9 December 1999
George F. Wilhere
Washington State Department of Natural Resources
P.O. Box 47014
Olympia, WA 98504
360-902-1018; FAX 360-902-1789; E-mail george.wilhere@wadnr.gov
RH: Spatially-Realistic Population Models
A Spatially Realistic Population Model for Informing Forest Management Decisions
GEORGE F. W1LHERE, Washington State Department of Natural Resources, P.O. Box 47014,
Olympia, WA 98504, USA
NATHAN H. SCHUMAKER, U.S. Environmental Protection Agency. 200 SW 35th Street,
Corvallis. OR 97333. USA
SCOTT P. MORTON, Washington State Department of Natural Resources, 411 Tillicum Lane,
Forks, WA 98331, USA
Abstract: Spatially realistic population models (SRPMs) address a fundamental problem
commonly confronted by wildlife managers predicting the effects of landscape-scale habitat
management on an animal population. SRPMs typically consist oi* three submodels: (1) a
habitat submodel. (2) a movement submodel, and (3) a demographic submodel. We descnbe the
submodels and data requirements for the typical SRPM. The most frustrating problem with
SRPMs is the lack of data needed to relate movement and demographic parameters to habitat
quality. We developed a SRPM to evaluate the relative effects of different habitat management
strategies on the spotted owl subpopulation of the Olympic Peninsula. This case study
documents some plausible assumptions we made to circumvent the data problem, and explains a
novel approach called "parameter tuning" that we used to generate parameter values.
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Key words: spatially explicit population model, population modeling, northern spotted owl,
habitat management
The Washington State Department of Natural Resources (DNR) has developed a habitat
conservation plan (DNR 1997) for 107,000 hectares of state lands on the western Olympic
Peninsula that emphasizes the habitat needs of the northern spotted owl (Siri.x occidentalis
caurina). The plan will alter landscape conditions across more than 4000 km2 of inter-mixed
state, federal, and private land, and thus influence the fate of the Peninsula's spotted owl
suhpopulation. The critical question was how much of an influence? Specifically, would the
conservation plan appreciably reduce the likelihood of survival and recovery of spotted owls on
the Peninsula? In addition, since Washington's State Environmental Policy Act dictates that
state agencies shall consider more than one alternative when planning large projects. DNR
needed to answer questions about the relative effects of different habitat management strategies.
During development of the plan, spatially realistic population models (SRPMs) were emerging as
a practical approach for answering these types of questions (McKelvey 1992, Raphael et al.
1994), so the DNR funded the development of a new SRPM that offered some advantages over
existing models (Schumaker 1995, DNR 1996). We will refer to the model of Schumaker (1995)
as SOS for "Spotted Owl Simulator/' SOS is a pre-cursor to the model known as PATCH
(Schumaker 1998).
AN INTRODUCTION TO SPATIALLY REALISTIC POPULATION MODELS
Spatially realistic population models address a fundamental problem commonly confronted
by wildlife managers predicting the effects of landscape-scale habitat management on an
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animal population. SRP.Vls are a type of spatially explicit population model (Hanski and
Simherloff 1997). Spatially explicit models "keep track of the exact positions of plants and
animals" (Kareiva and Wennergren 1995), but most types of spatially explicit models are based
on simplistic, stylized landscapes (Roloff et al., this volume). In contrast, a SRPM uses
empirically-derived habitat data that are referenced to real geographic coordinates. These
"realistic'* landscapes can be manipulated to represent conditions likely to result from future
habitat management. SRPMs are usually individual-based models. That is, location, birth,
death, reproduction, and movement are "observed" and recorded for every individual in the
simulated population. The behavior and fate of individuals are stochastic. This means that most
actions or events occur randomly according to probability distributions that are either estimated
from empirical data or based on plausible assumptions. SRPMs are typically comprised of three
submodels: (1) a habitat submodel, (2) a movement submodel, and (3) a demographic submodel.
The habitat submodel creates an abstract representation of a real landscape. SRPMs are
usually limited to two spatial dimensions (X and Y coordinates), a third dimension related to
habitat quality, and a fourth dimension is time, which implies that habitat changes over time.
The habitat submodel must interface with the demographic and movement submodels. That is.
the submodel should delineate landscape units that have demographic significance, such as
territories, or that may be relevant to movement behavior, such as habitat corridors. Also, a
habitat submodel must provide metrics of habitat quality that can be used by habitat dependent
functions in the other submodels.
A common approach to representing landscapes uses a hexagonal grid to define landscape
units (Pulliam et al. 1992, McKelvey et al. 1993). A hexagonal structure is often adopted for its
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geometric simplicity, and because, unlike a rectangular or triangular grid, the distances between a
polygon center and centers of all adjacent polygons are equal. This simplifying assumption - that
the spatial distribution and connectivity of habitat can be adequately represented by a hexagonal
grid - obviously imposes some limitations on realism of the habitat submodel. The most
significant limitations are that (1) the number of hexagons sets the carrying capacity of the entire
landscape, (2) the hexagon size determines the minimum territory size, and therefore, the
maximum local territory density, and (3) and habitat quality is usually characterized by one only
variable some type of index calculated for each hexagon.
The data requirements of a habitat submodel correspond with its multiple dimensions. An
intermediate data product must be a habitat map showing the location of various vegetation
classes or habitat categories. The simplest map could consist of two categories habitat and
nonhabitat (e.g., Raphael et al. 1994, Holthausen et al. 1995). Such maps may be generated
through remote sensing methods (e.g,. aerial photography or satellite thematic mapper imaging),
through on-the-ground habitat surveys, or most likely some combination of both. The habitat
map is digitized using a geographic information system and the habitat submodel translates the
digitized map into a simulated landscape. Forest growth models or information about future land
use patterns can be used to create maps of likely changes in habitat conditions over time.
Ideally, a movement submodel would simulate realistic movement behavior. That is, metrics
of simulated movement, such as total distance moved, net distance moved, net direction moved,
linear auto-correlation (i.e., the tendency to move in a straight line), and habitat preference would
be statistically representative of real movements. Certainly, habitat quality must influence
movement behavior, as must interactions with conspecifics, but unfortunately, our understanding
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of such behavior is crude and the cost of improv ing our understanding has been prohibitive.
Consequently, a common approach has been to simply intuit the cognitive mechanisms, such as
"memory", habitat "selectivity", and intraspecific conflict "aversion", that reputedly manifest
movement behaviors (Pulham et al.1992, McKelvey et al. 1993).
If a habitat submodel uses a hexagonal grid to define landscape units, then movement paths
consist of a sequence of steps from hexagon to hexagon. At each hexagon, an individual can
move in one of six directions or not move at all. Submodel parameters define how "cognitive
mechanisms" influence individual movement decisions. Movement submodels in SRPMs
usually allow a range of behaviors from totally random to completely directed by habitat quality
and the presence of conspecifics. Because long-distance dispersal is considered a risky behavior,
some SRPMs incorporate dispersal related mortality into the movement submodel (e.g., Pulliam
et al. 1992, Bart 1995)
The most vexing problem with SRPMs has been a lack of movement data (Ruckelshaus et al.
1997). Movement data should be collected such that parameter estimates can be related to
habitat quality...Mark-recapture studies can yield some information on animal movements, but
the most efficient means of studying movement is radio-telemetry. Understanding how
conspecific interactions influence movement behavior would require detailed knowledge of a
local population.
The demographic submodel defines the population structure and deals with changes in
population size over time. SRPMs can be two-sex or one-sex. The population is often broken
into stage classes, such as juvenile, subadult, and adult (McKelvey et al. 1993). The birth and
death of individuals are usually modelled as stochastic processes with the probabilities of nesting
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success or producing a certain number of offspring or death being functions of local habitat
quality (e.g., Pulliam et al. 1992, Holthausen et al. 1995). The crux of the demographic
submodel is developing these quantitative relationships between demographic parameters and
habitat quality.
The most important data for the demographic submodel are those needed for estimates of
stage-specific mortality and maternity parameters. These data are obtained through mark-
recapture studies and observations on the number of offspring produced per breeding female (or
breeding pair), respectively. Ideally, demographic data would also provide information on the
nonbreeding portion of the population, e.g., floaters. Demographic data should be collected such
that parameter estimates can be related to habitat quality.
The basic output of SRPMs is the same as other population models - the number of
individuals over time. SRPMs generate an output that other populations models do not the
spatial distribution of individuals over time. One can compare the likely outcomes of different
habitat management strategies, which could be useful for optimizing land management (Hof and
Raphael 1997). An optimal strategy might be one that maintains a desired population density for
the minimum cost.
In general, SRPMs are not mathematically sophisticated, but they are computationally
complex. Well-honed computer programming skills are indispensable for tackling the task of
model development. There are no standards for mode! structure, but modular, top-down, object-
oriented programming is highly recommended. For most applications, a spatially realistic,
individual-based model will require large computer memory and huge on-line data storage
because: (1) information on every living individual in the population is maintained during a
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simulation, and (2) GIS data, particularly rastcrized data, can occupy gigabytes of nonvolatile
memory. High CPU speeds are also very desirable.
AN EXAMPLE: THE SPOTTED OWL SIMULATOR
The Spotted Owl Simulator was developed to evaluate the effects of different habitat
management strategies on the spotted owl subpopuiation of the Olympic Peninsula. With respect
to the abundance and richness of data, the Olympic Peninsula was an excellent place to attempt
analyses using a SRPM. The Peninsula's owl subpopuiation has been the subject of intensive
study and the results of numerous investigations were available (Forsman 1990, 91, 92; Carey et
aL 1992; Seaman el al. 1992, 1996; Lehmkuhl and Raphael 1993; Mills etal 1993).
Demographirpararaeter estimates had been published (Burnham et al. 1994, Forsman et al.
1996). Habitat use versus habitat availability studies (E. D. Forsman, U.S. Forest Service,
unpublished data), and juvenile dispersal studies (E.D. Forsman, U. S. Forest Service, personal
communication) had been conducted. A gross estimate of population size had been issued in a
draft report (Holthausen et al. 1994). Data for habitat maps were also available. Landsat
Thematic Mapper 
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The Habitat Submodel
SOS uses a hexagonal grid to represent the spatial distribution of owl habitat. Six parameters
govern the translation of rasterized habitat maps to a hexagonal landscape: hexagon size,
i
''territory expansion", a "territory threshold", and the relative habitat values of three land cover
categories. The hexagon size corresponds to the minimum home range area of an owl pair. We
assumed that the smallest home ranges on the Peninsula would exist in the high quality habitat of
Olympic National Park. The density of owl pairs in the low-elevation old-growth forests of the
Park was estimated to be 0.08/100 ha (Seaman et al. 1996). This density is equivalent to an
exclusive home range of 1250 ha/pair, and we equated the size of the exclusive home range to
the minimum home range. The minimum home range is probably not equivalent to the exclusive
home range, but theoretically, in a sparsely populated region composed of high quality habitat it
should be nearly so.
The classified Landsat TM data (WDVV 1993) had eight discrete forest categories, but only
three categories (old-growth, large-saw, and small saw) were assumed to have value as spotted
owl habitat - an assumption based on Forsman et al. (1984) and Carey et ai. (1992). A habitat
utilization index (HUI) was calculated for each forest category. It is defined by a ratio: (percent
of owl relocations within a category) / (percent of home range area in that category).
HUI describes habitat preferences. If HUI is greater than 1.0, then owls expressed a
preference for that forest category. The ratio of two HUI quantifies the relative habitat value of
two forest categories. HUIs were calculated using radio-telemetry data collected from 20 owl
home ranges on the western Olympic Peninsula (E. D. Forsman, U. S. Forest Service,
unpublished data). The shortcomings of indices based on habitat use versus habitat availability
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were known to us (see Van Home 1983, Hobbs and Hanley 1990). but the data available to us
precluded any other approach.
The hexagon habitat scores were calculated with the following equation:
HS =- HV0(jA(K, + HVlsAls - HVSSASS
where H V\ is the relative habitat value of either old-growth (OG), large-saw (LS), or small-saw
(SS) forest, and Ax is the proportion of a hexagon covered by that forest category. Hexagons
having scores above a threshold value are classified as potential owl territories. The threshold
value was determined by applying the same equation to the 20 owl home ranges studied by
Foreman, where Ax refers to the proportion of a home range. We found that setting the threshold
value to the mean habitat score of these 20 home ranges (which was less tham the median score)
yielded an acceptable spatial distribution of potential territories when compared to the known
locations of territorial owls on the Olympic Peninsula (H. I). Foreman, U.S. Forest Service,
unpublished data; D.E. Seaman, National Biological Service, unpublished, data; S. P. Horton,
DNR, unpublished data). The minimum and first quartile scores each yielded a worse
correspondence between predicted potential territories and known locations.
The maximum home range of an owl pair is determined through an expansion parameter.
This parameter represents two aspects of owl behavior. First, in areas of fragmented habitat,
owls expand the size of their home range, and second, the home ranges of neighboring owls may
overlap (Carey et al. 1992). The expansion parameter represents the maximum amount of
neighboring hexagons that may be included in a home range. For 20 owl home ranges studied on
the "western Olympic Peninsula (E. D. Foreman, U. S. Forest Service, unpublished data), the
maximum home range size was 11248 ha, but the third quartile size was 6301 ha. With a
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hexagon size of 1250, the maximum home range that can be modeled is 8750 ha (a hexagon plus
its six neighboring hexagons). The expansion parameter value was assigned its maximum value.
The difference between the observed maximum home range and the maximum size that can be
modelled will cause the number of potential territories to be underestimated.
Hexagon "expansion" is a novel aspect of SOS. Expansion does not actually increase the
score or size of hexagons. It is simply a mechanism that allows hexagons with low scores to
function as territories by laying claim to unallocated habitat present in adjacent hexagons. The
expansion of a sub-threshold hexagon continues until it reaches the potential territory threshold
or until it reaches the expansion limit. Only hexagons that are below the threshold expand, and
hexagons with low scores require more expansion to become potential territories. This process
does not effect the score of any hexagons. The habitat submodel produces three types of
hexagons: supra-tlireshold potential territory, sub-threshold potential territory, and not a potential
territory.
The Movement Submodel
The simulated landscape in SOS is a hexagonal grid. From each location, owls can move in
only six directions and every move must be the same length, from hexagon center to hexagon
center. For hexagons of 1250 ha, the "step" size is about 3.80 km. Owls stop moving when a
territory or mate is found, or a maximum number of steps has been taken.
The submodel requires specification of the minimum number of steps that must be moved by
dispersing juveniles. The minimum movement distance is ignored by moving adults. This
assumption was made because no data on minimum movement distances exist for adults. The
ratio of total distance to net distance for owl dispersal equals about 2 (Thomas et al. 1990), and
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the minimum net dispersal distance observed for juveniles on the Peninsula is 8.67 km (h'.D.
Forsman. V. S. Forest Service, unpublished data). So, the minimum number of steps equaled
approximately two times the net dispersal distance divided by the mean step size, or about four
hexagons. Likewise, the maximum net. dispersal distance observed for juveniles on the Peninsula
is 58.25 km, and so the maximum number of steps was set to 31.
The degree to which owl movements are guided by habitat quality is specified by the "Bias to
Quality" parameter. This parameter determines the frequency at which owls move to the adjacent
hexagon with the best habitat quality. If Bias to Quality equals 0.60, then owls move to the
hexagon with the highest habitat score about 60 percent of their steps. If an owl does not
consider habitat quality when moving, then the "Linearity" parameter specifies the probable
direction of the next step. It determines the tendency to move in a forward direction. When
Linearity equals zero, there is an equal probability of moving to any of the neighboring six
hexagons. As Linearity increases from zero, the simulated owls have a greater tendency to move
in a straight line. The values of Bias to Quality and Linearity were determined through parameter
tuning (described below).
Little is known about the behavioral mechanisms that direct the movement of individual
animals across landscapes. Hence, the strategy for developing the movement submodel was to
avoid parameters that are behavioral. This is contrary to the modeling strategy recommended by
others (e.g., Conroy et al. 1995) who believe that parameters should be biologically meaningful.
At least one parameter, namely Bias to Quality, was needed to link habitat quality to movement.
The other movement parameters minimum and maximum number of steps and Linearity - are
basically statistical descriptors of the movement path. Our current understanding is that males,
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females, juveniles, and adults probably exhibit different movement behaviors (Greenwood and
Harvey 1982, Johnson and Gaines 1990)- However, besides the minimum movement distance,
all movement behavior was modeled the same way, regardless of sex or stage class. A lack of
data motivated this simplification.
No mortality occurs during movement. When juvenile owls are dispersing substantial
mortality probably occurs and it presumably is a function of habitat quality and dispersal
distance. But, having no data with which to develop such a relationship, we elected to lump all
death into a single annual mortality.
The Demographic Submodel
The Spotted Owl Simulator has a two-sex, three stage-class population structure. As w ith
other spotted owl population models the stage classes are juvenile, subadult, and adult.
Estimates for demographic parameters were available (Forsman et al. 1996), but the crux was
developing quantitative relationships between these demographic parameters and habitat quality
- a challenging task with no habitat data. The first step was to select the form of the
relationships. A logistic function is intuitively appealing, but it requires five parameters to define
completely. A logistic function may be approximated with a three-segment, piece-wise linear
function that requires only four parameters. We assumed that the least important domain of this
function was the Hat segment over lower quality habitat. Hence, we eliminated this segment and
adopted a two-segment, piece-wise linear function with only 3 parameters. The shape of this
function was based on the plausible assumption that above some value of habitat quality,
survivorship (the complement of mortality) and maternity do not increase appreciably and can be
considered constants. This same assumption was adopted by Holthausen et al. (1995). The value
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at which survivorship and maternity become constants is known as the "saturation value" of
habitat quality.
Adult and subadult stage classes had separate habitat dependent functions for the probability
of death and the probability of nesting success.: The values for the minimum and maximum
parameters were determined through parameter tuning (described below). Juvenile survivorship
was not a function of habitat quality because there is considerable uncertainty about the value of
this parameter (Forsman et al. 1996). Instead, separate simulations were run using different
constant values of juvenile survivorship. These runs represented a range of plausible scenarios
from worst case to best case, and were a form of sensitivity analysis for juvenile survivorship.
Parameter Tuning
The values of some model parameters, such as fledgling sex ratio, came directly from
published studies of spotted owls (e.g., Forsman ct al. 1984). The value of other model
parameters, such as minimum number of steps for movement, were calculated using available
data. Unfortunately, SRPMs require types of information that are often difficult to acquire, such
as the relationships between habitat quality and.demographic parameters. SRPMs also entail
modeling processes that are poorly understood, such as dispersal behavioral. For these situations
there were no data with which to derive parameter values directly, but there were data that
allowed us to iteratively search for values such that the average characteristics of the simulated
population approximated known characteristics of the real population. This is parameter tuning.
For example, to determine values for the movement parameters, simulations were run on SOS
with all otherparameters assigned fixed values. Upon completion of a simulation, statistical
descriptors of the simulated dispersal paths w ere compared to empirical data. Based on this
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comparison. Bias to Quality and Linearity were adjusted, and the process was repeated until the
mean net dispersal distance was approximately equal to the mean observed on the Peninsula (24
km; E. D. Forsman, U. S. Forest Serv ice, unpublished data) and the ratio of mean net distance to
mean total distance was approximately 2 (Thomas et al. 1990). To enable tuning of the dispersal
parameters, mean net distance and mean total distance had to be model outputs.
To establish the relationship between demographic parameters and habitat quality, a
maximum value.was assumed using available information (Holthausen et al. 1995) and the
minimum value was determined through parameter tuning. The minimum parameter value was
iteratively adjusted until the realized mean parameter value of the simulated population was
approximately those reported by Forsman et al. (1996). To enable tuning of the demographic
parameters, adult and subadult mortality and mean maternity had to be outputs of the model
Conclusions
Spatially realistic population models are an exciting new technology in wildlife management,
but the excitement is somewhat tempered by their extraordinary data requirements. Part of the
excitement surrounding SRPMs undoubtedly arises from the array of pow erful new technologies
for the collection and analysis of spatial data satellite thematic mapper imaging, global
positioning systems, improved microelectronics for radio-telemetry, and geographic information
systems. Yet, even with this technology, the extraordinary data requirements of most SRPMs are
difficult to satisfy, and this has elicited some concerns about model reliability (Doak and Mills
1994, Bart 1995, Conroyetal. 1995, Wennergrenetai. 1995. Ruckelshaus et al. 1997). Many of
these concerns can be assuaged by thorough explication of model assumptions, rigorous model
evaluation, thoughtful interpretation of results, and cautious use of the results for decision
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making- But, for those who choose to develop a SRPV1 for analyzing their wildlife management
problems, grappling with insufficient data remains a vexing challenge.
Developing a SRP.V1 will invariably require assumptions about the population or species
autecoJogy. Assumptions will be necessary to circumvent insufficient information or to make
computer programming a practical task, but each assumption or simplification made during
model development can introduce poor judgement or bias. Nearly all other categories of models
familiar to wildlife biologists - habitat suitability indices, matnx models, equations derived from
statistical regression, etc. have well-established principles or methods for their development,
and much of their credibility as decision-making tools derives from the process of model
formulation that reduces subjective judgements. Likewise, the credibility of a SRPM depends
upon the handling of subjective judgements, i.e., assumptions, by the modeller. The most
satisfactory approach to dealing with model assumptions is collecting the data needed to
eliminate them. When this is impractical, each assumption should be explicitly stated and
justified, and a thoughtful consideration of its potential effects on model output should be
documented. The effects of£ach assumption can be rigorously evaluated through sensitivity
analyses.
Models which link habitat quality to population demographics are a relatively new tool. This
may account for the scarcity of critical data needed by SRPMs. In fact, considering the needs of
nongame species at large spatial scales is a relatively recent conceptual breakthrough in wildlife
management. A critical mass of research in landscape ecology, albeit predominately conceptual
or theoretical, has been attained during the past 15 years (Harris 1984, Forman and Godron 1986,
Turner 1989, Bissonette 1997). As is often the case, empirical research has not matched the pace
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of theoretical research, nor has it matched the pace of the technological developments that have
enabled SRPMs. Nevertheless, the outlook is promising. Awareness of important processes that
take place at the landscape scale has begun to direct field research in wildlife biology and data
needed by SRPMs will accumulate.
ACKNOWLEDGMENTS
We gratefully acknowledge the reviewers of this paper, Erie Forsman and John Dunning Jr.,
whose comments motivated major revisions. Timothy Quinn added considerable polish through
his conscientious editing. We thank Dave Johnson for the opportunity to present our work.
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21
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NHEERL-COR-WED-00-092
WED-00-92
TECHNICAL REPORT DATA
(Please read instructions on the reverse before completing)
1. REPORT NO.
EPA/600/A-00/073
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
A Spatially Realistic Model for Informing
Forest Management Decisions
5. REPORT DATE
6. PERFORMING ORGANIZATION
CODE
7. AUTHOR(S) George F. Wilhere1, Nathan H. Schumaker2, Scott P. Horton3,
8. PERFORMING ORGANIZATION REPORT
NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
'Washington State Department of Natural Resources 2 U.S. EPA NHEERL WED
P.O. Box 47014 200 SW 35'h Street
Olympia, WA 98504 Corvallis, OR 97333
2Washington State Department of Natural Resources
411 Tillicum Lane
Forks, WA 98331
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
US EPA ENVIRONMENTAL RESEARCH LABORATORY
200 SW 35th Street
Corvallis, OR 97333
13. TYPE OF REPORT AND PERIOD
COVERED
14. SPONSORING AGENCY CODE
EPA/600/02
15. SUPPLEMENTARY NOTES:
16. Abstract: Spatially realistic population models (SRPMs) address a fundamental problem commonly confronted by wildlife
managers-predicting the effects of landscape-scale habitat management on an animal population. SRPMs typically consist of
three submodels: (1) a habitat submodel, (2) a movement submodel, and (3) a demographic submodel. We describe the
submodels and data requirements for the typical SRPM. The most frustrating problem with SRPMs is the lack of data needed to
relate movement and demographic parameters to habitat quality. We developed a SRPM to evaluate the relative effects of
different habitat management strategies on the spotted owl subpopulation of the Olympic Peninsula. This case study
documents some plausible assumptions we made to circumvent the data problem, and explains a novel approach called
"parameter tuning" that we used to generate parameter values.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED
TERMS
c. COSATI Field/Group
Monitoring design,terrestrial surveys,
integrating surveys, CENR framework, EMAP


18. DISTRIBUTION STATEMENT
19. SECURITY CLASS [This Report)
21. NO. OF PAGES:
20. SECURITY CLASS {Thispage)
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION IS OBSOLETE
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