vvEPA
          United States
          Environmental Protection
          Agency
               Office of Research and
               Development
               Washington, DC 20460
EPA/600/R-98/135
September 1998
A Users Guide to the
PATCH Model

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                                              EPA/600/R-98/135
                                               September 1998
       A Users Guide  to the
             PATCH Model
                       by
                Nathan H. Schumaker
          U.S. Environmental Protection Agency
National Health and Environmental Effects Research Laboratory
              Western Ecology Division
                Corvallis, OR 97333
National Health and Environmental Effects Research Laboratory
          Office of Research and Development
          U.S. Environmental Protection Agency
           Research Triangle Park, NC 27711
                                              Printed on Recycled Paper

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                               Notice

The  information  in this  document has  been funded in  part by the  U.S.
Environmental Protection Agency. It has been subjected to the Agency's peer
and administrative review, and it has been approved for publication as an  EPA
document.  Mention of  trade  names  or  commercial products  does  not
constitute  endorsement  or recommendation for use. The development  of
PATCH was also  supported by the U.S. Forest Service through grant number
PNW 90-340, the U.S. State Department through grant number 1753-000574,
and the National Science Foundation through grant number BIR9256532.
                         Preferred Citation:

           Schumaker, N.H. A users guide to the PATCH model.
         EPA/600/R-98/135. U.S. Environmental Protection Agency,
          Environmental Research Laboratory, Corvallis, Oregon.

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PATCH is an excellent tool that will take a lot of the guesswork out of predicting the
impacts of different habitat management scenarios on species' populations. Although
the model seems complicated, it is actually the best "pre-packaged" spatial module we
have seen. There are no shortcuts in spatially explicit models, and it would be
intellectually dishonest and misleading to contrive a model that did not have the depth
or flexibility of PATCH. Users will not master PATCH in a few hours, but neither will
they need to be computer wizards. PATCH has the potential to stimulate breakthroughs
in landscape-based resource management. It will do this because it makes biology and
clear thinking the hurdle, not computer programming.

   Peter Kareiva
   Professor of Zoology
   The University of Washington
PATCH is an excellent tool for applied ecologists seeking to predict the effects of land
use change on populations of concern. PATCH is a vast improvement over any similar
program of which we are aware. PATCH was clearly designed to address and
overcome the most serious concerns voiced by critics of spatially-explicit,
individually-based models. In our view, PATCH succeeds admirably in this goal,
providing a modeling framework that will allow the intelligent and informative use of
complicated simulation models to address environmental problems.

    Daniel Doak
    Associate Professor, Environmental Studies
    The University of California at Santa Cruz
We found PATCH very easy to use, the manual to provide good documentation, and the
examples to be sufficient to illustrate the most common applications of the model. The
model should prove quite useful for exploring spatial solutions to the conservation of
threatened and endangered species. Given that most species of concern are at risk due
to habitat loss and fragmentation, the focus of the model on linking demography to
habitat quality and geometry is highly appropriate. The model's integration with
actual landscapes via a GIS interface is a unique strength that makes PATCH
particularly relevant to "real world" conservation problems. We believe that many
population and conservation biologists will make wide use of PATCH.

    Barry Noon
    Associate .Professor, Fisheries and Wildlife
    Colorado State University

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                              Table of Contents
Preface       	viii

Chapter 1     PATCH Basics	1

               Getting Started	1
               File Name Conventions	1
               Numeric and Text Fields	2
               Mouse Conventions	2
               Selecting the Active Window	3
               The Zoom-Box	3
               Window Names	3
               Control Windows	4
               Graphics Windows	4
               Using GIS Imagery	5
               Loading an Lnage	6
               Creating Images with Arc/Info	7
               Caveats and Concerns	7

Chapter 2     Model Inputs	8

               Introduction	8
               GIS Data	8
               Habitat Affinities	8
               Territory Size	9
               Vital Rates	9
               Movement Behavior	9

Chapter 3     Model Outputs	10

               Introduction	10
               Landscape Pattern	11
               Home Range Analysis	11
               Demographic Information	12
               Observed Movement Rates	12
               Observed Occupancy Rates	12
               Source-Sink Analysis	13

Chapter 4     Patch Identification	14

               Introduction	14
               Habitat Weights	14
               Adjacency	14
               Measurement Conventions	14
                                                                        IV

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                Identifying Patches	15
                Statistics Output	....	16
                Using the Zoom-Box	17
                Displaying the Results	17
                Selecting a Patch	17

Chapter 5      Territory Allocation	18

                Introduction	....	18
                Scores and Breeding Status	;18
                Territory Min and Max	18
                Habitat Sharing	19
                Linking to Life History	20
                Identifying Territories	20
                Using the Zoom-Box	21
                Displaying the Results	21
                Selecting a Hexagon	22
                Adjusting Min and Max Sizes	22
                Aligning the Hexagon Grid	22
                Hexagon Borders	22
                Editing the Hexagons	23
                Hexagon Compression	23
                Changing the Resample Rate	24
                      *
Chapter 6      The Movement Module	25

                Introduction	. .25
                Movement Behavior.	25
                Random Walks	26
                Walk Linearity	30
                Nonrandom Movement	31
                Site Fidelity	32
                Reflecting Boundaries	33

Chapter 7      The Life History Module	34

                Introduction	34
                Survival and Reproduction	35
                Linking to Habitat Quality	36
                Demographic Stochasticity	38
                Environmental Stochasticity	38
                Miscellaneous Parameters	40
                Running a Simulation	 .40
                Life History Output Files	 .41
                Using Movement Limits	43
                Selecting Starting Sites	45
                Time Series Analysis	45

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                The Parameters Window	46
                The Functions Window	47
                The Life History Functions	47

 Chapter 8     PATCH Utilities	49

                Introduction	49
                Reading and Viewing Imagery	49
                Miscellaneous Functions	51
                Zoom-Box and Image Window	53
                Tracking and Resampling	54
                Zoom-Box Placement	54
                Habitat Controls Files and Tables	55
                Patch Identification	56
                Hexagon Editing	58
                Territory Construction	60
                Life History File Names	62
                Time Series Editor	63
                Visualization and Initialization	63
                Life History Controls	65
                Life History Parameters	69
                The Projection Matrix	72
                Interpolation Functions	73
                Movement Functions	75

Example 1     Patch Identification	77

                Introduction	77
                Starting PATCH	77
                Reading GIS Data	78
                Displaying GIS Data	78
                Setting the Zoom-Box Size	78
                Using the Zoom Window	78
                Moving the Zoom-Box	79
                Setting the Legend Weights	80
                Identifying Habitat Patches	81
                Picking Four or Eight Neighbors	82
                Locating Core Habitat Areas	82
                Saving the Results	82
                Patch Statistics	83
                Loading a Patch Map	83

Example 2     Territory Allocation	85

                Introduction	85
                Starting PATCH	85
                Reading GIS Data	86
                                                                             VI

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                Displaying GIS Data	86
                Setting the Zoom-Box Size	 .86
                Using the Zoom Window	87
                Setting the Legend Weights	87
                Setting the Hexagon Size	87
                Building a Territory Map	88
                Adding a Border	89
                Selecting a Hexagon	89
                Territory Min and Max	90
                Saving the Results	91
                Locating Core Habitat Areas	91
                Hexagon Statistics	91
                Hexagon Compression	92
                Hexagon Grid Alignment	94
                Editing Hexagon Scores by Range	94
                Editing Hexagon Scores by Hand	95
                Randomizing the Territory Map	96
                Changing the Resample Rate	97

Example 3     Demographic Simulations	98

                Introduction	98
                Getting Started	98
                The Projection Matrix	100
                The Vital Rates Factor	 .101
                Runs, Years, and Utility	103
                The Initial Population Size	104
                Movement Parameters	104
                Visual Feedback	106
                Specifying an Output File	107
                Running a Simulation	107
                The Output Statistics	108
                The Main Life History File	109
                The ".statsO" File	 .109
                The ".statsl" File	110
                The ".stats2" File	110
                Displaying the Output Data	Ill
                The Output Imagery	112
                The Occupancy Rate Map	..112
                The Source-Sink Maps.			112
                Editing Output Imagery	113
                Environmental Stochasticity	114
                Including Habitat Change	117
                                                                              Vll

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                                             Preface
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          This  manual  provides  instructions  for  using  a  spatially  explicit
          demographic simulator called PATCH (a Program to Assist in Tracking
          Critical Habitat).  The model was designed to project populations of
          territorial terrestrial vertebrate species through time, but it can perform
          other analyses as well. PATCH  is ideal for investigations involving
          wildlife species that are mobile habitat  specialists  because  it pays
          careful attention to habitat pattern and quality.  Where the details of
          landscape pattern  are relatively unimportant, a different model may be
          preferable.  PATCH is a single species, females only model, thus it
          cannot track intra-specinc interactions, or complications associated
          with mate finding  or sex ratio. In spite of these limitations, PATCH can
          accommodate a broad range of analyses,  and it should be useful  for
          both theoretical and applied investigations.

          I began work on  the precursor to PATCH while attending a summer
          school on Patch Dynamics organized by S. A. Levin, T. M. Powell, and
          J. H. Steele and held at Cornell University in the summer of 1991. I
          continued the development of the  model from  1991 to  1995 at  the
          University of Washington. Funding constraints encountered during this
          period resulted in the model becoming  essentially a  life  history
          simulator for the Northern Spotted  Owl. From 1995  to 1998, I
          transformed the spotted owl simulator into the present PATCH model. I
          wrote PATCH entirely in the C programming language,  and worked
          hard to keep it user  friendly and bug free. The source  code to  the
          PATCH model is not being released for two reasons.  First, the source
          code consists of about 40,000 lines of text. This code is modular and
          straightforward, but it would be difficult for anyone other than  the
          author to modify  it correctly. Second, having a single home  for  the
          PATCH source code guarantees  that copies of the  model with  the
          identical version numbers are truly the same.

          PATCH'S data requirements  are  minimal.  It must be supplied with
          habitat maps, typically from  a geographic information system (GIS),
          and data specifying habitat use (territory size and habitat affinity), vital
          rates (survival and reproduction), and the movement behavior of the
          species of concern. PATCH requires that its GIS data be stored in Sun
          Rasterfiles.  The model is guaranteed to run correctly only on a Sun
          Microsystems computer runnrng the OpenWindows window manager.
          Problems may arise if  it is  used with  Sun's Common Desktop
          Environment. This manual assumes some familiarity with both the Sun
          operating system and the OpenWindows window manager.
                                                                      vm

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                     Models are never perfect, and PATCH is no exception. Errors in a
                     model's outputs can result from poor or inadequate design, mistakes
                     made during its construction, and from limits on input data quality and
                     assumptions.  The  PATCH  model has been  designed to help  you
                     investigate and minimize sources of error. PATCH was put through an
                     extensive debugging process  in  which  the  performance  of every
                     algorithm was carefully validated. This  bug checking process  was
                     intended to eliminate poor construction as a source of model error. In
                     addition, PATCH  is designed to require as few  input parameters as
                     possible, and it brings a minimum of complexity to the simulation of
                     organism's life histories. But ultimately, it is up to  you to ensure that
                     PATCH is used responsibly. In order to  take full advantage of this
                     program it is important that you understand the implications of altering
                     the assumptions behind the simulations. Take the time  to conduct and
                     explore sensitivity analyses and alternative parameterizations to get a
                     grasp of how strongly your results are effected by the particular set of
                     assumptions and life history values you choose.  The confidence you
                     place in PATCH'S projections should reflect the reliability of the data
                     and assumptions you build into its simulations.

                     PATCH'S pattern  identification module simply quantifies landscape
                     pattern, and as such is not subject to design flaws. But errors in the GIS
                     imagery can be expected to propagate through the pattern identification
                     process. PATCH'S territory allocation  module analyzes GIS landscapes
                     and provides input to the demographic subroutine. Errors in the  GIS
                     imagery will also  be reflected in the territory maps that you construct.
                     The design of the territory allocation  module is straightforward, but it
                     restricts the model's use to territorial species. The territory allocation
                     module allows you to carefully test the sensitivity of the model results
                     to uncertainty in its input parameters.

                     Concerns about the accuracy of the model outputs can be expected to
                     focus primarily on PATCH'S life history simulator. But the life history
                     module's simplicity  and flexibility should help you  to assess your
                     confidence  in its  results. The life history  module is based upon a
                     population  projection  matrix and,  in an optimal  landscape with
                     abundant breeding sites, its projections are going to closely match those
                     from  a matrix model. Population-level  attributes such as  density
                     dependence emerge directly from the model's explicit use of space, and
                     are never hard wired in the source code. Other than the vital rates used
                     in a matrix  model, you need only supply habitat  affinities, territory
                     sizes,  and rules defining movement  behavior. Uncertainties in these
                     parameters can be explored directly through sensitivity analysis.

                     The PATCH model is distributed on a compact disk (CD). The contents
                     of the CD include the directories  "bin", "man", and "gis". The "bin"
Preface
                                                                                     IX

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Chapter 1
                             PATCH Basics
Getting Started
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Sun Microsystem's OpenWindows window manager must be running
before the PATCH model can be started (the Common Desktop
Environment may not work correctly with PATCH). First, move to the
root directory of the CD or to the appropriate location on the hard disk
if PATCH has been copied off the CD. At the UNIX prompt, type
"bin/PATCH". This calls up the initial window, referred to as the title
window (Figure 1). Next, click anywhere in the title window, which
causes PATCH to display its control windows in an array at the upper
left of the screen. This collection of windows is shown in Figure 2.
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                 Figure 1.   The title window. This window is displayed when PATCH
                 is first started, and it is used to call up all of the other control windows.
                 The header of the title window displays the version of PATCH that you
                 are using (not shown here).
                 PATCH reads from and writes to the location in the file system at which
                 the model was called up, unless absolute path names are used. In some
                 circumstances, PATCH automatically appends extensions to the end of
                 file names. Model output can always be directed to a file. If an output
                 file name is not specified, PATCH writes its data directly to the monitor.

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Figure 2.   PATCH'S  control windows. Two additional  panels and
another control window are hidden behind those displayed above. The
hidden panels can be viewed by clicking the "Display Next Panel" and
"View  Next Panel" buttons in the main and habitat controls windows,
respectively.  The hidden window can be  displayed by  clicking  the
rectangular bar shown in the lower right hand corner. Right clicking in
the appropriate area also displays the hidden window or panels.
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                    Table 1 displays the various consequences associated with clicking the
                    mouse buttons in PATCH'S graphics windows. The features mentioned
                    in Table 1 are discussed in subsequent sections of this manual.
                                 Table 1: Clicking in Graphics Windows
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Legend
Window
Image
Window
Zoom
Window
Analysis
Window
Double Click

Paint
Window
Paint
Window
Paint
Window
Left Click
Increment
Weighting

Edit
Pixel
Edit Patch,
Hexagon
Middle Click
Start Image
Editing
Move
Zoom-Box
Select
Pixel
Select Patch,
Hexagon
Right Click
Decrement
Weighting
Stretch
Zoom-Box
Move
Zoom-Box
Move
Zoom-Box

Selecting the
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Active Window
Sun Microsystem's OpenWindows and Common Desktop Environment
window managers provide you with two mechanisms for selecting the
active window. The active window is the window that receives the
commands you enter from the keyboard or the mouse. The options for
making a window active are to either click on it or move the mouse
pointer into it. When using PATCH, you should always make sure that
the active window is defined by the location of the mouse pointer. Some
of PATCH'S utilities  do not work correctly  when a mouse click is
required to specify the active window.


PATCH allows you to perform analyses on any rectangular subset of a
GIS image. The  portion of the image to  be used is  specified by the
placement of a small rectangular box in the principle graphical window
(the image window). This  rectangular  box is referred to  as the
zoom-box, since PATCH allows you to zoom into the data within it. The
zoom and analysis windows display only the  GIS  imagery present
within the zoom-box, which can be enhanced using a magnification
parameter that appears in a control window called the main window.


Windows in PATCH that contain buttons and text fields are referred to
collectively as control  windows. Windows that contain images are
referred to collectively as graphics windows. Every window in PATCH
has a name, and these  names are  displayed  in the window headers.
However,  exceptions  to this rule are made for the  title and legend
Chapter 1   PATCH Basics

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                    windows. The title window is the very first window that comes up when
                    the model is started. The title window header displays the version of
                    PATCH being used. The legend window displays the classes present in
                    the GIS data. The legend window header displays the name of the GIS
                    data set being used. Moving the mouse pointer into the image, zoom, or
                    analysis window causes its header to display the name of the GIS data
                    set being used. When the mouse pointer is removed from the window,
                    the window header redisplays the window name.
Control
Windows
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Each control window is designed to facilitate a particular  class of
operations. The title window is used to iconify the entire PATCH
interface and to recall other control windows that have been removed
from the desktop. The main window permits you to read, display, and
modify GIS data. The habitat controls window allows you to  quantify
landscape pattern and to construct and edit a territory map.  The life
history windows are used to drive the demographic analysis.


The PATCH model  contains  four  graphics  windows. The image
window displays a subsampled version of the entire GIS image. The
size of the image window is set using a numeric field called Image
Window Sampling in the main control window. A sampling value of n
forces the image window to be constructed from every nth row and nth
column of the GIS image.  Hence smaller values of n result in larger
image windows that display more detail. The legend window  displays
the colors and names of each category present in the GIS image. The
size of the legend window is set automatically by the model. The zoom
window  displays  the  contents  of  the  zoom-box  at  a  specified
magnification  (see  the Degree  Of Magnification field in the main
control window). The analysis  window  displays the results of  any
analysis conducted with the model, and is also linked to the zoom-box
and the magnification parameter.

The legend window is always painted automatically by the model. This
is not true for the image, zoom, and analysis windows. To repaint these
windows, it is necessary to double click within the window. However, if
the zoom or analysis  window dimensions do not equal the zoom-box
size times the magnification value, then a double click  resizes the
window (this is not the case for the image window, whose size can be
altered only by using the Image Window Sampling field). A second
double click paints the image after a  window has been  resized.
Throughout this manual, the term up to date is used to describe a
window that is displayed on the screen, has the correct size,  and has
been painted with an image.
Chapter 1  PATCH Basics
                                                             4

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             Ss
Different portions of your GIS imagery can be viewed in the zoom and
analysis windows by changing the size and placement of the zoom-box.
The zoom-box size and placement can be modified using any of the
many fields in the main control window that specify its  location within
the GIS data. The edges of the zoom-box can also be moved to the
location of the mouse pointer by right clicking in the image window. In
addition, the zoom-box location can be altered by middle clicking in
the image window. The zoom-box can also be moved by left clicking in
either the zoom or the analysis window. In these instances, you specify
the direction in which the zoom-box moves by clicking in one of four
quadrants, delineated by connecting opposite corners  of the window
along diagonals (Figure 3). The zoom-box moves a distance equal in
pixels to the value of the numeric field in the main control window
labeled Set Zoom-Box Increment. However, if this field is set to zero,
the zoom-box moves exactly its own width, or height.
                                 Left Quadrant   / \  Right Quadrant
                                       /
                                         /
                                           /
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                                   /
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                   Figure 3.    The  zoom-box  can be  moved incrementally by  right
                   clicking in either  the zoom or the analysis window.  The zoom-box
                   moves up, down,  left, or right, depending on if the mouse pointer is
                   located in the top, bottom, left, or right quadrant, respectively.
                   To begin using PATCH, it is first necessary to load in a GIS image.
                   PATCH only reads images  that  have  been  formatted  as  8-bit,
                   uncompressed, full color Sun Rasterfiles. However, most standard GIS
                   applications create Sun Rasterfiles of this  type, or another raster data
                   format (e.g., GIFF, TIFF) that can be  converted to a Sun Rasterfile.
                   PATCH also stores some necessary ancillary data in a text file referred
                   to as a control file. If this text file does not exist, PATCH creates one,
Chapter 1  PATCH Basics

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 Loading an
 Image
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 but you must then edit it to supply meaningful values for the Universal
 Transverse Mercator (UTM) coordinates associated with the image's
 edges, the size in meters of the data pixels, and the names of the legend
 categories. The UTM information is not critical to running the model.


 You can begin by reading one of the sample images provided with the
 PATCH distribution. To do this, it is necessary to provide a directory
 and a file name that describe the location of the imagery in the UNIX
 file system. If the PATCH program is started from the CD, then the
 sample imagery should be found in a directory called "gis". Load the
 imagery by entering its directory and name into the main window, and
 then click on the button labeled Read The Data File (Figure 4). Next,
 click on the button in  Figure 4 labeled Show Image Window. This
 window initially  is painted black. Double  click in this black  area to
 display the GIS data set that you have loaded into the model. This small
 window can be increased in size by lowering the value of the text field
 labeled Image Window  Sampling that  appears just below the color
 palette  in Figure 2. You always  have to read a GIS  data set before
 running analyses with PATCH.
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Figure 4.   The top panel in PATCH'S main window. The buttons on
the right side of this panel are used to access three of PATCH'S four
graphics windows. The "Read The Data File" button loads a GIS image
into the model. Clicking on "Display Next Panel" sends this entire panel
to the background,  and brings a second set  of  buttons into  the
foreground (this can also be accomplished  by  right  clicking in  the
panel).  The colored boxes (depicted here as in gray-tones) at  the
bottom of the panel are used to modify the color of the zoom-box and
of the hexagon grid in the zoom window.
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Chapter 1  PATCH Basics

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witfrArc/Iitfb:"
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Arc/Info is an extremely popular GIS program written by ESRI. This
software package has a raster modeling toolkit called GRID. You can
use GRID, and the instructions provided below, to convert an Arc/Info
raster coverage into a 8-bit Sun Rasterfile with an imbedded colormap
suitable for use  with  PATCH. You must first construct a table that
assigns colors to the pixels in the GRID image. The first column of this
table must be a list of the data values present in the GRID image. An
8-bit Sun  Rasterfile cannot be created if any of these data values lie
outside the range from 0 to 255. The remaining columns in  the table
specify the red (R), green (G), and blue (B) levels to be associated with
each data value. These RGB levels must also lie in the range from 0 to
255, and all of the entries in this table must be separated by spaces. The
Arc/Info SAVECOLORMAP command can be used to construct this
table. The Arc/Info command you use to generate the Sun Rasterfile is:

GRIDIMAGE   
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 Chapter  2
                                                      Model Inputs
Introduction
                 This chapter presents a brief description of the data necessary to drive
                 the PATCH model. PATCH can quantify landscape pattern using only
                 GIS data as input. The model can also perform a home range analysis
                 using  GIS  data  and information  specifying habitat affinities and
                 territory sizes. Source-sink analyses can be developed from habitat
                 affinities, territory sizes, and estimates of vital rates. Li order to conduct
                 demographic  simulations,  you must also provide  PATCH  with
                 information describing a species' movement behavior.
GIS Data
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Habitat Affinities
The imagery supplied to the PATCH model must come in the form of
an 8-bit, uncompressed, Sun Rasterfile with square pixels.  This  file
must be given a name that ends in ".sun" in order for the model to
locate it. PATCH stores some ancillary data in a text file that is always
assigned the same name  as  the Sun  Rasterfile, minus  the  ".sun"
extension. These text files, hereafter referred to as control files, provide
a mechanism for you to supply Universal Transverse Mercator (UTM)
coordinates for the edges of the data, the pixel size (in meters), and the
names and colors associated with each data category. If a control file is
missing, PATCH automatically creates one that contains default values
for every  field except for  the colors, which  are assigned the  values
actually present in the Sun Rasterfile.

Every 8-bit, full color Sun Rasterfile contains an embedded colormap.
As mentioned previously, when PATCH builds a missing control file,
this colormap is used to assign red, green, and blue values to the image
categories. This is the only situation in which a rasterfile colormap is
accessed by the model. Thus if the colors in the control file are altered,
PATCH'S  graphics windows display this  change. In addition, when
PATCH creates a new Sun Rasterfile, it constructs  its imbedded
colormap from the color table present in the control file being used.


Habitat affinities in PATCH are integer weighting values between 0 and
99  associated with each habitat class present in the GIS data.  These
weights (also referred to as habitat utility indices) are relative measures
of a habitat's importance to the species under study. They are  assigned
by clicking in the legend window. Categories present in the  imagery
that are assigned weights of zero are totally inhospitable to the species.
Habitat  classes having  the largest of the assigned weights  serve as
optimal  habitat for the species. The data necessary to specify habitat
                                                                                  8

-------
pHlr4*^ f?-"'€
                    weights can be hard to come by. Ideally, you should specify the weights
                    based upon field data that directly measure a species' preference in
                    different habitat types. An alternative that you can use if field data are
                    not available is to survey experts and  request that they  rank  the
                    importance of available habitats for the species in question. In any case,
                    remember that the habitat weights are relative, not absolute, measures.


                    The territory size parameter is designed to be set to the typical size of a
                    territory for the species being modeled. In addition, estimates can be
                    provided for the minimum territory size (expected in optimal habitat),
                    and a maximum territory size (expected in marginal habitat).


                    PATCH'S vital rates are estimates of survival and fecundity (the number
                    of female offspring per female) supplied in the form of a Leslie or
                    Lefkovitch projection matrix.  Because PATCH  uses  projection
                    matrices, you must determine whether the species under study is best
                    described with an age or stage based model. Separate survival and
                    fecundity values are required for each age or stage class identified in
                    the species' rife history. The survival rates (or transition probabilities)
                    within any one column of the projection matrix must sum at most to
                    one. PATCH'S life history module incorporates a post-breeding census,
                    which means that the first age or stage class always consists exclusively
                    of newly recruited individuals that are not yet of breeding age. Thus the
                    upper left entry in PATCH'S projection matrix is always fixed at zero.


                    Movement behavior  is  defined  collectively  through  a  series  of
                    parameters. Movement events occur when young of the year (those
                    individuals born in the last breeding pulse) disperse in search of vacant
                    sites in which  to set  up  territories. In   addition,  floaters  (older
                    individuals without territories) must also search the  landscape  for
                    breeding sites. Territorial individuals may or may not elect to move,
                    and this behavior is controlled by the site fidelity parameter and the
                    quality of the site the individuals presently occupy. The movement
                    process can  involve  a  pseudorandom walk, or it can  assign  the
                    organisms a complete knowledge of some portion of the landscape and
                    then let them move directly to vacant breeding sites. If a random walk
                    is being employed, you must indicate the species' movement ability
                    and  supply parameters  that  influence  the linearity  in  searcher's
                    movements, and their tendency to move up gradient from low to high
                    quality habitats. Otherwise, you  must specify  a search radius and
                    whether individuals  should  attempt to  obtain the best or closest
                    available site. Regardless of the movement  strategy employed, three
                    degrees of site fidelity can be imposed.
Chapter 2   Model Inputs

-------
 Chapter 3
                                   Model Outputs
Introduction
J
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              - 1
 Outputs  from the PATCH model fall into two general categories:
 pattern-based metrics and demographic analyses. Pattern-based outputs
 include patch-by-patch descriptions of landscapes, assessments of the
 number,  quality,  and  spatial  orientation of breeding  sites,  and
 map-based  estimates of  the  occupancy  rate and the source-sink
 behavior of the breeding habitat. The principal demographic outputs
 generated by the PATCH model include several measures of population
 size as a function of time, realized survival and fecundity rates (rates
 that reflect the limitations on a population  imposed by habitat quality
 and landscape pattern), and assessments of the  occupancy rate and
 source-sink behavior of the breeding sites present in a landscape.

 PATCH'S pattern-based outputs help you to  quantify  landscape
 structure and quality. These outputs vary in the extent to which they are
 sensitive to species' life history. Patch-based analyses  might reflect
 only species' habitat preferences,  while territory-based metrics  also
 consider  estimates of territory size. Occupancy rate and source-sink
 analyses  go  further to  incorporate estimates of  species' vital rates.
 PATCH'S demographic  outputs  include estimates of population size,
 age structure, and spatial distribution. PATCH'S life history module can
 also help you quantify the impacts of landscape change on population
 viability, estimate changes in vital rates corresponding to habitat loss or
 fragmentation, and identify source and  sink  populations within  a
 landscape. PATCH'S source-sink analysis, coupled with its capacity to
 incorporate  landscape change through time, allow you to identify,
 track, and modify clusters of habitat that  play a critical role in the
 maintenance of a population. This is the model's most unique feature
 and the reason it is called a Program to Assist in Tracking Critical
Habitat, or PATCH, for short.

A great  deal of interest has recently developed  in exploring the
performance of indices of landscape pattern as predictors of ecological
quality and function. Because PATCH both quantifies landscape pattern
 and projects population trends,  it is ideally suited to  this type of
investigation. For example, PATCH will make it easy for you to search
for measures of landscape pattern  that  are  well correlated  with
estimates of dispersal success or population persistence.

The ecologies and life histories of most species are poorly known. In
the common situation where data are sparse and parameter values less
                                                                                 10

-------
Landscape
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than certain, you will have to find creative ways to make the most of
what PATCH can offer. Many approaches are possible. You can begin
with very  simple habitat-based analyses and  add Me  history  and
behavioral information iteratively. An assessment of landscape quality,
in the  simplest case, could consist only of counting the number of
pixels of habitat of various qualities. A slightly more detailed analysis
might be performed by examining the size structure of the habitat
patches present  in the landscape. Supplying territory size estimates
would allow you to assess the number of high quality breeding sites.
Vital rates  could be specified and the numbers of source and sink
habitats identified. All of this  data, and more, can be collected from
PATCH without even running a life history simulation. Still, sensitivity
analyses should always be performed to examine the consequences of
your assumptions and specific model parameterizations.


PATCH can generate a histogram showing the frequency of each habitat
type present in any rectangular subset of the landscape.  PATCH can
also quantify habitat pattern on a patch-by-patch basis. The module that
does this will supply you with  a table that includes the area, weighted
area, core area, arid perimeter of each patch. Area is measured as the
number of pixels of habitat present. Weighted area is measured as the
sum of the weighting values (habitat affinities) assigned to each pixel in
a patch. Core area is computed based on a edge width that you provide
(in pixels).  A patch's core area is equal  to the number of pixels
separated from the patch's perimeter by a distance equal to at least one
edge width. These pattern-based measures can be used (outside of
PATCH)  to  develop  indicators  of  habitat  quality,  such  as
perimeter / area ratios or estimates of fractal dimension. In addition to
generating these numerical outputs, PATCH also displays the results of
the patch identification process in a graphics window.


PATCH'S home  range  analysis  complements the  assessment  of
landscape pattern described above. The home range analysis is also an
important part of the process of conducting demographic  simulations.
The key procedure involved in PATCH'S home range analysis, termed
territory allocation, involves intersecting a GIS image with an array of
hexagonal cells.  PATCH was designed with the  intent that the area of
these hexagons  would equal the typical size of a territory for the
species being modeled. In  addition to setting the  hexagon size, you can
also specify a minimum and a maximum territory  size. The design of
the territory allocation module is such that the minimum territory size
is observed in optimal habitat,  and the maximum territory size is
observed in more marginal habitats.
Chapter 3   Model Outputs
                                                              11

-------
                     One output from the territory allocation process is a new raster data set
                     displaying each individual hexagon and its breeding status (suitable vs.
                     unsuitable). A second output resulting from territory allocation is  a
                     table that displays  every hexagon's  score  (the mean  value  of the
                     weights assigned to each of its pixels), the overall amount of habitat it
                     contains, its weighted habitat area, its  breeding status, and the amount
                     of core and edge habitat it contains (computed patch by patch).
Demographic
Information
When conducting demographic simulations, PATCH compiles a table
exhibiting a year-by-year tally of the floater and breeder populations,
the number of individuals in each age or stage class, and the overall
population size. To facilitate  analyses  involving  multiple replicate
simulations, the means and standard deviations of these quantities
(taken over every replicate run) are computed  as well. PATCH also
tracks the effective aggregate survival rates and fecundities, on an age
or stage class basis, as mean values computed from every replicate run.
These observed vital rates can be used  to construct a time series of
projection matrices that can together exactly  recreate  the population
trajectory generated by the simulation model.
Observed
Movement Rates
              *t
Observed
Occupancy Rates
For every year of a demographic simulation, PATCH compiles the
mean dispersal distance and reports it as both the total distance moved
and the net straight-line displacement from the starting point. The term
dispersal is used to describe only the movements of young of the year
(individuals born in the last breeding pulse). The distances moved by
older individuals are not reported in any of the output files generated by
the PATCH model.


PATCH examines whether or not each breeding site is occupied at the
end of the final year of each replicate simulation. These data are stored
and used to generate three different types of outputs. First, PATCH
constructs a map that displays the relative occupancy rate of each
breeding site present in the landscape. This map can be used to glean a
general picture of the overall patterns of occupancy exhibited by the
model species. Second, the model creates a numeric output that pairs
each hexagon's total occupancy rate (again, gathered once per replicate
run, at the end of the final model year) with information quantifying its
quality.  These data can be used to segregate patterns of occupancy
based on measures of habitat quality. Third, PATCH allows you to
examine the  population density that existed  in  any subset of a
landscape.  This  feature can  be used to generate a distribution of
occupancy rates built  up from multiple replicate  simulations.  This
output is  designed to be compared directly to  density estimates
gathered in the field.
Chapter 3   Model Outputs
                                                              12

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Source-Sink
Analysis
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Throughout this manual, demographic sources are defined as sites in
which  reproduction   exceeds  mortality.   If   mortality  exceeds
reproduction, then a site is referred to as a sink. PATCH compiles
estimates of both the expected and the observed source-sink behavior
of each breeding site present in a landscape.

PATCH can conduct a source-sink analysis using only data describing a
species' habitat affinities, territory size,  and vital rates.  In a typical
landscape,  survival and reproductive rates change from site to  site
because habitat quality varies. PATCH uses this information to compute
the mean steady-state replacement rate (as the dominant eigenvalue of
the associated projection matrix) for the model species in each breeding
site.  With this information, expected demographic sources and sinks
are identified throughout the landscape. This source-sink  analysis  can
be used as an initial estimate of the importance of different regions of
the landscape for the model species. Deviations from these expected
outcomes result primarily from limitations inherent in an organism's
searching behavior.

PATCH also tracks immigration  into  and emigration from each
breeding  site,  and uses  this  information  to   identify  observed
demographic  sources and  sinks throughout the  landscape. PATCH
accomplishes this by incrementing a counter each time an individual
leaves a breeding site, and decrementing the same counter each time an
individual enters the site. Individuals that simply  pass through  a  site
produce no net change in the counter's value. On the other hand, when
individuals are born in and subsequently disperse from a breeding site,
the counter's net value is incremented. When individuals  move into a
breeding site and die, the counter's net value is decremented. These
counters can be held at zero until a specified number of years  has
passed (so that transient effects resulting from the initial conditions can
die down), and they can also be averaged across replicate simulations.

PATCH'S source-sink analysis is presented to you in three files. The
first  file contains a table that displays the score and the expected  and
observed source-sink behavior of each  breeding site, as  described
above. The second and third files  are Sun Rasterfiles  that provide a
visual representation  of  the expected  and observed  source-sink
behavior. Each  hexagon in these images is displayed as a 2 x 2 pixel
square. Constructed this way, these output images are easier to compare
visually to the GIS input data from which  they were derived.
Chapter 3   Model Outputs
                                                               13

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 Chapter 4
                                              Patch Identification
Introduction
                    It is often desirable to identify aggregate features of landscape pattern
                    that correlate with measures  of ecological quality such as habitat
                    connectivity or  population viability. PATCH facilitates this  type of
                    analysis because it  includes  a  module  devoted  specifically to
                    quantifying landscape  pattern. PATCH'S approach to providing this
                    information is to break a landscape up into a collection of individual
                    patches of habitat, and then to provide a limited amount of information
                    about each one. Many different metrics can then be developed (outside
                    of PATCH) from such measures of landscape pattern.
Habitat Weights
J  i
          t    - 1
                    For the purposes of patch identification, PATCH requires that each
                    legend category be assigned a weighting value (i.e., a habitat affinity),
                    which takes the form of an integer between 0 and 99. Every pixel
                    belonging to a category that has been assigned a nonzero weight is
                    treated as habitat, whereas those with zero weights are considered
                    non-habitat. Habitat weights are entered into the legend window by
                    clicking on the different categories displayed there. A weighting value
                    of zero  is displayed in the legend  as an empty box.  The patch
                    identification process treats all habitat classes with nonzero weights
                    identically when computing patch shapes, sizes, perimeters, and core
                    areas. However, the model also computes a weighted area, and this
                    quantity can  be used to  rank patches  based on the amount of
                    high-quality habitat they contain.
Adjacency
i      ...  -Mr
                    A patch consists of any collection of pixels that touch, and that all have
                    been assigned nonzero weights. PATCH provides you with two ways to
                    define what it means for pixels to touch each  other.  One choice
                    specifies that, for the purpose of patch identification, only a pixel's four
                    adjacent neighbors (top, bottom, left, and right) actually touch it. The
                    other option includes pixels touching at corners as well. Based on the
                    rule applied, PATCH assigns every habitat pixel to one, and only one,
                    patch. The areas, weighted areas, core areas, and perimeters assigned to
                    the landscape's patches can all be affected by adjacency rule used.
            _ ,
Measurement
'Conventions
                   PATCH area is measured as the number of pixels of habitat. Weighted
                   area is measured as the sum, taken over every pixel in a patch, of the
                   weighting values assigned to each pixel. Core area is computed based
                   on a edge width that you supply, specified as a number of pixels. A
                                                                                14

-------
  f „ •« '*'
  •>. »v I
Identifying
Patches   "
patch's core area is defined as the number of pixels separated from the
patch's perimeter by a distance equal to at least one edge width in every
direction (regardless of the adjacency rule being used). The actual
values for patch area, weighted area, and core area can be obtained by
multiplying these values by the area of a pixel  (in square meters).
Perimeters are measured as the total number of pixel edges present in a
patch. Patch perimeters can always be converted from pixels to meters
by multiplying by the length of a pixel. This is also true for the edge
width parameter.

Many well known indices of habitat pattern can be built up from the
measures just described. Examples include perimeter-area ratio, shape
index, and estimates of fractal dimension.  More  importantly, this
analysis provides you with the raw  data necessary  to  search for
measures of landscape pattern that function well as effective indicators
of ecological quality. PATCH itself does not construct such metrics, but
many other programs are capable of doing so using PATCH'S outputs.


A panel in the habitat controls window is  devoted to the process of
patch identification  (Figure 5).  This panel  allows  you  to specify
whether data pixels are to be treated as having four or eight touching
neighbors.  This panel also allows you  to run the patch identification
process entirely in memory (RAM) or to store the relevant tables on the
hard disk (Disk). The data generated by the patch identification process
can always be saved to the disk after the process has completed, and the
usual reason for setting the location switch to Disk is that not enough
memory is available to build the tables in RAM. A write protect feature
is also provided that helps to prevent data from being unintentionally
overwritten. A numeric field is included in the panel for setting the
edge  width used in computing patch core areas.  Core  areas  are
computed automatically any time that the edge width field is set greater
than zero, including when the territory allocation process is running.
                     Figure 5.   The panel within the habitat controls window that governs
                     the patch identification  process. See the text for descriptions of the
                     panel's various fields, settings, and buttons.
Chapter 4   Patch Identification
                                                               15

-------
r
                Statistics Output
                     The button in Figure 5 labeled Statistics Output is used to generate a
                     summary report describing the results  of the patch identification or
                     territory allocation process. These reports differ slightly, depending on
                     whether patches or hexagons are present. The reports contain a list of
                     the settings used to generate the data, and provide a summary of the
                     model's description  of each patch or hexagon.  Figure 6 provides an
                     example of the statistics output file that results from running the patch
                     identification process. If the Define Edge Width field is set greater than
                     zero, then PATCH identifies all  of the core habitat  present  in the
                     landscape prior to generating the statistics output file.

                              „.-.«
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                                                  Input File Name Used
                                                  Analysis Is For Rows
                                                  Analysis Is For Cols
                                                  Edge Width In Pixels
                                                         clayoquot
                                                         1741 - 1840
                                                         2335 - 2434
                                                         4
                                                  Total Number Patches
                                                  Landscape Patch Area
                                                  Sum Of Patch Weights
                                                  Sura Patch Core Areas
                                                  Total Landscape Edge
                                                         11
                                                         5186
                                                         22022
                                                         1110
                                                         1366
                                                  Legend Value, Weight
                                                  Legend Value, Weight
                                                  Legend Value
                                                  Legend Value
                                                  Legend Value
                                                Weight
                                                Weight
                                                Weight
                                                  Legend .Value, Weight
                                                  Patch   Patch   Patch '. -Core
                                                  Number  Area    Weight^ Area
                                    Figure 6.   A report generated using the "Statistics Output" button in
                                    the habitat controls  window.  Only  legend weights  that  have been
                                    assigned non-zero values are listed  in the header. This format of this
                                    report changes slightly if it is developed from a territory map instead of
                                    a collection of habitat patches.
               Chapter 4   Patch Identification
                                                                                     16

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Using the ;
_••,   -f <*. •• -„•"
-Zoom-Box'
PATCH runs its patch  identification  process on the subset of the
imagery contained within the zoom-box. If the zoom-box is 1000 pixels
or more in width ,j,pr height, then the patch identification process  is
conducted separately in rectangular blocks between 500 and  1000
pixels on a side. After the analysis has been performed on every one  of
these blocks, the results  are pieced back together into a single data set
describing the patches present in the landscape. As individual patches
are identified, their bounding rectangles are displayed within the image
window (the window that displays the zoom-box). This visual feedback
helps you to monitor the progress of the patch identification routine.


The  results of the patch identification process are displayed in the
analysis window. The  analysis window is  accessed using  a button
located in the habitat controls window.  The analysis window tracks the
zoom-box just as the zoom window does, and patches are displayed  in
this  window using  a revolving scheme of four colors. There is no
significance to the choice of colors assigned to patches in the analysis
window, and  adjacent patches  often have identical colors. When the
patch identification process is run on a large part of a GIS image, the
results often cannot be displayed all at once because they would then
extend beyond the edges of the monitor. However, the zoom-box can be
decreased in  size and moved around after the patch identification
routine has run, and in this way the results can be viewed a bit at a time.


The  PATCH model keeps track of  each  patch located by the patch
identification routine. When the results are displayed in the analysis
window, you can middle click on a patch to  display a summary of its
properties in the window footer. When a patch is selected in this way, it
is highlighted (painted white) and the analysis window footer displays
the patch's number, its  area (in pixels),  and its perimeter  (in pixel
edges). The patch number can then be cross-referenced to data supplied
in PATCH'S output files.
Chapter 4   Patch Identification
                                                              17

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 Chapter 5
                          Territory Allocation
Introduction
Before  PATCH'S  demographic analysis  can be  conducted,  it  is
necessary to break a landscape into an array of territory-sized units.
This process, termed territory allocation, involves intersecting the GIS
image with an array of hexagonal cells. PATCH was designed with the
intent that each hexagon's area would be set equal to the typical size of
a territory for  an  individual of the species  being modeled. PATCH
allows you to define minimum  and maximum territory sizes as well.
Setting the minimum or maximum territory size to a value other man
the hexagon size tends to eliminate artifacts associated with the exact
placement of the grid. Weighting values (habitat affinities) are used to
incorporate habitat quality into the territory allocation process, just  as
they are in the patch identification routine.  The territory allocation
module also includes a hexagon editing facility designed to  help you
explore the consequences for wildlife species of landscape change.
Scores and
Breeding Status
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  erritory' Min
When the territory  allocation process is  run,  a territory  map  is
generated and displayed in the analysis window. Each hexagon in this
map has two attributes: its score and its breeding status. A hexagon's
score is computed as the  arithmetic average of the weighting values
assigned to each of the data pixels contained within it. The scores are
real numbers between zero and the maximum weighting value assigned
to any of the categories present in the GIS imagery.  A hexagon's
breeding  status  is a binary  attribute  that  dictates whether or not
breeding is allowed at the site. Breeding status is determined based on
the minimum and maximum territory sizes.


The  Territory Min  and  Territory Max parameters influence the
allocation of breeding sites across a  landscape.  The minimum size
corresponds to the size of a territory in optimal habitat, whereas the
maximum territory size is realized in marginal habitats. The territory
minimum and maximum sizes do not affect the hexagon areas. Instead,
these parameters govern the degree to which habitat is shared across
hexagon boundaries, as the model allocates breeding sites throughout a
landscape. The territory allocation algorithm proceeds in several steps.
Initially, PATCH computes a threshold score using the equation


     threshold score  = max weighting value x "^  m or^ slze.
                                            hexagon size
                                                                                 18

-------
Habitat Sharing
^mm^:^
This relationship defines the threshold score as the score assigned to a
hexagon containing  exactly the  minimum territory  size  worth  of
optimal habitat, and no other habitat whatsoever. Any hexagon with a
score of at least this threshold value is automatically labeled suitable
for breeding. Hexagons that do not meet this threshold value still have a
chance to be classified as breeding sites, as long as they contain some
habitat. However, breeding status can be automatically  assigned  to
every hexagon with habitat simply by setting the minimum territory
size to zero. As a rule, hexagons that contain no habitat can never be
suitable for breeding. The next step in the territory allocation process is
governed by the maximum territory size parameter.


PATCH determines the extent to which habitat can be shared across the
hexagon boundaries using the expression

                         maximum territory size   ., ~
            expansion = 	-	-—*	1.0.
                             hexagon size

The  expansion  parameter defines the maximum amount of habitat
(expressed in fractions of a hexagon) that a hexagon can borrow from
its six immediate  neighbors. The maximum territory size  is never
allowed to exceed seven times the size of a single hexagon,  and thus the
expansion parameter can never exceed  the  area of a  hexagon's six
neighbors.  After  identifying every hexagon that  contains enough
high-quality habitat to automatically qualify as a breeding site, PATCH
builds a list of all remaining sites that have any habitat at all. These
hexagons are sorted by score, in decreasing order. The hexagons are
then allowed, in turn from best to worst, to borrow habitat from then-
neighbors  up to the  limit set by  the expansion parameter. For each
hexagon in this list, lending continues until the hexagon either meets
the suitability threshold, reaches the borrowing limit, or exhausts the
habitat available in its neighborhood. Habitat can only be lent once,
except that when hexagons are unable to expand up to the suitability
threshold, they return any habitat they have borrowed  in the process.

The amount of habitat that can be borrowed depends on  whether the
lending hexagon is suitable for breeding. Suitable hexagons are allowed
to lend only what they hold in excess of the threshold score, whereas
unsuitable hexagons  can lend  all of their habitat. Borrowing begins
with the neighbor having  the largest amount of habitat to lend, and
concludes  with  the neighbor having the least. This  process, coupled
with the initial  sorting of the borrowing hexagons by score, roughly
optimizes the allocation of suitable breeding sites across the landscape.
Chapter 5   Territory Allocation
                                                              19

-------
Linking to Life
liistory '  '	 .•;'•*
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b

Identifying
Territories
 Setting the expansion parameter to 2.5 would tell PATCH that portions
 of each neighbor could be borrowed until a total of 1.5 hexagons worth
 of the neighboring habitat had been claimed. The borrowing process is
 conducted under the assumption that each lending hexagon's habitat is
 distributed uniformly throughout its area. Though this is not always the
 case, the use of this assumption allows PATCH to avoid following the
 borrowing process on a pixel-by-pixel basis within hexagons, and at the
 same time does not significantly compromise the results. It is important
 for you to remember that the process  of borrowing habitat does  not
 change any features of a territory map other than the classification of
 hexagons as suitable or unsuitable for breeding.

 The additional energetic  costs of foraging  in, and defending larger
 territories are approximated through the borrowing process because
 hexagons labeled suitable for  breeding by virtue of having borrowed
 habitat have lower scores than those that had sufficient habitat on their
 own. These lower scores typically translate into higher mortality rates
 and lower reproductive output in the demographic analysis.


 PATCH'S use of territory maps is  designed to keep the life history
 simulator as straightforward and general as possible. The structure of a
 territory map is  simple compared to the GIS imagery from which it is
 derived. And from the standpoint of demographic modeling, PATCH is
 concerned only with each hexagon's score, whether or not  it is suitable
 for breeding,  and  who its neighbors are. Information about habitat
 patterns within each hexagon is not used by the demography module,
 and is left out of the internal description of the territory maps. Habitat
 patterns are still preserved in the visual display of territory maps, as
 long as they are not compressed. Editing territory maps is easy because
 it only  entails modifying individual hexagon scores.  The hexagon
 editing tools  are designed to  facilitate the generation of temporal
 sequences  of maps that can  be used to  investigate demographic
 consequences of landscape change. A territory map can constitute  the
 final product  of an analysis, or it  may simply  be a necessary step
 towards performing demographic simulations.


 The territory allocation controls are accessed through a panel in  the
 habitat controls window (Figure 1). This panel allows you  to construct
 a new territory map. It also makes it possible to alter an existing map (if
 the territory size  settings have been  updated)  and to  compress a
 territory map. If the current working data set consists of either a patch
map or a territory map that  has  been compressed using  PATCH'S
hexagon compression routine, then clicking on the Build The Territory
Map button simply removes these existing data. Otherwise, clicking on
this button always builds a new territory map.
Chapter 5   Territory Allocation
                                                              20

-------
                     Figure 7.    The panel in the habitat controls window that contains the
                     territory allocation routines. See the text for descriptions of the panel's
                     various fields, settings, and buttons.
                    Territory maps are constructed using the subset of the GIS imagery that
                    falls within the zoom-box. If the zoom-box contains a portion of the
                    imagery that is too large to display on the screen at one tune, then after
                    constructing the map, it can be reduced and moved around so that the
                    results can be examined a bit at a time.
                    The results of the territory  allocation process can be viewed in the
                    analysis window (use the button labeled Analysis Window shown in
                    Figure?).  The  analysis  window is always  set  to  the  size  of the
                    zoom-box, given the current magnification value. By displaying the
                    analysis and zoom windows side by side, you can compare a territory
                    map directly to the GIS data used in its construction.

                    The result of the territory allocation process is a map of hexagonal cells
                    displayed  in one  of  three  colors, depending on  the  amount  of
                    high-quality habitat hi their vicinity. Hexagons that contain no habitat
                    (no pixels with a weighting value greater than zero) are painted black.
                    Hexagons that  contain some habitat, but  that are  not  suitable for
                    breeding, are painted gray. Hexagons suitable for breeding are painted
                    green. This visual presentation is designed to help you quickly grasp
                    the character of the results. Each hexagon is also assigned a score, and
                    you should keep in mind that a hexagon's color (black, gray, or green)
                    does not necessarily reveal a lot about its score.

                    PATCH locates core areas within a territory map just  as it does with a
                    patch map. Core areas  are defined relative to an edge width that you
                    supply. They are  computed  on  a patch-by-patch basis, since the
                    hexagon boundaries do  not typically fall along habitat edges.
Chapter 5   Territory Allocation
21

-------
 Selecting a
 Hexagon
 Once the territory allocation process has been run, individual hexagons
 can be selected and a few of their properties observed. To  select a
 hexagon, simply middle click on or near it in the analysis window. The
 hexagon is highlighted (painted white), and its number, area (in pixels
 of  habitat), and score are  displayed in the  analysis window footer.
 When the mouse button is released, the hexagon returns to its original
 color and the analysis window footer displays its standard information.

 When a hexagon is selected, the threshold score and the mean distance
 separating  neighboring hexagons are  displayed in the footer of the
 habitat controls window.  The  mean  distance between  neighboring
 hexagons is computed as

                     (4 x Horiz) + (2 x Diag)
                                6

 where "Horiz" and "Diag" refer to the horizontal and diagonal distance
 between neighbors, respectively.  You  will need  to  know  this mean
 distance when parameterizing PATCH'S life history simulator.
Adjusting Min
and Max Sizes
Aligning the
Hexagon Grrid
            i
Hexagon Borders

          '
 IS™:™"1.11!.1!!; ssw. '"|ijiiii:'-"^;r^^~—."^
  ^»L;«i:;^
The button labeled Adjust Min & Max Sizes (Figure 7) updates the
territory map if the territory minimum or maximum value is altered
after the map has been constructed. This does not change individual
hexagon scores, only their designation as suitable or  unsuitable for
breeding. When this button is used, the analysis window is repainted.

The Align Grid To setting allows you to align the hexagon grid to the
zoom-box, and hence to the zoom window (the Window option), or to
the edges of the current territory map (the Data Set option).  This
feature is useful when the dimensions of the zoom-box are not equal to
those of the territory map. In such a situation, the hexagon grid should
be aligned to the edges of the entire hexagon data set, not to the edges
of the zoom-box. But if a new map is to be constructed later using a
different zoom-box size or placement, the hexagon grid must then be
aligned to the zoom-box.  Otherwise, the new map will be constructed
using the zoom-box settings from the previous patch or territory map.


The Set To Data Edge button sets the zoom-box to exactly the size and
placement of the current patch or territory map. The Add Hxgn Border
button expands the zoom-box slightly beyond the edges of a hexagon
data set in order to add a small border around the sides  of the map.
However, if this feature is used with a patch map, it simply sets the
zoom-box to the data edges.
Chapter 5   Territory Allocation
                                                             22

-------
Hexagons
             .'j^jv ,'
             **&&n-- •'
*, ^,^^-K-:-^^^^
r***
                    The PATCH model contains an editor that you can use to  alter a
                    territory map (Figure 8). Using this tool, alternative future landscapes
                    can be developed, or "what if' questions addressing the consequences
                    of specific habitat modifications can be pursued. PATCH also makes it
                    possible to randomize the placement of hexagons  within  a territory
                    map, and you can use  this feature  to  test hypotheses  about the
                    importance of a particular orientation of habitat across a landscape. The
                    hexagon editor is accessed by clicking on the button labeled View Next
                    Panel in Figure 5, or by right clicking in the panel.
                    Figure 8.   The hexagon editor. The fields and buttons on the left
                    side of the panel are used to modify hexagon scores. The buttons on
                    the right side of the panel are used for randomizing hexagons and for
                    saving results obtained using the hexagon editor.
                    The hexagon compression routine converts a standard territory map
                    into a new map composed entirely of 12-pixel hexagons. All of the
                    routines involved in running PATCH'S demographic simulations work
                    correctly with compressed territory maps. There are three reasons for
                    you to take advantage of this routine.

                    First, many territory maps cannot be displayed in full on the computer's
                    monitor because they simply extend beyond the screen's borders. If
                    such a map is  composed of large territories (much greater than 12
                    pixels), then the result of running the hexagon compression routine is a
                    new map with dimensions in pixels significantly smaller that those of
                    the uncompressed map. A compressed territory map often fits entirely
                    on  the computer screen. The second reason for using the hexagon
                    compression facility is that it is a prerequisite to running the hexagon
                    randomization routines. Finally,  when  working with large territory
                    maps, it is often desirable to use the compression facility to save disk
                    space. When a  territory map is saved to the disk, the size of the file
                    containing the map itself (the ".patch" file) is approximately 4 bytes x
                    #rows x # columns.  Saving  such files can quickly consume large
                    amounts of hard disk space. If a territory map is compressed first, the
                    demands on storage space can be reduced considerably. The difference
Chapter 5   Territory Allocation
                                                                                  23

-------
f:.-:	'  ;:.;::..;^;
r ' • ' '>„ i f "" ;   '':
I r:;
i.",',."
j..^
 • :;.' -""   f fKi;
i	,  -"-'." v -«si«i i
	' *  i1"'.'1"." -" :.,„ ::'"
3v:...v	;s"'-'5r
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i	   „„   „ ,
|i:	:  	:„   ni, ' ',
Changing the
Resample Rate
        ', ;',. *" , '"-: Tii~-«
         «  '" ~
will be proportional to the ratio of the compressed hexagon size (12
pixels) to the original hexagon size. Since some territory maps take a
long time to build, you might want to first save the original data to the
hard disk and compress it using a UNIX compression routine.

When the hexagon compression routine is used, a new territory map is
constructed  and substituted  for the  original one.  The new  map is
composed of 12-pixel hexagons, but the scores and breeding status of
the new  hexagons are  exactly the same as their counterparts in the
uncompressed map.  All habitat pattern  is lost in the compressed
territory  map, and its hexagons are  painted entirely black, gray, or
green. Li compressed territory maps there is no within-hexagon habitat
pattern to track. This is why only compressed maps can be randomized.

When  a territory  map  is compressed,  the  one-to-one   spatial
correspondence between the GIS habitat coverage and the territory map
is lost. To avoid creating misleading visual cues, the zoom window is
disabled when a territory map is compressed. This also applies when a
compressed territory map is loaded into the model. The image window
and zoom-box still work when a compressed territory map is used.

PATCH can be taken out of this mode  by clicking the Build The
Territory Map button. This removes the compressed territory map from
PATCH'S memory and  reestablishes the  one-to-one correspondence
between the zoom and analysis windows. A second click builds a new
uncompressed territory map. When the Build The Territory Map button
is used to remove a compressed territory map, the zoom-box size and
location,  the legend weights, and the hexagon and territory sizes are all
set to the values used to construct the original uncompressed map.

Running  the hexagon compression routine on a 12-pixel territory map
is allowed in spite of its having no  advantage from a  display or storage
standpoint. This is permitted because only compressed  territory maps
can be used with the hexagon randomization routines.  It can also be
easier to  see some of the patterns  in compressed territory maps since
every hexagon is painted a solid color. When a territory  map is
compressed, the hexagon grid conforms to the pixel boundaries. This is
intended to serve as a visual reminder that the data are compressed.


PATCH contains a mechanism, the Resample Rate parameter, that you
can use to split data pixels into  finer units. This  feature is useful
primarily when the desired territory size cannot be obtained using the
original pixel dimensions. If the resample rate is set to n (an arbitrary
integer), every pixel in the GIS data set is split into an n x n array of
pixels. The Resample Rate parameter is located in the main window.
Chapter 5  Territory Allocation
                                                                            24

-------
Chapter 6
                    The Movement  Module
  ,;, ; 's  'i'' &?i
Introduction
 Three different movement routines  are available within the PATCH
 model. In addition, three choices are available for defining site fidelity
 behavior (the likelihood that an individual remains on a breeding site
 from one year to the next). The options  for simulating movement
 include a directed random walk, selection of the  best available site
 within a search radius, and selection of the closest available site within
 a search radius. These movement routines require  that you  specify a
 minimum and a  maximum movement  ability, in  terms of the total
 number of steps that can be taken from a hexagon to one  of its six
 neighbors. It is also necessary to define just how random the movement
 is when  a  random  walk is taken.  The degree  of  randomness is
 determined by parameters that control the amount of linearity and the
 attraction to high quality habitat exhibited during random walks. The
 options for site fidelity are termed high, medium, and low.  High site
 fidelity implies that organisms possessing territories never relinquish
 them. Low site fidelity dictates that every  territorial individual  must
 search yearly for a new breeding site. If site fidelity is set to medium,
 then the decision regarding whether or not to remain on a territory is
 made based upon the quality of the habitat at that site. This chapter
 discusses all of these features.

 There is no mortality associated with movement in PATCH.  This was
 done because the data necessary to link mortality to movement is
 almost never available. However, PATCH does link survival to habitat
 quality, and individuals dispersing into poor habitats will experience
 lower survival rates  than those  settling  in high quality  sites. If
 population-wide estimates of dispersal mortality exist, you can always
 approximate this loss by lowering a species' fecundity values.


 The movement routine is called twice per year. It is used in the fall to
 control the dispersal of the year's new recruits (referred to as young of
 the year or juveniles) and in the spring to drive the movements of older
 organisms (referred to as adults) just prior to the breeding pulse. The
 implementation of the movement routine differs slightly depending on
 whether juveniles or adults are involved. Every juvenile is obliged to
 disperse from its  natal site, whereas adults may or may not elect to
move. Decisions  regarding adult  movement are made based upon
 whether the individual is territorial or a floater, the quality of habitat
 currently  being  occupied  (for  territorial individuals), and the site
                                                                               25

-------
                    fidelity parameter. The success of the dispersal process is evidenced in
                    part by the number of floaters in a population. PATCH keeps track of
                    the number of floaters and reports this information on a yearly basis.

                    The edges of PATCH'S territory maps act as reflecting boundaries. In
                    addition,  you can force any  nonbreeding  hexagon to behave  as  a
                    reflecting boundary. This can be done on a hexagon by hexagon basis,
                    but PATCH also has a routine that performs this function automatically
                    along edges present in the landscape. This facility is designed to help
                    you restrict movement paths in the presence of large bodies of water,
                    mountain ranges, etc. The PATCH model does not make use  of
                    wrapping or absorbing boundaries.

                    Every juvenile and every floater is required to undergo a yearly search
                    for a territory.  Further, because the minimum movement distance is
                    always at least one hexagon, individuals who qualify for movement are
                    obligated to  actually  do so. The only exception to this rule is that
                    floaters are allowed to take over the site at which they are presently
                    located in the event that the owner of the territory dies or leaves. (This
                    is technically possible for juveniles too, but it never happens because
                    there is no opportunity for the parent to move or die  in the period
                    separating the breeding pulse and  the juvenile  dispersal event.)
                    Regardless of the movement behavior being specified, individuals are
                    not allowed to settle until they have gone at least the minimum distance
                    you have specified.  Throughout the movement process, reflecting
                    boundaries are respected and movement paths are adjusted accordingly.
                    Movement paths are not affected by the presence of other individuals.

                    As a whole, this scheme provides you with the flexibility necessary to
                    apply the model to a variety of organisms using only a small number of
                    parameters. Figure 9 depicts the sequence of decisions that are made
                    when the movement routine is called.
 Random Walks

                   When a random walk is used for the movement routine, individual
                   organisms take a series of steps, from the hexagon currently occupied,
                   to one of its six neighbors. The direction of the walk is influenced by
                   the Search Randomly and Walk Up Gradient parameters. Individual's
                   tendency to move up gradient is in turn influenced by the quality of the
                   habitat within which the movement is taking place.  Before taking a
                   step,  individuals performing a random  walk first look to  see  if a
                   neighboring hexagon is both suitable for breeding and available. If so,
                   they determine whether or not to settle in that site.  This decision  is
^—--.^.^•ss^si^t   Dased upon the site's quality and on the distance already moved. The
•^^^^"Wi*Sl   better the quality of the site, the more likely an individual is to settle in
                   it. At the same time, individuals become less selective as their ability to

Chapter 6   The Movement Module
                                                                                26

-------
              Juvenile or Adult Floater
        No
                                Territorial Adult
 Individual's Present Site
is Suitable and Available ?
          Select Closest / Optimal
          Available Breeding Site
        Site Within Distance Limits
         is Suitable and Available ?
                     No
          Settle in Site (Stochastic
        Function of Site Quality) ?
                     No
                               Use the Random Walk
                               Routine for the Search
                         Next Step
Step < Min ?
                                                        Yes
                                           Step > Max ?
                                                        Yes,
                                                Stop (Floater)
                               Select Best Neighbor that
                               is Suitable and Available
             Stop (Territorial)
                                       Yes
                               Settle in Site (Stochastic
                              Function of Site Quality) ?
                                    Each
                                  Neighbor
                                                                       £<._,
                                                                       f|
                              Select a Neighbor based on
                               Up Gradient Parameter ?
                            Yes
                                            Select any Neighbor based
                                            on the Linearity Parameter
Figure 9.   A schematic of the movement routine. The term "juvenile" refers to individuals
born in the previous breeding pulse. The symbol A, denotes the dominant eigenvalue of the
projection matrix associated with a hexagon. The random walk routine's "Settle in Site" box is
passed  over if there are no available breeding sites to  be colonized. Notice that a path
connects the exhaustive search strategies (closest and optimal) to the random walk routine.
Chapter 6   The Movement Module
                                                                     27

-------

                    continue searching diminishes. If more than one neighbor is suitable for
                    breeding and unoccupied, the highest quality site is considered first for
                    settling. Ties are handled randomly.

                    PATCH uses a settling probability to determine whether an individual
                    taking a random walk should stop and occupy an available breeding
                    site. The settling probability is computed based on the quality of the
                    target hexagon, the maximum possible site quality, the distance already
                    moved, and the maximum  movement distance. A random number
                    between zero and one is then selected, and if the random number is less
                    than the settling probability, the site is colonized. Otherwise it is passed
                    up and the individual continues to search. The settling probability is
                        p      _ hexagon score
                        ^settling -   max score
                              '- _ step number^  step number
                                   max steps )   max steps
                    Early in a random walk, a searcher's probability of colonizing  an
                    available breeding site is determined almost entirely by the breeding
                    sites scores. But the  likelihood of settling increases (eventually to
                    100%), as the step number approaches the maximum number of steps,
                    regardless of breeding  site quality.  In the absence of unoccupied
                    breeding habitat, individuals taking a random walk select a neighbor in
                    a more  or less random fashion. The extent to which the choice of
                    neighbors is made at random is influenced by a general tendency to
                    move towards, but not necessarily to remain in, higher quality habitats
                    (the Walk Up Gradient parameter), and by the amount of linearity built
                    into the movement paths (the Search Randomly parameter).

                    The probability that an individual elects to move up gradient from
                    lower to higher quality habitat is proportional to the difference between
                    the score of the currently occupied hexagon and the neighbor being
                    considered. A decision to move up gradient is made if
where     T(x, z) =
   r
-------
                    Thus, the attraction to a  neighboring site  grows stronger as the
                    difference increases between its score and that of the site presently
                    occupied. This process always considers a hexagon's highest quality
                    neighbors first so that individuals are most likely to move into the best
                    adjacent site. The equations governing up gradient movement generate
                    a family of curves. Each curve corresponds to a value of the Move Up
                    Gradient parameter (Figure 10). Individuals never elect to move up
                    gradient when this parameter is set to zero.  The probability that an
                    individual moves  up gradient increases smoothly as the Move Up
                    Gradient parameter is increased (Figure 10). Individuals always move
                    up gradient when the parameter is set to 100%.
                    I
            ~s~~n-    £P
                r    53
                ?    *
       I  /*     
-------
 Walk Linearity
                     The amount of linearity in  a random walk  is  controlled by the
                     parameter labeled  Search Randomly. This parameter takes on values
                     between 0 and 100%. When Search Randomly is set to 100%, the
                     choice of which of a hexagon's six neighbors to move into (Figure 11)
                     is made completely randomly (in the absence of reflecting boundaries
                     and decisions to move up gradient). When this parameter is set to zero,
                     an  individuals  always moves in the direction of the previous step
                     (again, in the absence of boundaries and up gradient motion). The
                     resulting movement paths then become completely linear.

  .«:	 	Kjji" ' ^wtf* i ^TiiiS S
  ta»,,,»p,; |f S	=:r:u :=::§ |f
 ; f;-'ps !'S	i;i?,f| ffcaSliS
 i f*i MhTf "i pfii |
I' *"»'.•.'"" 3 i-i,,1;;,,,.' SsI»
f*^;-;!^^;pS^
1,-^., _,^	_'..;"; i-^!, "--r.,r) -•;—•--"-—•--<—"•
       ' 5 ^ SSL T^iffc »*
	 -f?	»!•! .• i	if S3S
  —•- r^ -y- t j| ™	a?1
   *  * " E '"""!l1

1 lv J./^%_'
                     Figure 11.  The naming conventions that PATCH uses to describe the
                     movement choices available to individuals in motion. The direction of
                     the previous step is indicated by the  arrow. The  labeled hexagons
                     indicate the directions corresponding to the six movement choices that
                     can be  made in  the subsequent move. The abbreviations used for
                     these directions, moving clockwise from "Directly Ahead", are: DA, AR,
                     BR, DB, BL, and AL.
                     The  influence of the  Search Randomly parameter  on a searching
                     individual's  movement  path  is  mediated  through  a  series  of
                     probabilities that govern the  likelihood of moving  in each of the
                     different available directions. Let the six possible movement directions
                     be referred to as directly ahead (DA), ahead and left or right (AL, AR),
                     behind and left or right (BL, BR), and directly behind (DB).  These
                     naming conventions  are always  relative  to  the  previous  move
                     (Figure 11). Each time an individual in motion prepares to take a step,
                     probabilities are assigned to each of the six possible directions, and this
                     in turn governs the likelihood of each neighbor being  selected. The
                          US£d for assigning these probabilities are:
Chapter 6   The Movement Module
                                                                                   30

-------
                                                  _ x(2-x)
                                                           ~
                                                             2.467
V f'~> 7 ' S?^'*' •  7f'i''^*" '^
                    and
                          1 - PAL ~ PAR ~ PEL
PEL ~ PDB »
                    where
                         _ the Search Randomly parameter
                      X  ~             100%
^2
                    The probabilities PDA, PDB, PAL> PAR, PBL, and PBR, are all smoothly
                    varying curves that  together sum to  one,  as  long as the Search
                    Randomly parameter is held between zero and 100% (Figure  12). When
                    the Search Randomly parameter is set to 100%, each of the six possible
                    movement directions  has an equal probability of being chosen. As this
                    parameter decreases, the direction selected becomes steadily  more
                    biased toward  forward movement (Figure 12).  When the Search
                    Randomly parameter  is set to 50%, PDA = PAL + PAR (hence the odd
                    exponent assigned to PAL and PAR> above). When the Search Randomly
                    parameter is set to zero, searchers not interacting with a reflecting
                    boundary or moving up gradient always elect to travel directly ahead.

                    The  behavior  of  the Search  Randomly  parameter  can also  be
                    characterized by its affect on the observed diffusion rate in the absence
                    of influences due to habitat quality or reflecting boundaries. Figure 13
                    displays the relative diffusion rate of individuals as a function of the
                    Search Randomly parameter. Relative diffusion rate is measured here as
                    an individual's displacement from its starting point divided by the total
                    distance  moved. The  data points used to  construct  the  curve  in
                    Figure 13 were generated from a sample of 100 individuals each taking
                    exactly 100 steps without reflecting boundaries or up gradient motion.


                    When individuals searching for breeding sites are instructed to select
                    the best or closest available site within a search radius, the movement
                    process takes on an appearance different from that of a random walk.
                    The search radius becomes the annulus, centered on the current site,
                    defined by the minimum and maximum movement abilities.  If the best
                    site is  to be selected, the quality and  availability of every hexagon
                    within the search radius is examined. If the closest available site is to be
Chapter 6   The Movement Module
                                                                     31

-------
I T-:
                    !
                    Is
                    •S
                    t,
                    .0
                                             Dkectly Ahead
                                                                    Dkectly Behind
                                     20         40          60
                                              Parameter Value (%)
                                                                     80
                                                                               100
                     Figure 12.  The influence of the Search Randomly parameter on the
                     probabilities governing choice of movement direction. The probability
                     of moving ahead (behind) and  left equals the probability of moving
                     ahead (behind) and right. When the  Search Randomly parameter is
                     set to 50%, the probability of moving directly ahead equals the sum of
                     the probabilities of moving ahead to the left and ahead to the right.
       -j il j::i  sf
           Si.	 I ii
                    selected, then  the search radius  is  expanded iteratively  from the
                    minimum to the maximum until a suitable hexagon is located, hi either
                    case, if more than one suitable site is found at the same distance, then
                    the best  site  is always taken. If two equidistant sites have the same
                    score, the decision of which to occupy is made randomly. Reflecting
                    boundaries are always respected,  and if the searching individual is
                    unable to locate a suitable site, a random walk must be taken. For this
                    reason, the Search Randomly and Walk Up Gradient parameters should
                    to be supplied even if a random walk is not being explicitly used.


                    The behavior of PATCH'S movement algorithm is also controlled by the
                    site  fidelity parameter.  Site fidelity governs the probability that  a
                    territorial adult (or a floater poised to take over a site who's owner has
                    died) elects to  abandon its  breeding site in search of  one  of higher
                    quality. If the site fidelity parameter is low, then every adult abandons
                    its territory (if it holds one) and searches for another site. If site fidelity
                    is high,  individuals holding territories remain on them indefinitely.
Chapter 6   The Movement Module
                                                                                  32

-------
                    CO
                    I
^^^^^S?g"™.
w^r-mxn^-?"-'
'MZ-^iWi? if
£#•55 $« , , ,
                                    20          40         60
                                             Parameter Value (%)
                                                                   80
                                                                              100
                    Figure 13.  The relative diffusion rate as a function of the Search
                    Randomly parameter. The net movement distance is the straight line
                    distance connecting the start and end of an individual's movement
                    path.  The  sum  movement distance  is  the actual length  of the
                    movement path, measures as a series of jumps between hexagons.
                    The data points used to construct this curve were generated from a
                    sample of 100 individuals each taking exactly 100 steps in the absence
                    of reflecting boundaries or up gradient motion.
                    When the site fidelity parameter is set to medium, individuals move
                    away from demographic sinks, but remain on demographic sources. In
                    this context, demographic sinks and sources refer  to  sites having
                    dominant eigenvalues (A, values) that are less than 1.0  and greater than
                    or equal to 1.0, respectively.


                    Individuals in motion reflect off the edges of PATCH'S territory maps.
                    Li addition, you can force any nonbreeding hexagon to behave as a
                    reflecting boundary. This feature allows you to prohibit movement
                    beyond a coastline  or over  a mountain range, etc. You can enter
                    reflecting boundaries by  hand  (using  the  life history  window's
                    Movement Limits  button)  or they  can  be located  automatically at
                    interfaces present within the landscape (using the life history window's
                    Automatic Limits button). The PATCH model does not allow you to
                    insert wrapping or absorbing boundaries.
Chapter 6  The Movement Module
                                                                                 33

-------
Chapter 7
                The Life History Module
Introduction
             *P"™
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             ?* t
                "I
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                *
               .4

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               3
The life history simulator is the centerpiece of the PATCH model. It is
designed for use with a range of wildlife species. The  life cycle is
modeled as a series of discrete events taking place on a yearly basis.
Each year a cohort of new recruits is generated during a breeding pulse.
PATCH has a post-breeding census, so these new recruits (subsequently
referred to as juveniles) are not of breeding age when they are initially
censused. All of the older (and potentially reproductive) individuals are
referred to for simplicity as adults. PATCH is a single-sex model, and
as such it cannot simulate an Allee effect. For this reason, PATCH may
underestimate the risk experienced by populations that are  subject to
periods of extremely low density.

PATCH'S life cycle begins in the winter  with an assessment of  the
year's  mortality. Next comes spring and  the optional movement of
adults, which is followed by a summer breeding pulse.  Juveniles
disperse in the autumn,  and finally the census is taken. The cycle then
repeats starting with the winter of the following year. For simplicity, all
mortality is collapsed  into the yearly  survival  event. There is  no
mortality associated with the movement process. As mentioned above,
the timing of events in PATCH'S life history simulator is designed to
mimic a projection matrix with a post-breeding census. However,  the
census is placed after the dispersal event so that juveniles  are included
in the counts of floaters and breeders. The absence of mortality in  the
movement process ensures that the census still accurately records  the
number of new recruits. PATCH'S life cycle is displayed in Figure 14.

PATCH'S life history simulator  was  designed  with the intent that it
would carefully incorporate spatial pattern into its predictions, while
being as parsimonious as possible. None the less, you may not have the
data necessary to  supply all of the parameters  with  confidence,
particularly the interpolation  functions, the vital rates factor, and the
parameters  controlling  random walk  behaviors. But all of these
parameters  emerge directly from the spatially explicit nature  of the
model. If, for example, the interpolation routines were not  selectable
from the model interface, PATCH'S  connection to GIS maps  would
dictate that their functionality still existed in some form. By providing
you with control over these parameters, instead of simply hard-wiring
them into the model code, PATCH makes it possible for you to conduct
sensitivity analyses  and test the various assumptions that you will
inevitably end up making.
                                                                                34

-------
                                    Increment Year
                                 Read New Hex Maps
                                         i.
                                       Survival
                                   Adult Movement
                                      Breeding
                                  Juvenile Dispersal
                                  Census Population
Start Up Model
    Winter
    Spring
   Summer
   Autumn
Tabulate Data
                    Figure 14.  The timing  of events  in the life history simulator. The
                    census is placed between the breeding pulse and the survival routine
                    so that it records the actual number of new recruits to the population.
                    The dispersal event is placed before the census so that juveniles are
                    included in the  counts  of floaters and breeders.  The movement
                    routines do not subject individuals to any additional mortality.
                    Survival and reproductive rates are loaded into PATCH in the form of a
                    projection matrix. If an entire landscape consists of optimal habitat, and
                    if breeding sites are unlimited, then PATCH'S projected population
                    sizes will agree almost perfectly with those obtained using  a matrix
                    model. However, to the extent that high-quality habitat is  limiting,
                    PATCH'S results will  differ from those of a projection matrix.
                    Differences arise because PATCH is individual based, spatially explicit,
                    and because its  survival, reproduction, and movement modules all
                    incorporate  some  stochasticity.  Decisions  regarding   survival,
                    reproduction, and movement behavior are made on an individual basis
                    using  a random number generator.  These events can be significantly
                    influenced by the quality of habitat present  at an  animal's current
                    location. Variability in the  survival and reproductive rates  resulting
                    from the use of a random number generator approximates demographic
                    stochasticity. PATCH also allows you to incorporate environmental
                    stochasticity into its simulations.
Chapter 7  The Life History Module
                  35

-------
Linking to
Habitat Quality
             ""V
PATCH  does not assume that survival and reproductive rates scale
linearly with habitat quality. Instead, you are provided with a set of six
generic  functions (linear,  logistic, concave,  convex,  constant, and
piecewise constant) that can be used to compute species' vital rates
from habitat quality. But PATCH cannot carry  out these computations
unless you also tell it what quality of habitat is to be associated with the
vital rates supplied as input parameters. That is, PATCH needs to know
if the vital rates in its input matrix are to be realized in the best habitat,
or the worst, or some intermediate value. This information is brought to
PATCH by the Vital Rates Factor parameter. Of course, you also need
to select specific survival and reproduction interpolation functions. The
six interpolation functions are described mathematically in Table 2. hi
each equation, hexagon quality is introduced through the relation

                    _     Hexagon Score
                                          Maximum Hexagon Score'

                     The value of each interpolation function is represented in Table 2 by
                     the symbol "y". The minimum survival and reproductive rates always
                     equal zero, and they are realized in hexagons having scores of zero. The
                     maximum survival and  reproductive rates are realized in hexagons
                     having scores  equal to  the largest weighting value specified in the
                     legend. These maximum vital rates can be calculated from the input
                     data using the relationship
                           maximum rate =
                                                vital rate entered into matrix
                                            INTERPOLATE-
                                        Vital Rates Factor
                                             100%
            -«*!
            , - I i
               -,-j
            ',f»l
where "INTERPOLATE" is replaced with the appropriate interpolation
function from Table 2. The  argument of the interpolation function
represents the extent (expressed as a number between zero and one) to
which the best possible hexagon score exceeds the score associated
with the vital rates entered into the matrix. For example, you might
specify  that the yearly adult  survival probability is 0.60 in hexagons
that have scores equal to 75% of the highest possible value (i.e., vital
rates factor = 75). If the interpolation function is linear, then the value
of adult survival ranges between zero, in hexagons having scores of
zero, and
                                           0.60
                                    0.60
                                      LINEAR{0.75}    0.75
                                                             = 0.80
             1*1!
Chapter 7   The Life History Module
                                                              36

-------
                     in  hexagons  having  the  best  possible  score.  However,  if  the
                     interpolation function is concave, then this maximum value equals
                                          0.60
0.60
                                   CONCAVE{0.75}    (0.75)3
                                                                = 1.44.
                     Because this represents a survival rate greater than one, PATCH would
                     refuse to  run until you either  lowered the matrix value for adult
                     survival, raised the quality of habitat associated with the input matrix,
                     or changed the interpolation function used for survival.  To make this
                     sort of assessment easier, PATCH displays the maximum vital rates any
                     time you middle click in the Life History Parameters window.
                                    Table 2: The Interpolation Functions
Name
Linear
Logistic
Concave
Convex
Constant
Piecewise Constant
Mathematical Description
y = x

' , HH
1+e

3
v ~ x
y = l-(l-x)3
y = l
y = 0 x e [0 ,
y = 1/2 x e [1/3
y = 1 x e (2/3
1/3)
,2/3]
,1]
                     The above rules governing survival probabilities are modified slightly
                     for floaters. Floaters are adults or post-dispersal juveniles that do not
                     possess a territory. By definition, floater reproductive rates are fixed at
                     zero. The survival rates for floaters are computed the same as for
                     territorial  individuals, except that floaters' maximum survival rate is
                     capped at the threshold score. The threshold score is given by:
Chapter 7   The Life History Module
                          37

-------
                         ,.   ,  , j                . , ,.     ,     min territory size
                         threshold score = max weighting value x —;	-.	.
                                                                  hexagon size

                     The logic behind this is simple. Floaters in the vicinity of high-quality
                     sites occupied by territorial individuals cannot be expected to reap the
                     same benefits  from these  habitats  (i.e., they  should have  higher
                     mortality) as those who are breeding there. At the same time, floaters in
                     habitats that cannot support breeding do  not necessarily experience
                     intra-specific  competition,  and  in   those  situations  it  might be
                     inappropriate to lower their survival rates. The threshold score is the
                     break-point between habitat that can and cannot support breeding (in
                     the absence of habitat sharing between sites) and as such it provides a
                     natural vehicle for fixing an upper bound on the survival rate of floaters.
Demographic
Stochasticity

       :*„* fi
       '-*— - '
Life history simulations conducted with PATCH always incorporate
demographic Stochasticity,  the random fluctuations in survival and
reproductive rates that occur between individuals. This results from the
model's use of a random number generator to evaluate the outcome of
specific survival and reproduction decisions. In the case of survival, a
uniform random number between zero and one is selected. If this
number is less than the sum of the probabilities of making a transition
between the current stage (or age) class and every other class, then the
individual dies. Reproduction  is stochastic only to the extent that a
random number is selected to force the brood sizes take on integer
values. Let the expected rate of reproduction for a particular hexagon
be represented by the real number x. Refer to brood sizes equal to the
closest integers less than x and greater than x as n" and n+, respectively.
The probability of producing a brood of  size n" is set  to n+-x.
Similarly, the probability of producing a brood of size n+ equals x - n".
Only broods of these two sizes  exist as possible  outcomes for
individuals breeding in this hexagon. This scheme for reproduction is
simplistic, but it only a single parameter per stage (age) class.
Environmental

Changes to the mean survival and reproductive rates resulting from
fluctuations  in  environmental conditions  (good  and  bad  years,
catastrophes,  etc.)  can be assumed  to influence every member of a
population in a similar way. This type of variability is referred to as
environmental Stochasticity, and it frequently plays a significant role in
the dynamics of wildlife populations.  PATCH allows you  to  build
environmental Stochasticity  into its demographic  simulations. You
accomplish this by constructing a table  of vital rates  that reflect the
level  of environmental Stochasticity to be simulated. PATCH can
upload the data in this table as long as the data are formatted correctly
and contained in a  file that has an appropriate name. Each column of
the table signifies a specific survival or reproduction rate. Every row of
Chapter?   The Life History Module
                                                              38

-------
                    the table must contain the entire set of survival and reproductive rates
                    necessary to construct a projection matrix.
                                     i-          -'-
                    Matrix  elements set to zero  in  the  model interface  cannot be
                    represented in the table of vital rates, and as such they must remain zero
                    indefinitely. Each year the model is run, a row from the table is selected
                    at random and used to fill the projection matrix for the species being
                    simulated. Thus, you can include any amount of correlation between
                    age or stage classes by constructing the table's rows appropriately. The
                    name of the file holding this table has to be built up from two parts. The
                    first part must be identical to the name of a data file containing the other
                    demographic parameters describing the species. The second part must
                    contain  the string ".random". Figure 15 provides an illustration of the
                    format that PATCH expects for tables of vital rates.
                    Figure 15.   The data format for entering environmental stochasticity
                    into the PATCH model.  Each nonzero entry in the projection matrix
                    (shown on the left) defines a column of the data table (shown on the
                    right). The columns in the data table are numbered in increasing order
                    from left to right. A row from the data table is selected randomly at the
                    start of each year, and  is used to define a new projection matrix to
                    govern that year's survival and reproduction decisions. You can create
                    as many rows as desired,  but the survival  values within  a single
                    column of any potential matrix must never sum to more than one. This
                    calculation includes the influence of the vital rates factor.
Chapter 7   The Life History Module
39

-------
Miscellaneous
Parameters
Other than specifying the model organism's movement behavior, you
must provide only a few remaining parameters. It is necessary to
specify the duration of each simulation in years, and the number of
replicate simulations to be conducted. PATCH must also be told where
to locate the initial population of organisms, and what age or stage class
to assign to them. You can also make specific nonbreeding hexagons
function as reflecting boundaries. Lastly, a transient period  can  be
established  during  which  information  about the  emigration and
immigration into breeding sites is not to be compiled.
Running a
Simulation
  -
  i»3"
rilJtillt
The PATCH model can be used to conduct demographic simulations
after a territory map has been installed and the parameters in the life
history  windows have  been  specified. A simulation  is started by
clicking the Run Simulations  button in the bottom panel of the life
history   window (Figure 16).  If the  visualization  toggle is on
(Figure 17), and if the analysis  window is  up to date,  then the
simulation is displayed on the screen as it progresses. It is possible for
one simulation to start up at the point where the previous one left off,
but this can be done only when the number of runs is set to one, and
only if  the Tally Utility From  field is set to zero. Otherwise, the run
number and year are automatically reset to zero at the start of each new
simulation. Altering any model parameter except the number of years
or the visualization setting causes PATCH to reset the run number and
year to zero.  This  design allows  you  to run  the model for a  large
number of years with the visualization check-box turned off, and then
subsequently for a few more years with the visualization on.

The Write Parameters button (Figure 16) can be used to write a copy of
the current set of demographic parameters to the computer's  monitor,
or to a file. The Read Parameters button loads demographic data from a
file and sets the parameters in the life history windows. This utility can
be used to read output generated from the Write Parameters button, or
it can read output from a previous run of the model. This works because
every time a demographic simulation is conducted, the model begins by
printing out the full set of life history parameters currently being used.

While a simulation is being conducted, PATCH tracks the number of
individuals  in each age or stage  class, the number of floaters and
breeders, and the mean values  of both the  net and sum dispersal
distances (for juveniles only). The net dispersal distance is the length of
the  straight line connecting the  starting and ending points on the
movement path. The sum dispersal distance  is the actual  distance
moved,  measured as a series of straight lines from one hexagon center
to another. PATCH  also tracks the effective survival and reproductive
rates and it  provides you with a year-by-year record of the dominant
Chapter?   The Life History Module
                                                              40

-------
        > ^ * * 1
       -, » jit t '  x

                     Figure 16.  The panel in the life history window that is used to control
                     PATCH'S demographic simulations.
                     eigenvalue (the  anticipated steady-state growth  rate, or A,)  of the
                     projection matrix derived from these vital rates. An example of the data
                     generated by running the model with a two-stage projection matrix is
                     provided in Figure 18.  The results shown are averages taken over 10
                     replicate runs. Only part of the model output is shown in Figure  18.
                     Figure 17.  The  panel in the  life history window that controls the
                     visualization and  initialization options. The R, B, and L refer to the
                     random,  best, and locked options of the routine used to locate the
                     initial breeding population within the landscape.
                     If an output file name has been specified in the life history window,
                     then model results are written to this location. If a file name has not
                     been provided, then the output is sent to the monitor. The output data
                     include a run-by-run, year-by-year summary of the population. If an
                     output file has been provided, and if the number of runs is greater than
                     one or the Track Utility From parameter is not zero, a binary output file
                     ending  in  ".statsO"  is  generated.  This  file  contains  the  data on
                     occupancy rates. If the Track Utility  From parameter is not zero, two
                     more text files are also generated. One of these ends in ".statsl", and
                     contains the means and standard deviations of various measures of the
                     population computed from the collection of replicate runs. The second
                     file ends in ".stats2" and stores occupancy rates and source-sink data.
Chapter?   The Life History Module
41

-------
                      I  §
                                  Population Size
                              10
                                   20
                                        30

                                      Year
                                                   50
                                            Observed Vital Rates
                                                               10
                                                                    20
                                                    30

                                                  Year
                                                                               40
                               Observed Lambda Values
                ii
               	I":
ST.;
          -?'!'„, rjSi f~~
        ''iiiiypift'i ii'V-r-.
               ,
         n KJ, ""',|,|, W .jftlE sS
         \-'^ * ;''"'~Jli f
      ll(l"™'* '^fil" 1 ..... FV%
       l
     :T 11 ...... 11
         TI1i*>"vni
         -'•'- ....... ! ..... , ...... ';""• Mill's "I
                                                              Observed Source Sink Behavior
                              10
                                        30    40
                                                   50
                                      Worst
                                      Sink
               Best
        Neutral   source
Expected Behavior
Figure 18.   Example output, averaged over 10 replicate simulations,
generated  using  a  two-stage  projection  matrix.  Each  replicate
simulation was run for 1000  years, but only years 5 through 50 are
shown  in the figure. Every breeding  site was initially filled,  and the
population is shown declining to  a stable size. The source-sink data
are  averages  for  years  500-1000.  PATCH does not create these
graphs, it only generates the data that can be used to construct them.


Three additional output files containing occupancy rate and source-sink
information can also be generated by clicking on the Get Output Maps
button in Figure 16. The first of these ends in ".imageO" and it displays
the observed occupancy rates.  These occupancy rates are gathered from
the final year of a  model simulation, and are summed across every
replicate  model run.  Each breeding  site is assigned an occupancy
register that is incremented by one if the site is occupied at the end of a
given replicate run. When the occupancy rate map is generated, the
occupancy register totals are collected and rescaled to lie between zero
and ten. The more frequently occupied sites are assigned the higher
values. Breeding sites that were used  the least are displayed in red in
the occupancy maps. The sites that were used the most are displayed in
blue. Intermediate rates of occupancy are displayed using a gradient of
colors that shift smoothly from red to blue.

The second output map ends in ".imagel", and it displays the expected
source-sink properties of each breeding site. This image is constructed
Chapter?  The Life History Module
                                                                 42

-------
''••  &• ^ *i&!«fe £s I
  ="  • • : 2*~£f^'~ i 'f^9,5
;x.;^|j^^l
,  -   - "'--"; "*.:.;   ;<.,-
                    directly from the territory map and the survival and reproductive rates
                    supplied. It does not incorporate any results from a simulation. Instead,
                    it provides an anticipated source-sink distribution for the landscape. In
                    contrast, the third output map (ending  hi  ".image2") displays  the
                    observed  source-sink  properties  that   actually emerged  from a
                    simulation. In both cases, the source-sink evaluations are made only for
                    the breeding sites present in a landscape. The expected source sink map
                    is  built  from  the  dominant  eigenvalues  (A/s)  of the  population
                    projection matrices associated with each breeding site, given its score.
                    The  observed  source-sink map is  generated from a tally of  the
                    immigration and emigration events observed at each breeding site. The
                    actual data values used to generate these maps are stored in a text file
                    (the ".stats2" file) that is automatically generated by the model.

                    The  expected and  observed source-sink maps  are constructed by
                    breaking the original continuous source-sink data into discrete color
                    classes. The maps are designed to distinguish between sources, sinks,
                    neutral sites (neither a source nor a sink), and sites that are unsuitable
                    for breeding. Sources  and sinks are further broken down into 100
                    classes each. Every one of  these classes represents  an interval, one
                    percent in width, within the observed range for all sources or all sinks.
                    The  scheme used to construct these images is illustrated in Table 3.
                    Initially, all of the sources are displayed in green, and all of the sinks
                    are displayed in red. But you can easily change these color schemes and
                    identify sources and sinks based on their severity. A new copy of the
                    expected source-sink map can always be  generated  by loading a
                    territory map, entering the vital rates, the vital rates factor, the survival
                    and  reproduction interpolation  functions, and then clicking the Get
                    Output Maps button. A new copy of the observed source-sink map can
                    be generated by loading a territory map and a demographic output data
                    set that includes a ".stats2" file. Once PATCH has uploaded the data
                    contained in the ".stats2" file,  you can  click the Get Output Maps
                    button to recreate an observed source-sink map.


                    PATCH allows you to insert reflecting boundaries into a territory map.
                    These boundaries are defined on a hexagon-by-hexagon basis, and are
                    used to prevent movement across bodies  of water or high mountains,
                    etc.  You can start this process by clicking on the Movement Limits
                    button (Figure 16), but this only works if the analysis window is up to
                    date. Once the button has been clicked, and after the mouse pointer has
                    been moved into the analysis  window, reflecting boundaries can be
                    inserted by clicking on any hexagon that is painted either black or gray.
                    The  assignment of boundaries works like a toggle, hence a second click
                    removes a boundary that has previously been added. This process ends
                    when the mouse pointer is removed from the analysis window.
Chapter 7   The Life History Module
                                                                                   43

-------
                                     Table 3: Source-Sink Map Structure
Pixel
0
1
2
Interpretation
1. 00 x Worst Sink > Value > 0.99 x Worst Sink
0.99 x Worst Sink > Value > 0.98 x Worst Sink
0.98 x Worst Sink > Value > 0.97 x Worst Sink
 :.vv- V/V,/:	":S!i
 j|	;,  'l-i'iVpT	:,;.:; S~a 3
1 -V	'•:  """ -i~v*;j ft^f ~
 T ?	•' 	M *"	3 S
		« ,: ij,,-* «(
f ?'•'•« "iijr: 4 TV Hfc *f
II t:Mf '	£'••.•, IB.; I	';..;"«"«,
i| : -i:',,  ,v~ „•*«« 1 ('ifv .HI i
  '   '--
               ;:,:!;,!,
98
99
100
101
102
0.02 x Worst Sink > Value > 0.01 x Worst Sink
0.01 x Worst Sink > Value > 0.00 x Worst Sink
Neither Source Or Sink
0.00 x Best Source < Value < 0.01 x Best Source
0.01 x Best Source < Value < 0.02 x Best Source
198
199
200
201
202
0.97
0.98
0.99

x Best Source <
x Best Source <
x Best Source <
Hexagons That Do
Value
Value
Value
< 0.98 x
< 0.99 x
Best Source
Best Source
< 1. 00 x Best Source
Not Contain Any
Non-Breeding Hexagons
Containing
Habitat
Habitat
        "'" ""•-"• -a™ " 7il!l'Jii 'S
           '
  §jw
  r
I E*-3''l!|r. .,,,.«..,„

llliMlll" »,"»"'"'ill1 =, ^iiii *'; Ai!7^,i(;*ii5raJi.;M-j|i
The life history window also has a button labeled Automatic Limits that
inserts  reflecting  boundaries into the landscape for you. Recall that
hexagons with no habitat are painted black. Hexagons with habitat are
painted green if they are suitable for breeding, and gray otherwise. If no
reflecting boundaries are present, clicking the Automatic Limits button
initially places a boundary at every black hexagon that has  a gray or
green  neighbor.  Clicking  on this  button  a  second  time  places a
boundary at every gray hexagon  that has a neighbor has a black or
green neighbor. A  third click locates a boundary at every site that
qualified under either of the two scenarios just described. A fourth click
removes all of the reflecting boundaries. The Automatic Limits feature
only works if the analysis  window is up  to  date. The locations of
reflecting boundaries are stored in the life history parameters files.
Chapter?   The Life History Module
                                                                 44

-------
          -
Starting Sites^b
PATCH  provides three mechanisms for specifying the size and
locations of  the initial breeding  population. PATCH  cannot be
initialized with nonbreeders. The initial population can be distributed
randomly across the breeding sites, it can be placed preferentially into
the highest quality neighborhoods (a neighborhood is a hexagon plus
its six neighbors), or it can be located by hand using the mouse. In
addition, any configuration of initial locations can be locked into place,
and thus applied to every one of a series of replicate simulations. These
three options (random, best, and locked) correspond to the R, B, and L
check-boxes found in Figure 17.

If the random or best neighborhood options are being used, then it is
necessary to specify only the size  of the initial population. If the
starting sites are to  be selected by hand, then the Specify Locations
button must be used. Click on this button, move the mouse pointer into
the analysis window, and then click on each of the sites that  is to be
initialized. For this to work, the analysis window must be up  to date,
and the sites selected must be suitable for breeding.  Once the mouse
pointer is moved outside of the analysis window, the procedure ends.
This process can be  used in combination with either of the other two
methods of selecting starting sites. Any time you set a starting location
by  hand, the Initialization  parameter (Figure 17) is automatically
locked. You can always view the  current placement of initial breeders
in the analysis window by  clicking on the Reset & Initialize and
Display Locations buttons. If you have already run a simulation, you
may have to press this button twice to generate a new initial population.


PATCH  provides  you with  a  way  to alter the landscape  while a
demographic simulation is running. You do this by telling the model to
load new territory maps at specific years. The life history window
contains  a time series editor (Figure 19) that exists for this purpose. To
use the time series editor, first select the desired year. If a territory map
has already been entered for that year, then the name of map appears in
the panel's text fields.  Otherwise, enter the location and name of the
map you want to use.  An  existing  map  can  be removed using the
Remove This Entry button. A new map can be installed using the Add
This Entry button. The list of active maps can be examined using the
Search Backward and  Search Forward buttons. If multiple replicate
simulations are being conducted, you must install a territory map at
year zero. This prevents the model from starting a new replicate using
the ending map from the previous replicate. The life history window
footer informs you about any actions taken by the time series editor.
Chapter 7   The Life History Module
                                                              45

-------
     Parameters
Window
    .
  .\'\ :
ijliiii ...... r ....... ill iii,, i,
T ......
   ".'',,,:':.; S'
  i"j» v ti f
  ff3 IS.;!..,];!1
IS
       	;	:i"	";-::-»i!4	-'3
       ;	:	,	:-:	rrfi;	••'••>•'
                                                  "     /
                              Get Hes Map At year?   0
                                          .    '  '  . ^ <*,„ _
                              Directory  :  __,	^
                              File  Name  :
                                Remove This
                                Search Backward^ x
                     Figure 19.  PATCH'S time series editor. The utilities in this panel allow
                     you to alter  the  landscape while a simulation is  running.  PATCH
                     accomplishes this by loading new territory maps at specified times.
     The majority of the information used to describe a species is entered
     into PATCH through the life history parameters window (Figure 20).
     The life history parameters window contains two panels. The left panel
     holds ten different model parameters and  the  right panel holds  a
     projection matrix. The ten parameters include the number of runs and
     number of years per run to be used in the simulations. It is also where
     you specify the starting population size, the age or stage class of the
     starting population, and the minimum and maximum movement ability
     of the species. This panel holds two parameters (Search Randomly and
     Walk Up Gradient) that govern the behavior of random walks. It is also
     where you set the year in which the tabulation of source-sink data for
     the species  begins (the  Tally Utility From parameter). Lastly, this is
     where you define the percent of the maximum habitat quality that is to
     be associated with the vital rates entered into the projection matrix. You
     specify this using the field labeled Vital Rates Factor.
                             /" life. History parameters
 Totn) MBdel Wns : 0_
 NnmfetrOfVoars

* inttlil PapuIaMori
, Jnrtlalliat1onA»B
 S»«Tt MinintBin
• S««rt* Maximum
       WmikUftCradiejrt
       Vita) Kxt« ftctsr
,jtW
 **VJ
:m
-jua
-itel
-JEtl
-T
                :$
                     Figure 20.   The life history parameters window. The left panel holds a
                     variety of parameters that describe a species and set up the properties
                     of a simulation. The right panel holds a 10 x 10 projection matrix.
Chapter 7   The Life History Module
                                                                   46

-------
              if'
             r  *
             V",*
The right panel of Figure 20 is where the population projection matrix
is supplied to the model. This panel can accommodate up to a 10 x 10
matrix. The rows and columns of this matrix, and hence the age or
stage classes, are numbered 0-9. You must provide a projection matrix
with at least two age or stage classes, but it is not necessary to fill the
entire 10 x  10  matrix present in the model.  PATCH'S life history
module incorporates a post-breeding census, which means that the first
age or stage class  always consists exclusively of newly recruited
individuals that are not yet of breeding age. Thus the upper left entry in
PATCH'S projection matrix is necessarily fixed at zero. The vertical bar
on the right hand side of Figure 20 is used to display the life history
functions window (Figure 21). You can also right click in  the life
history parameters window to call up the life history functions window.
The Functions
Window, ,  /
     W «h "
     1 .^"l* ,
PATCH uses interpolation functions to compute the expected survival
and reproductive rates associated with hexagons of an arbitrary quality.
These functions are accessed through the rife history functions window
(Figure 21). The functions provided are linear, logistic, concave (cubic
growth), convex (cubic decay), constant,  and  piecewise  constant.
Hexagons  with a score of zero are always assigned survival and
reproductive rates of zero. Hexagons having  a  score equal to that
specified by the Vital Rates Factor parameter are assigned the survival
and reproductive rates appearing in the projection matrix. Survival and
reproductive rates for hexagons with all other scores are obtained from
the interpolation functions.

If the constant function is used, then the survival and reproductive rates
appearing in the projection matrix are applied to every hexagon that has
a score greater than zero. Hexagons  with scores of zero are assigned
vital rates of zero. The break points for the piecewise constant function
are at 1/3 and 2/3 of the maximum hexagon score. Hexagons with less
than 1/3 of the maximum score are assigned survival and reproductive
rates of zero. Hexagons with more than 2/3 of the maximum score are
assigned the survival and reproductive rates entered into the projection
matrix. All other hexagons are assigned vital rates equal to 1/2 of the
values entered into the projection matrix. The maximum hexagon score
is always equal to the maximum weight assigned to any of the image
categories in the legend, even if no hexagon actually has a score that
high. A hexagon would have to consist entirely of the habitat that was
assigned this maximum weight in order to attain the maximum score.


The life history interpolation functions are included in PATCH to give
you control over the way survival and reproductive rates scale with
habitat quality.  Most spatially explicit models ignore this  issue by
assuming a constant or piecewise constant functional  form. While
Chapter 7  The Life History Module
                                                              47

-------
                                               '- life History Functions
                     Figure 21.  The life history functions window. The left and  center
                     panels allow you to select interpolation functions to be used with the
                     survival and reproductive routines. The right panel is used to select a
                     movement strategy and the site fidelity behavior.
,ih	.;•
• '); i. ."
             ; A
             ;;ill

                     PATCH'S additional flexibility in this area may  seem like a burden,
                     there are at least  three approaches you  can take to selecting  the
                     interpolation functions. Ideally, field data can be used to fit survival and
                     reproductive rates directly to estimates of habitat quality. If this is
                     possible, the interpolation functions can be chosen that most closely
                     match the curves fitted to the field data. A second approach is to use the
                     interpolation functions as free parameters to help you rune the observed
                     population-wide  vital rates.  The  observed  vital rates  reflect  the
                     influence of habitat quality on the population as a whole. You might,
                     for instance,  supply PATCH  with  biological upper limits  for  the
                     survival and reproductive rates of a species,  and then associate these
                     values with optimal habitat using the Vital Rates Factor, Interpolation
                     functions can then be chosen so that the observed aggregate vital rates
                     or Vs agree with field-based estimates. A third alternative is simply to
                     use the life history interpolation functions in sensitivity analyses.  Some
                     of the functions may  be ruled out in  advance  using plausibility
                     arguments. The remainder can be examined  to see how significant a
                     role they play in controlling the results of your life history simulations.
  i:i £••••:• 'f v
                 i
  f!:'!"!! fti!:1™:;1"1" ;K ^ i;!-j5il> *f
Chapter 1   The Life History Module
                                                                                  48

-------
Chapter 8
                                           PATCH  Utilities
Introduction
Reading and  ;
^Ti'*"7' '." *  :'Jff tti*fZVf.
•Viewing Imager
            This chapter contains an exhaustive list of the utilities present in the
            PATCH model. Each section begins with an image of one of PATCH'S
            control panels. The remainder of the section describes the function of
            each button and field located within the panel.
F/s

                   This is the first panel you interact with. The directory and file name
                   fields are used for  loading GIS imagery,  and  also by PATCH'S
                   histogram routine. This panel also provides you with access to three of
                   PATCH'S graphics windows, and is where you exit the program.

                                            This button is used to load a GIS data set
                                            into PATCH. Pushing this button also
                   resets most of the model parameters to their default values. You cannot
                   conduct any analyses until a GIS data has been successfully loaded.

                                            This button calls up a hidden panel that
                                            contains 10 additional buttons.

                                            This button exits PATCH. You will not be
                                            given the option to cancel this command.

                                               This button  calls  up  the  image
                                               window. The image window displays
                   a subsampled  version of the entire GIS  data  set.  The level  of
                                                                            49

-------
         1,  -L
         "**«
              p >
             ",£*!
                    subsampling is set using the Image Window Sampling field. When this
                    field is set to n (an arbitrary integer), every nth row and every nth
                    column from the GIS data set are  shown in the image window. As n
                    decreases, the window gets larger and more data is displayed.
   how
                                                       butt°n  calls  ?P  the,. zoom
                                                 W1ndow. The zoom wuidow displays
                    the contents of the zoom-box. The zoom-box is shown in the image
                    window, and can be moved around and resized in a variety of ways. The
                    data displayed in the zoom window are shown in their entirety (unlike
                    the image window), and they can be magnified using the Degree  Of
                    Magnification field. Only the data within the zoom window are used
                    when the patch identification or territory analysis routines are run.
                             This  button calls  up the  legend
                             window. The legend window displays
the category names and colors present in the control file. Entries in the
control file that do not contain a category name are  skipped in the
legend.  The legend window also contains  a facility for  assigning
weights (habitat affinities) to classes in the GIS data. These weights are
needed by the patch identification and territory allocation routines.
Habitat weights are assigned by clicking on the legend categories. A
left click increments a weighting value, while a right click decrements
it. If the left and right buttons are used together, the weighting value is
set to zero. Note that a weight of zero is displayed as an empty box in
the legend window. Middle clicking on a legend category inserts the
editing arrow. The editing arrow is used to define a target habitat class
for use with PATCH'S pixel and patch editing procedures. The editing
arrow can only be inserted if the GIS file has UNIX write permission.

                             The color bar (shown throughout the
                             manual in  gray-tone)  is  used  to
change the color of the zoom-box  and of the hexagon grid in the zoom
window. You click on the desired color, and it is automatically applied
to both features. However, selecting the white color cell removes both
the hexagon grid from the zoom window and the zoom-box from the
image window. If the size of the zoom-box exceeds that of the territory
or patch map, use of the white color cell also produces a white box in
the zoom window that shows you the extent of the map.

            '! '
Chapter 8  PATCH Utilities
                                                             50

-------
            us
           »»M re
Functions t ;
L '•-""? «&••: ' '~"*'~'. J '
                    This panel is obtained by clicking on the main window's Display Next
                    Panel button. The buttons labeled Get Habitat Controls, Life History
                    Controls, and Life History Settings  simply call  up other control
                    windows. The button labeled Display Initial Panel recalls the panel that
                    was  originally  displayed  in this  part  of  the main window. The
                    remaining utilities have more complex functions.

                                                 This button causes PATCH to generate a
                                                 histogram  showing  the  number   of
                    occurrences  of  each habitat class within the  area enclosed by  the
                    zoom-box. The  histogram  includes a record of the row and column
                    values of the zoom-box edges used in its construction. It also includes a
                    list all of the habitat classes, the class names, and a tally of the number
                    of pixels and hectares of each class found in the data. The histogram is
                    written to the computer screen unless a file name is provided in  the
                    main window. The histogram routine never overwrites an existing file.

                                                 This  button  generates  a  new  Sun
                                                 Rasterfile  containing only  the image
                    present in the zoom window. This routine is  identical to the one
                    accessed  with the Zoom Rasterfile  button  (located  in the habitat
                    controls window),  except that this utility creates a rasterfile whose
                    colormap contains every entry  present  in the legend  window. In
                    contrast, the Zoom Rasterfile button strips out legend colors not used in
                    the image. This utility  works only if an output file name has been
                    provided in the habitat controls window.

                                                 The   resample   rate    provides   a
                                                 mechanism for splitting the data pixels
                    into finer units. This is useful primarily when the desired territory size
                    cannot  be obtained using  the original pixel dimensions. When  the
                    resample rate is set to n (an arbitrary integer), every pixel in the GIS
                    data set is split into an n x n array of pixels. Patch or territory  maps
                    constructed using the same GIS data but different resample rates are  not
Chapters  PATCH Utilities
                                                                                  51

-------
	ii.;:4^;:
•i" Hi- ,iij I	
   	: r-" ; .-,:	i -i , ^ •	ry «[
   inn In..;™-- ««i 	- - liip 4
                    identical. At a minimum, their extent in pixels is different. For this
                    reason, PATCH must store the resample rate that was used to construct
                    a territory or patch map. This information is recorded in the ".patch"
                    file. When  you attempt to  load a patch or territory map, PATCH
                    compares the resample rate stored in the ".patch" file to that currently
                    set through  the model interface. If the two values do  not match, then
                    PATCH alerts you and aborts the load.

                    In some very special cases, you might want to alter the  value of the
                    resample rate as it is stored in the ".patch" file. This  can be done by
                    setting the resample rate field in the main window to the value desired,
                    entering the name of an existing patch or territory map in the habitat
                    controls  window (use the input fields but do not load the  data), and
                    clicking  on  the Alter Resample Rate button. In  order for  the edited
                    patch or habitat map to be useful, you must ensure that its row and
                    column boundaries do not lie outside the range defined by the  GIS
                    imagery and the new resample rate.
                             Pixels By
                             °" -^-  *
                                                          of the tools  available for
                                               using PATCH to edit GIS imagery. This
                   utility only works when the GIS file being used has UNIX write
                   permission, and when the patch identification routine has been run. To
                   proceed, you  must first insert the editing arrow at one of the legend
                   entries by clicking the middle mouse button on the desired category.
                   When the Alter Pixels By Patch button is pushed, every pixel in every
                   patch present in the landscape is changed to the legend value containing
                   the editing arrow. This change is made directly to the GIS imagery, so it
                   is permanent.  The patch map is discarded after the process has finished,
                   since the underlying data from which it was built has been altered.
                       HUH A Random FHel This utility buUds a new Sun Rasterfile
                       ^"^"""•••"' •'•"—=	~	•	=-^ based on the image present in the zoom
                    window. The new image has the same extent as the zoom-box, and
                    contains only the habitat classes actually found the zoom window. The
                    habitat classes are assigned randomly to the pixels in the new image, so
                    the class frequencies in the new image all end up roughly identical. You
                    must provide an output file name in the habitat controls window.

                                                This utility is similar  to the Build A
                                                Random File routine described above. It
                    also constructs a new Sun Rasterfile based on the image present in the
                    zoom window. The new image has the  same extent as the zoom-box,
                    and contains  only  the habitat  classes actually found in  the zoom
                    window. The  new image becomes a randomized  version of the old
                    image, and the numbers of pixels in each habitat class are preserved.
                    You must provide an output file name in the habitat controls window.
Chapter 8   PATCH Utilities
                                                                                52

-------
                                                 ^s button sunPty redisplays the panel
                                               that originally appeared at this location.
       HilbltSt Controls^
        ------- — * " ,"  - — /
                                                    Button recalls me habitat controls
                                               window if it has been removed.
ftife 41 fstory
^& - ^
                                               ™s  button  recaUs the
                                               controls window if it has been removed.
                                               This  button  recaUs ^  Ufe
                                               parameters and functions windows.
Zoom-Box and
      f    t    
-------
                    in the zoom or analysis window. If this field is set  to  zero, the
                    zoom-box moves a distance equal to its current height or width. This
                    feature makes it easy for you to move quickly through a large GIS data
                    set. Since the analysis window also tracks the zoom-box, this technique
                    can also be used to efficiently search large patch or territory maps.
                                                         This  sets the magnification
                                                         value to be  used with the
                                                         zoom and analysis windows.
Tracking and
Resampling
    Tracking:
Resamate*Rai9:??
"I'
I:
When the zoom window is sized correctly, it is repainted every time the
zoom-box is moved. At times, you may want to move the zoom-box but
not wait for PATCH to repaint the  zoom window. This can be
accomplished  by  removing the  check  mark from the  Tracking
check-box. When tracking is off and the zoom-box is moved, the zoom
window simply goes blank. A second click replaces the check mark and
turns tracking back on again.
^corn-Box
"•--,--:: "• ".'' ,-" ::
Placement
  r.-jr.ea7.'* lk 'KS
k:-- :.

    : ....... i Ijf.fffi, j
    "'

             -~.;.::~.y:
               :•«::»
     ,3 V '— •-=:
The TOP, 5OT, LFF, and RGT fields are used to set the zoom-box's top,
bottom, left, and right edges to specific row and column values within
the GIS data set. The N, S, W, and E (north, south, west, and east) fields
are used to set the zoom-box's  top, bottom,  left,  and right edges to
specific Universal Transverse Mercator (UTM) coordinate values. The
UTM coordinates are associated with the centers of the data pixels. The
fields  specifying UTM  information are  disabled  if  the UTM
coordinates for the edges of the GIS data set have not been entered into
the control file. All of these fields are disabled if a compressed territory
map is being used. Otherwise, these fields are updated any time the
zoom-box is moved.  Thus  you can record the placement  of the
zoom-box at any time by reading these values off of the panel.
Chapters  PATCH Utilities
                                                            54

-------
Files' andTbes
                    The ability to save patch and territory maps to the hard disk and load
                    them in later is central to the PATCH model. This panel contains the
                    tools used to perform these tasks. The input and output file name fields
                    are used to specify the names of existing patch or territory maps to be
                    loaded,  or of new maps to be saved to the hard disk. These fields are
                    also used by a few other routines and are mentioned elsewhere in this
                    manual. The three pairs of buttons in the center of this panel are
                    unlikely to be of much interest to you. Much of the information they
                    generate can be obtained in a more concise format using the Statistics
                    Output button (also located in the habitat controls window).

                                        These buttons load existing patch or territory
                                        maps, or to save new maps as files on the hard
                                        disk. Every patch and territory map consists of a
                                        ".patch" and a ".index" file. Territory maps also
                    include  a ".hexgn" file. These  files are all binary, so you cannot read
                    them directly. The write protect feature present in the habitat controls
                    window can be used to prevent the  Save All  Files utility from
                    overwriting an existing data set.
                                           The Zoom Rasterfile button generates a new
                                           Sun Rasterfile containing the image present in
                                           the zoom window. This routine strips out any
                                           habitat classes that do not appear in the zoom
                    window's image. The Hxgn Rasterfile button is used to generate a new
                    Sun Rasterfile that contains the portion of a territory map present in the
                    analysis window. This feature does not work with patch maps. The
                    hexagon grid is not included in either of the output images. Core areas
                    are not displayed in the image created using the Hxgn Rasterfile button.
                    You must provide an output file name hi the habitat controls window.
                               These buttons print out ascii versions of the image data
                               imbedded in a patch or territory map. The button labeled
                               Patch prints a summary, while the button labeled Array
                               prints the full data array. These utilities read  from a
Chapters  PATCH Utilities
55

-------
 t •' ........... • i -,"'*r~
      _...
    "ill, '.',!, 'I*. ;iS=S:I;!L:»SB"JM
                      ".patch" file if a valid input file name is provided in the habitat controls
                      window. Otherwise they read the data stored in memory, if any exists.
                      These utilities write to an output file if one is provided in the habitat
                      controls window. Otherwise, they write to the screen.
                                 Th£se buttons print out ascii versions of the location and
                                 properties data imbedded in a patch or territory map. The
                                 button labeled Index prints a summary, while the button
                                 labeled Array prints the full data array. These utilities read
                     from a ".index" file if a valid input file name is provided in the habitat
                     controls window. Otherwise they read the data stored in memory, if any
                     exists. These utilities write to an output  file if one is provided in the
                     habitat controls window. Otherwise, they write to the screen.
                                 These buttons print  out  ascii versions of the  hexagon
                                 specific data  imbedded in  a territory map.  The  button
                                 labeled Hxgn  prints a summary, while the button labeled
                                 Array prints out the  full  data array. These utilities read
                     from a ".hexgn" file if a valid input file name is provided in the habitat
                     controls window. Otherwise they read the data stored in memory, if any
                     exists. These utilities write to an output file if one is provided in the
                     habitat controls window. Otherwise, they write to the screen.

                     This panel is where the routines controlling the patch identification
                     process are located. It is not necessary for you to master these utilities
         .in sSSSS   before using PATCH'S life history simulator.
                                      These check-boxes specify the rule used to group
                                      collections of pixels into patches. Setting this field to
                                      Eight implies that every  pixel has  eight neighbors
                                      (four adjacent and four diagonal pixels). Setting it to
                                      Four implies that every pixel has only four touching
                                      neighbors (the four adjacent pixels).
	/>;>:;, Ji±¥
i1	<" -•"•'. V-"!-, ^3':;:ri"   ...  .
&'*	::"V:»S	5?=""^*^ %
X...	 	:'' MI* '• .i,,pn •  _  _
H-r		--"~i, •"f,-=if-,=f-i.- ^
^:^~fm^~h'*^'r*
Chapter 8   PATCH Utilities
                                                                                     56

-------
          .
          '&JF,,' ' '?,"?%&
                                  This check-box specifies the location of the image data
                                  generated  during  patch   identification  or  territory
                                  allocation. This utility is designed to help you construct
                                  patch or territory maps that are too large to be stored in
                                  the computer's memory. Setting the check-box to RAM
                                  forces the image data to  be stored in the computer's
                                  memory. If an attempt to build a patch or territory map
                     in  memory produces an error message  stating Memory  Allocation
                     Failed - Use Disk File, then the location check-box should be set to
                     Disk. This forces the  image data to be written directly to the hard disk
                     (as a ".patch" file). PATCH uses disk  files that are too large to fit in
                     memory by treating them as  virtual memory. When the Location
                     check-box is  set to  Disk, the ".index"  and ".hexgn" files  are also
                     automatically written to the hard disk. PATCH'S write  protect feature
                     can be used to prevent this utility from overwriting an existing data set.
                                        This check-box controls PATCH'S write protect
                                        feature.  It  is  provided  to  help  you  avoid
                                        accidentally overwriting patch or territory maps
                                        when using Save All Files or building a map
                                        directly on the hard disk. Existing data are safe
                                        when the check mark is placed on Protected.
                                                            This field  sets  the  edge
                                                            width used to identify core
                                                            habitats.  Edge widths are
                     measured in pixels, and core (interior) habitat pixels must be separated
                     from non-habitat by  a distance of at least one edge width in every
                     direction. Core areas are identified and displayed any time this field is
                     greater than zero, including when territories are being constructed.

                                            Clicking on this button displays the panel
                                            containing the hexagon editing routines.
                        This button starts the patch identification
                        routine. When each new patch is identified,
its bounding rectangle is displayed in the image window (if the window
is up to date). This feature helps you follow the routine's progress. The
patch identification algorithm breaks very large landscapes up into
blocks that are between 500 and 1000 pixels in width and height. It then
proceeds within each of these subregions, and reconnects the  results
when it has finished. The patch identification routine is quite fast, and
you should not hesitate to use it on large GIS data sets.
                                            This button P™1*8 a reP°rt mat describes a
                                            patch or territory map. The report contains a
Chapter 8   PATCH Utilities
                                                              57

-------
                    subset of the information found in the ".patch", ".index", and ".hexgn"
                    files. The format of the statistics output varies  a bit depending on
                    whether patches or territories are present. This utility writes to a file if a
                    valid file name is provided in the habitat controls window. Otherwise, it
                    writes to the computer screen. If the Define Edge Width field is set
                    greater than zero, then PATCH identifies all of the core habitat present
                    in the landscape prior to generating the statistics report.
                                            TWS button makes PATCH locate the core
                                            ,.   •  \  •*  •* •             • i •
                                            (interior)  habitat present within a patch or
                    territory map. PATCH recognizes core areas as habitats separated from
                    non-habitat by a distance of at least one edge width in every direction.
                    These core areas are displayed in cyan if they are  associated with a
                    patch map, and in yellow if they are associated with a territory map.
Hexagon Editing
                      i| ftssign Score To Hxgns Integjajr*  \
                     " O.QOO  . o Hex Score < *
                      New Hexagon Score is:
                      [    ~ T   I.,   »4*ff JT s  -^
                      ifftsstgtt Score To Se
                                                             /*' ^
                                                                            'r^^-L
              L...J," ,,1

               '""
These utilities allow you to edit territory maps. You can not alter the
scores of hexagons with no habitat. The randomization utilities  can
only  be used on  territory maps that have been compressed  using
PATCH'S hexagon compression utility.

                                         j These fields allow you to
                                          select a target range of
                                         , hexagon  scores, and to
                                          specify a new score to be
applied when editing hexagons. The target range includes its  lower
bound but not its upper bound. The New Hexagon Score Is field cannot
be set higher than the largest weight used to construct a territory map.
                              Score ToJHxgns'-In;F
                                         Pushing this button edits
                                         every hexagon that lies
entirely within the zoom-box and that has a score falling within the
target range (see discussion immediately preceding). Each of these
hexagons is assigned the new score specified in the New Hexagon Score
Is field.  After the hexagon scores have been changed, the habitat
sharing routine is rerun. This makes PATCH re-evaluate the breeding
status of every hexagon in the landscape that contains some habitat.
Chapter8  PATCH Utilities
                                                              58

-------
           ,n
           £*••' I
.V'.;

                                                            This button allows you to
                                                            modify a  territory map.
                    After this button is'pushed, move the mouse pointer inside the analysis
                    window.  The  window  header should read  CHANGE  HEXAGON
                    SCORES. You can then select (left click) hexagons to modify them.
                    Selected hexagons are painted blue and their scores are changed to the
                    value of the New Hexagon Score Is field. These hexagons can be reset
                    to their original value by clicking on them a second time. When the
                    mouse pointer is moved outside  the analysis window, the window
                    header returns to normal, the editing process terminates, and the habitat
                    sharing routine is rerun. This causes PATCH to re-evaluate the breeding
                    status of every hexagon in the landscape that contains some habitat.
                                              This button redisplays the panel
                                              that was originally located here.
                                                      This   button  writes  a   new
                                                      ".hexgn" file to the hard disk.
                    You may want to do this after editing a territory map to make the
                    changes permanent. Saving just the ".hexgn" file is much quicker than
                    rewriting an entire territory map to the disk. You must provide an
                    output file in the habitat controls window.

                                                      This routine randomly arranges
                                                      all of the hexagons in a territory
                    map. The locations of the hexagons change, but their areas and scores
                    stay the same. After the territory map has been randomized, the habitat
                    sharing routine is rerun. This causes PATCH to re-evaluate the breeding
                    status of every hexagon in the landscape that contains some habitat.
                    This randomization routine works only with compressed hexagons.

                                                      This routine randomly arranges
                                                      all of the hexagons in a territory
                    map that contain some habitat  (those  painted gray and green). The
                    locations of the hexagons change, but their areas and  scores stay the
                    same. If you  want to preserve  features  such  as a coastline, but
                    randomize everything else, then this routine should be selected over the
                    one labeled Randomize Every Hexagon. After the territory map has
                    been randomized, the habitat sharing  routine is  rerun. This causes
                    PATCH to re-evaluate the breeding status of every hexagon in the
                    landscape that contains some habitat. This randomization routine works
                    only with compressed hexagons.
Chapter 8  PATCH Utilities
                                                                         59

-------
Territory
Construction
                               '       ^
                       » Build The Territory Map J

                               Min & Max
                       •Reset Parameter Values J
                      ,^ Ap p Jy Hex Compression J
                      ^i^iirnHe^^&nGrltdOn	)
                     ^Turn Hexagon Grid Off J
Align Grid To /^Anajygte Whicto»/jT

Window  Sf"'Jet?">Dttta ElfisY"
      X    rmrnnrr   ^mnmamuuuwumi'wi'i'wmuiiiiiiiiiiimiiiiiiiiwiw'i^liii'ii'if^
Dala tot'" J "'  Add Hngn,
                                                  Hexagon Area .:  0
                                                  — —  ~, , /*   ™~~%
                                                           /..   .,   gf
                                                                            »« -'^ •*;- '•:-'


    .•r:U¥ri.--r -~	-
ii!	
iiwi
It'll	I!!J4A^^^^^^^^^^^
II!,'!!*..,.!!!»1!.!	' .. '. ':!!!!!!!!:»!!!!!i!i!!!i!»:i!i!l!!!'!.!!!lI"™"!!!!!.!'!".!!l!,l!i,i:,, i,,!1' |
            HI
                     This panel contains the utilities used to construct territory maps. It is
                     important to become familiar with all of these features unless PATCH is
                     to be used only for displaying GIS data and constructing patch maps.
                              ir

                             fin Area
                                 1B8HMMW
                                 ^^Bi^^K
                                  Max.
                                  si, — -;< These fields allow you to specify the hexagon
                                           size and the range of territory sizes used in
                                           constructing a territory map. You cannot alter
                                           the hexagon area after  a territory map has
                                           been constructed. In contrast,  the territory
                     minimum and maximum can be changed at any time. When hexagons
                     are incremented (decremented) in size, PATCH increases (decreases)
                     their width by two pixels at a time in order to keep them symmetric.
                     This means that the hexagon area can not be set to any arbitrary value.

                     The smallest hexagon that PATCH constructs has an area of 12 pixels.
                     The hexagons then increase in size to 36,  90, 168, 270 pixels, and so
                     on. If you cannot obtain the desired hexagon size, the resampling rate
                     can be increased until PATCH produces the intended  value. But this
                     strategy has  a cost: setting the resampling rate  to 2  is the same as
                     working with a  data set four times as large. Setting it to 3 produces a
                     data set nine times as large, and so on. Under such scenarios, PATCH'S
                     analyses run more slowly, and its output files are larger.

                     The number of hexagons and the hexagon size in hectares are shown in
                     the habitat controls window footer. If the territory minimum or territory
                     maximum is not equal to the hexagon size,  then these quantities are
                     displayed in the footer  as  well. The  territory minimum  cannot be
                     changed until at least one legend weighting value has been provided.

                     The Hexagon Area field gets locked  any time a territory map is
                     compressed,  or if a compressed map  is loaded into  the model. To
                     remove PATCH from  this state,  you must click once on the button
                     labeled Built The Territory Map. This causes the compressed map to be
                     discarded but does not construct a new territory map.
Chapter 8   PATCH Utilities
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           IB- * "3-
                                                   This button makes PATCH build a
                                                   new  territory  map.  However,  if
                    either a patch map or a compressed territory map currently resides in
                    PATCH'S memory, clicking on this button simply removes the patch or
                    territory data. In these situations, a second click builds a new territory
                    map.  If a compressed territory map is  removed  in  this way,  the
                    zoom-box size and location are likely to change.
                               ff  the  m?™™  or  maximum
V.i» «*-*•**>.. "^ - ^ *>. / territory size is  altered after  a
territory  map has been constructed, pushing  this  button propagates
these changes through the map. Running this utility causes PATCH to
re-evaluate the breeding status of every hexagon that has some habitat.

                               This button resets the hexagon size,
                               territory minimum and maximum,
and the habitat weights to the values used to construct a territory map.

                               This   button  runs the   hexagon
                               compression procedure. This utility
only works  when an uncompressed territory  map is present in the
model. The result  of running this utility is  a new territory map
constructed  entirely from  hexagons 12 pixels in  area.  From the
standpoint of the life history simulator, the new map is identical to the
old one.  But, if the original map was built from hexagons  that were
greater than  12 pixels in area, then the compressed map takes up much
less space in memory and on  the computer screen. Every hexagon in
the compressed map is painted a solid  color  (either black, gray, or
green) since the patch structure present in the original map is lost.

Large territory maps can sometimes take a long time to build, and if
they are compressed the original data are lost. Therefore, you may want
to save uncompressed territory maps before running the compression
routine. If the uncompressed data are taking up too much disk space,
they can always be compressed with a UNIX file compression routine.

                               This displays the  hex grid in the
                               zoom and analysis windows.
                                                   This removes the hex grid from the
                                                   zoom and analysis windows.
Chapters   PATCH Utilities
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                                     This feature is useful when the zoom-box size is
                                     not equal to the size of a  territory map being
                                     viewed. When you examine a territory map, you
                                     want the hexagon grid tied to the territory data,
                                     regardless  of the  size  and location  of  the
                                     zoom-box. Clicking on the Data Set check-box
                  aligns the hexagon grid to the territory map's boundaries. But if you are
                  going to construct a new map, you typically want to link the hexagon
                  grid to the zoom-box (and hence the zoom window) instead of an old
                  territory map. This can be accomplished by clicking on the Window
                  check-box. If a new territory map is constructed with the Data Set box
                  checked, it is built from the region used to construct the previous map.
                                           If a patch or a territory map is present in
                                           memory, then clicking on this button sets
                    the edges of the zoom-box to the edges of that map. This provides you
                    with an automatic way to zoom out and view an entire patch or territory
                    map (assuming it fits on the screen). When this button is pushed, the
                    Align Grid To check-box is set to Window.
                                           ^ a Patck maP *s Present> this button works
                                           the same as the one labeled Set To Data
                    Edge. However, if a territory map is present, clicking on this button sets
                    the edges of the zoom-box slightly beyond the edges of the map (as
                    long this does not exceed the limits of the GIS data). This tends to make
                    it a little easier to see the territory map. When this button is pushed, the
                    Align Grid To check-box is set to Data Set.
                                           Clicking this  button  causes  the  analysis
                                           window to be displayed.
 .ife History File
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                  The fields in this panel allow you to specify the locations of life history
                  parameter files to be  stored or  retrieved. These fields  are used
                  frequently when demographic simulations are being conducted.
Chapter 8  PATCH Utilities
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                    The time series  editor is used to introduce landscape change to
                    PATCH'S demographic simulations. PATCH approximates landscape
                    change by installing different territory maps at specified points in time.

                                                  These utilities allow you to specify
                                                  territory maps to add or remove from
                                                  PATCH'S time series facility. When a
                                                  year is selected, any territory map to
                                                  be installed at that time is shown in
                                                  the directory and file name fields. As
                    the model runs, the time series editor's year field tracks the model year.
                    If a file name linked to that year comes up in the editor, the model stops
                    and loads the territory map with that name. Once the new map has been
                    installed, the model continues the simulation where it left off.

                                              This button removes a territory map that
                                              has been placed in the time series editor.
                                           This button loads a territory map into the time
                                           series editor at a specified year.
                                              This makes the time series editor search
                                              backward for a year with an installed map.
                                           This makes the time  series  editor search
                                           forward for a year with an installed map.
Chapter 8  PATCH Utilities
63

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PATCH'S life history simulator can display the location and movements
of  individual members  of  a population as  the model runs. The
visualization check-box provides a mechanism  for you to turn this
feature on or off. The model runs much more slowly if the visualization
is on, so you probably want to keep it off most of the time. If a single
replicate is being conducted, and if the Tally Utility From parameter is
set to zero, you can conduct part  of a model run with the visualization
parameter off, and part of it with the option set on. If the visualization
parameter is on, the current population, and any reflecting boundaries,
are displayed every time that the analysis window is repainted.

The initialization check-box allows you to control how the starting
population is distributed throughout a landscape. This feature is used
with the Initial Population  and Initialization Age parameters. The
initial  population  always  consists  exclusively of breeders. You can
force PATCH to reselect the starting population at any time by cricking
the Reset  & Initialize button.  You  can make  PATCH display the
locations of the initial population in the analysis window by clicking
the Display Locations button. If the initialization check-box is set to .R
(random),  PATCH selects  the  locations  of  the initial  population
randomly from the  breeding sites present in the landscape.  If this
check-box is set to B (best), PATCH places the initial population in the
landscape's best neighborhoods.  For this purpose, PATCH  defines a
neighborhood as a breeding site and its six immediate neighbors. The
best neighborhoods are those with the largest cumulative scores.

You can also manually enter the initial population. This  is done using
the Specify Locations button, and this feature can be used to modify any
existing initial distribution. Li addition, it can be used to modify a final
population distribution resulting from a simulation. When the Specify
Locations button is  pushed, the initialization  check-box is set to L
(locked), and the present distribution of breeding individuals is locked
into place.  While this lock is  on,  you cannot modify the  initial
population except by using the Specify Locations utility.  Setting the
lock on also ensures that every model run begins with the same initial
population.  Any  starting  locations entered by hand are  lost  if the
initialization lock is taken off. Therefore, if you have put a lot of time
into selecting starting locations by hand, it is a good idea to save this
data to a life history parameters file using the Write Parameters button.
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Chapter 8   PATCH Utilities
                                                                64

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Controls 1
                                   ST^* ™^;M-I !-/mW"?.?t *'T"£TO*V 'JSS*W?WIW?A T« fK1 »f^i.J»?" 'Of-

                    The tools in this panel control PATCH'S life history simulations. These
                    utilities are accessed every time the model is run, and you should
                    become familiar with them as soon as possible.

                                            Clicking on this button makes PATCH load
                                            a life history parameters file. An input file
                    name must first be entered in the life history window. Feedback and
                    error messages are sent to the life history window footer. If a ".stats2"
                    file is present, and if its prefix is the same as the name of the life history
                    parameters file being read, then PATCH loads the data contained in it as
                    well.  This feature allows you  to generate occupancy rates and  an
                    observed source-sink map from the results of a previous simulation. If a
                    ".random" file  is present, and if its prefix has the name of the life
                    history parameters file being read, then PATCH loads this data too. This
                    feature allows you to add environmental stochasticity to a simulation.

                                            This  button  makes  PATCH write  a life
                                            history  parameters file. If an  output file
                    name has been entered into the life history window, then these data are
                    written to that file. Otherwise, the data are sent to the computer screen.

                                            This button allows you to enter reflecting
                                            boundaries by  hand.  After pushing this
                    button, move the mouse pointer inside the analysis window. PATCH is
                    ready to assign reflecting boundaries if the  analysis window header
                    changes to SELECT REFLECTING SITES. A reflecting boundaries can
                    be applied by selecting (left clicking) a hexagon. A reflecting boundary
                    can be removed by selecting the hexagon a second time. Sites that are
                    suitable for breeding cannot be assigned reflecting  status. This function
                    only works if the analysis window is up to date. The locations  of
                    reflecting boundaries are stored in the life history parameters files.
                                            This  button allows you to automatically
                                            locate reflecting boundaries throughout a
Chapters   PATCH Utilities
65

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                     territory map. If no reflecting boundaries are present, clicking this
                     button initially places a reflecting boundary at every black hexagon
                     (those having no habitat) that has a neighbor with some  habitat (the
                     gray or green hexagons). Clicking on this button a second time places a
                     reflecting boundary at every gray hexagon (those having habitat but not
                     suitable for breeding) with a neighbor that is either black (no habitat) or
                     green (suitable for breeding). A third click locates a reflecting boundary
                     at every site that received one as a result of either the first or second
                     clicks. A fourth click removes all of the reflecting boundaries. This
                     feature only works if the analysis window is up to date. The locations
                     of reflecting boundaries are stored in the life history parameters files.
                         This button allows you to enter the locations
                          _ ,    ..  .•        i *.•    i   i   JAJ^
                         of the  starting  population  by hand. After
pushing  this button,  move the  mouse pointer  inside the analysis
window. PATCH is ready to assign reflecting boundaries if the analysis
window header changes to SELECT STARTING SITES. You can add a
member of the starting  population  by  selecting (left clicking)  a
hexagon.  Selecting the hexagon a  second time will  remove  the
individual. Only sites that are suitable for breeding can be assigned a
member of the starting population. This  function only works if the
analysis window is up to date. The locations of the starting population
are not stored in the life history parameters  files unless the Initialization
check-box is set to L (locked). However, PATCH sets the Initialization
check-box to L any time you set a  starting location by hand.
           Loca
                '
                                                  ^utton  mates PATCH  display  the
                                             location of every  member of the current
                    population. If a simulation has not yet been run, or if the life history
                    module has been reset, you are  instead shown the locations of the
                    starting population.  In either case, the  locations of  all reflecting
                    boundaries entered into the landscape are shown as well.
                                 Dels it|T)  This t)utton P™1*8  a distribution of ending
                                          ^  population densities for the portion of the
landscape contained within the zoom-box. When this button is pushed,
PATCH first identifies every hexagon that is both suitable for breeding
and  contained  entirely within the zoom-box. These hexagons  are
painted blue (in the analysis window) so you can see which ones are
included in the tabulation. Next, PATCH reads the ".statsO" file with the
prefix specified in the life history window's input file name field. If a
".statsO" file with this name does not exist, then density estimates are
not made. Otherwise, PATCH counts up the total number of breeders
that were present in the target hexagons at the end of every replicate
run, and reports this data on a run-by-run basis. PATCH also writes out
the row and column values of the zoom-box's edges, and the mean and
Chapter 8   PATCH Utilities
                                                              66

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                    standard deviation of the density values, computed across the collection
                    of replicate runs. Lastly, PATCH writes out the statistics present in a
                    ".stats2" file, but for just the breeding sites contained entirely within
                    the zoom-box. This information is provided to help you summarize the
                    importance of a specific collection of breeding sites. If an output file
                    name is provided, PATCH sends all of this information to a file with
                    that prefix, but that ends in  ".statsS". If an  output file name is  not
                    provided, PATCH sends the data to the computer's monitor. Changes to
                    the image  in the  analysis  window made by this  routine  are  not
                    permanent. You can restore the original  image using the window
                    manager's refresh feature, or using the Turn Hexagon Grid On button.
                                            This  button  makes  PATCH  write  three
                                            output maps to the hard disk.  These maps
                    are placed in files that end in ".imageO", ".imagel", and ",image2". The
                    first of these maps (".imageO") displays the occupancy rates observed
                    at the end of each replicate simulation, but averaged across all of the
                    replicate runs.  The second and third maps (".imagel" and ".imageZ")
                    contain  the   expected  and  observed  source-sink distributions,
                    respectively. The expected  source-sink distribution can be generated
                    without first running a simulation. A simulation must be conducted
                    before the occupancy rate or observed source-sink maps  can be
                    compiled. To generate an expected source-sink map, you must supply a
                    territory map and specify the vital rates, the vital rates factor, and the
                    interpolation  functions. The data  used  in  building the  observed
                    source-sink map are compiled only if the Tally Utility From field is set
                    greater than zero. The data used in building the occupancy rate map are
                    compiled if the Tally Utility From field is greater than zero,  or if the
                    number of runs is greater  than one. You can recreate the observed
                    source-sink or occupancy rate maps from the data stored in the ".stats2"
                    output file. PATCH automatically uploads this data any time  a life
                    history parameter file is read, provided a valid  ".stats2" files exists.
                    Once these data have been uploaded, you can push the Get Output
                    Maps button to recreate the observed source-sink and occupancy maps.

                    The  occupancy rate maps  are Sun Rasterfiles composed of 4-pixel
                    "hexagons" that are derived from territory maps. Each hexagon in an
                    occupancy rate map is assigned to  a color class. Hexagons with no
                    habitat are displayed in white. Hexagons that have habitat but are not
                    suitable for breeding are displayed in black. All other hexagons (the
                    breeding sites) are assigned a color from a spectrum that shifts from red
                    to blue. The color assigned to a hexagon depends on its  relative
                    occupancy rate. Sites with a relative occupancy rate of zero (the
                    minimum) are displayed in 100% red,  and  those with a  relative
                    occupancy rate of ten (the  maximum) are shown in  100% blue. The
                    colors vary smoothly for sites in-between. The relative occupancy rates
Chapters  PATCH Utilities
                                                                                  67

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                      are constructed from tallies of the breeders present in the final year of
                      each (or a single) replicate simulation. At the end of each replicate, a
                      breeding site's occupancy register is incremented if the site is occupied,
                      and is left unchanged if it is not. When the occupancy map is built, the
                      values in these registers are rescaled to lie between zero and ten.

                      The expected source-sink map is a Sun Rasterfile composed of 4-pixel
                      "hexagons" that is derived from a territory map. Each hexagon in an
                      expected source-sink map falls into one of five classes. Hexagons may
                      have no habitat, have habitat but be unsuitable for breeding, or they can
                      be classified as sinks, sources,  or as neutral sites. The source or sink
                      designation (which applies only to  breeding  sites)  is based on the
                      dominant eigenvalue (A,) of the projection matrix associated with each
                      hexagon. This projection  matrix is  constructed from the vital rates
                      entered into the model interface, the vital rates factor, the interpolation
                      functions you selected, and from a hexagon's score. If this value is less
                      than one the site is classified as a sink. If it is greater than one the site is
                      listed as a source. Sites that have a dominant eigenvalue of exactly one
                      are considered neutral. This source-sink designation is not affected by
                      the  presence  or absence of the  data  tables  used to  introduce
                      environmental stochasticity into the model. The data used to create the
                      expected source-sink map  are  stored in the ",stats2" file under the
                      heading Lambda. A new expected source-sink map can be always  be
                      built by loading a territory map and a set of Me history parameter files
                      that include a  ",stats2" file. The expected source-sink  map is not
                      affected when a simulation is conducted.

                      The observed source-sink map is also a Sun Rasterfile composed of
                      4-pixel "hexagons" that is derived from a territory map. Each hexagon
                      in an observed source-sink map falls into one of five classes. Hexagons
                      may have no habitat, have habitat but be unsuitable for  breeding, or
                      they can be classified as sinks, sources, or as neutral sites. The source
                      or sink designation (which  applies only to breeding sites) is based on
                      the number of immigration and emigration events observed at a site
                      during a simulation. Any time an individual enters a breeding hexagon,
                      an immigration event is recorded for that site. Similarly, an emigration
                      event is recorded whenever an individual exits a site. These tallies are
                      made on  a  hexagon-by-hexagon  basis. The  process  of  tallying
                      immigration and emigration events can be started at a specific  year
                      using the Tally Utility From field in the life history parameters window.

                      When the number of immigration events is greater than the number of
                      emigration events, a  site is classified as  a sink. If emigration events
                      exceed immigration  events,  a site  is considered  a source. When
                      immigration and  emigration  are exactly balanced, a site is labeled
                      neutral. Most neutral sites fall into this category because  immigration
Chapter 8   PATCH Utilities
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                      and emigration both equal zero. The data used to create the observed
                      source-sink map are stored in the ",stats2" output file under the heading
                      Utility. The utility values are computed as the emigration rate minus the
                      immigration rate. Thus, sites with utility values less than zero are sinks,
                      while those greater than zero are sources. If the Tally Utility From field
                      is set to zero, or to  a value greater than the number of model-years, then
                      immigration and emigration tallies are not made. Li these cases, every
                      site's utility value equals zero. The immigration and emigration tallies
                      are summed across replicate model runs.

                      Sinks and sources in both the expected and observed source-sink maps
                      can be distinguished  based on their severity.  PATCH makes  this
                      possible by taking the observed range of the sinks, and the observed
                      range of the sources,  and splitting  each into 100 uniform intervals.
                      Each of these intervals is one percent in width, and is represented by a
                      unique class in the source-sink  map's color  table. Hexagons  are
                      assigned to these classes when the maps are constructed. The ranges,
                      and hence the interval sizes, used for the sources and sinks are usually
                      not the same. All sinks are  painted red and  all sources are painted
                      green.  Only hexagons  that are suitable for breeding can qualify as a
                      source, sink, or neutral site. Hexagons that do not contain any habitat
                      are painted white. Hexagons are painted black if they have habitat but
                      are not suitable for breeding. Only the hexagons that are suitable for
                      breeding are recorded in the ".statsl" files.

                                               This button sets the run number and year to
                                               zero, and inserts  the starting population.

                                               Pushing this button initiates a simulation.
Chapter 8   PATCH Utilities
                                                                                     69

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This  panel is used to  supply many  of PATCH'S  demographic
parameters. Familiarity with an organism is not required to specify the
panel's top three fields. Simulation results are often insensitive to the
initial population size and age, so you may be able to justify picking
these values arbitrarily. The Search Randomly and Walk Up Gradient
parameters can only be estimated, and PATCH'S animation facility is
designed to help you perform this  task. Model results  tend to be
sensitive to the remaining parameters, particularly the vital rates factor.

                             This  field  specifies the  number of
                             replicate model runs to be conducted.
                             If this field is greater than one, the run
number and year are set to zero when a new simulation is initiated.

                             This field sets the duration in years of
                             each  model  run. This parameter can
                             be  altered without  resetting  the life
history module. Altering any other parameter, except the visualization
check-box, causes PATCH to reset the run number and year to zero. If
the number of runs is set to one, and the Tally Utility From field is set to
zero, then you can make PATCH conduct a simulation in increments.
For  instance,  the  model  could be run for  100  years with  the
visualization check-box set off. Then you could turn the visualization
on and run the model for an additional 10 years.

                             This field specifies the model year in
                             which the immigration and emigration
                             data  are  first  recorded.  These  data
make up  the  observed source-sink  map, and  you  should use this
parameter to delay tallying them until any transient behaviors resulting
from the initial conditions have had a chance to die down. If the Tally
Utility From parameter  is set to  zero,  then  the  immigration and
emigration data are not collected at all. If this parameter equals one or
more, the  run  number and year are automatically reset to zero every
time you initiate a demographic simulation. PATCH'S occupancy rate
data are only collected only if the Tally Utility From parameter is set
greater than zero, or if the number of replicate runs is greater than one.

                             This field sets the size of the starting
                             population. However, this field  gets
                             locked if the initialization check-box
is set to L. This parameter is incremented or decremented if you add or
remove starting individuals using the Specify Locations button.

                             Starting  populations  consist of a
                             single cohort of breeding individuals.
Chapter 8   PATCH Utilities
                                                              70

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                    This field is used to specify the age or stage class of this cohort. PATCH
                    numbers its ages and stage classes from zero to nine.
                                     >*          *#
                                                 This parameter specifies the minimum
                                                 distance  an  individual  must  move
                                                 before a vacant breeding site can be
                    colonized. If the movement strategy selected does not involve a random
                    walk, this parameter defines a disk about the starting site inside which
                    hexagons  are  not available for colonization. Individuals taking  a
                    random walk are obligated to move  a number of steps that is at least
                    equal to the value of this parameter. You must specify the minimum
                    search distance as a number of steps from a hexagon to one  of its
                    immediate neighbors.  It is usually convenient to know the distance
                    between hexagons in meters when assigning a value to this parameter.
                    PATCH displays the mean distance between neighboring hexagons (the
                    step size) in meters any time you middle click on a hexagon in the
                    analysis window. This information is sent to the habitat controls
                    window footer. The step size is reported as a mean value because the
                    distances separating each hexagon's horizontal and diagonal neighbors
                    are slightly different.

                                                 This parameter limits the maximum
                                                 distance any individual can move in
                                                 search of a vacant breeding site. If the
                    movement strategy does not involve a random walk, then this parameter
                    defines a disk  about the starting site outside which a hexagon is not
                    available for colonization. In such cases, if a vacant site does not exist
                    within the search radius, a random walk is taken. Individuals taking  a
                    random walk move a number of steps mat is at most equal to the value
                    of this parameter. You must specify the maximum search distance as  a
                    number of steps from a hexagon to one of its immediate neighbors. It is
                    usually convenient to know the distance between hexagons in meters
                    when assigning a value to this parameter. PATCH displays the  mean
                    distance between neighboring hexagons (the step size) in meters any
                    time you middle  click on a hexagon in the analysis window. This
                    information is sent to the habitat controls window footer. The step size
                    is reported as  a mean value because the distances separating each
                    hexagon's horizontal and diagonal neighbors are slightly different.

                                                 This   parameter   influences   the
                                                 behavior  of  individuals  taking   a
                                                 random walk. Decreasing  its  value
                    makes movement paths more linear. As this parameter is increased,
                    movement paths become more random. If this parameter is set to zero,
                    individuals travel  in straight lines. If this parameter is set to 100%,
                    individuals select  movement directions entirely at random.  However,
Chapters  PATCH Utilities
71

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JT&e Projection
                        alk Up Gradient
                        ^K'l)iSaiiHS:i&i!*:5av:»gilks^^*i;:,I!;S!fMs!*
the influence of  this parameter is  overridden by  an individual's
tendency to move up gradient from lower to higher quality hexagons. If
you want to simulate a true random walk, you must set this parameter
to 100% and set the Walk Up Gradient parameter to zero. Extremely
low values of this parameter may produce unrealistic movement paths.

                              This   parameter   influences   the
                              behavior  of  individuals  taking  a
                              random walk. It governs the tendency
to move up gradient from lower to higher quality hexagons. When this
parameter is set to zero,  individuals never attempt to move into better
quality  sites. As  the value of this  parameter is  raised, individuals
become increasing likely to move into higher quality habitats.  When
this parameter is set to 100%,  individuals  always  select the best
neighboring site to move into, as long as that sites' score is higher than
the hexagon  currently  occupied. Extremely high  values of  this
parameter produce unrealistic movement paths.

                              The  vital rates factor determines the
                              quality of habitat to be associated with
                              the survival and reproductive values
you supply. Hexagons with scores of zero are always assigned survival
and reproductive rates of zero. Hexagons having the score indicated by
the vital rates factor  are assigned the survival and reproductive rates
entered into the model's projection matrix. Survival and reproductive
rates for hexagons with  all other scores are obtained  using  PATCH'S
interpolation functions.  The vital rates factor must  be  set to  a
percentage of the maximum possible hexagon score. The maximum
score is always equal to the largest weighting value used in the legend
window, even if no hexagon actually has a score this high. For instance,
a vital rates factor of 80% implies that the survival and reproductive
rates you entered are to be realized in hexagons having a score equal to
80% of the maximum value. The vital rates factor also governs the
survival  and reproductive rates   experienced  by individuals  when
environmental stochasticity is included in a simulation.
                                                                     0   0.205 0.339
                                                                   0.258   0     0
                                                                     0   0.844 0.844
                     Population projection matrices are entered into PATCH through the
                     panel on the right side of the lif e history parameters window. This panel
Chapter 8   PATCH Utilities
                                                               72

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,__
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contains a 10 x 10 array of fields that can each hold a single vital rate.
Rates set to zero are not displayed. These survival and reproductive
rates are associated with hexagons having scores specified by the vital
rates factor. The maximum  survival and  reproductive rates (those
observed in hexagons having the highest possible score) are displayed
any time you click the middle mouse button in  the projection matrix.
The survival and reproductive rates experienced by an individual are
influenced as well  by the interpolation functions you  select. The
survival rates present in any column of PATCH'S projection matrix
must sum at most to one,  and this is also true of the matrix used for
survival and reproductive decisions in the best habitats. PATCH'S  life
history  module incorporates a post-breeding census, which means that
the first age or stage class  always  consists exclusively  of newly
recruited individuals that are not yet of breeding age. For this reason,
the upper left entry in PATCH'S projection matrix is always fixed at
zero. If a  table of vital rates has  been  supplied  for  simulating
environmental stochasticity, then PATCH randomly selects a projection
matrix from this table at the start of each model year. In such cases, the
randomly selected  vital rates are  displayed  in PATCH'S projection
matrix for the duration of that model year. When the simulation ends,
PATCH redisplays the vital rates you entered into the model interface.
                     PATCH allows you to specify the relationships Unking the survival and
                     reproductive rates to habitat quality. The influence of habitat quality
                     can  be ignored  by selecting the constant function,  or  it  can be
                     minimized by picking the piecewise constant function. The simplest
                     nontrivial option is a linear relationship. You can also choose between
                     logistic, concave, and convex  functions. The mathematical definitions
                     of these interpolation functions are provided in Table 2.
Chapter 8   PATCH Utilities
                                                               73

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                                     This option makes either survival or fecundity a linear
                                     function of habitat quality. A minimum rate of zero is
                                     realized in hexagons with a  score  of zero.  The
                                     maximum rate is realized in hexagons having a score
                                     equal to the largest habitat weight.
                                     This option makes either survival or  fecundity  a
                                     logistic function of habitat quality. A minimum rate
                                     of zero is realized in hexagons with a score of zero.
                                     The maximum rate is realized in hexagons having a
                                     score equal to the largest habitat weight. It is possible
                                     for no hexagon to have a score this high.


                                     This option makes either survival or  fecundity  a
                                     concave function of habitat quality. A minimum rate
                                     of zero is realized in hexagons with a score of zero.
                                     The maximum rate is realized in hexagons having a
                                     score equal to the largest habitat weight. It is possible
                                     for no hexagon to have a score this high.
                                     This  option makes either  survival or  fecundity  a
                                     convex function of habitat quality. A minimum rate of
                                     zero is realized in hexagons with a score of zero. The
                                     maximum rate is realized in hexagons having a score
                                     equal to the largest habitat weight. It is possible for no
                                     hexagon to have a score this high.


                                     This option assigns the survival or fecundity values
                                     entered into the  model's projection matrix to every
                                     hexagon with a score greater than zero. Survival or
                                     fecundity are set to zero in  every hexagon that has a
                                     score of zero. The role of the vital rates  factor is
                                     suspended when this function is used.


                                     This option assigns a survival or fecundity value of
                                     zero to every hexagon with a score less than one-third
                                     of the largest habitat weight.  In  hexagons having
                                     scores greater than two-thirds of the largest habitat
                                     weight, survival  or fecundity  are  set to the  values
                                     entered into the model's projection matrix. In all other
                     hexagons, survival or fecundity are set to one-half of the values entered
                     into the model's projection matrix. The role of the vital rates factor is
                     suspended when this function is used.
Chapter 8   PATCH Utilities
74

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Functions
 'F11
                    PATCH  allows you to choose between  three  different movement
                    strategies. The button labeled RANDOM WALK forces individuals to
                    search for available breeding sites using a pseudo-random walk. The
                    button  labeled SELECT  OPTIMAL allows  individuals  to travel
                    immediately  to  the best  available  breeding site  within a  search
                    neighborhood.  The  button  labeled  SELECT  CLOSEST  allows
                    individuals to take the closest available breeding site within a search
                    neighborhood. In latter two cases, if more than one option exists at the
                    same distance, then the best of these is colonized.  Ties  are handled
                    randomly. A  random walk is always used by individuals that cannot
                    locate an available breeding site with one of the other strategies.

                    PATCH also provides you with three options for specifying site fidelity.
                    The site fidelity  parameter controls the likelihood  that  territorial
                    individuals (or a floater poised to take over a site who's owner has died)
                    remain in the breeding sites they have colonized. When site fidelity is
                    high, individuals never give up their territories. When site fidelity is
                    low, each individual gives  up its territory and relocates every year. At
                    the intermediate value of site fidelity, decisions regarding whether or
                    not to remain in a territory  are made based upon hexagon quality.
This button forces individuals searching for available
breeding sites to use a  pseudo-random walk. The
behavior  exhibited  during  a  random  walk  is
influenced by the minimum and maximum movement
ability, the linearity in searcher's movements, and by
their tendency to travel up gradient.
Chapter 8   PATCH Utilities
                                               75

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                       SELECT
                      OPTIMAL
                                    This choice of movement allows individuals to move
                                    directly to the best available site falling within an
                                    annulus  specified by the minimum and maximum
                                    movement distances. This is the slowest of the three
                                    available movement routines.
                       SELECT
                      CLOSEST
                                    This choice of movement allows individuals to move
                                    directly to the closest available site falling within an
                                    annulus  specified by the minimum and maximum
                                    movement distances. This option is faster than the
                                    optimal site selection algorithm, but it is still slower
                                    than a random walk.
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                                    When site fidelity is set to low, each individual gives
                                    up its breeding site every year, regardless of the site's
                                    quality. The individual is then obligated to search for
                                    a new site.
                                    When site  fidelity  is  set to medium,  individuals
                                    relinquish breeding sites that can be expected to
                                    function as  sinks, and retain breeding sites expected
                                    to behave neutrally or as sources.
                                    When site fidelity is set to high,  territory holders
                                    always remain on their sites indefinitely.
Chapter 8   PATCH Utilities
                                                                                   76

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Example 1
                        Patch  Identification
Introduction'
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Reading CIS
Data
              Click on the button labeled Read The Data File, This makes PATCH
              read the GIS data set. If the clayoquot image has been successfully
              loaded, the main window footer displays the number of rows and
              columns present in the data. The clayoquot image contains 3731 rows
              and 4301 columns. If PATCH has trouble reading the clayoquot data set
              or its control file, it writes error messages to the main window footer.
Displaying GIS
Data
              Call up the image window by clicking on the button labeled Show
              Image Window.  Now double click in  the image window. PATCH
              displays every 28th row and 28th column of the clayoquot data set. The
              image window is designed to subsample the GIS data and generate a
              dithered version  of the entire image. In contrast, the zoom window is
              designed to display part, or all, of the GIS image without dithering.

              Change the Image Window Sampling field from 28 to 10 (remember to
              use the "Return" key). This expands the size of the image window, and
              paints it black. Double click on the image window to display every 10th
              row and every 10th column of the clayoquot data. Drag the image
              window to a convenient location on the desktop.
Setting the
Zoom-Box Size
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             Change the fields  labeled Modify Zoom-Box Height  and Modify
             Zoom-Box Length to 200 pixels each. Notice how the zoom-box size
             changes (in the image window) as this is done. Make sure that the field
             labeled Set Zoom-Box Increment is set to zero. Lastly, set the Degree Of
             Magnification field to 2 (remember to use the "Return" key). Click on
             the cyan color cell in the main window. It is just to the left of the white
             color cell. This changes the color of the zoom-box.

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the Zoom    Call up the zoom window by clicking on the button labeled Show Zoom
             Window. Double click once in the zoom window to set its size. Double
             click a second time to display the data within the zoom-box. Drag the
             zoom window to a convenient location on the desktop. Select a data
             pixel by clicking and holding the middle mouse button anywhere in the
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Example 1   Patch Identification
                                                                         78

-------
                    zoom window. While the mouse button is held down, the selected pixel
                    is highlighted (painted white) and the zoom window footer displays its
                    row and column values and indicates which legend entry it belongs to.
Moving the
Zoom-Box
           -Tir
Imagine breaking the zoom window into four quadrants by connecting
its opposite corners  with two diagonal lines. For the purpose of this
discussion, label the resulting triangular regions top, bottom, left, and
right. When the right mouse button is clicked in one of these quadrants,
the zoom-box moves incrementally. The increment size is specified in
pixels,  and is  set by the Set Zoom-Box Increment field. If the Set
Zoom-Box Increment field is set to zero, however, the increment size
equals either the height or width of the zoom-box.
                    Place the mouse pointer over the zoom window's top quadrant and
                    click the right mouse button three times. Because the Set Zoom-Box
                    Increment field is set to zero, each click moves the zoom-box vertically
                    a distance equal to its height (200 pixels). Now place the mouse pointer
                    over the zoom window's left quadrant, and right click three times. This
                    moves  the  zoom-box a distance of 600 pixels  (three times the
                    zoom-box's width) to the left. The zoom window is repainted each time
                    the zoom-box is moved. This happens only when the tracking switch is
                    on and the zoom window is sized correctly.

                    Now change the field labeled Set Zoom-Box Increment to 10 (remember
                    to use the "Return" key). Again, place the mouse pointer over the left
                    quadrant of the zoom window. Click right once. Then click right twice
                    in the bottom quadrant of the window. A small island should be visible
                    in the upper hah0 of the zoom window.
Example 1   Patch Identification
                                                            79

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                    The  zoom window footer  should read Rows 1186-1385  []  Cols
                    1441-1640. If this is not the case, modify the location of the zoom-box
                    directly by altering the fields in the main window labeled TOP, EOT,
                    LFT, snARGT. Change these fields to 1186,1385,1441, and 1640.
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Display the legend window by clicking on the button labeled
Legend Window. Place the mouse pointer on the category labeled
Growth and click the left button three times. The uppermost white box
within the legend window should now contain a 3. Move the mouse
pointer to Open Canopy Forest and click left once. Old growth and
open canopy forest should now have weights of 3 and 1, respectively.
Every other habitat class should have a weight of 0. Weights that are set
to 0 are displayed in the legend window as empty boxes.

Move the mouse pointer to the habitat controls window. Call up the
analysis window by clicking on the button labeled Analysis Window.
Double click in the analysis window to update its size, Dsag the
analysis window to a convenient location on the desktop.
Example 1   Patch Identification
                                                            80

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           _
Habitat Batches
  I.-.1S I
                          Old  Growth
                          Open  Canopy  Forest
          s?2*#^#,CiiKa
Click the button in the habitat controls window labeled Find Every
Patch. This makes PATCH locate every patch within the  zoom-box
composed of old growth, open canopy forest, or both. These patches
are displayed in the analysis window, and the analysis window footer
reads Number Of Patches: 160. Take a look at the zoom-box while the
patch counting routine is running. As each separate patch is located, its
bounding rectangle is drawn  within the zoom-box. This  feature is
designed to help you follow the progress of the patch counting routine.

Move the mouse pointer into the analysis window. Select the large
patch covering most of the right hand side of the image by clicking the
middle mouse button on it. As long as the mouse button is held down,
the patch is highlighted (painted white), and the analysis window footer
should read Number 1 [] Area 6580 [] Edge 3014.
Example 1   Patch Identification
                                                          81

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Picking Four or
Eight Neighbors
Locate  the check-box labeled Neighbors in the  habitat controls
window. When this check-box is set to Four, only adjacent pixels are
considered to be  touching.  When it is set to Eight,  neighbors at
diagonals are assumed to  touch as  well. Patches are built up from
collections of pixels that touch and that have all been assigned nonzero
weighting  values.  The value of the Neighbors  check-box controls
PATCH'S definition of what it means for pixels to touch, thus it  can
greatly influence the results of the patch counting routine.

Change the Neighbors check-box from Eight to Four. Click again on
the button labeled Find Every Patch.  The analysis window footer
should show that 364 separate patches have now been identified. Select
patch number 1 again. Its area has decreased from 6580 pixels to 6437.
Locating Core
    itaf. Areas' '
Reset the Neighbors check-box to Eight, and set the field labeled Define
Edge Width to 1 (remember to use the "Return" key). Again, click on
the button labeled Find Every Patch. A large quantity of core habitat
should become visible in the analysis window. Core habitat identified
during patch counting is always painted cyan.

Now increase the edge width to three pixels, and click on the button
labeled  Find Core Areas. PATCH removes the previously displayed
core habitats and replaces them with the subset that is at least thee
pixels from an edge in every direction.
Saving -the \ \    Enter a directory and file name into the habitat controls window Output
jtesulls ,. \,'''{v-:::^:|   Directory and Output File Name fields. For the sake of this discussion,
t i,;	a i-siE^yi fitfifjf J   let's assume you have entered "/tmp" and "test" for the directory and
Example 1  Patch Identification
                                                              82

-------
         l3W:
Patch Statistics
^ j™-?"?^ .-™.* £ ~v^^-; 5; j.?^"*. S=^f
jLoadmg a Patcli;;:;
                    file name fields, respectively. Set the write protect feature to Override if
                    a patch or territory map with this name already exists.
                                    ~       ' • &'
                    Now click on the button labeled Save All Files. PATCH attempts to save
                    the results of the patch identification process. If it is successful, the
                    habitat controls window footer reads test Successfully Written. This
                    causes PATCH to create two binary (hence not readable) files named
                    "/tmp/test.patch" and "/tmp/test.index".

                    Click on the button labeled Statistics Output. This creates a file named
                    "/tmp/test", assuming you have supplied the output directory and file
                    name fields suggested above. This file contains a general description of
                    the results  of the analysis run thus far. The first few lines of this
                    statistics file should contain the text displayed here.
                              Input File Name Used
                              Analysis  Is For Rows
                              Analysis  Is For Cols
                              Edge Width In Pixels

                              Total Number Patches
                              Landscape Patch Area
                              Sum Of Patch Weights
                              Sum Patch Core Areas
                              Total Landscape Edge

                              Legend Value,  Weight
                              Legend Value,  Weight
                                                       clayoquot
                                                       1186  -  1385
                                                       1441  -  1640
                                                       3

                                                       160
                                                       17660
                                                       41228
                                                       2526
                                                       10532
                                                         0,
                                                         1,
                                 3
                                 1
                                               Patch   Core
                                               Weight  Area
                                                                 Patch
                                                                 Perim
6580
3493
1
1
1
16078
8045
1
1
1
1219
301
0
0
0
3014
2198
4
4
4
Patch   Patch
Number  Area
                              1
                              2
                              3
                              4
                              5
                    Quit PATCH by clicking on the button in the main window labeled Quit
                    PATCH Model. Then call PATCH up again and enter the location of
                    PATCH'S sample GIS data in the main window Directory field. Enter
                    "clayoquot" into the main window File Name field. Load the GIS
                    image using the button in the main window labeled Read  The Data
                    File. Next, set the Input Directory and Input File Name fields in the
                    habitat controls window to the names used for storing the patch map
                    mat was built earlier in this example (e.g. "/trap" and "test").
Example 1   Patch Identification
                                                                                83

-------
        I I
Reload the patch map by clicking on the Load All Files button in the
habitat controls window. All of the information describing the original
patch map, except for the core areas, are restored from the ".patch" and
".index" files when the data set is loaded. If the edge width is nonzero,
then the core areas are recomputed. If the zoom and analysis windows
are sized correctly, they are automatically repainted when the patch
map is loaded.

PATCH does not automatically fit the zoom-box to the boundaries of an
imported map. Therefore, you may want to adjust the zoom-box size
and location after a patch map is loaded. Fortunately, you do not have
to set the zoom-box size and location by hand. Instead, you can simply
click on the button in the habitat controls window labeled Set To Data
Edge. This alters the zoom-box size and location to match the extent of
the patch map. Click on this button, and then change the magnification
parameter to 2. Next, call up the zoom and analysis windows. Double
click on each window once to set its size, and a second time to paint it.
Examine the patch map that has just been loaded. It should be identical
to the map constructed earlier in this example.
        1.,,
Example 1   Patch Identification
                                                             84

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Example 2
                        Territory Allocation
Introduction
This example introduces  the territory allocation module.  It is also
intended to help familiarize you with PATCH'S utilities for reading and
writing data, and for displaying imagery and modeling results.

Windows in PATCH that contain buttons and text fields are referred to
collectively as  control  windows. Windows  that contain images are
referred to as graphics windows. Every window in PATCH has a name,
displayed in the window header. However, there are exceptions to this
rule for the title and legend windows. The title window is the very first
window that comes up  when the model is started.  The title window
header displays the version of software being used. The legend window
displays the classes present in the GIS  data. The legend window header
displays the name of the GIS data set being used.  Also, moving the
mouse pointer into the  image, zoom, or analysis window  causes its
header to display the name of the GIS data set being used.

Many of PATCH'S control and graphics windows also have footers.
Footers, always located at the bottom of the windows,  are used to
display data and error messages generated by the model's utilities. You
should get into the habit of monitoring PATCH'S window footers.

Begin by starting PATCH and clicking on the title window. This makes
all of the control windows  visible. Enter the location of PATCH'S
sample GIS data in the main window Directory field. Enter "clayoquot"
into the main window's File Name field.
                                                                            85

-------
Reading GIS
Data
         Click on the button labeled Read The Data File. This makes PATCH
         read the GIS data set. If the clayoquot image has been successfully
         loaded, the main window  footer displays the number of rows and
         columns present in the data. The clayoquot image contains 3731 rows
         and 4301 columns. If PATCH has trouble reading the clayoquot data set
         or its control file, it writes error messages to the main window footer.
Displaying GIS
Data
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   )m-Box Size
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         Call up the image window by clicking on the button labeled Show
         Image  Window. Now  double click  in the image window. PATCH
         displays every 28th row and 28th column of the clayoquot data set. The
         image window is designed to subsample the GIS data and generate a
         dithered version of the entire image.  In contrast, the zoom window is
         designed to display part, or all, of the  GIS image without dithering.

         Change the Image Window Sampling  field from 28 to 10 (remember to
         use the "Return" key). This expands the size of the image window, and
         paints it black. Double click on the image window to display every 10th
         row and every 10th column of the  clayoquot data. Drag the image
         window to a convenient location on the desktop.
                        Modify Zoom-Box Height'%
                                Window Sajn*}lp^'-lg
                                 Zoom-BoK
                                            /fc/
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         Change the fields labeled Modify  Zoom-Box Height and  Modify
         Zoom-Box Length to 750 pixels each. Notice how the zoom-box size
         changes (in the image window) as this is done. Then, set the Degree Of
         Magnification field to 1 (remember to use the "Return" key). Click on
         the cyan color cell in the main window. It is just to the left of the white
         color cell. This changes the color of the zoom-box.

         The zoom window footer should read Rows 1491-2240 [] Cols
         1776-2525. If this is not the case, modify the location of the zoom-box
         directly by altering the fields in the main window labeled  TOP, BOT,
         LFT, and RGT. Change these fields to 1491, 2240,  1776, and 2525,
         respectively. Remember to use the Return key.
Example 2  Territory Allocation
                                                                     86

-------
VT  \ *" *- ;'££"•  -:*?=*- rr,
Using the Zoom
•Window  ""i-""'^

." *;:-e^IS3i'a f- "^"J^j
. , \;^ ,* $M:f>FS S7 1^, ^'^? 0
r; r.-v-'s f?S*-f-.'* fe*« jS 1
                                                      H im&mi5T^\^,i
                                                       * i§44704fc>;* 3g;
                    Call up the zoom window by clicking on the button labeled S/zcw Zoom
                    Window. Double click once in the zoom window to set its size. Double
                    click a second time to display the data within the zoom-box. Drag the
                    zoom window to a convenient location on the desktop.

                    Select a data pixel by clicking and holding the middle mouse button
                    anywhere in the zoom window. While the mouse button is down, the
                    selected  pixel is highlighted (painted white),  and the zoom window
                    footer displays its row and column values and indicates which legend
                    category it belongs to. Close the zoom window to get it out of the way.


                    Display the legend window by clicking on the button labeled Show
                    Legend Window. Place the mouse pointer on the category labeled Old
                    Growth and click the left button six times. Move the mouse pointer
                    down to Open Canopy Forest and click left five times. Then click twice
                    on Muskeg Forest, once on Bonsai Forest, four times on Natural Mature
                    Forest, and three times  on Natural Deciduous Forest. The first six
                    classes present in the legend should now be assigned nonzero habitat
                    weights. The other classes should all have weights of zero.
                                     Old Growth
                                     Open Canopy Forest
                                     Muskeg Forest
                                     Bonsai Forest
                   Display the zoom window again by clicking on the Show Zoom Window
                   button. Move to the habitat controls window and click on the button
                   labeled Turn Hexagon Grid On. The hexagon grid should appear on top
Example 2   Territory Allocation
                                                                              87

-------
     I,	If",	;' .  ,1!!'. ill!

         . , '.  _-..) ^
               - 'r "s;



FH;'.;';1'.,^v;;:   'II'}

i iil*	.iS! jjjii/ii;;-1' il i
   ......       ,
Building a
 .'.,' .'";,":,';> •..,; - ......... ! ......... It, TiSfir s-i*
1..-.!..- .. - - ., „   ........... ~  .I,,, (,,= _T, :: ....... J,
        '   ~
        ,
1) flSii r-Ti-ffl!* II ck/jft ^
4 i..«m : -s ....... B.I ..... is-' S ill! US""* it
              '
j.1'!' I1' "-"'"••'"• '.— .[rt. - "!,!' ""!	Ji a" '~"!''' -™"1"-*
     •-
of the image hi the zoom window. Each hexagon should be 12 pixels in
size and difficult to make out at this magnification.

With the zoom window visible, increase the hexagon area considerably
(e.g., to 10044 pixels or larger), then decrease it all the way down to 90
pixels. Use the increment or decrement widgets (       ) or the up and
down arrow keys on the keyboard. (The cursor must be inserted in the
Hexagon Area field in order for the up and down arrow keys to work.)
Each time the hexagon area is altered, its new value is automatically
assigned to the Territory Min and Territory Max fields.

The habitat controls window footer should now read 6342 Hexagons
and 8.10 Hectares. This indicates that 6342 hexagons, each  with an
area of 8.10 hectares (or 90 pixels), can  fit within the portion of the
image specified by the zoom-box.


Now click on the button labeled Build The  Territory Map.  PATCH
constructs a territory map and aligns the hexagon grid to its edges. To
see the results, call up the analysis window using the button (also in the
habitat controls window) labeled Analysis Window. Double click once
on the analysis window to set its size. Double click a second tune to
display the new territory map.

Example 2   Territory Allocation
                                                                88

-------
 .^^SA^KSSS
 ;.-•••  ,..- / fc^l,".-' =«?"• *•
 Adding a Border
 The analysis window footer should read 6342 //ex. [] 4420 Sites [] 154
 Terr., indicating that the map has a total of 6342 hexagons, that 4420 of
 them contain at least some Habitat (are painted either gray or green),
 and that 154 of them are territories (painted green), which implies that
 they are suitable for breeding.


 Now click on the button labeled AddHxgn Border. Pushing this button
 expands the zoom-box size slightly. Consequently, the analysis window
 is no longer up to date, and PATCH paints it black. Double click on the
 analysis window once to resize it, and a second time to repaint the
 territory map. The territory  map and hexagon grid should now be
 entirely  visible within the analysis window. A small black border
 should separate the outer edge of the hexagon grid from the window
 edges. This border region lies outside of the portion of the image used
 to generate the territory map.


 Place the  mouse pointer over one  of the  hexagons present in the
 analysis window.  Select  the hexagon by pressing and holding the
 middle mouse button.  As long as the mouse button is held down, the
 hexagon is highlighted (painted white) and the analysis window footer
 displays its number, area in pixels, and score. Hexagon  numbers are
 simply assigned sequentially  from top  to bottom, and left to right. A
 hexagon's area is equal to the number of pixels of habitat it contains.
 Habitat is defined as any legend class that has been assigned a nonzero
 weight. A hexagon's score is equal to the mean value of the weights
 assigned to every pixel it contains.

 When  a hexagon is  selected, the  habitat  controls window footer
 changes  to display the threshold score associated with  the territory
 map. This value is the same, regardless of which hexagon is selected.
 The threshold score is the minimum score  a hexagon must have to
 qualify as suitable for  breeding. Remember that hexagons can borrow
habitat from their neighbors in order to attain this threshold value. The
threshold score for this territory map is equal to 6.0 (the largest weight
entered into the legend) because the Territory Min field has been set
equal to the hexagon area.

When a hexagon is selected,  the habitat controls window footer also
displays  the  mean step  size.  This  is the  average center-to-center
distance separating a hexagon and each of its six neighbors. The reason
for reporting  the step  size as a mean value is  that PATCH'S raster
hexagons are not entirely symmetric. The distances between horizontal
and diagonal neighbors differ slightly. Knowing the  mean step size is
useful when parameterizing the life history simulator. The mean step
size is always reported  in meters (305.91 meters in this case).
Example 2   Territory Allocation
                                                              89

-------
IFerritory Min
and Max
                      Now change the field called Territory Min to 80. The habitat controls
                      window footer changes to indicate that the minimum territory size has
                      been set to 7.20 hectares. Click on the button labeled Adjust Min &
                      Max Sizes, This changes the threshold score from 6.00 to 5.33, and thus
                      increases the number of breeding sites present in the landscape from
                      154 to 1079. This change should be apparent in the analysis window.
                *	
                i
mm
              111
              	|'H ••
     -.••	i_, ,4
  a,, f ,,,i, "ii'inn  ilil |i,,,;< JiE.miiii1.
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nil i	I fit;™* in fft. _*! v
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I i=Cli1|SSi|l
  §!!!!l!!!:!ll:!!f  !	,!!• Ihj!!! ^,,'f,	Si ajEji: S1 "'
  IHIII j|i| i	Ji It j	|BiESjjiS!. l|l!|; *
b^iML '^•^.^WyEiiiwfc.ji
(llniiilir •)«» .'"i'li"1 '»'£iiHlilJjilll—Sin'' J|fl""''u«ll5iiiiiill!iiiii: '*S* III! .ii1,;.
„„, „„ „''„ „,.. .;..:.!'*• ••;!:-v*ii	Mipiiii. >J	i,,i«" |iHi * AllgiuGrill Tip  ; ft nalysls Window J

                          Adjust Mi n& Max Sizes)  ' Winiliiw-  *J,
                         *"" ;  ' : ; ••--v-v-v\;^jiimij™mm;:v;v:;--v-:jjiw)wijijjMjjjMMjjjJrrir^
                         jRessf Parameter Vftjuro/'
                         v-:" "~^   :   "" --^j^- •---""•-•- ...... • ..... -••"• ...... «"-• j"--''-- - '- " -•*
                                Hex Com press ion )

                                                                      ftdd
                          Turrt
                                                                    .
                          Turn Hexagon Grid Off/  Territory Max. :" ^100
                        Threshold Score; S.333
                      Now change the field called Territory Max to 100. The habitat controls
                      window footer changes to indicate that the territory maximum has been
                      set to 9.00 hectares. Click the button labeled Adjust Min & Max Sizes.
         asHBSiiissa;
Example 2   Territory Allocation
                                                                                         90

-------
 Saving the
 Results
 Locating
 f<^ms^,.^  *
    >iiat*reas
 This further increases the number of breeding sites present in the
 landscape from 1079 to 1493. This change should also be easy to spot
 in the analysis wmdow. ThstfTerritory Min  and Territory Max fields
 control the number of hexagons designated as suitable for breeding.
 Altering them does not change the hexagon scores or sizes.


 Enter a directory and file name into the habitat controls window Output
 Directory and Output File Name fields. For the sake of this discussion,
 let's assume you have entered "/Imp" and "test" for the directory and
 file name fields, respectively. Set the write protect feature to Override if
 a map with this name already exists. Now click on the button labeled
 Save All Files. PATCH attempts  to  save the results of the territory
 allocation process. If it is successful, the habitat controls window footer
 reports test Successfully Written. This causes PATCH to create three
 binary   (hence  not   readable)   files  named  "/tmp/test.patch",
 "/tmp/test.index", and "/tmp/testhexgn".


 Set the field labeled Define Edge Width to 10 (remember to use the
 Return key), and click on the button called Find Core Areas. A  small
 quantity of core habitat becomes visible in the analysis window. The
 process of locating core habitat in patch and territory maps is the same,
 and the presence of the hexagon boundaries does not affect the results.
 But the core habitats identified within a territory map are reported on a
 hexagon-by-hexagon basis. This makes it possible for you to rank
 hexagons based on  the quantity of core habitat they contain.  Core
 habitat identified during territory allocation is always painted yellow.


 Now decrease the edge width to six pixels, and click on the button
 labeled Statistics Output. PATCH recomputes the core areas before it
 generates the output file. Because the edge width was decreased, a large
 number of additional core habitat is added to that previously displayed.
 When PATCH is done identifying core habitat, it creates a file named
 "/tap/test" that contains a general description  of the results of the
 analysis run thus far.

 This  statistics file is similar to  those generated from patch maps. It
 begins with a header indicating the GIS data set being used. The rows
 and columns corresponding to the boundaries of the zoom-box are also
 included.  The file then records the edge width used to make the core
 area computations. Summary statistics describing the landscape as a
 whole are displayed next, followed by data characterizing the overall
properties of the hexagons contained within the landscape. The header
ends  with a  description of the legend  weights you provided. The
remainder of the statistics table consists of a record of the attributes of
Example 2  Territory Allocation
                                                              91

-------
                    every hexagon present in the landscape that has a score exceeding zero.
                    The first few lines of this statistics file contain the text displayed here.
1,



, „ I
ili" '"."•.
	 	 • ' • 	 	
:» ' 	 • .
; 	 ' • - :
gmgUL ,,..,,. in, , ' , •', . II


,,,,, 	 	 ' 'N ,"
111":: ' ••: ,' «?;>;;;+ 	 !V;
j 	 : 	 "v •-;'>'3l":::;' '**'':;



MJ. •:• ...^ ,'.-•*, IJ'..niV;i!Mii)iJ|iii'i,:b

5^{>?;-'fi l':±v:3 :,;"'
"*..,. - 	 '. - 	 ,,iV: 	 rm'\rm. 	 S-. i
llliliik!' iriinnl!1! n1 t^illlil'"!!!,!,!1,;,:11 Ir .iii^^
lit -flfi IP l|5f
1 ^Tif'si f iilii^ ISP %
•I"'..1 " 'T1'1!:. ;,"".... , ',„;;;;;; ,,:r ,,a r^isr'™.*

lL"t!l';\;l^!^f??5!!?^
I-'—:- v- 	 	 7***'&T?J?:1
;ii • • fV 	 f! !»•• »j fl'-ijiniP J» &
1 22-1 li=;~|fl!| 1? jig 1
- 	 ' 	 '•'•-[• 	 ! 	 ; 	 ;;,;7 	 ".T-t"2?
£r^ w^rw'^twSi-*
B, r-^3^^;*^1. |?| |
"if 	 'i"1'"' - -"""! 	 f j|i ' " , "1 	 ' /"i :!!!ili:*M 4
Input File Name Used
Analysis Is For Rows
Analysis Is For Cols
Edge Width In Pixels
Landscape Patch Area
Sum Of Patch Weights
Sum Patch Core Areas
Total Landscape Edge
Hexagon Size (Pixels)
Hexgn Threshold Value
Hexgn Expansion Value
Dist Between Hexagons
Total Nbr Of Hexagons
Hexagons With Habitat
Number Breeding Sites
Legend Value, Weight
Legend Value, Weight

Legend Value, Weight
Legend Value, Weight
Legend Value, Weight
Legend Value, Weight

Hexgn Hexgn Hexgn
Number Score Area


13 3.400 51
14 4.878 74
15 4.933 74
16 4.911 74
17 4.911 74
18 3.922 74
19 0.778 20
20 0.011 1
clayoquot
1491 - 2240
1776 - 2525
6
285416
1390538
103281
45840
90
5.333
0.111
305.91
6342
4420
1493
0, 6
1, 5

2, 2
3, 1
4, 4
5, 3

Hexgn Core Hexgn Breed
weight Area Perim In Hex


306 0 17 NO
439 10 10 YES
444 14 10 YES
442 14 10 YES
442 14 10 YES
353 8 10 NO
70 0 14 NO
1 0 4 NO
•*• •liliiniinr » "
||,  11 Jf 'l||
..... » ....... J'f-si.
tt«'
H       ^
Compression
exagon ^ :--i,-
The table above begins with hexagon number 13 because the statistics
file lists only hexagons that have some habitat. The score, area, weight,
core area, and perimeter of empty hexagons always equals zero. Empty
hexagons also never qualify  as breeding sites. Now set the edge width
to zero. This makes PATCH  stop locating core areas and consequently
speeds up any subsequent analysis.


The hexagon compression routine is useful for shrinking the size of a
territory map. PATCH'S compression routine works by constructing a
new territory map from 12-pixel hexagons. It then copies the scores and
breeding status from each hexagon present in the original territory map
Example 2   Territory Allocation
                                                                                 92

-------
                    over to the corresponding site in the compressed map. The compressed
                    and  uncompressed maps  are  identical  to PATCH'S life  history
                    simulator, but compressed maps are easier to display, take up less space
                    on the hard disk, and can be randomized with the hexagon editor.

                    Compress the territory map by clicking on the button labeled Apply Hex
                    Compression. When this is done, set the magnification parameter in the
                    main window to 2  (remember to use the Return key). Double click in
                    the analysis window once to change its size, and again to display the
                    compressed territory map. The compressed hexagons are each 12 pixels
                    in size, and the cells in the hexagon grid now have a slightly different
                    shape. Also, the hexagons in the compressed map are all painted a solid
                    color. The within-hexagon habitat pattern present in the uncompressed
                    map is lost when the compressed image is constructed.
                    Notice that the uncompressed hexagon size (90 pixels) is still displayed
                    in the Hexagon Area field, even though the hexagons themselves have
                    shrunk to 12 pixels each, hi order for this feature to work, the Hexagon
                    Area field must be locked any time that a territory map is compressed,
                    or if a compressed map is loaded into the model. To remove PATCH
                    from this state, you must click once on the button labeled Build The
                    Territory Map (don't do this now). The Territory Min and Territory
                    Max fields can still be modified when a compressed territory map is
                    being used.  The  habitat  controls  window  footer  displays  the
                    uncompressed hexagon and territory sizes.

                    The original territory map was 750 pixels tall and 750 pixels wide. The
                    compressed map is 251 pixels tall and 300 pixels wide. The zoom-box
                    appears  unchanged even though its height and width have become
                    much smaller. PATCH accomplishes this by translating the zoom-box
                    coordinates used to display the compressed map into the corresponding
Example 2  Territory Allocation
93

-------
r, '."i;,1.1 ^.".Cji.1^1	S;*;;{!: !•!!
Hexagon Grid
Jill, i'Si	I, i ,K 	' .""	••'
Alignment
     ', -:,f , S/^ii-.2;iL".ji
  	  ,'	\M'  .
Editing Hexagon
Scores by Range
values for the uncompressed map. The zoom-box is displayed with the
uncompressed coordinates while the analysis window is displayed
using the compressed values. The algorithm that does this cannot map
the contents of the zoom-box onto the zoom window, thus the zoom
window is disabled when a compressed territory map is being used.

Move the zoom-box around by clicking the middle mouse button in the
image window. This alters the image displayed in the analysis window.
The zoom-box can be moved only as far as the edges of the territory
map (if this is done, the  analysis window is painted almost entirely
black). This limitation is imposed by the routine that translates between
new (compressed) and old  (uncompressed) zoom-box coordinates.
When you are done, click on the button labeled Add Hxgn Border to
center the image in the analysis window.


Move the Align Grid To check-box from Data Set to Window and back
again. Notice how the habitat controls window footer changes to reflect
the grid alignment. The Align Grid To feature  allows you to link the
hexagon grid to the territory map or to the zoom-box.

Now change both the zoom-box's height and its length to 50 pixels by
editing the Modify Zoom-Box Height and Modify Zoom-Box Length
fields in the main window. Set the Degree Of Magnification field to 10
(remember to use the "Return" key).  Use the middle mouse button to
move the zoom-box around in  the  image window. Every time  the
zoom-box is moved, the analysis window is repainted. Change the grid
alignment to Window and then back to Data Set.  Lastly, turn  the
hexagon grid off and back on again, using the buttons labeled Turn
Hexagon Grid Off and Turn Hexagon Grid On.


Set the Degree Of Magnification field back to 2, and click on the button
labeled Add Hxgn Border. Then  double click on the analysis window
once to resize it, and a second time to display the entire compressed
territory map. Now click on the button in the center left of the habitat
controls window  labeled  View Next Panel (alternatively,  right click
anywhere in this panel). This displays the hexagon editor.
                      Hew Hexagon $$or» ter0*600-^ ^ jRannfeajfas^^n^tj^smn }/>
                      .L,.-d,,,jH-ljn,LwJ,*J.,4, , dL^jHHMH.Nli™™,*,,™ K.K, „  ,/ ,  '	*   ^1,mi1./^M1,1,.,rMUfaMm^rf/.rfA^^1^flhrt».H^m^^            5
Example 2  Territory Allocation
                                                            94

-------
tffXji
   »s»^~.-
    jrfP2 !
                     Locate the two numeric fields in the hexagon editor that are placed
              jjp |   adjacent to the text <= Hex Score <. These fields are used to define a
             7"  -T:   target set of hexagons that are to be altered as a group. Change the
             •-•/.'%    numeric fields so that the lower end of this range equals zero, and the
               / ;   upper end of the range equals six. None of the hexagons in the territory
              /.  f   map can have a score greater than six because the largest weighting
             \:[  S   value was set to six in the legend window. Now set the field labeled
               >,t    New Hexagon Score Is to 0.0. Once this is done, click on the button
                     labeled Assign Score To Hxgns In  Range. PATCH identifies every
              tp" 1   hexagon lying entirely within the zoom-box (all of the hexagons in this
              ««, ,^    case) that has a score greater than or equal to zero, but less than six.
              |_,,rjg   The model then changes the scores of these hexagons to zero.
Examine the results as they are displayed in the analysis window. Only
154 sites remain suitable for breeding. These are the hexagons that
originally had (and still have) a score of exactly six. Only hexagons
having a score less than six were modified in the preceding step. Select
a few of these hexagons, using the middle mouse button, to confirm that
they really do have a score of six. Examine some other hexagons as
well. They should all have  scores  of  zero. Notice that hexagons
containing habitat are never painted black, even after their scores have
been changed to zero.

This territory map has the same spatial distribution of breeding sites as
was present in the original map, when the territory minimum and
maximum were equal to the hexagon size. In both cases, only hexagons
with scores of exactly six qualified as  breeding sites. Now increase the
upper end of the range of target hexagon scores to seven. The hexagon
editor's range  fields should read 0.0 <= Hex Score < 7.0. Leave the
New Hexagon Score Is field  at zero, and click again on the button
labeled Assign Score To Hxgns In Range. The territory map should no
longer contain any sites suitable for breeding.

Click the middle mouse button on a hexagon in the analysis window.
While the mouse button  is held down, the habitat controls window
footer displays the threshold score. This value is 5.333, and is equal to
the minimum score a hexagon must achieve in order to be suitable for
breeding. Hexagons can borrow habitat from their neighbors to reach
the threshold score, but the amount that can be lent is limited by the
maximum territory size.
                    Now change the value of the field labeled New Hexagon Score Is to
                    5.334. Click on the button labeled Assign Score To Selected Hxgns and
                    move the mouse pointer into the analysis window. The analysis window
                    header should change  to read CHANGE HEXAGON SCORES.  This
Example 2  Territory Allocation
                                                             95

-------
      ,
Randomizing the
II*!!!!!*1 ill";!!!!!!! lli"!I *!!(*!!	.:" 	•	 •	
Territory Map
ilSi"	i,;;,;,!, >iifi'i! Iiii!:!!t«!j';;;
jiiii	I' J	J. :nu! i».	.;--:.:	---.


        "Ill
             JMC,'
             ~
j^..:.^±.,, Jli!,;^,.1j—,r^-:
 Uv	?*••••?	f
 i1!1 in vn	i."! mi"", f ni	i1".i"n	liiuF'"!!!! oniiinur in

    ,
indicates that PATCH is ready for you to modify hexagon scores by
hand. Click left on any of the gray hexagons. They should turn blue,
indicating they have been selected for modification. If you click on a
blue hexagon, PATCH removes it from the list of sites to be modified
and  restores its original color. The scores of hexagons that do not
contain any habitat (those painted black) can not be changed with this
routine, or by using the Assign Score To Hxgns In Range button.

Next, move the mouse pointer out of the analysis window. PATCH
applies the new score to all of the hexagons that were selected,  and
reruns the habitat sharing algorithm. The only breeding sites present in
this modified landscape should be the sites that were just altered using
the Assign Score To  Selected Hxgns button. No other hexagons  can
achieve breeding status by borrowing habitat, since the New Hexagon
Score Is field is set right at the threshold score.


Now type the name of the saved territory map into the habitat controls
window input file location. If you used the file name suggested earlier
in this example, then this means  you should place "/trap" into the
directory field, and "test" into the file name field. Now click on the
button labeled Load All Files. This loads the uncompressed territory
map that was constructed previously.

Now click on the Apply Hex Compression button. When the process
finishes, the entire compressed territory map should be displayed in the
analysis window. Next, click on  the button labeled Randomize When
Area > 0. This randomizes the location of every hexagon that has at
least some habitat. The black regions in the image do not change.
Lastly, click on the button labeled Randomize Every  Hexagon. This
randomizes every hexagon in the territory map.

When a territory map is randomized, every hexagon's location changes,
but the scores stay the same. However, the randomization process can
change the number of territories  present in a landscape because each
hexagon's ability to share habitat  is influenced by the quality of its
neighbors.  Click the Randomize Every  Hexagon  button a few more
times and watch the analysis window footer. The number of territories
present in the landscape should change with the landscape pattern. Now
set the territory maximum to the hexagon area (90 pixels) and click the
Adjust Min & Max Sizes button. Randomize the landscape a few more
times and watch the analysis window footer. The number of territories
should stay constant because habitat sharing has been precluded.
Example 2  Territory Allocation
                                                              96

-------
Changing the  ",
Resample Rate  t
« ikv .=--:,--« 6 y;v -M &
w O»:': *^M M l;/^>4^ ^
t e-.'... v;t,-*3 r/|'-» 1=^5 g--
 '- ."c iK»"~ «_ '•• *' i " ! ^^ tj&
                    Reset PATCH'S fields to their default values by clicking on the Read
                    The Data  File button  in  the main  window. The territory map  is
                    discarded. Go to the habitat controls window and increment the value
                    of the Hexagon Area field  using the increment or decrement widgets

                    (t!SZ|) or tne up and down  arrow keys on the keyboard. Each time
                    the hexagon  size is increased to  a new value, its size in hectares  is
                    displayed in the habitat controls window footer. You should observe a
                    sequence of hexagon sizes beginning with 1.08 hectares at 12 pixels per
                    hexagon/Next you should see 3.24 hectare hexagons composed of 36
                    pixels, then 8.10,15.12,24.30 hectares, and so on.

                    Now change the Resample Rate field in the main window to 2. Repeat
                    the process  of incrementing  the hexagon  size and observing the
                    corresponding areas  in hectares.  The  sequence  described  above
                    changes so that it now progresses through 0.27, 0.81, 2.02, 3.78, and
                    6.08 hectares. You may want to repeat this process for other values of
                    the resample rate parameter to see how the sequence of hexagon sizes  is
                    further modified.

                    The resample rate is designed to help you obtain a particular hexagon
                    size (in hectares). Use of the resample rate field forces PATCH to  divide
                    each pixel in the GIS data set into an  array of smaller subpixel units.
                    When the resample rate is  set to  2, each data pixel is divided  into  a
                    2-by-2 array of subpixels. A resample  rate of 3 causes PATCH to split
                    each pixel into a 3-by-3 array, and so  on. Change the resample rate a
                    few times and notice the number of rows and columns reported in the
                    main window footer. These  values grow in a predictable manner as the
                    resample rate is increased.

                    With the resample rate set greater than one, open and display both the
                    image and zoom windows.  Now move the zoom-box until the  image
                    displayed in the zoom window includes an isolated pixel of a  single
                    color. Left click on this pixels to observe the effect of the resample rate
                    parameter. Repeat  this process one more tune with an even  larger
                    resample rate.
Example 2  Territory Allocation
                                                                                 97

-------
Example 3
                            Demographic  Simulations
Introduction
               This example is designed to introduce PATCH'S life history simulator.
               It is assumed that the reader has worked through the previous two
               examples and thus already possesses a basic understanding of the
               organization and  use  of the PATCH model. This example does not
               come close to  illustrating  every possible approach to working with
               PATCH'S life history simulator. Many other applications remain for you
               to identify and explore.  The utilities discussed here are flexible and
               much more can be done with them than is illustrated. For better or
               worse, the possibilities are pretty much limitless.
Getting Started
;r r	~:
•4 «	I4i;^ ;
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               Begin by loading the clayoquot GIS data set (this is one of the sample
               images included with the PATCH distribution). Then set the zoom-box
               size to 500 x 500 pixels. If the zoom-box location has not been altered,
               then its top, bottom, left, and right edges (in pixels) should be equal to
               1616, 2115, 1901, and 2400, respectively. If this is not the case, then
               make the appropriate changes to the TOP, EOT, LFT, and RGT fields in
               the main window.
                     «,,»ui. ;240$
                     rt'
Once the zoom-box is in place, call up the legend window and specify
the habitat weights. Working from the top of the legend down to the
bottom, set the weights to 10,4,1,1,8,6,0,0,0,0,7,5,3,1,1,1,0,0.
As was the case in the previous two examples, these legend weights are
completely arbitrary.  Li a real investigation, you should specify the
legend weights based upon field  data that directly measure a species'
preferences in different habitat types. An alternative approach that you
can take if field data  are not available is to survey experts and request
that they rank the importance of available habitats for the species in
question. Recall that  the left mouse button increments the weighting
values and the right button decrements them.
                                                                            98

-------
 ? "f,l'..-K'il4^ss'»-*'"-
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is
                                          Old  Growth
                                          Open Canopy Forest
                                          Muskeg Forest
                                          Bonsai Forest
                                          Natural Mature Forest
                                          Natural Deciduous Forest
                                          Lightly Vegetated
                                          Bare / Rock / Sand
                                          Misc. Non-Forest    ''••".-•
                                         Logged / Ofcban / Rural
                                         Water
                     Next, set the hexagon size to 36 pixels, and the territory minimum and
                     maximum to 26 and 46 pixels, respectively. Then build a territory map.
                     The territory map should contain 7056 hexagons, of which 2310 should
                     be suitable for breeding. Click on the Add Hxgn Border button (found
                     in the habitat controls window) and change the magnification level to 1
                     (found in the main window). Then call up the analysis window and
                     double click in it once to resize it, and a second time to paint it. This
                     displays the territory map that was just constructed.

                     Place the mouse pointer over one  of the hexagons present in the
                     analysis  window. Select the hexagon by pressing and  holding the
                     middle mouse button. As long as the mouse button is held down, the
                     hexagon is highlighted (painted white) and the analysis window footer
                     displays  its number, area hi pixels, and  score. When a hexagon is
                     selected,  the habitat controls window footer changes to display the
                     threshold score  associated with the territory map.  The footer also
                     displays the mean step size when a hexagon is selected.
Example 3   Demographic Simulations
99

-------
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                     Now that  a territory map has  been created, you can begin  to use
                     PATCH'S life history simulator. But before going on, save the territory
                     map you just built. Choose a directory and name for the map. Later on
                     in the example, this territory map is referred to as "old_map",  so you
                     may want to specify that name now.


                     If a life history parameters file already exists, you can simply  upload
                     the data and immediately run a simulation. Otherwise, it is best to begin
                     preparing for a simulation by specifying the parameters in the life
                     history parameters  window. There are  10  parameter fields  in this
                     window, plus a 10 x 10 population projection matrix. PATCH'S life
                     history module simulates a post-breeding census, which means  that its
                     first age or stage class always consists exclusively of newly recruited
                     individuals that are not yet of breeding age. Thus the upper left entry in
                     PATCH'S projection matrix is always fixed at zero.

                     Start preparing to run a simulation by entering a projection matrix into
                     the panel at the right of the life history parameters window. Remember
                     that the survival rates present in any column of PATCH'S projection
                     matrix must not sum to more than one. More importantly, this must also
                     be  true of  the  corresponding  matrix used to make  survival and
                     reproductive decisions in the best habitats.
Example 3   Demographic Simulations
                                                                                   100

-------
                                                                             0   0.50
                                                                            0.25 0.75
 Enter the simple 2x2 population projection matrix,
 shown to the right,  into  the  life history parameters
 window.  You  can3 think of mis  matrix as defining a
 two-stage system of juveniles and adults. According to
 this matrix, juveniles  (who, by definition, do  not reproduce) have a
 relatively high rate of mortality. Adults (who do reproduce at a mean
 rate of 0.5 females  per female per year) experience a relatively low
 mortality rate. These vital rates were simply made up for this example.
 The
 Factor
The vital rates factor determines the quality of habitat to be associated
with the survival and reproductive values you supply. Hexagons with
scores of zero are always assigned survival and reproductive rates of
zero. Hexagons having the score indicated by the vital rates factor are
assigned the survival  and reproductive rates entered into the model's
projection matrix. PATCH uses the interpolation  functions to  find
survival and reproductive rates for hexagons with other scores. As the
vital rates factor is lowered, the vital rates associated with  the  best
habitats increase. You can examine  the  projection  matrix associated
with the best habitats by holding down the middle mouse button in the
panel containing PATCH'S projection matrix. Of course, holding down
the middle  mouse button will not  change the values displayed in
PATCH'S projection matrix unless the vital rates factor is set to a value
less than 100%.  Set the vital rates factor to 100% (the default value),
but don't  supply values to any of the other life history parameters
present in the window.
                    Next call up the life history functions window by clicking on the yellow
                    bar on the left (alternatively,  right click anywhere in the window).
                    Select the linear options for the survival and fecundity interpolation
                    functions  (these are the default options). Then bring back the life
Example 3  Demographic Simulations
                                                              101

-------
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                    history parameters window. Provide an output file name in the life
                    history controls window and click on the button labeled Get Output
                    Maps. Pushing this button after a simulation has been conducted would
                    generate three different image files. But two of these (".imageO" and
                    ".image2") are built from the results of a simulation and are not printed
                    if a simulation hasn't been run (unless a ".stats2" file containing utility
                    and density information has been loaded into the life history module).

                    At present,  you should obtain only a single image file ending  in
                    ".imagel". This is the expected source-sink map. PATCH also prints
                    out a ".stats2" file (unless one with the specified prefix already exists).
                    This is where PATCH stores the raw data used to construct its output
                    image files.  Examine the expected source-sink map  (".imagel") that
                    has just been created. You can do this by changing its name so that it
                    ends in ".sun" and then reading it into PATCH. Alternatively, you can
                    examine the file using other raster image viewing packages such as XV,
                    Xloadlmage, or Sun's snapshot or imagetool programs.

                    Non-habitat is displayed in white on the source-sink map. Sites that
                    have habitat but are not suitable for breeding are displayed in black.
                    Breeding sites are displayed in red if they can be expected to behave as
                    sinks and in green if they are expected to behave as sources. Notice that
                    all of the breeding habitat displayed in this image is colored red, which
                    alerts you that the result of combining the current territory map with the
                    population projection matrix, the vital rates factor, and the interpolation
                    functions  specified above,  is a landscape containing no  source sites
                    whatsoever.  You can be confident that any model species is going to
                    decline rapidly to extinction in a landscape containing  only  sinks.
                    Remember  that   sources  and  sinks  here  are  evaluated  on  a
                    hexagon-by-hexagon basis.

                    If the species being modeled is not experiencing a rapid decline in
                    numbers, then the above analysis should be sufficient to alert you that
                    something is already amiss. Assume the  survival and reproduction
                    values being used  have been  taken from  the  literature  and are
                    reasonable for the species. Assume also that the GIS map is accurate
                    and that the selection of habitat weights is  appropriate. You  may then
                    conclude that the vital rates factor is  set too high. This simple analysis
                    thus  suggests that if the model species is to have any chance at
                    persistence, the survival and reproductive rates specified above must be
                    realized in suboptimal  habitat. When the  vital  rates factor is  set to
                     100%, altering  the interpolation functions  does  not improve the
                    species' performance in the best habitats.

                    Now set the vital rates factor to 85%. This tells PATCH to  associate the
                    survival and reproductive rates entered above with hexagons that have
Example 3   Demographic Simulations
                                                                                   102

-------
                      scores of 85% of the maximum value of 10, or 8.5. As a result, the vital
                      rates  experienced  (ignoring stochasticity)  in hexagons with scores
                      greater than 8.5 exceed those entered into PATCH'S projection matrix.
                      This will allow some of these sites to function as demographic sources.
                      Leave the interpolation functions as they are (both linear), and click
                      and hold the middle mouse button on PATCH'S projection matrix. The
                      adult fecundity, juvenile survival, and adult survival should change to
                      read 0.5882, 0.2941, and 0.8824 respectively. These are the  survival
                      and reproductive rates now  realized in the  highest quality habitats.
                      Click on the button labeled  Get Output Maps and examine the new
                      copy of the expected  source-sink map  (".imagel")  that  PATCH
                      constructs. Many of the breeding sites previously classified as sinks
                      (red) should now be classified as sources (green). This combination of
                      parameters is more likely to produce a stable population.
                          Vital Rates Factor = 100%
Vital Rates Factor = 85%
                     After  supplying  the  projection matrix,  specify  the  remaining
                     parameters present in the life history parameters window. It is usually a
                     good idea to begin by setting the number of runs to 1, and the number
                     of years to a small value such as 10, Otherwise, if the model population
                     begins growing rapidly, the  simulation can  take a long time to
                     complete. Use the field labeled Tally Utility From to specify a year for
                     PATCH to begin tracking the observed source-sink data. It is reasonable
                     to begin by setting this field to zero.

                     The life history parameters selected for this example are designed to
                     produce simulations that progress relatively quickly. So for the time
Example 3   Demographic Simulations
                       103

-------
                     being, ignore the cautions mentioned above and set the number of runs
                     to 10, the number of years to 200, and the Tally Utility From field to
                     101. This instructs PATCH to perform 10 replicate runs of 200 years
                     each, and to tally the observed source-sink properties of each breeding
                     site for the final 100 years of each simulation.
The Initial
Population Size
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Function
                     maximum limits the total distance that can be traveled. The search
                     minimum and maximum are specified as a number of steps from a
                     hexagon to one of its immediate neighbors. This step size is displayed
                     in kilometers in the habitat controls window footer when a hexagon is
                     selected (using the middle mouse button) in the analysis window. This
                     mechanism is provided to help you translate actual dispersal estimates
                     into numbers of steps within a territory map.

                     The parameters labeled Search Randomly and Walk Up Gradient are
                     used only when the search  strategy  involves a  random  walk. But
                     remember that a random walk is always taken by individuals that fail to
                     locate an available breeding site using the alternative search strategies.
                     Thus the Search Randomly and Walk Up  Gradient parameters should
                     be specified regardless of the search strategy being implemented. Both
                     of these parameters range between 0 and 100%. If the Search Randomly
                     parameter is  set to  0, movement paths become  straight lines. If this
                     parameter is set to 100%,  the choice of movement direction  is made
                     randomly.  Movement  paths  vary  continuously  from  linear  to
                     completely random as this parameter is increased from 0 to 100%.

                     When the parameter labeled Walk Up Gradient is set to 0, individuals
                     taking a random walk ignore habitat quality all together. The character
                     of the random walks is then controlled entirely by the Search Randomly
                     parameter. When the parameter labeled Walk Up Gradient is set to
                     100%, individuals always  attempt  to  move  to the best neighboring
                     hexagon (as long as it is better than  the current site). As this parameter
                     is increased from 0 to 100%, searchers exhibit an increased propensity
                     to move up gradient to better habitats. Decisions based on the Walk Up
                     Gradient parameter always  take precedence over decisions based on the
                     Search Randomly parameter. For this example, set the search minimum
                     and maximum to 1 and 10,  respectively. Then set the Search Randomly
                     and Walk Up Gradient parameters both to 50% (their default values).
          Values have now been assigned to all of the fields in the life history
          parameters window. Next call up the life history functions window by
          clicking on the yellow bar that appears to the left of the projection
          matrix (alternatively,  right click anywhere in the window). The life
          history functions window lets you specify the interpolation functions
Example 3  Demographic Simulations
                                                                      105

-------
                     for survival and reproduction, the movement strategy, and the level of
                     site fidelity. The interpolation functions for survival and reproduction
                     were both set to the linear option earlier in this example. Leave these
                     the way they are, but set the movement routine to Random Walk and the
                     site fidelity to medium (these are both the default settings).
                       Tatml Hodol Ram :
                       Number Of ¥«are :
                       Tolly Utility From ;
                       initial Popnlitlon :
                       lnlti«lfaitlon
                       S««rl. Hlnlmom
                       Starch Maximum  : 10
                       S««rcb JUndomly  t 80
                       Walk Up Gradient  : S0
                       Vttml Rates Factor  : BS
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                     This forces every individual to use a random walk when searching for
                     an available breeding  site, hi addition, setting  the  site fidelity to
                     medium  obligates  territorial individuals occupying sinks to search
                     yearly  for a  new breeding site. Territorial individuals occupying
                     sources remain on their sites  indefinitely. When the  site  fidelity
                     parameter is set to low, every territorial individual searches yearly for a
                     new site. When it is set  to high, all territorial individuals remain on
                     their sites indefinitely.

                     PATCH can display the locations and movements of every member of
                     the simulated population  in the analysis window. This visual feedback
                     is informative, but the process of displaying it  makes  the model run
                     much more slowly. You can turn these graphics off and on  using the
                     Visualization check-box present in the life history window. It  is usually
                     best to  begin with the visualization check-box off.

 'IS!
Example 3   Demographic Simulations
                                                                                  106

-------
 Specifying an
 Output File
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Running a'
Simulation
 The last thing to consider before running a simulation is whether or not
 to save the results to a disk file. The life history window contains output
 file name fields that can be ustd to save the life history parameters and
 model results. This window also contains input file name fields that can
 be used to upload life history parameter files that have previously been
 saved. It is usually not necessary to enter an output file name in the
 early stages of a simulation. PATCH simply sends the output data
 directly to the computer's monitor. However, the life history simulator
 can generate seven additional  files (".statsO",  ".stats 1", ".stats2",
 ".stats3",  ".imageO",  ".imagel",  and  ".image2"),  that  are  only
 constructed if an output file name is supplied. For now, select an output
 directory and file name and enter them in the life history window. Let's
 assume you have selected the file name "/tmp/test" for this purpose.
Before  starting a simulation, call up and paint the analysis window.
Then go to the life history window and push the Reset & Initialize
button. The life history window footer should change to read Selected
Initial Sites. If it does not do this, push the reset button again. Next
click on the button labeled Display Locations. This displays every
member of the initial population  in  the  analysis  window.  These
individuals  are all territorial,  and  are  shown in red.  A  territorial
individual should  appear in every breeding site because the initial
population was set equal to the number of breeding sites. Check that the
vital rates factor is at 85%. If this parameter is mistakenly set to 100%,
the population can be expected to die out in about 50 years.

Now push the button labeled Run Simulations. This starts a model run.
The left side of the life history window footer displays the run number
and year as the simulation progresses. The right side of the footer
displays the function currently being implemented.  The simulation
results are sent to the specified output file, or to the UNIX command
window from which PATCH was called up.
Example 3   Demographic Simulations
                                                              107

-------
                    If the visualization check-box is set on and the analysis window is up to
                    date, you can observe the simulation superimposed  on the  territory
                    map. Dispersing juveniles are displayed as white lines. The movements
                    of floaters, if there are any, are  displayed as yellow lines.  Heaters
                    themselves are displayed as yellow borders surrounding the hexagons
                    in which they are located.
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                                 i
                                "test"
                            Basic Outputs
I i
"test.statsO"
Density

1
"test.stats1"
11, a

*
"test.stats2"
Site Quality
                        Assuming the  above naming scheme was used, the file named "test"
                        contains the parameters provided to the life history module, and the
                        simulation results on a run-by-run and year-by-year basis. This file can
                        be used to display the net and sum movement distances, the number of
                        floaters and breeders, and the number of individuals in each stage class.
    Lift History *»*n*
        To Create fhis File
                          *• parameter File for Die.
                          * the Coverage 'clayaquoti
                                      1 -I'-tO^BO 60 8S^Q':0p_1l»3"'lQ4''*04 Tdl TOT 801802
0,0000 -» 0,5000
0,2500   0,7500
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       0.0000
       0,0000
       0,8000
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0,0030*
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0,0800.  0,0080
0.0000
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0,0000
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8,0008
0,0080
0,0800
0,0000
0,0000
0,0000
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0,0000
8,0000
0,0000
0,0000
0,0008
0,0000
0.0008
0.0000
0,0000
0.0000
0,0000
         0,0000
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                                      0,000
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                                      0/403
                                      0,383
                                      0,345
                                      0,332
                                      0,325
                                      0,332
                                      0,328,
                        The file called "teststatsO" contains a record indicating whether or not
                        each breeding site was occupied at the end of the final year of every
                        replicate simulation. The ".statsO" files are written in a binary format,
                        and because of this you cannot read them directly. PATCH accesses the
                        data in a ".statsO" file when the button labeled Estimate Density is used.
                        When this button  is pushed, PATCH extracts  the  density information
                        corresponding to the breeding sites currently enclosed in the zoom-box,
                        and it generates a list showing the number of breeders present in that
                        region at the end  of each simulation. PATCH highlights the breeding
                        sites being used in the  calculation so  you can make sure that  the
                        occupancy data being gathered actually correspond to  the intended
Example 3   Demographic Simulations
                                               109

-------
                       region. When this utility is used, the appropriate file name must appear
                       in the life history window's input file name field.
The ".statsl" File
                       The file called "teststatsl" can be used to display the yearly means and
                       standard deviations of the population size, the number of floaters and
                       breeders, and the number of individuals in each stage class. This file
                       also records  the  mean  effective  survival and  reproductive  rates,
                       presented as elements of a projection matrix. PATCH  also records the
                       dominant eigenvalue (A)  corresponding to  each effective projection
                       matrix. Each value  in a ".statsl" file  is  computed using the  entire
                       collection of replicate runs generated during a simulation.
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                                  0
                                  1
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                                  3
                                  4
                                  5
                                  6
                                  7
                                  8
                                  9
                                 10
                                      2310,00
                                      2538.30
                                      2228.00
                                      1883.20
                                      1815.20
                                      1673,40
                                      1538,40
                                      1521.30
                                      1448.00
                                      1402.70
                                      1341.30
    0,00
    38.13
    37.34
    4B.97
    37,78
    25,00
    22.53
    18,93
    29,86
    34,81
    35,43
    0.00
  343,00
  216.50
  144.70
  101.70
   80.90
   70,60
   55.90
   48.00
   48^30
   38,30
     0,00
    25,05
    25,88
    25.28
    21,39
    14.48
     6,70-
    10. BO
    13,48
    13,01
    12,09
     2310,00
     2189,30'
     2012,50
     1848.SO
     1713. SO
     1582. SO
     1527.80
     1465,40
     1400,00
     1354.40
     1302.40
        0.00
       15,68
       24,12
       24.71
       24,67
       22,52
       15,71
       22,92
       26,60
       30.65
0.8804
0^7269
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0,8399
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                       The file called "test.stats2" can be used to  display the breeding site
                       scores, their expected and observed source-sink properties, and their
                       observed occupancy rates. Nonbreeding sites do not appear in ",stats2"
                       files. The observed source-sink properties are compiled for every year
                       of every replicate run that is greater than or equal to the value of the
                       Tally Utility From parameter. In contrast, the observed occupancy rates
                       are gathered  strictly from the population distributions present at the
                       final model year of each replicate simulation.

                       The first two columns in a ".stats2" file contain identifying numbers
                       unique to each hexagon.  PATCH uses the numbers in the first column
                       when a ",stats2" file is uploaded into the life history module. You can
                       ignore these values. The  numbers in the second column correspond to
                       the numbers displayed in  the analysis window footer when a hexagon is
Example 3   Demographic Simulations
                                                                                            110

-------
'&«• *

                       selected (using the middle  mouse button). The  next two columns
                       contain the hexagon scores and lambda values. The lambda values are
                       computed from the scores using the life history parameters you supply,
                       and they indicate each hexagon's expected source-sink behavior. The
                       next column contains utility values, which describe each  hexagon's
                       observed  source-sink behavior. The last column in a  ".stats2" file
                       displays the number of times each hexagon was occupied by a breeder
                       on the final year of each replicate model run.
                                     I Patch-*   Hex-* „  scores   LamtJa   -utility occupancy j
                                          .
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                      PATCH does not generate graphical displays of any of its output data.
                      Instead, a S-PLUS macro called "plot" has been provided specifically
                      for this purpose. S-PLUS is a statistics package produced by MathSoft,
                      Inc. The S-PLUS macro reads and plots all of the data present in the
                      main life history output file as well as the ".stats 1" and ",stats2" files.


                      The S-PLUS macro is complex, but it is easy to use. It prompts you for
                      all of the information it needs. You must open a graphics window in
                      S-PLUS (e.g., issue a  motif command) before using the macro. If
                      possible, use the S-PLUS macro to view the results from the simulation
                      you just conducted. The S-PLUS macro accesses the data stored in the
                      ".stats 1" file if you ask it to  plot replicate number 0.  Otherwise, it
                      displays only the data corresponding to a specific model replicate (data
                      contained in the main life history output file). The S-PLUS macro is
                      also useful for  generating  data sets  that  can  be used to introduce
                      environmental stochasticity into PATCH'S simulations.
Example 3  Demographic Simulations
                                                                         111

-------
                                 Total Population Size <
                                                                    Floaters & Breeders (test)
                                                                  Number of Source Hexagora
is
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                                  Survival & Fecundity (test)
                                                                              (1881)
                                Observed Lambda Values (tost)
                                     Statistics For File : "test" (Years 101 to 200)

                                     Mean Population Size For Years 101 to 200 la : 896.7
                                     Mean Number Breeders For Years 101 to 200 Is : 875.1
                                     Mean Number Floaters For Years 101 to 200 Is ;  21.7
                                     Mean Value Of Lambda For Years 101 to 200 Is : 0.999

                                     Mean Matrix Elements For Years 101 to 200

                                        0.000 0.569
                                        0.251 0.856
Next, push the button in the life history window labeled Get Output
Maps. This makes PATCH print out three output image files, assuming
that the appropriate data have been compiled during the simulation, and
also that a file name has been specified in the life history window.
These three image files end in ".imageO", ".imagel", and ".image!".


The ".imageO" file displays the  occupancy rate of breeding habitat
throughout the landscape. The data displayed in the occupancy map are
gathered during the final year of each replicate simulation. However,
this information is compiled only if the number of runs conducted was
greater than 1 or the Tally Utility From parameter was set greater than
0. In the construction of this map, the occupancy rate data are rescaled
to lie in the range from 0 to  10. The resulting occupancy rates are then
displayed using a color spectrum that shifts from red to blue. The least
used sites appear in pure red, and the most frequently used sites appear
in pure  blue. The data used to create  this image  are  essentially  a
summary of the information stored in the ".statsO" file. But PATCH
does not consult the ".statsO" file when it constructs a ".imageO" map.

The ".imagel" and ".image2" files contain the expected and observed
source-sink maps. As discussed earlier, the ".imagel" file (the expected
source-sink map) can be generated before a simulation has been run. In
contrast, the ".image2" file (the observed source-sink map) can be
created only after a simulation has been performed. But the data used to
Example 3   Demographic Simulations
                                                                  112

-------
   '

                     construct the ".image2" file will be compiled only if the Tally Utility
                     From parameter is  set greater than 0 and less than or equal to the
                     number of simulation years. All sinks in these maps are painted red,
                     and all sources are painted green. But you can alter this color scheme
                     because both images contain 100 sink and 100 source classes.

                     The figure below provides a list of the output image files that PATCH
                     can construct before and after a life history simulation is performed.
                                                Simulation

V
# Runs > 1
-or-
Utility > 0
V
"tesUmageO"
Observed
Occupancy
Rates
Get Output Maps

^

r
"test.imager
Expected
Source-Sink
Distribution
\
r
0 < Utility <# Years
i
r
"test.image2"
Observed
Source-Sink
Distribution

                     The occupancy and source-sink data are stored in the ".stats2" file, and
                     can be uploaded along with a life history parameters file using the Read
                     Parameters button. This feature can be used to generate new copies of
                     the  three output  images at any  time after a simulation has been
                     conducted. To rebuild the image files, you need only load a life history
                     output file paired with an existing ",stats2" file. When a ".stats2" file is
                     successfully imported, the life history window footer adds the text
                     + stats2 to  the message that would otherwise be displayed. At this
                     point, you can click on the button labeled Get Output Maps to generate
                     new copies of PATCH'S output images.


                     PATCH'S source-sink maps are  designed to be customized.  The
                     expected and observed source-sink maps both use the  same  color
                     scheme. Sources and sinks are broken into 100 classes each, with every
                     sink initially painted red, and every source painted green. You can alter
                     this color scheme to highlight the best sources or the worst sinks. A key
                     to this color scheme is included with PATCH'S sample GIS data in the
                     files   "source_sink"   and  "source_sink.sun".   The  control  file
                     ("source_sink") can be copied and used with one of PATCH'S output
Example 3  Demographic Simulations
113

-------
.fit',	 i; IT i "" " Ji!!1 1
                     source-sink images. Because the control file has been designed for this
                     purpose, the resulting legend categories are meaningful.

                     A second option exists for customizing an observed source-sink map.
                     The key to this method lies in the fact that PATCH  can upload a
                     ".stats2" file along with a life history parameters  file, and the data
                     stored in it can then be used to generate a new observed source-sink
                     map. The observed source-sink map can be customized by editing the
                     ",stats2" file so that it contains only the information you want to display
                     in the ".image2" file. Hexagons corresponding to lines removed from
                     the ".stats2" file are considered neutral and painted blue. Using this
                     method, you can select specific hexagons  or groups of sources and
                     sinks to be highlighted in the observed source-sink map.
 environmental
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               PATCH  allows you to  build  environmental stochasticity into  its
               demographic simulations. You accomplish this by constructing a table
               of vital rates that reflect the level of environmental stochasticity to be
               simulated. PATCH can upload the data in this table as long the table is
               arranged correctly and contained in a file that has an appropriate name.
               Each column of the table holds a specific survival or reproductive rate.
               Every row of  the table must contain the entire set of survival  and
               reproductive rates necessary to construct a projection matrix.

               Matrix elements that have been set to zero in the model interface cannot
               be represented in the table of vital rates, and as such they remain zero
               throughout a simulation. Nonzero elements in the matrix are read from
               top to bottom and left  to right, and  (in this order) they define the
               columns of the table used to simulate environmental stochasticity. Each
               year a simulation is run,  a row from the table is selected at random and
               used  to build the projection matrix for the model species. Remember
               that survival rates present in any column of PATCH'S projection matrix
               must sum at most to one, and this is also true of the matrix used for
               survival and reproductive decisions in the best habitats. Every matrix
               contained in a table of vital rates used to  simulate  environmental
               stochasticity is subject to these constraints. If any of the matrices fail to
               meet these conditions, the entire table is discarded.

               PATCH expects a table of vital  rates to have the same  name as a life
               history parameter file, except that it must end in ".random". If a table of
               vital  rates is successfully loaded (using the Read Parameters button),
               PATCH indicates this in  the life history window footer by  adding
               + random to the message that would otherwise be displayed. You can
               practice constructing and using  tables of vital rates by  building these
               data sets by hand. A valid table  of vital rates may have  as little as one
               line. There is no upper limit to the number of lines a table may contain.
Example 3   Demographic Simulations
                                                                              114

-------
                     The S-PLUS plotting program included with the PATCH distribution
                     includes a flexible tool for constructing tables of vital rates. If you enter
                     the text "random" when the S-PLUS macro asks for the replicate run
                     number, the program's vital rates generator is initiated.

                     Add environmental stochasticity to the simulation conducted earlier in
                     this example by constructing  a table of vital rates. If the life history
                     output file created earlier was named "test",  then this  table should be
                     called "testrandom". The table  of vital rates has  three columns
                     corresponding to the three nonzero entries used in PATCH'S projection
                     matrix. The first column specifies  the adult fecundity. The second and
                     third columns specify the juvenile and adult survival rates, respectively.
                     A copy of the table of vital rates intended to be used with this example
                     is displayed below. This table is not intended to be realistic.
                                                              continued from left..,
                            continued on right...
                     After constructing  the table of vital rates, load it and the existing
                     demographic output files into PATCH'S life history module by clicking
                     the Read Parameters button. But first, be sure to type the correct name
                     into the life history window input file name field. Because a simulation
                     has already been conducted, a ".stats2" file should be present with the
                     same prefix as the ".random" file that was just created. PATCH attempts
                     to upload this file, along with the main life history parameter file and
                     the table of vital rates.  If PATCH successfully reads these  files, a
                     corresponding message appears in the life history window footer.
Example 3   Demographic Simulations
115

-------

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Select a new name to be used for the life history output files that
include environmental stochasticity. Let's assume here that you have
chosen the name "random" for this purpose. Enter the new name in the
life history window  output  file name field.  Assuming the Read
Parameters operation was successful, PATCH is now ready to conduct
a new simulation in which everything is the same as before except for
the addition of environmental stochasticity. Start this new simulation by
clicking the button labeled Run Simulations.

At the beginning of each model year, PATCH selects a row at random
from  the table of vital rates.  This information is used to construct a
projection matrix for  that year, which is then placed  into PATCH'S
graphical interface.  As a result, the vital rates displayed in PATCH'S
projection matrix change constantly as a simulation progresses. This
feature  makes  it  easy to  verify  the  presence  of  environmental
stochasticity in the model. When the simulation has finished, compare
the  statistics  files  to  those  generated   without   environmental
stochasticity.  A  great  deal more variability  should be  present in the
model outputs, and the various measures of population size most likely
have decreased as a result.

Environmental variation in PATCH'S vital rates is always going to be
synchronized across a landscape.  This  simplification becomes less
realistic as the size of your landscape increases. You can work around
this spatial synchronization by creating a time series of territory maps
that  exhibit  the patterns and  ranges  of environmental variability
desired. The time series of territory maps can then be  substituted for
PATCH'S traditional approach to environmental stochasticity (the use
of ".random" files), or the two techniques can be combined.
Example 3  Demographic Simulations
                                                            116

-------
   bitat Change
                                Total Population Size (random)
                                                        !l
                                                                  Floaters & Breadars (random)

                                Survival & Fecundity (random)
                                                                 Number Per Stage Class (random)
                                                           ^X^fos:^^^^^
                               Observed Lambda Values (random)
                                                                         100     ISO
                                                          Statistics For File : "random" (Years 101 to 200)

                                                          Mean Population Size For Years 101 to 200 Is ; 278.4
                                                          Mean Number Breeders For Years 101 to 200 Is : 260.1
                                                          Mean Number Floaters For Years 101 to 200 Is : 18.3
                                                          Mean Value of lambda For Years 101 to 200 Is : 1.000
                                                          Mean Matri:
                                                             0.000  0.598
                                                             0.261  0.843
A principal feature of the life history module is its ability to simulate
landscape change through time. PATCH models landscape change by
loading different territory maps at specified points in time. A tool called
the time series editor is available in the life history window for this
purpose. The time series editor allows you to create  a schedule of
territory maps to be installed at specific times during a simulation. The
process of loading territory maps during a simulation works correctly
whether or not multiple replicate runs are being conducted. However, if
the number of replicates is greater than one, PATCH insists that you
install a territory map  at  year zero. PATCH loads the  year  zero
landscape at the beginning of each new replicate and inserts the initial
population into this landscape.

Any reflecting boundaries that have been entered into the landscape (or
uploaded along with  a life  history parameters file) are replaced  each
time a new territory map is installed. However, hexagons suitable for
breeding cannot be made into reflecting boundaries. Thus,  if suitable
breeding sites are gained when a new territory map is installed, then it
is possible to lose some reflecting boundaries. On the other hand, if
suitable breeding sites are lost, reflecting boundaries may appear where
they previously did not exist. This feature can be used to simulate the
creation or destruction of obstacles to movement.

In order to take advantage  of PATCH'S ability to simulate landscape
change, you must first create a sequence of territory maps. You have at
Example 3   Demographic Simulations
                                                                 117

-------
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 least two options for accomplishing this.  PATCH'S habitat controls
 window contains  a  hexagon editor. With this tool, you can quickly
 generate a series of territory maps that illustrate any number of subtle
 or dramatic landscape changes. The resulting territory maps may then
 be imported directly  into PATCH'S time  series  editor.  The  second
 option for creating a time series involves editing the GIS imagery and
 then rebuilding the  territory maps.  A  GIS image  can always be
 modified using the program that  created it. But it is also possible to
 modify a GIS image from within PATCH. You can change the  habitat
 class assigned to  a pixel, a patch, or a collection of patches. These
 utilities are straightforward to use, but they work only on GIS files that
 have UNIX write permission.

 To edit individual pixels, first identify the class in the legend window
 that is to be applied to the modified cells. Next, click the middle mouse
 button on this legend window category. If the GIS file is writable, the
 editing arrow appears in the box next to the specified legend category.
 Once the editing arrow has been placed, you can modify individual
 pixels by left clicking on them in the zoom window. Any pixel selected
 in this way is changed to the  legend  class indicated by the editing
 arrow. The editing arrow can be relocated as often as desired, and the
 process continued. Click either the right or left mouse button anywhere
 in the legend window to remove the arrow and end the editing session.

 To edit patches, a patch map must first be  constructed. You  can then
 place the editing arrow in a legend category  and left click on any of the
 patches present in the analysis window. Each time a patch is  selected,
 every pixel in it is changed to the  habitat class specified by the editing
 arrow. You can also automatically modify every habitat patch present in
 the landscape by clicking on the button labeled Alter Pixels By Patch.
 This button is in the hidden panel at the top of the main window.

 This example now illustrates the use of the hexagon editor for creating
 new territory maps. Recall that a territory map was constructed in the
 beginning of this example, and it has been used in all of the simulations
 conducted thus far. Let's assume  here that  this original territory map
 was  named "old_map" (i.e., it consisted of the files "old_map.hexgn",
 "old_map.index", and "old_map.patch"). If this territory map has not
 been loaded, do so before proceeding.

 The  legend weights used in  constructing the original territory  map
 ranged between 0 and 10. All of the hexagon scores therefore also fall
 within this range. Call up the hexagon editor by clicking on the View
Next Panel button located in the center of the habitat controls window.
 Alternatively, right click  anywhere in the habitat controls  window
middle panel. Set the lower end of the range of target hexagon scores to
Example 3   Demographic Simulations
                                                             118

-------
                     5, and the upper end to 10. Then set the New Hexagon Score Is field to
                     10. Next, make sure that the entire territory map is  visible  in the
                     analysis window. You accomplish this by clicking on the button in the
                     habitat controls window labeled Add Hxgn Border (the Set To Data
                     Edge button also suffices). Then click on the button labeled Assign
                     Score  To Hxgns In Range. This causes PATCH to identify every
                     hexagon contained entirely  within the zoom-box  that has a  score
                     between 5 and 10. It assigns each of these hexagons a new score of 10.
                     This modified territory map should contain 2658 breeding sites.

                    Next, save the resulting territory map using the name "newjtnap". Do
                    so by entering this name in the habitat controls window output file
                    name field and then pushing the button labeled Save All Files. Many of
                    the hexagons  in the territory map named "new_map" have higher
                    scores  than their counterparts  in the map named "old_map".  Now
                    upload  the demographic  output  files   generated  earlier  ("test",
                    "test.stats2", "testrandom") into PATCH'S life history module. Make
                    sure that  PATCH  successfully reads  the  table  of vital  rates
                    ("testrandom"). Then insert the original  territory map, presumably
                    named "old_map", into the life history window time series editor at
                    year 0. Next, insert the territory map named "new_map" into the time
                    series editor at year 50. To add an entry into the time series editor, first
                    set the year, then specify the directory and file name information, and
                    finally click on the Add This Entry button. PATCH provides  all of the
                    relevant feedback in the life history window footer.
Example 3  Demographic Simulations
119

-------
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                     Leave all of the other life history parameters as they are. Lastly, enter a
                     new file name in the life history window output file name field. Let's
                     assume here that you have selected the name "old_+_new"  for this
                     purpose.  Then  begin the new  simulation by clicking on the button
                     labeled Run Simulations. The  new model  output incorporates both
                     environmental stochasticity and landscape change. In the absence of
                     environmental stochasticity, the model population could be expected to
                     improve dramatically after the  new landscape is installed at year  50.
                     However,  a considerable amount of  environmental stochasticity is
                     represented in the table of vital rates created earlier. As a consequence,
                     these new results are likely to be highly variable.
                               Replicate 2 of 10
Replicate 3 of 10
                                50
                                     100
                                     Year
                                           150
                                                 200
                                                                 50
                                                                      100
                                                                      Year
                                                                            150
                                                                                  200
                               Replicate 6 of 10
                                                        §
                                                        9
                                                        |
                                                                Replicate 8 of 10
                                                      (D O
                                                      II
                                50    100    150    200
                                     Year
                                                                 50    100    150    200
                                                                      Year
                     The changes to the landscape that take place at year 50 should be
                     dramatic enough  to quickly  and  positively influence the  model
                     population in most of the replicate simulations. At the same time, the
                     fluctuations   in  population  size  resulting  from  environmental
                     stochasticity most likely keep the extinction probability from dropping
                     to zero. On average, the population size will probably remain larger
                     than it did when it was confined to the original landscape.
Example 3   Demographic Simulations
                                                                                    120

-------