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
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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.
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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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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
-------
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
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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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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.
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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
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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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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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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
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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
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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
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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
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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 „ •« '*'
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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
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Total Number Patches
Landscape Patch Area
Sum Of Patch Weights
Sura Patch Core Areas
Total Landscape Edge
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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
-------
Using the ;
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-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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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
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Linking to Life
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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
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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
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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
i^'-P^l^- ->'
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"™
***
?* t
"I
I - *
*
.4
i-i1;
«*j
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
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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
-------
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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
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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
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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'
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ff3 IS.;!..,];!1
IS
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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
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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
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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
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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
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.
'&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
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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
/*' ^
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'""
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
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,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
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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
— — ~, , /* ™~~%
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»« -'^ •*;- '•:-'
.•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
60
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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
61
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'-••; - ;'; - ^:13' 3
:":l ~ l"'1 'li:; 3 '* 'a '?" .fU^
i'S'.' -UTM i a »---,fifg m
Tfri
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
Barnes "'•"•-" ^"
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Input Dir j ^
Filename": '_J_
Output Pir is
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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
62
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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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i1!
1 . . - :1 '
ill iHlllr 'I 1':,, 111 .VII ,:' ;' .HI,, ,„ jUlllll'UI *!'
IB'1" i'5 j.V.i :i ;'**^yiiiit-p
; *»
' \i i ll"!i,a'"=!+ -i I-- i! jsij n
S'=-- !.,;!"""• ':: ..... ' I ..... ^-".iis
«;«{," IB ...... . '*;" •"„ -Tiii ',;» ..... ™,rs*
•lil'lillliM'IPI" , In fir ..... iliFiiii,1 ' ....... ' ..... ' m li lulilllipL
fS''1'li,l!l!'.*.'St • L"1!1;1.:1:;-:";," '"fl
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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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j i :>v'« -'liiis
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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
-------
ijliVjiiiLiinii i1
11 "•?'' ~';\.: Sj
iif ' if!
" '' " '
KSir"
»«:.} i '",
yjHiHiiilnMii
ll'""V f'^ilB'" y'fr'"'iS'T*]™ *f™jf
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S'll 1: IP ll f
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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i -Sij^JW? I
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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
68
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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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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
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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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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
-------
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
-------
_
Habitat Batches
I.-.1S I
Old Growth
Open Canopy Forest
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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
-------
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
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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
-------
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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3 :'•:".•:*v|;;:;»' ••-.•,;,'" "« ^!
ft::: ft''ii; ::- r rf 7:;"!i I
liSi;'" i!™"*?-"* iSis i=r*«a
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/
",%'
"*•""• Ml *
r I *, \,,
Degree Of
H^t
m»m*'£****£ &
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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
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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
-------
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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
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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,
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lit -flfi IP l|5f
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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 » "
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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
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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
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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
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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.
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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
-------
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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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Density
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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
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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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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.
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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
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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
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r
"test.imager
Expected
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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
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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
-------