Modeling spatial use patterns of white-tailed deer in the Florida Everglades

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Modeling spatial use patterns of white-tailed deer in the Florida Everglades
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White-tailed deer -- Habitat -- Florida -- Everglades   ( lcsh )
Spatial behavior in animals -- Computer simulation   ( lcsh )
Wildlife Ecology and Conservation thesis, Ph. D   ( lcsh )
Dissertations, Academic -- Wildlife Ecology and Conservation -- UF   ( lcsh )
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Thesis (Ph. D.)--University of Florida, 2000.
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Includes bibliographical references (leaves 212-222).
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by Christine Steible Hartless.
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MODELING SPATIAL USE PATTERNS OF WHITE-TAILED DEER
IN THE FLORIDA EVERGLADES














By

CHRISTINE STEIBLE HARTLESS


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2000































Copyright 2000

by

Christine Steible Hartless
































To Glen--my husband, my soulmate, my lifemate--
for his ability to help me see the 'big picture'
and his unending encouragement and love.















ACKNOWLEDGMENTS


Funding was provided by the National Park Service (Cooperative Agreement No.

CA-528039013) and by the Agricultural Women's Club Scholarship and the William &

Elyse Jennings Scholarship.

I would like to thank Drs. Ronald F. Labisky and Kenneth M. Portier, my

committee cochairs, for their support, guidance, and patience as I delved deeper into

building the simulation model. Thanks also go to the other members of my committee,

Drs. Michael P. Moulton and George W. Tanner, and especially to Dr. Jon C. Allen for

his generous donation of countless hours of computer time running simulations in his lab.

I am immensely grateful to Margaret Boulay, Kristi MacDonald, Karl Miller,

Robert Sargent, and Jodie Zultowsky--the graduate students who came before me and

conducted the field research that is the foundation of the work in this dissertation. My

thanks also go to the staff of Everglades National Park and Big Cypress National Preserve

who were involved in the field research. Patty Cramer and Brad Stith helped me through

the initial shock of C++ and programming IBSE simulations.

My parents, Dan and Barbara Steible, are owed my deepest gratitude for their

constant support and encouragement. I also wish to thank Emily Clark for reminding me

that there is life outside graduate school and Mike Steible for helping me nurse my ailing

car through the last several years.
















TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ................................................ iv

ABSTRACT .......................................................... vii

1 INTRODUCTION ................................................. 1

1.1. Simulation Models as Research Tools ............................. 3
1.2. Objectives .................................................... 6
1.3. Dissertation Structure ........................................... 7

2 EVERGLADES ECOSYSTEM AND THE STUDY AREA ................ 8

2.1. The Everglades Ecosystem ....................................... 8
2.2. Study Area ................................................... 10

3 WHITE-TAILED DEER MODEL CALIBRATION DATA ............... 24

3.1. Data Collection Methods ....................................... 24
3.2. Data Summary Methods ........................................ 25
3.3. Data Summary ................................................ 30
3.4. Discussion ................................................... 36

4 DEVELOPMENT, CALIBRATION, AND EVALUATION OF THE
SIMULATION MODEL ........................................... 39

4.1. Approach and Technique ....................................... 39
4.2. Initial Model Parameterization ................................... 53
4.3. Model Calibration Experiments ................................. 63
4.4. Final Movement Model .......... .............................. 82
4.5. Evaluation Approach for the Final Movement Model ................. 90
4.6. Evaluation of the Final Movement Model for Females ................ 91
4.7. Evaluation of the Final Movement Model for Males ................ 104










5 WHITE-TAILED DEER MODEL VALIDATION DATA ................ 117

5.1. Data Collection and Summary Methods .......................... 117
5.2. Data Summary ............................................... 119
5.3. Discussion .................................................. 126

6 VALIDATION OF THE SIMULATION MODEL UNDER
FLOOD CONDITIONS ........................................... 128

6.1. Approach to Model Validation .................................. 128
6.2. Model Validation Results ...................................... 131
6.3. Discussion .................................................. 148

7 CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS ............ 157

7.1. Applications of the White-tailed Deer Movement Simulation Model .... 158
7.2. Contributions to the Field of Ecological Modeling .................. 159

APPENDICES

A CALIBRATION DATA SET ...................................... 162

B DESCRIPTION OF PARAMETER SYMBOLS USED IN THE
CALIBRATION EXPERIMENTS ................................. 175

C SUMMARY OF CALIBRATION EXPERIMENTS FOR FEMALES ....... 177

D SUMMARY OF CALIBRATION EXPERIMENTS FOR MALES ......... 195

E VALIDATION DATA SET ....................................... 204

LITERATURE CITED ................................................. 212

BIOGRAPHICAL SKETCH ............................................ 223















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

MODELING SPATIAL USE PATTERNS OF WHITE-TAILED DEER
IN THE FLORIDA EVERGLADES

By

Christine Steible Hartless

August 2000

Chair: Dr. Ronald F. Labisky
Cochair: Dr. Kenneth M. Portier
Major Department: Wildlife Ecology and Conservation

As reliance on ecological simulation models increases, proper tools to facilitate

their calibration and to increase their reliability become more important. Computer

simulations enable scientists to model the effects of environmental catastrophes or

management strategies on target populations without conducting expensive or difficult

field experiments.

Fractional factorial experiments and response surface methods are presented as

design and analysis tools to optimize a simulation model with respect to competing

algorithms and parameter values. Issues involving simulation "bum-in" time, the number

of iterations required for a simulation to reach a steady-state, and its estimation are

discussed. Use of discrepancy functions as quantitative measures of model fit and

parameter estimation are examined. Predictive p-values are presented as a tool for










evaluation of the performance of a simulation model, relative to observed field data.

Finally, these tools are integrated into an iterative approach for development of

simulation models.

An individual-based, spatially explicit (IBSE) simulation model of adult white-

tailed deer (Odocoileus virginianus seminolus) movement patterns in the wet

prairie/hardwood tree island habitat of the Florida Everglades illustrates the use of these

techniques. Radio-telemetry data obtained from white-tailed deer on the boundary

between Big Cypress National Preserve and Everglades National Park during three

normal-to-dry years (1989-92) were used to develop and calibrate the IBSE simulation

model. Radio-location data from this same population of deer collected just prior to and

during a severe flood (1993-95) were used to validate this simulation. The simulation

model can help predict impacts of changes in water management strategies and the

impacts of floods and hurricanes on white-tailed deer in the Florida Everglades.















CHAPTER 1
INTRODUCTION


The Florida Everglades is home to a diverse mixture of temperate and sub-tropical

flora and a broad collection of fauna, including the Florida panther (Puma concolor

coryi), the American alligator (Alligator mississipiensis), many species of wading birds,

and the white-tailed deer (Odocoileus virginianus seminolus). The Everglades serves as

an example of how anthropogenic activities can drastically change the appearance and

function of an ecosystem. National attention was focused on the Everglades when

Douglas (1947) described its natural and cultural history in her book, The Everglades:

River of Grass, and when the Everglades National Park was established that same year.

Since then, many scientists have focused their research on understanding the effects of the

human-induced changes on this ecosystem and on finding ways to slow or reverse

degradation of this unique ecosystem.

White-tailed deer are an ecologically, culturally, and economically valuable

wildlife resource throughout the United States (Langenau et al. 1984). White-tailed deer

play an important role in the Everglades ecosystem, serving as the major prey of the

endangered Florida panther (Maehr et al. 1990) and the bobcat (Lynx rufus) (Maehr and

Brady 1986). These deer are non-migratory (Loveless 1959b) and exhibit extreme site

fidelity, even under adverse environmental conditions (MacDonald 1997, Labisky et al.

1999). The cyclic rising and falling of water levels in this marginal habitat influences










spatial movements (Sargent and Labisky 1995, Zultowsky 1992), habitat use (Hunter

1990, Miller 1993) and reproductive phenology (Loveless 1959b, Richter and Labisky

1985, Boulay 1992).

Historically, the primary goal of deer managers was that of increasing herd

productivity and health. Today, throughout much of the United States, managers have the

task of controlling deer populations because inflated densities are exerting negative

impacts on the landscape. However, in the Everglades, where white-tailed deer maintain

low-density populations, managers must insure that deer populations persist. Thus, the

maintenance of this deer population is one of the many goals of the large multi-agency

research and restoration effort currently in progress in the Florida Everglades (Fleming et

al. 1994, USGS 1997, DeAngelis et al. 1998). Part of this restoration effort is the

development of the suite of simulation models, Across Trophic Level System Simulation

(ATLSS), to predict and compare the effects of alternative hydrologic scenarios on this

ecosystem. This suite of models, covering approximately 2.6 million ha, includes physical

models (landscape hydrology and topography), process models (e.g., macro- and meso-

invertebrates and vegetation), size-structured population models (e.g., fish and

amphibians), and individual-based models (e.g., wading birds, white-tailed deer, and

Florida panthers) designed to work interactively.

In this dissertation, I explored movement patterns of white-tailed deer in the wet

prairie/tree island habitat of the Florida Everglades. An individual-based spatially explicit

(IBSE) simulation model was developed to simulate their movement patterns under

normal and high water conditions. This model was designed to predict changes in the








3

movement patterns of the deer population under extreme flood conditions and alternative

water management scenarios.

1.1. Simulation Models as Research Tools

Simulation models are important tools in wildlife ecology and conservation, and

their use is increasing continuously. Computer simulations enable scientists to model the

effects of environmental catastrophes or management strategies on target populations

without conducting expensive or difficult field experiments. Early population simulation

models ranged from simple growth models, such as logistic growth (Pearl and Reed 1920,

Renshaw 1990) to stage- or age-based matrix models (Leslie 1945, Lefkovitch 1965).

More recent population models incorporated a spatial component, such as spatial

dispersion models (Skellam 1951) and metapopulation models (Levins 1969, Hanski and

Gilpin 1996). In the continuing evolution of simulation models, individual-based models,

those using individuals as the basic unit (DeAngelis and Gross 1992, Grimm 1999), are

the current state of the art. Within this large class of models, IBSE models are used to

simulate individual movement processes and interactions over a heterogeneous landscape.

This ability to model interactions among individuals and interactions between individuals

and their environment provides insight into many ecological processes (Huston et al.

1988, Ims 1995). Furthermore, these models are used to make or defend management

decisions (DeAngelis and Gross 1992, Bart 1995, Conroy et al. 1995, Dunning et al.

1995, Turner et al. 1995). As computing power and speed increase and computer costs

decrease, more complex IBSE models become feasible.

In individual-based simulations, in which each individual in a population is

monitored, stochastic decision rules are developed to control the behavior and choices of










each individual. These models are particularly advantageous when studying populations

with few individuals as well as when the study of individual behavior is important.

Spatially explicit models allow simulation over a heterogenous environment, making it

possible to define spatial relationships among habitat patches and other landscape

features such as boundaries and corridors; therefore, the effect of a heterogenous

environment on the organism of interest can be investigated. Saaremaa et al. (1988: 125)

described the advantages of models using artificial intelligence as "(a) studying

population processes based on individual levels of behavior, (b) modeling spatial

heterogeneity, (c) building event-driven models, (d) providing a conceptual clarity to

model construction, (e) and providing a structure equally well suited to simulating

resource management." Intertwining animal movement dynamics and spatial patterns to

reveal the larger picture can be accomplished with simulation models. Furthermore, these

models comply with two basic doctrines of biology: that individual organisms are

represented rather than being combined and represented by one variable (i.e., population

size), and that these models distinguish among the locations of individuals (Huston et al.

1988).

Early simulation models of individual animal movements were developed using

random walks and correlated random walks (Rolfe and Davenport 1969, Siniff and Jessen

1969, Holgate 1971, Bovet and Benhamou 1988). Effects of communication between

individuals on movement patterns also have been explored. Montgomery (1974)

expanded Siniff and Jessen's (1969) model to include the impact of communication (i.e.,

tactile, visual, scent, and vocal) among red fox (Vulpes vulpes) dyads on home range

formation. Lewis and Murray (1993) modeled territory formation and location of wolf










(Canus lupus) packs as a function of scent marks left by neighboring packs and deer

densities in the area.

Recently, simulation models have been used to explore the effects of spatial

heterogeneity on the dynamics and movements of animals. Effects of various timber

harvesting schemes on Bachman's sparrow (Aimophila aestivalis) populations in the

southeastern U.S. were simulated and evaluated (Pulliam et al. 1992, Liu 1993, Liu et

al. 1995). A model developed for the California spotted owl (Strix occidentalis caurina)

explored the effects of habitat connectivity, quality, and quantity on population dynamics

(Verner et al. 1992). Turner et al. (1994) developed a model to explore movements of

ungulates in Yellowstone National Park in response to fire. Riesenhoover et al. (1997)

designed a simulation model to predict impacts of alternative deer management strategies

on a population. Cramer (1999) developed an IBSE model to predict movements of

Florida panthers in north Florida, should a reintroduction program be enacted. Although

these simulations are predictive and often are not fully validated, they may still aid in

understanding the dynamics of species and landscape interactions.

The increasing reliance of management decisions on simulation models drives the

necessity to develop tools to adequately calibrate and validate these models. Most

individual-based models incorporate a large number of parameters (Grimm 1999). Some

model parameters, such as number of offspring or survival rate, are estimated from

published values. In contrast, parameters characterizing movement patterns of individuals

in a simulation rarely can be estimated from published values or even derived from

measurable variables on study animals. These parameters (e.g., distance an individual can

'see' when making a movement decision or the effect of previous movements on the










current movement decision) are either difficult or impossible to estimate from field data.

However, the best-fitting movement algorithms and associated parameter values can be

determined by evaluating discrepancies in measurable outcomes (e.g., home range size)

between study animals and simulated animals.

Bart (1995) and Conroy et al. (1995) suggested guidelines for model development

and testing that included the need for clearly stated model objectives, a description of the

model structure, and a sensitivity analysis to assess effects of parameter uncertainty on

model outputs. In addition, model development also requires verification, calibration, and

validation. As defined by Rykiel (1996), verification is a demonstration that the model

form is correct, calibration is the estimation and adjustment of model parameters to

improve agreement between model output and observed data, and validation is a

demonstration that a model possesses the accuracy required for its intended applications.

Although individual-based models ought to be more testable than state-variable

models (Murdoch et al. 1992), only 36% (18 of 50) of the individual-based modeling

papers reviewed by Grimm (1999) explicitly discussed validation or corroboration of the

presented models. Statistical tools for validation of simulation models have been

developed primarily in two fields of research: ecological process and population models

(e.g., Van der Molen and Pinter 1993, Rykiel 1996) and operations research and industrial

engineering settings (e.g., Sargent 1984, Kleijnen 1987).

1.2. Objectives

The main objective of this dissertation was to develop an IBSE simulation model

of movement patterns of adult white-tailed deer in the Florida Everglades. The model

provides a means of exploring patterns of spatial use of deer in response to environmental










catastrophes (e.g., tropical storms) and to different management regimes (e.g., water

control). Furthermore, the statistical methodologies used to calibrate and validate this

IBSE model provide a foundation for the development of future simulation models.

The specific objective of the simulation model was to predict how temporal

landscape changes (i.e., rising and falling water levels) affect movement patterns of deer

in the Florida Everglades. The simulation model was calibrated with radio-telemetry data

collected from 1989 to 1992 under dry-to-normal hydrological conditions. The same

simulation model also was run under flood conditions, like those experienced during the

flood that began in the fall of 1994, to evaluate the changes in movement patterns during

an environmental catastrophe. In the development stages of this model, several calibration

issues were addressed: (1) development of an approach to test the IBSE model relative to

observed data with the use of discrepancy measures, (2) development of an effective

approach for calibrating an IBSE model with sequential experimentation, and (3)

evaluation of the predictive abilities of an IBSE simulation with predictive p-values. The

model was validated with radio-telemetry data collected just prior to and during the flood

of 1994-95.

1.3. Dissertation Structure

In Chapter 2, the Everglades ecosystem and the study area are described. In

Chapter 3, the white-tailed deer calibration data are discussed in detail. The statistical

techniques employed to calibrate the IBSE model and details of the final model are

discussed in Chapter 4. In Chapter 5, the white-tailed deer validation data are presented

and in Chapter 6, details of model validation are discussed. Conclusions and implications

of the simulation results are discussed in Chapter 7.















CHAPTER 2
EVERGLADES ECOSYSTEM AND THE STUDY AREA


Understanding the ecosystem under consideration is essential prior to simulation

development. In this chapter, the Everglades ecosystem and the study area are discussed.

Development of the temporal-spatial hydrology map is described.

2.1. The Everglades Ecosystem

2.1.1. Climate and Topography

The Everglades ecosystem is characterized by a subtropical climate with

alternating dry winters (November-April) and wet summers (May-October). Mean

monthly temperature ranges from 14 C in January to 28 C in August. Mean annual

precipitation is 136 cm, two-thirds of which falls between May and October (Duever et

al. 1986). The onset, duration, and intensity of the wet seasons are highly variable; thus,

periods of either drought or flooding occur. Tropical cyclones (hurricanes and tropical

storms) occur in this region of Florida at a rate of one every 3 years (Gentry 1984), and

often exacerbate the severity of floods. Frost occurs infrequently, and a severe freeze

occurs at a rate of one every 10 years (Drew and Schomer 1984).

The Everglades region is nearly flat, with an overall gradient on the order of 2

cm/km in a north-south direction with steeper gradients at smaller spatial scales

(Gunderson 1994), and is characterized by a southwestward sheet flow of water (Duever










et al. 1986). The range of elevations between the lowest and highest vegetation

communities is approximately 1.5 m (Gunderson 1994).

2.1.2. Flooding and Water Control

The historic Everglades, a 3.6 million ha mosaic of marsh, slough, tree islands,

and pinelands, extended from central Florida (Kissimmee Chain of Lakes) southward to

the Florida Bay. "Replumbing" of the Everglades watershed began with the Swamplands

Act of 1850, which authorized the transfer of 8.1 million ha of the Everglades to the state

of Florida for the purpose of drainage and reclamation. In the 1880s, a millionaire

entrepreneur purchased and drained more than 20,000 ha in the Kissimmee basin and

built the first canals through the Everglades, demonstrating that the land was very

productive and could be lucrative for agriculture (Blake 1980). To control the impacts of

devastating floods and hurricanes on human populations and to further agricultural

production, drainage of the Everglades and flood control measures on Lake Okeechobee

continued into the early 1900s. The Central and Southern Flood Control District, later

renamed the South Florida Water Management District (SFWMD), was formed in 1949,

consolidating water management functions into one entity. Between 1950 and 1973, the

SFWMD and the Army Corps of Engineers constructed a network of canals, pumps, and

other water control structures. In the northern Everglades, the Water Conservation Areas

were created to hold water away from the populated coastal areas and retain it for

agricultural and municipal needs (Light and Dineen 1994). During periods of high

rainfall, overflows from these areas were released southward often creating artificially

high water levels in the Everglades National Park and surrounding protected areas.










Approximately half of the original Everglades ecosystem remains today (Davis

and Odgen 1994), but, in many places, the hydrologic regimes bear little resemblance to

the historic predrainage flows (Light and Dineen 1994). Hydrology is the most important

force shaping the Everglades, and it is the force that was most altered and has most

affected the remaining system (Brandt 1997). Water control measures have exacerbated

the effects of floods and droughts in the remaining natural system, and changes in

hydroperiod length and intensity have altered vegetative communities. Modifications in

hydrologic patterns have contributed to changes in plant communities, changes and

decreases in wildlife populations, and changes in the historic functioning of the

Everglades (Loveless 1959a, Alexander and Crook 1984, Davis et al. 1994, Odgen 1994).

2.2. Study Area

The 30,000 ha study area (Fig. 2.1) is located in the wet prairie/tree island

ecosystem that extends from the Stairsteps Unit of the Big Cypress National Preserve

(BCNP) south into Everglades National Park (ENP). It is bounded on the north by Loop

Road, on the west by Lostmans and Dayhoff Sloughs, and on the east and south by Shark

River Slough. The habitat map (Fig. 2.2) was developed by Miller (1993); it depicts ten

habitats (Table 2.1), using 20-m x 20-m pixels (referred to as "20-m pixels") with an

estimated accuracy of 80.4%. Miller (1993) discussed the details of development of this

map and its accuracy evaluation.

2.2.1. Vegetation Classification and Hydroperiod Length

Soil depth and type, hydroperiod (length of annual inundation), and fire are the

primary factors in the development of plant occurrences in the wet prairie habitat of the

Everglades (Duever 1984). Various vegetation classifications of the Everglades region are









reported in the literature (see Olmsted and Armentano [1997] for summary). The

vegetation classification scheme used in this study follows the broad classifications of

Duever (1984): forested uplands, non-forested wetlands, and forested wetlands.


Big Cypress
National Preserve


Miami


N

0 40
kilometers I
kilometers


Figure 2.1. Location of study area within Big Cypress National Preserve (BCNP) and
Everglades National Park (ENP), Florida. The study area is marked by the hashed lines.

































8608 16 Kilometers


/BCNP I ENP boundary
Habitat N
Wet Prairie
Herbaceous Prairie
I Tree island
SWillowldense sawgrass W E
Dwarf cypress prairie
SCypress strand
Pine S
Mangrove/prairie transition
Mangrove


Figure 2.2. Habitat within the study area of BCNP and ENP, Florida. Map developed by
Miller (1993).








13

Table 2.1. Areal coverage of the habitats in the study area, BCNP and ENP, Florida [after
Miller (1993)].
Area
Habitat (ha) (%)
Wet prairie 21758 62.9
Herbaceous prairie 5001 14.5
Tree islands 2201 6.4
Willow/dense sawgrass 1469 4.2
Dwarf cypress prairie 2045 5.9
Cypress strand 399 1.2
Pine 143 0.4
Pine with dwarf cypress 248 0.7
Mangrove/prairie transition 568 1.6
Mangrove 735 2.2


2.2.1.a. Forested uplands

Hardwood tree islands, including hardwood hammocks and bayheads, account for

approximately 6.4% of the study area (Miller 1993). Many of these tree islands are

characterized by an elongated shape, as formed by the flow of surface water, although

some in the drier prairies have a more rounded shape. Size of tree islands in the study

area is variable (0.04-208 ha), but most (83%) are <1 ha (Fig. 2.3). Tree islands have a

closed dome canopy of 6-20 m high.

Hardwood hammocks are elevated above the surrounding prairie 1 m, often on a

bedrock outcrop (Craighead 1984). Hammocks are composed primarily of flood

intolerant species including live oak (Quercus virginiana), wild tamarind (Lysiloma

latisiliqua), gumbo limbo (Bursera simaruba), and strangler fig (Ficus aurea) (Duever et

al. 1986). Bayheads are elevated above the surrounding prairie, but less so than hardwood

hammocks, and are composed of flood tolerant temperate and tropical hardwoods











>100.0
10.0-100.0
5.0-10.0 I
3.0-5.0
S2.75-3.00
S2.50-2.75
()
N 2.25-2.50 I
2.00-2.25
1.75-2.00
S1.50-1.75
1.25-1.50 |
I- 1.00-1.25
0.75-1.00 /
0.50-0.75 1
0.25-0.50 I
0.00-0.25 + 1

0 200 400 600 800 1000
Frequency
Figure 2.3. Histogram of size of tree islands in the study area. Note that not all the widths
of size categories for tree islands are the same.


including red bay (Persea borbonia), wax myrtle (Myrica cerifera), cocoplum

(Chrysobalanus icaco), and dalhoon holly (Ilex cassine). Common ground cover in tree

islands includes royal fern (Osmunda regalis), swamp fern (Blechnum serrulatum),

bloodberry (Rivina humilis), and greenbriar (Smilax spp.) (Duever et al. 1986).

Inundation of hardwood hammocks is rare; however, partial inundation of

bayheads is frequent. Between 1953 and 1978, the hardwood hammocks in the Pinecrest

region of Big Cypress National Preserve were estimated to have been inundated only 2

days (Gunderson and Loope 1982a). Schomer and Drew (1982) estimated a hydroperiod

length of <1 month in hardwood hammocks. Shallow inundations lasting 0.3-1.5 months

in hardwood hammocks and bayheads in BCNP were reported by Duever et al. (1986).









15

Slash pine (Pinus elliottii var. densa) forests are restricted to the extreme western

edge of the study area. Pine forests have a grassy understory, commonly Muhlenbergia

spp. and Andropogon spp.; drier forests often have a saw palmetto (Serenoa repens)

understory (Duever et al. 1986). Hydoperiods are often non-existent, but if present, they

average <2 months in length (Duever et al. 1986, Olmsted et al. 1980).

2.2.1.b. Non-forested wetlands

Non-forested wetlands, principally sparse sawgrass (Cladiumjamaicensis)

marshes and muhly grass (Muhlenbergiafilipes) prairies, comprise 77.4% of the study

area (Miller 1993). Sparse sawgrass marshes, which comprise 62.9% of the study area,

are dominated by sawgrass, but also contain maidencane (Panicum hemitomon),

spikerush (Eleocharis spp), muhly grass, as well as other grasses, sedges, and rushes

(Duever et al. 1986). Patches of pickerelweed (Pontederia spp.) and arrowhead

(Sagittaria spp.) are found in slight depressions in the marsh. Muhly grass prairies, also

termed 'herbaceous prairies', constitute 14.5% of the study area and occur at slightly

higher elevations than sparse sawgrass marshes (Miller 1993). These prairies support a

higher diversity of herbaceous forbs and grasses, sedges, and rushes than sparse sawgrass

marshes.

Estimates of hydroperiod length in sparse sawgrass marshes and muhly grass

prairie vary depending on geographic location and habitat classification. Annual

hydroperiod estimates for sparse sawgrass in Shark Slough ranged from 6-12 months

between 1953-1980 (Olmsted and Armentano 1997) and from 2.2-7.6 months in Taylor

Slough between 1961-1977 (Olmsted et al. 1980). Annual hydroperiod estimates for

muhly grass prairie ranged from 1.0-4.9 months in Taylor Slough between 1961-1977








16

(Olmsted et al. 1980), from 0.0-6.7 months in the Turner River area between 1964-1978

(Gunderson et al. 1982), and from 1.0-3.6 months in Deep Lake Strand between 1973-

1980 (Gunderson and Loope 1982b). Duever et al. (1986) defined wet prairies in BCNP

to have hydroperiods of 1.7-5.0 months and freshwater marshes to have hydroperiods of

7.5-9.0 months. Kushlan (1990) defined wet prairies to have hydroperiods of<6 months

and sawgrass marshes to have hydroperiods of 6-9 months.

2.2.1.c. Forested wetlands

Willow (Salix caroliniana) forms dense thickets in flowing water sites, often

surrounding tree islands and forming "tails" following the direction of water flow. Stands

of tall (1-3 m) dense sawgrass are frequently found in association with willow thickets.

These tall dense sawgrass strands frequently occur at slightly higher elevations than the

surrounding prairie, and exhibit a reduced hydroperiod (Kushlan 1990). However,

Olmsted and Armentano (1997) noted that east and west of Shark Slough, tall sawgrass

strands are often found at lower elevations than the surrounding sparse sawgrass or

spikerush marsh and exhibit hydroperiods of 6-8 months. In southern Taylor Slough, a

willow/sawgrass stand had an estimated hydroperiod of 9.0-10.3 months between 1961-

1977 (Olmsted et al. 1980).

Cypress domes and strands (Taxodium spp.), which are restricted to the

northwestern portion of the study area, occur in circular or elongated depressions in the

bedrock and are characterized by an understory of herbaceous and woody species, such as

bladderwort (Utricularia spp.), swamp fern (Blechnum serrulatum), buttonbush

(Cephalanthus occidentalis) and willow (Salix caroliniana). Hydroperiods in cypress

strands and domes average 8.3-9.7 months (Duever et al. 1984). Dwarf cypress forest is










an open forest with stunted, widely spaced cypress tress and a herbaceous understory.

Hydroperiods in dwarf cypress forests range from 4-12 months (Flohrschutz 1978,

Gunderson and Loope 1982a).

Red mangrove (Rhizophora mangle) forests are restricted to the southwestern

edge of the study area. These tidally submerged woodlands occur along the coast and

inland along coastal rivers (Scholl 1968). Water in these swamps is <60 cm deep; and

many interior areas are not inundated during an average high tide. The swamp floor is

submerged entirely during extreme high tides, and many areas are exposed subaerially

during low tide.

2.2.2. Hydrology Patterns

Hydrology patterns were inferred using historical data from hydrologic station P-

34, which was located centrally in the study site in an area characterized as wet prairie or

sparse sawgrass marsh (Fig. 2.4). During the period of record (1953-1995), data were

missing for the following 4 months: October 1980, May 1991, January 1993, and

February 1993. These missing data were estimated with an analysis of covariance, using

water depths from a neighboring water gauge as the covariate. Three water gauges were

identified as potential covariates (Fig. 2.4). NP-205, located 13 km northeast of P-34 in a

drier prairie, had water levels strongly correlated with levels at P-34 (r=0.876, n=251);

however, the period of record did not start until October 1974, and data were not

available for January 1993 and February 1993. P-35 was located 18 km south of P-34 in

southern Shark Slough; however, the correlation between water depths was not as strong

(r=0.675, n=511). Measurement of water depths at P-36, located 17 km southeast of P-34














NP-205










UP-P33


Shark-ilough



.P-35
10 0 10 20 Kilometers

/ BCNP I ENP boundary
Habitat
Wet Prairie
Herbaceous Prairie N
Tree island
Willowidense sawgrass
F-7 Dwarf cypress prairie
Cypress strand W E
Pine
Mangrovelprairie transition
Mangrove S


Figure 2.4. Study area with locations of neighboring hydrologic gauges, P-34, NP-205, P-
35, and P-36.








19

in central Shark Slough, began in February 1968 and the correlation with water depths at

P-34 was the strongest (r=0.904, n=331).

Based on the quantity of available data and strength of correlation, P-36 was

chosen to predict water depths during the 4 missing months. The model included water

depth at P-36 as a quantitative covariate with year and month included as qualitative

factors. The inclusion of year and month improved the model fit (adjusted R2=0.817 for

model with P-36 and adjusted R2=0.888 for model with P-36, year, and month). Other

models that accounted for the temporal correlation of the data and the cyclical nature of

the water depths were fit to the data. However, these models did not provide improved fit,

possibly because of the intrinsic random nature of rainfall patterns and changes in water

control measures during the period of record.

Relative to four other gauging stations in wetland communities in ENP, P-34 had

the lowest water levels and the shortest period of annual inundation; however, it also had

the largest range of water level fluctuations (Gunderson 1990). Between 1954-1985,

hydroperiods ranged from 2-12 months with a historical mean of 6.6 months. No

differences in hydropattemrn among community types were detected because of high year-

to-year variability.

From 1989 to 1992 (during the first field study), wet seasons appeared typical;

however, dry seasons were much drier than average (Figs. 2.5 and 2.6). Hurricane

Andrew, a relatively dry hurricane, moved through the study area in August 1992 and

caused extensive damage to the tree islands by blowing down and completely defoliating

most trees in its path (Labisky et al. 1999). The second field study was conducted from

1993 to 1995. The fall of 1994 was extremely wet, with >100 cm of rain occurring











90 -


60 -.


-30 -

D 0 ........ ........0

0-30-


-60 -...


-90 -
I I I I I I I I I

1953 1958 1963 1968 1973 1978 1983 1988 1993

Year


Figure 2.5. Mean monthly water levels recorded at P-34 hydrologic station, Everglades National Park, Florida, January 1953-
December 1995. Depths were predicted for October 1980, May 1991, January 1993, and February 1993.













90- Observed monthly mean A
Historical monthly means --
6 0 . . . . . . . . . . . . . . ..... .... .. .. .. .... ............ ........... I. . . ......




-60


-90
~-30-






I I I I I I !
Jan 1989 Jan 1990 Jan 1991 Jan 1992 Jan 1993 Jan 1994 Jan 1995
Year
Figure 2.6. Mean monthly water levels recorded at P-34 hydrologic station from January
1989 to December 1995 and historical monthly means from 1953-1985. Depths were
predicted for May 1991, January 1993, and February 1993.


between August and November, culminating with Tropical Storm Gordon in November

1994 which contributed >20 cm of rain. Water levels remained high in the study area

throughout 1995.

A relative elevation map was created to simulate changes in water depths over

time. Elevation of each habitat, relative to P-34, was derived from a literature review and

estimation of annual hydroperiod length for various elevations (Table 2.2). The 20-m

pixel elevation map was created from the habitat map and the estimated elevations (Fig.

2.7). To allow for gradual changes in elevation on habitat edges, nearest-neighbor

averaging was performed on the elevation map.











Table 2.2. Estimated elevation of each habitat, relative to P-34 hydrologic stations, and
estimated minimum, median, and maximum hydroperiod lengths (months per year) for
each habitat.
Estimated Estimated hydroperiod 1953-1995
elevation relative
Habitat to P-34 (cm) mmin med max
Wet prairie 0 2 7 12
Herbaceous prairie 20 0 3 12
Tree islands 80 0 0 2
Willow/dense sawgrass -15 5 9 12
Dwarf cypress prairie 5 0 6 12
Cypress strand -10 5 9 12
Pine 80 0 0 2
Pine with dwarf cypress 30 0 0 12
Mangrove/prairie transition -5 3 8 12
Mangrove -20 6 12 12
a P-34 hydrologic station was located in wet prairie habitat (Fig. 2.4).




































8 0 8 16 Kilometers

'/uBCNP I ENP boundary
Elvaon classes (cm)
-20--lO N
40-o-0
So0-10
10 -20
20 -30 W E
30-40
40-50
M50-60 s
Ss60-70o
M 70 -80


Figure 2.7. Estimated elevation map (relative to P-34 hydrologic station) within the study
area.















CHAPTER 3
WHITE-TAILED DEER MODEL CALIBRATION DATA


The white-tailed deer population on the BCNP/ENP study site was the subject of

intensive investigation from 1989-1992 (Boulay 1992, Sargent 1992, Zultowsky 1992,

Miller 1993, Sargent and Labisky 1995, Labisky et al. 1999). The white-tailed deer data

used for model calibration were analyzed to provide a starting point for the development

of the simulation model. During the collection of this calibration data, environmental

conditions ranged from mild drought to typical (Fig. 3.1). The simulation model

developed in Chapter 4 reflects the movement patterns and habitat use dynamics explored

in these analysis.

3.1. Data Collection Methods

White-tailed deer were captured exclusively by helicopter-netgunning (Barrett et

al. 1982, Labisky et al. 1995). Each captured deer was aged, measured, and marked with a

radio-transmitter/collar, equipped with motion-sensitive activity (2X signal pulse) and

mortality (4X signal pulse) modes (Wildlife Materials, Inc., Carbondale, IL). Due to the

inaccessibility of the study area, all radio-monitoring was conducted during daylight

hours from a fixed-wing aircraft. To obtain unbiased temporal monitoring, radio-locations

for each deer were evenly distributed among four daylight periods: sunrise to 2 hours

post-sunrise, 2 hours post-sunrise to noon, noon to 2 hours pre-sunset, and 2 hours pre-

sunset to sunset. By stratifying the radio-locations across the entire day, any diurnal









25


90-"
Observed monthly mean -
Historical monthly means --
6 0 . ... ........... . . . . . . . . . . . . . . . . . . . . . . . . . .

30-

0 ... ......... .- .. . .. . . .

..6O
~-30 -qf



-90
II I I
Jan 1989 Jan 1990 Jan 1991 Jan 1992
Year
Figure 3.1. Mean monthly water levels recorded at P-34 hydrologic station, and historical
monthly means from 1953-1985. Depths were predicted for May 1991.


patterns present in movement characteristics or habitat associations would be equally

represented and, thus, not impact annual and hydrologic season summary statistics. Each

deer was located, on average, once every 5 days. The location error associated with aerial-

based telemetry, estimated from blind placement of dummy radio-collars, was <30 m

(Miller 1993).

3.2. Data Summary Methods

A deer was classified as a resident of either BCNP or ENP if >75% of its radio-

locations were located in one of the management units. Data were summarized on an

annual basis with the annual cycle defined to begin on April 1 of the calendar year. This

annual cycle was divided into four periods based on reproductive phenology (Labisky et

al. 1995). Weaning and pre-rut occur from April through June. Males are in rut and

females in estrus from July through September. Post-rut and pregnancy occur from









26
October through December, coinciding with the peak hunting season in BCNP. Fawning

and antlerogenesis occur January through March, and all deer were assigned arbitrary

birthdates of April 1. For the calibration data set, data were collected for 3 annual cycles

[1989 (1 April 1989-31 March 1990), 1990 (1 April 1990-31 March 1991), and 1991 (1

April 1991-31 March 1992)]. Deer included in an annual cycle were required to have a

minimum of 50 radio-locations, be monitored for a minimum of 9 months during that

annual cycle, and exhibit no dispersal movements.

Differences in the measured parameters between hydrologic seasons also were

estimated. Sufficient data were collected for 5 hydrologic seasons [89DRY (1 November

1989 30 April 1990), 90WET (1 May 1990 31 October 1990), 90DRY (1 November

1990 30 April 1991), 91WET (1 May 1991 31 October 1991), and 91DRY (1

November 1991 30 April 1992)]. Deer included in these analyses were required to have

been monitored for a minimum of 2 sequential hydrologic seasons and exhibit no

dispersal movements during those seasons. Each included deer had a minimum of 30

radio-locations and was monitored for a minimum of 5 months in each season. That

condition was relaxed in 91DRY to a minimum of 24 radio-locations and 4 months of

observation because radio-monitoring ended on 31 March 1992.

3.2.1. Annual Cycles

Annual home range size was calculated using the 95% fixed kernel estimator with

least squares cross validation (Silverman 1986, Worton 1989, Seaman and Powell 1996).

Distance between centers of annual home ranges was calculated to access the degree of

site fidelity. Mean distance between radio-locations for each deer was used as a proxy for

the distance that a deer traveled during a 5-day interval. This statistic cannot be used as a









27
measure of the total distance that a deer traveled over a 5-day interval, but can be used as

an indicator of the minimum distance a deer traveled over 5 days. Percentage of radio-

locations in each habitat was used to establish habitat selection patterns. Sample means

were weighted to account for deer with multiple years of observations.

Resource selection was evaluated using chi-square analyses (Neu et al. 1974,

Manly et al. 1993) for sample design II (multiple observations on same individual,

assume same habitat availability for all individuals) and sample design IIl (multiple

observations on same individual, estimate habitat availability for each individual) as

defined by Thomas and Taylor (1990). To insure deer with multiple years of observation

did not unduly influence summary statistics, 1 year of observational data from each deer

was randomly selected for inclusion into these analyses. The original study and deer

captures focused on tree islands and prairies of the study area; therefore, the few deer

spending a large portion of their time in the pine, cypress, and mangroves were not

included in these analyses. Separate summary statistics were calculated for females and

males.

For the sample design II analyses, habitat availability was assumed equal for all

deer. After removing pine, cypress, and mangrove areas from the map, wet prairie,

herbaceous prairie, tree islands, and willow/sawgrass accounted for 72%, 16%, 7%, and

5% of the study area, respectively. The notation used for the habitat analyses was:

it, = known proportion of habitat i in the study area,

UY = number of observations of thefP animal in the ith habitat,

%, = total number of observations of all n animals in the ih habitat,

u+j = total number of observations of the!" animal in all habitats, and











u,, = total number of observations.

Selection ratios for each habitat were calculated. Each ratio was proportional to the

probability of the given habitat being utilized, assuming the individual had unrestricted

access to the entire distribution of habitats. The selection ratio and associated variance for

each habitat for this population of deer was estimated with



U.

u. )
,'iu/++



varn (1u- I u++ 2
y=1 n-1 +


Simultaneous Bonferroni confidence intervals for the selection ratios were calculated

using an a-level of 0.05. Those confidence intervals not including 1 indicated either

selection for (ratio >1) or against (ratio <1) a particular habitat, and confidence intervals

including 1 indicated no evidence of selection for or against a particular habitat. A second

sample design I analysis was performed, using the percentage of each habitat contained

inside the 100% minimum convex polygon (MCP) home range for each deer, rather than

the number of radio-locations in each habitat.

For the sample design III analyses, habitat availability was estimated individually

for each deer using the proportions of habitats contained inside the 100% MCP home

ranges. Notation was the same as defined above for design II except that n. was the

known proportion of habitat i contained in the home range of individuals. Population

selection ratios and associated variances for each habitat were estimated using











U.+
w.i = R

J=i

n )w2 n

var(w,) = n
In j)

\j=\


Simultaneous Bonferroni confidence intervals for these population selection ratios using

an a-level of 0.05 also were calculated.

3.2.2. Hydrologic Seasons

For each deer, home range size for each of the hydrologic seasons was calculated

using the 95% fixed kernel estimator with least squares cross validation. Mean distance

between radio-locations for each deer served as a proxy for the distance a deer traveled

during a 5-day interval. Mean home range size and distance between consecutive radio-

locations and their standard errors were estimated using the number of seasons each deer

was in the sample population as weights. Differences between the WET and DRY

seasons were tested using a mixed model analysis with deer as a random effect and

hydrologic season as a fixed effect.

Percentage of radio-locations occurring in each habitat was used to establish

differences in seasonal habitat selection. Deer observed in pine, cypress, or mangrove

habitats were not included in these analyses. The generalized Cochran-Mantel-Haenszel

test (Birch 1965, Agresti 1990) was conducted for each gender to test for an overall

association between hydrologic season and habitat selection. Additionally for each









30
deer, a chi-square test was performed to test the hypothesis that there was a difference in

the distribution of radio-locations across habitats between WET and DRY seasons.

3.3. Data Summary

Estimated white-tailed deer densities for 1990-1992 were 3.65 (se=1.47) deer/km2

for the hunted BCNP population and 4.68 (se= 1.00) deer/km2 for the non-hunted ENP

population (Labisky et al. 1995). The data set used for model calibration included

yearling and adult deer that were captured, radio-collared, and monitored between 1989

and 1992. Data from 46 yearling or adult deer were used for initial model calibration

(Appendix A). Twenty-four deer were radio-monitored for 1 year, 18 deer for 2 years, and

10 deer for 3 years. Ten deer were radio-monitored for 2 hydrologic seasons, 15 deer for 3

seasons, 12 deer for 4 seasons, and 6 deer for 5 seasons.

3.3.1. Annual Cycles

The mean annual home range size of females was 271 ha (se=20, n=29), with a

range from 90 ha to 600 ha. Male home ranges were slightly larger (316 ha, se=49, n=17)

ranging from 102 ha to 1086 ha. Distance between consecutive home range centers was

similar for both genders; females had a mean distance of 307 m (se=53, n=17) and males

had a mean distance of 243 m (se=56, n=9).

Time intervals between radio-locations ranged from 1 to 14 days; however, many

(46%) were 5 days in length. To ensure the length of the measurement interval was not

influencing the straight-line distance between locations, an analysis of covariance

(ANCOVA) was performed. Distance between consecutive measurements had a skewed

distribution (Fig. 3.2) and was log-transformed prior to analysis. In the ANCOVA model,

the fixed effects were year (1989, 1990, 1991), days between radio-locations (linear










0.25


0.20-


0.15-


*S 0.10-


0.05-


0.00-



0.25-


0.20-
C
4)
90.15-
*4=

13
9 0.10-


0.05-


n nn-


0 1000 2000 30C


I . .. . .



.........


Figure 3.2. Histogram of straight-line distances (m) between consecutive radio-locations
for (a) female and (b) male white-tailed deer.


0 1000 2000 30(


. . . . . .


(a)















O0 4000 5000 6000 7000 8000 9000 1000C

Distance, m

(b)
. . . . I . . . . . . I . . I . . .












0 4000 5000 6000 7000 8000 9000 10000

Distance, m


v=vv


)









32
covariate), and their interaction; the random effect was deer. Using an a-level of 0.05, the

fixed effects did not have a significant effect on distance between consecutive

measurements (Table 3.1). The mean distance between consecutive locations was 686 m

(se=29, n=29) for females and 779 m (se=79, n=17) for males. Most distances were <750

m (65%) and nearly all <1500 m (90%), but deer occasionally were recorded traveling

longer straight-line distances (maximum observed distance=10240 m).


Table 3.1. Results from the analyses ofcovariance for log-transformed distance between
consecutive radio-locations for female and male white-tailed deer.
Fixed Effect df numerator df denominator p-value
Female
YEAR 2 3034 0.4366
DAYS 1 3034 0.0766
YEAR*DAYS 2 3034 0.6011
Male
YEAR 2 1715 0.1924
DAYS 1 1715 0.5992
YEAR*DAYS 2 1715 0.1596


Based on simple summaries of percentage of occurrences in each habitat (Table

3.2), females appeared to select for wet prairie more strongly than males, and males

appeared to select for tree islands and willow/dense sawgrass more strongly than females.

Habitat-use patterns were evaluated quantitatively using selection ratios. When

evaluating habitat selection based on the choice of a home range (100% MCP), assuming

equal availability of habitat for all individuals, females exhibited no significant selection

for or against any habitat since all the confidence intervals included 1 (Table 3.3).

However, males selected home ranges with less wet prairie and more willow/dense

sawgrass than expected, based on availability in the study area (Table 3.3). When the










selection ratios were calculated using radio-locations and assumed equal habitat

availability for all individuals, both females and males demonstrated habitat preferences

(Table 3.4). Both genders selected against wet prairie, had no selection for or against

herbaceous prairie, and selected for tree islands and willow/dense sawgrass; however,

males tended to exhibit stronger selection for or against a particular habitat than females,

as evidenced by the more extreme selection ratios (i.e., selection ratios farther from 1).

These selection ratios were more extreme than those based on selection of home range

area (Table 3.3), which was expected because the analysis based on home range areas

assumed equal use of all the area contained inside the home range. Similar selection

trends were observed when habitat availability was estimated separately for each

individual using 100% MCP (Table 3.5). Both females and males selected against wet

prairie, selected neither for nor against herbaceous prairie, and selected for tree islands

and willow/dense sawgrass inside their home ranges. These results were similar to

Miller's (1993) findings.


Table 3.2. Mean percentage of radio-locations in each habitat for the study sample of
white-tailed deer in BCNP and ENP, April 1989 to March 1992.
Habitat Females Male
Wet prairie 53 (4)b 25 (4)
Herbaceous prairie 17 (3) 20 (3)
Tree islands 17 (2) 33 (4)
Willow / dense sawgrass 9 (1) 18 (2)
Dwarf cypress prairie 1 (1) 2 (2)
Cypress strand <1 (<1) 1 (1)
Pine <1 ( Mangrove 2 (2) 1 (1)
a Sample sizes: female (29), male (17).
b Standard error in parentheses.










Table 3.3. Selection ratios and 95% Bonferroni confidence intervals' using the design H
analysis for habitat inside 100% MCP for the study sample of white-tailed deer in BCNP
and ENP, April 1989 to March 1992.
Habitat Femaleb Male
Wet prairie 1.05 (0.90,1.20) 0.77 (0.56,0.98)
Herbaceous prairie 0.88 (0.08, 1.39) 1.51 (0.94,2.08)
Tree islands 0.74 (0.35,1.13) 1.67 (0.68, 2.66)
Willow/dense sawgrass 1.02 (0.58,1.46) 1.73 (1.13,2.33)
"Confidence intervals that do not include 1 indicate a selection against (selection ratio
<1) or a selection for (selection ratio >1) a given habitat.
b Sample sizes: female (26), male (12).


Table 3.4. Selection ratios and 95% Bonferroni confidence intervals" using the design II
analysis for radio-locations for the study sample of white-tailed deer in BCNP and ENP,
April 1989 to March 1992.
Habitat Femaleb Male
Wet prairie 0.75 (0.59,0.91) 0.35 (0.18,0.51)
Herbaceous prairie 1.15 (0.60,1.70) 1.14 (0.88,1.69)
Tree islands 2.41 (1.47,3.34) 5.29 (3.64,6.90)
Willow/dense sawgrass 2.14 (1.53,2.76) 3.96 (2.95,4.94)
"Confidence intervals that do not include 1 indicate a selection against (selection ratio
<1) or a selection for (selection ratio >1) a given habitat.
b Sample sizes: female (26), male (13).


Table 3.5. Selection ratios and 95% Bonferroni confidence intervals" using the design IIIl
analysis for the study sample of white-tailed deer in BCNP and ENP, April 1989 to
March 1992.
Habitat Femaleb Male
Wet prairie 0.72 (0.62, 0.83) 0.45 (0.30, 0.59)
Herbaceous prairie 1.28 (0.96,1.60) 0.79 (0.45,1.12)
Tree islands 3.16 (1.97,4.35) 3.19 (1.67,4.71)
Willow/densesawgrass 2.05 (1.13,2.97) 2.16 (1.44,2.89)
a Confidence intervals that do not include 1 indicate a selection against (selection ratio
<1) or a selection for (selection ratio >1) a given habitat.
b Sample sizes: female (26), male (12).










3.3.2. Hydrologic Seasons

Mean WET season home range size of females (n=26) was 211 ha (se=17) and

was significantly different (p=0.0025) from the mean DRY season home range size of

303 ha (se=36). The mean WET season home range size of males (n=17) was 301 ha

(se=48) and was significantly different (p=0.0007) from the mean DRY season home

range size of 187 ha (se=36).

Mean distance between consecutive radio-locations followed a pattern similar to

home range sizes. Mean distance between consecutive radio-locations in the WET season

for females (n=26) was 638 m (se=27) and was significantly different (p=0.0025) from

the mean DRY season distance of 722 m (se=34). Mean distance between consecutive

radio-locations in the WET season for males (n=17) was 866 m (se=67) and was

significantly different (p=0.0007) from the mean DRY season distance of 664 m (se=81).

There was no evidence of a change in habitat use between the hydrologic seasons

based on radio-locations for females (Cochran-Mantel-Haenszel test, p=0.75, df=3,

n=2702) (Table 3.6). Of the 24 females included in this analysis, only three had a

significant association between hydrologic season and habitat (chi-square test, p<0.05,

df=3), but there was no commonality in the associations between hydrologic season and

habitat. There was evidence of a change in the distribution of habitat use based on radio-

locations for males (Cochran-Mantel-Haenszel test, p=0.001, df=3, n=1498) (Table 3.6).

During the DRY season, males increased their use of wooded areas (tree islands and

willow/dense sawgrass) and decreased their use of wet prairie relative to WET season

habitat use. Of the 11 males included in this analysis, six had a significant association

between hydrologic season and habitat (chi-square test, p<0.05, df=3), and they typically









36

Table 3.6. Hydrologic season habitat use based on percentage of radio-locations in each
habitat for the study sample of white-tailed deer in BCNP and ENP, November 1989 to
March 1992.
Female" Male
Habitat WET DRY WET DRY
Wet prairie 55 (5)b 56 (5) 28 (5) 17 (4)
Herbaceous prairie 18 (4) 16 (3) 20 (4) 20 (4)
Tree islands 17 (3) 18 (3) 35 (3) 41 (4)
Willow/densesawgrass 11 (1) 12 (1) 17 (2) 22 (3)
"Sample sizes: female (24), male (11).
b Standard error in parentheses.


followed the same trend of increased use of wooded areas and decreased use of prairie in

the DRY season, relative to the WET season.

3.4. Discussion

3.4.1. Annual Cycles

The most conspicuous observation regarding any of the spatial-use summary

measures was the large variation among individuals and among years. Males tended to

have slightly larger mean annual home ranges and mean straight-line distances between

consecutive locations than females; however, this was negligible when individual

variability was taken into account. This high variability among individuals may be due to

a variety of factors such as resource availability (Byford 1969, Miller 1993), age (Gavin

et al. 1984, Nelson and Mech 1984), concealment cover (Sparrowe and Springer 1970),

weather (Michael 1970, Drolet 1976), and human disturbance (Sparrowe and Springer

1970). Local population dynamics such as density and social structure also may influence

spatial-use patterns (Sanderson 1966, Gavin et al. 1984, Zultowsky 1992, Miller 1993).

These deer exhibited a high degree of site fidelity, as evidenced by the small shifts in










annual home range centers, which measured <1 km for all deer. The strength of site

fidelity in this population of deer during the time frame of the calibration data set also

was discussed by Sargent (1992) and Zultowsky (1992). Labisky et al. (1999) noted the

continuous maintenance of home ranges, even after the passage of Hurricane Andrew in

August 1992.

The most prominent difference between spatial-use patterns of adult females and

males was habitat selection. Females were twice as likely as males to be radio-located in

the prairie, and males were twice as likely as females to be radio-located in a tree island

or willow/dense sawgrass areas. This differential preference between females and males

as evidenced by percentage of radio-locations in each habitat also is supported by the

magnitude of the selection ratios calculated using radio-locations in the study site (Table

3.4). For many ungulates, differential use of food and cover resources by gender occurs as

a result of differing energetic and reproductive strategies (Main and Coblentz 1990,

Miquelle et al. 1992). Hydrophytic forbs (notably swamp lily, Crinum americanum),

which contain high levels of crude protein (>15%) year-round (Loveless 1959a),

comprised 68% of the annual diet of females in the study area (Hurd et al. 1995). Isolated

patches of prairie that remain wet during the dry season support lilies and other forage

important for pregnant and lactating does (Hunter 1990). Increased use of prairies also

may provide protection against bobcat predation on fawns (Boulay 1992). Males consume

a higher proportion of the woody browse and ferns found in the tree islands and wooded

areas than females (Hurd et al. 1995). Males strive to maximize weight gain because

increased body size leads to higher reproductive success (Clutton-Brock et al. 1982). Due

to larger rumen size, males may require larger amounts of forage, but can subsist on










lower quality food (McCullough 1979, Shank 1982, Bowyer 1984, Beier 1987).

Therefore, males focus foraging efforts on tree islands, which probably support higher

forage biomass per unit area than other habitats (Miller 1993).

Females showed no significant trends for selection of home range content;

however, males selected home ranges containing less wet prairie and more herbaceous

prairie and wooded areas. Due to the polygynous nature of white-tailed deer, females are

organized into matrilineal groups and tend not to disperse as juveniles, whereas males

disperse from the family group at sexual maturity and establish new home ranges

(Marchington and Hirth 1984). Therefore, males had an opportunity to select home ranges

containing a higher proportion of their preferred habitats.

3.4.2. Hydrologic Seasons

Females traveled farther and had larger home ranges in the dry season than the

wet season, possibly because of limitations in nearby available forage during the winter

drought. Typically, white-tailed deer concentrate activities when food is plentiful and

expand activities when food is scarce (Byford 1969). However, no changes in the habitat-

use patterns of females between the wet and dry seasons were evident.

Males traveled more, had larger home ranges, increased their use of wet prairie,

and decreased their use of tree islands in the wet season relative to the dry season.

Because the wet season includes the rutting period, during which time males are

searching for females to breed, they travel greater distances to find females and utilize the

landscape matrix of wet prairie more heavily in those search efforts. During the seasonal

hunt, which occurs during the early dry season, males, especially those in BCNP, may

increase their use of wooded areas to obtain a higher degree of concealment cover.















CHAPTER 4
DEVELOPMENT, CALIBRATION, AND EVALUATION
OF THE SIMULATION MODEL


In this chapter, I present and demonstrate the approach developed to calibrate an

IBSE simulation model. Specific issues with regards to model calibration are addressed

and then introduced as steps of an iterative process to attain a satisfactory simulation

model. Finally, parameterization of the final simulation model is described. I developed

the simulation using C++ (Borland C++ Builder 3.0, Inprise Inc.) with object-oriented

programming techniques.

4.1. Approach and Technique

Determining correct model form (verification) involves evaluating the conceptual

structure and the transformation of the structure into computer algorithms (Bart 1995,

Conroy et al. 1995, Rykiel 1996). Model structure is often visualized through flow charts

(Fig. 4.1). Detailed literature review and analyses of additional data aid the verification of

correct conceptual model structure. Assuming the model structure is correct, the

calibration process consists of altering parameter values until the modeled system is

represented adequately. Model calibration also may reveal algorithms in the simulation

model that need to be modified if the optimum parameterization of the algorithm is not

sufficient. Updating algorithms and parameter values is an iterative process, requiring

constant reevaluation of the simulation model.













Read in habitat and elevation maps,
monthly water depths at gauging station


Initialize water depth map


Generate starting locations for each deer
4
Each deer evaluates surrounding pixels based on:
habitat
water depth
location relative to home range
etc.



Each deer chooses a new location and moves there


Each deer updates location coordinates
and memory of past locations


Output data to a file


SUpdate
depth m






No Yes


I Yes -
I ------ >|END


Figure 4.1. Simulation flow chart to aid in visualization of model structure. Example
depicts white-tailed deer movement in the Florida Everglades.










During the development of this model building process, I chose to focus on

several issues. Parameterization of the movement process is approached by quantitatively

and visually evaluating various movement algorithms. An approach for evaluation of

potential movement algorithms relative to the observed field data is presented. To address

algorithm and parameter value evaluation, simulation experiments are conducted, and

simulated and observed data are compared quantitatively with discrepancy measures.

However, before quantitative model evaluation is performed, the amount of time (i.e.,

number of iterations) the simulation must run before meaningful testing can occur must

be determined. Qualitative evaluation (e.g., visual comparison) also is an important

component of model calibration. Once the simulated data approach the observed data, the

robustness of the simulation to represent the observed data is evaluated.

4.1.1. Parameterization of Animal Movement

Observed movement patterns are a function of many possible factors, which vary

from individual to individual. Some of these factors may include age, predator threat,

availability of food and water, location of neighboring individuals (of the same or

different species), surrounding micro- and macro-habitat, weather, time of year, and time

of day. Differences in individual preferences and random chance also may influence

movement decisions. Many of these potential influences can be measured (i.e., weather

conditions and habitat availability), and potential relationships between these factors and

the movement patterns can be explored (i.e., correlation analyses and habitat-selection

ratios). However, often these factors cannot be measured on the scale appropriate for the

parameters of interest, and some factors may be unmeasurable or unknown.









42
Radio-telemetry data collected from individual animals can provide some of this

information (White and Garrott 1990). These data are used to evaluate individual patterns

of movement, home range size and shape, and habitat use. However, these summary

statistics are 'outcomes' resulting from the movement patterns generated by a multitude

of factors. Statistical analyses can identify associations between the environmental factors

and the measured outcomes. These associations help in formulating testable hypotheses

regarding how environmental factors may affect movement patterns, and, thus, affect the

measured outcomes. This approach is useful in developing a simulation of animal

movement patterns. Based on knowledge of the natural history of the species and the

results of the data analyses, rules to simulate movement patterns can be developed. These

rules then can be tested by comparing the measured 'outcomes' from the real individuals

and the 'outcomes' of the simulated individuals.

Simulating animal movement paths is accomplished with any of several

approaches. Vector-based models, in which a simulated individual chooses a movement

direction and, often, a movement distance for each step, constitute one approach. The

direction and distance for each move are chosen, based on those surrounding

environmental factors deemed important to movement decisions. Grid-based models, in

which simulated individuals move among pixels on a grid superimposed over the

landscape, constitute a second approach. These vector- or grid-based simulation models

can be either deterministic or stochastic. Deterministic models are designed such that the

individual always makes the 'best' movement decision (i.e., always moves in the

direction of best habitat). In contrast, stochastic models use random draws from various

probability distributions based on those factors that influence movement decisions, such








43
that individuals are most likely to make the 'best' choice. For the model presented in this

study, I used the grid-based stochastic simulation approach.

4.1.2. Measuring Model Fit

Model fit is evaluated by comparing simulated outcomes of the model and

observed outcomes of the field data. These quantities, often termed discrepancy measures

(DMs), quantify the difference between a simulated data set and an observed data set and

have the general form:

D(x) = g(P(x),o)


where P(x) is a summary statistic for one run of the simulation with parameter set x, x is

an element of X (the set of all feasible model parameters), and 0 is the summary statistic

computed for the observed data (Van der Molen and Pinter 1993). The objective of model

calibration is to minimize the DM(s). DMs may be calculated for summary statistics such

as average home range size or the percentage of time individuals are located in specific

habitat types.

One family of DMs takes the form:

D(x) = Ip(x)- o0


where 13>0 (Van der Molen and Pinter 1993). For example, if 13=1, D(x) is the absolute

value of the deviation between simulated and observed summary statistics, and if 13=2,

D(x) is the squared deviation between simulated and observed summary statistics.

Evaluation of summary statistics, such as mean annual home range size or mean distance










between consecutive annual home range centers, is accomplished with this family of

DMs.

A DM useful for evaluating a set of n dependent outcomes, such as the percentage

of radio-locations in each habitat, has the form:




D~x)(= Y, i
i=1 Oi

where 0, is the summary statistic for the observed data for the ith outcome, P(x) is the i'

summary statistic for a run of the simulation with parameter set x, and x is an element of

X (the set of all feasible model parameters). This DM approximates a chi-square

goodness-of-fit statistic with n-1 degrees of freedom where P,(x) and 0, are the

percentage of occurrences in habitat i based on simulated and observed individuals,

respectively. Mayer and Butler (1993), Power (1993), and Van der Molen and Pint6r

(1993) provide additional forms for discrepancy measures.

4.1.3. Visual Assessment

An additional component of model verification and calibration is the visual

comparison of simulation output and observed data. Even if the discrepancy measures

based on summary statistics demonstrate that simulation output is comparable to

observed data, movement patterns also must be visually realistic based on knowledge of

the natural history and ecology of the species.











4.1.4. Experimental Design

Simulation experiments are conducted to identify a set of algorithms and

parameter values that minimizes discrepancies between simulated and observed data. In

this setting, each algorithm and parameter value to be evaluated is a factor in the

experiment, and an experimental unit (EU) is one run of the simulation model. When

evaluating large numbers of model parameters, effects of each parameter on simulation

outcomes can be complicated and difficult to identify. Factorial experiments allow for the

simultaneous investigation of the effects of many factors (i.e., simulation model

parameters). Moreover, the ensuing analysis of variance (ANOVA) of the simulation data

can include interaction terms that explain the interrelationship among the simulation

parameters. However, as the number of investigated factors increases, the number of EUs

required to examine all factor combinations increases rapidly. For example, a factorial

experiment having p factors, each with k levels, requires / EUs for one replicate.

Experimental designs have been developed that make efficient use of resources by

requiring a minimal number of EUs. Response surface methodology (Khuri and Cornell

1987, Montgomery 1991) also provides a collection of specific experimental designs and

statistical techniques to facilitate the estimation of factor settings that optimize a response

variable.

Often a sequence of experiments is necessary to optimize simulation model

algorithms and parameters, with the analysis of each experiment dictating the particulars

of the following experiment. First-order designs are initial screening experiments used to

estimate and test main effects and interactions among the factors. Common designs are 2P

factorials and fractions of 2P factorials (Cochran and Cox 1957, Montgomery 1991).









46

Fractional factorials reduce the number of required EUs using the assumption that higher-

order interactions (i.e., 3- and 4-way interactions) are negligible. The response variables

from each EU are analyzed using ANOVA. For the model development process presented

in this study, the response variables are DMs (Section 4.1.2), and the goal of optimization

is to attain values of these DMs close to zero. If an optimum is not attained inside the

initial experimental region, the method of steepest descent is used to establish parameter

settings for a subsequent experiment more likely to contain a minimum (Khuri and

Comell 1987, Montgomery 1991). This process is repeated until a minimum is achieved,

which results in a sequence of experiments.

When statistical analyses indicate that the design settings are close to an optimum,

additional experimentation is performed to identify a set of parameter settings that

minimizes the DM (a local minimum). More specifically, a second-order design,

estimating main effects, first-order interactions and quadratic effects, is often required to

approximate the curvature of the true response surface. Common second-order designs

are central composite designs, Y factorials, and 3P fractional factorials (Cochran and Cox

1957, Khuri and Cornell 1987).

4.1.5. Simulation Burn-in Time

The "bum-in" period (Fig. 4.2) is the number of iterations required for the

simulation to reach a steady-state (Kleijnen 1987). A population-based stochastic model

is said to have a statistically stationary state if the probability distribution of population

size is constant over a long time interval (Nisbet and Gumrney 1982). When generalized to

all population- and individually-based simulation models, the bum-in period is completed

when a statistically stationary state is reached by all relevant outcome measures.


















0








Year


Figure 4.2. Example of burn-in time estimation for a simulation outcome measured on an
annual basis. Individual outcomes are plotted in grey; linear slope is significantly
different from zero when estimated for all years (heavy solid black line) and not
significantly different from zero when using data from years 2 through 10 (heavy dashed
black line).


Estimation of bum-in time is important for several reasons. First, if the goal of the

modeling effort is to explore the impacts of perturbations on the simulation outcomes, the

simulation must be in a steady-state before applying the perturbations. If it is not in a

steady-state, the effects of burn-in and the perturbations on the simulation outcomes are

confounded (i.e., confused and inseparable). Second, if the goal of the modeling effort is

to explore impacts of introduction or reintroduction of a species in a particular geographic

region, then determining if a steady-state is reached is essential. If it is determined that a

steady-state is reached, estimating the time until that steady-state is reached is also

important.










Bum-in time is estimated by running the simulation for an extended period of

time and examining temporal trends and autocorrelations of simulation "outcomes" for

each individual (Fig 4.2). The approach for this study utilizes repeated measures analyses

to identify significant time trends in the summary outcome (Diggle et al. 1994, Littell et

al. 1996, Vonesh and Chinchilli 1997). If no significant linear time trend over the entire

simulation interval is present, bum-in time has no effect on that particular outcome. A

significant linear time trend is evidence that simulation bum-in affects the outcome

measure. In this case, the test for a linear trend is repeated using all the time intervals

except the first. If the second test for a time trend is not statistically significant, bum-in

time is established at one interval; otherwise, the linear trend test is repeated excluding

the first and second time intervals. These steps continue until there is no longer a

significant linear time trend. If the simulation has not reached a steady-state until the end

of the simulated time period or never reaches a steady-state (i.e., simulation bum-in time

is equal to or longer than the time period of the simulation), further exploration of bum-in

time and the form of the simulation algorithms is necessary. For each test for linear trend,

an a-level of 0.01 was used. Because of multiple and sequential testing, this slightly more

conservative a-level was used to reduce Type I error rates.

4.1.6. Final Model Evaluation

In all model-building exercises, evaluating goodness-of-fit of the final model is

crucial. For models such as regression, analysis of variance, and generalized linear

models, fit often is evaluated with the coefficient of determination (R2), Akaike's

Information Criterion [AIC (Akaike 1974)], and chi-square goodness-of-fit tests.

However, these tools are not applicable for Monte Carlo simulations, such as the IBSE









simulation developed in this dissertation. To evaluate the simulation results, I test the

likelihood of values of the observed outcomes arising as realizations of the posited

stochastic model using estimated p-values from an estimated predictive distribution (Rao

1977, Bjornstad 1990, Gelman et al. 1995). First, the general approach is described, and

then the adaptation of this method used for evaluating the IBSE simulation model is

presented.

Let y, y2, y3 . y. be the observed data, where each yi is either a vector or a

scalar variable and n is the number of observations. Also let 0 be the vector of unknown

parameters in the model, andfy,,y2, y3, . y10) be the density (i.e., the joint

distribution ofy,, Y2, y3,... y, given 0). Inferences regarding some subsequent

observation, y*, can be made using the predictive density function (PDF):

f(y*JY, Y2 ,Y3,...,Yn,)


If 0 is known then the PDF provides all the information regarding inferences on y*. If 8 is

unknown, one approach to making inferences on y* is to estimate 0 and substitute the

estimate for 0 in the PDF. The parameter, 0, can be estimated from


f(ylY2 ,Y3,...,5Y,y0)


using maximum likelihood or some other estimation method. Using this estimated value

for 0, the estimated predictive density function (EPDF)

f(Y *aYou y iY3,... ,yno)


can then be used to make inferences about y*. Using the EPDF with a known form and an








50

estimated 0 to make inferences about y* is misleadingly precise and results in predictive

p-values that are more extreme than if 0 were known (Aitchison and Dunsmore 1975).

For the simulation model developed in this study, y,, y2, y3,..., y, represent the

summary outcomes (e.g., mean annual home range size and mean percentage of

observations in each of the habitats) from n runs of the simulation model, 0 is the vector

of unknown model parameters (e.g., number of steps per day, relative affinities for

habitat, and relative affinities based on water depths), and y* is the summary outcome

from observed field data. Of interest is the likelihood that the value ofy* could have

arisen as an outcome of the simulation model. Assuming y* is independent ofy, y2, y3,..

., y,, the EPDF simplifies to

f(y*\e)


where 0 is provided by the calibration process. The likelihood that the value of y* could

have arisen from the posited simulation model can be measured by the tail-area

probability:

min[Pr(y, y* ),Pr(Y > y*\O)]


Because the empirical form of the EPDF is unknown, the predictive p-value is estimated

by an approximate distribution obtained through Monte Carlo simulation. Multiple runs

of the IBSE simulation model are conducted and the distribution of the simulated

outcomes is used to estimate the tail-area probability (Fig. 4.3).




























Figure 4.3. Example of an approximate EPDF. Histogram represents the distribution of
100 outcomes obtained by Monte Carlo simulation. A subsequent observation, y*, is
represented by the vertical line and the approximate tail-area probability is 0.09.


4.1.7. Details of the Iterative Approach

An iterative process is used to calibrate the simulation model (Fig. 4.4). Initial

movement algorithms and parameter values are selected for the first experiment. Once the

experimental design is selected and the simulation runs are completed, burn-in time is

evaluated for each summary outcome for each EU. Experiment bum-in time is estimated

as the maximum bum-in time of all evaluated summary outcomes for all EUs. Statistical

analyses are performed on each discrepancy measure from the time interval (i.e., annual

cycle) following estimated experiment bum-in time. Based on the results of these

analyses and subjective opinions from viewing simulation output, settings for the next

simulation experiment are determined. Movement algorithms are changed or parameter

values are adjusted, as appropriate, in subsequent experiments. When the discrepancy

measures appear to be minimized, multiple runs of the simulation with the same








52
parameter values are conducted and the distributions of the simulated summary statistics,

relative to the observed summary statistics, are evaluated using predictive p-values.


( Calibration complete


Figure 4.4. Flow chart representing the iterative process of model calibration.










4.2. Initial Model Parameterization

This first series of calibration experiments focused on parameterization of the

adult female movement process. Once female movements were sufficiently calibrated, the

algorithms and parameters were adjusted for calibration of the male movement process.

In the movement process that was developed, each deer made multiple moves per

day. In order to make valid comparisons of the simulated data and the observed field data,

only some locations of the simulated deer (i.e., one radio-location every 5 days) were

used for calculation of the outcome summary statistics. These statistics included home

range size, distance between consecutive annual home range centers, distance between

two consecutive radio-locations (5 days apart), and percentage of observations in each

habitat.

Initial locations of simulated deer were representative of home range centers of

observed deer from the calibration data set. The habitat map over which deer moved was

a closed environment (i.e., deer could not move off the map); however, there was no

'repelling force' to prevent them from moving to the edge of the map. Simulated deer that

moved adjacent to the map boundary had fewer pixels from which to choose for their next

location since there was a zero probability of moving to a pixel not within the study area.

These deer that formed home ranges on the boundary of the habitat map may not have

had realistic movement patterns; therefore, they were removed from data analyses for

model calibration.

4.2.1. Movement Step Size

The habitat map was created using 20-m pixels; however, there were several

problems simulating deer movements on a scale that small. Simulated deer that moved a









54
maximum distance of one pixel per step (to one of the eight neighboring pixels or to the

current location) had to make a very large number of steps to cover a sufficient portion of

its home range over a 5-day period. Also, simulated deer were stranded in large regions of

continuous habitat (e.g., large areas of prairie) and wandered randomly, never finding

other habitats. Although some observed deer spent nearly all their time in the prairie, a

high proportion of the deer in early simulations exhibited this behavior. One alternative

possibility was to allow deer to move farther than one pixel per step. Although deer

traveled longer distances during one day, they would 'jump' from one location to another,

leaving 'holes' in the memory of its previous locations. These simulated deer tended to

wander over the entire landscape, probably because home range formation is partly based

on an algorithm using memory of previous locations.

To address this problem, a single iteration of simulated deer movement was

developed as a two-stage process. First, deer selected a new location, using pixels larger

than 20-m, and then selected a 20-m pixel within the large pixel. Because the dynamics of

the simulated movements changed drastically as the size of the large pixel changed,

evaluation of the potential pixel sizes quantitatively would require developing an

optimum set of parameters for each pixel size and then comparing the optimized models.

This approach was not feasible given the amount of computer time needed to optimize a

single simulation model. Thus, the size of the large pixel was chosen to be 60-m for

several more qualitative reasons. An average home range of 300 ha contained

approximately 7500 20-m pixels, 1875 40-m pixels, 833 60-m pixels, 469 80-m pixels,

300 100-m pixels, or 20 500-m pixels. Small pixel sizes required deer to make a large

number of movements to cover most of the home range during a reasonable time interval.











Large pixel sizes required fewer movements to cover most or all of the home range;

however, these large pixels also drastically reduced the resolution of the habitat map. Use

of a lower resolution when developing the habitat map would have caused the loss of

many of the small tree islands and other small features of the landscape (K. E. Miller,

personal communication). If the large pixels used in the simulation model were 'too

large', simulated deer were less likely to find and utilize the smaller habitat features. A

compromise between the two extreme scenarios was to develop the simulation with 60-m

large pixels, each containing nine 20-m small pixels (Fig. 4.5).

In summary, simulated deer made multiple movements over a 5-day interval, the

interval over which simulated 'radio-locations' were taken. In the first stage of each

movement iteration, using 60-m pixels, deer moved a maximum distance of one pixel in






--60 m -


Figure 4.5. Two-stage movement process of a simulated deer using large 60-m pixels.
The hypothetical deer moved from the upper left 20-m pixel in the center 60-m pixel to
the lower right 20-m pixel in the lower left 60-m pixel.


=i - =











any direction. During this stage, a deer evaluated its surroundings and determined the

probability of moving to each pixel based on habitat, water depth, and relative location in

its home range. The second stage consisted of selecting a 20-m pixel, based on habitat

and water depth, within the 60-m pixel.

4.2.2. 60-m Movement Stage

In the first stage of a movement step, each deer evaluated its surroundings based

on habitat, water depth, and relative location in its home range. A relative affinity score, a

continuous, ratio variable, was assigned to each pixel for each factor. For example, if a

deer had to choose between two pixels, with relative affinity scores of 5 and 10, it would

be twice as likely to move to the pixel with a relative affinity of 10 than it would be to

move to the pixel with a relative affinity of 5. These scores were converted to

probabilities of moving to given pixels and averaged, using methods detailed below. Final

values for the relative affinity scores for each factor were determined during the

calibration process.

4.2.2.a. Habitat

Each 20-m pixel was assigned a relative affinity score based on habitat contained

inside the pixel. Initial values for the relative affinities (Table 4.1) were updated

throughout the calibration process. Relative affinity scores for the 60-m pixels were

determined using the mean relative affinity of the nine 20-m pixels it contained. The

mean relative affinity score for each 60-m pixel was standardized by converting it to a

probability:











affinity
p -= 9
Saffinityj
j=1


forj = 1,2,3,... ,9 and where pj was the probability of moving to pixelj based solely on

habitat, and affinity was the relative affinity score for pixelj. For example, if the nine 60-

m pixels to which a simulated deer could move had relative affinity scores for habitat of

20, 30,40, 10, 10, 50, 50,20, and 30, then the probability of moving to each pixel based

on habitat would be 0.08,0.11,0.15, 0.04, 0.04, 0.19, 0.19,0.08, and 0.11, respectively.


Table 4.1. Initial habitat relative affinity scores.
Habitat Symbol Relative affinity
Wet prairie AWPR 10
Herbaceous prairie AHPR 20
Tree island AT- 50
Willow/dense sawgrass AWSA 50
Cypress prairie/strand Acys 10
Pine Ap 10
Mangrove AMWN 1


4.2.2.b. Water depth

Water depth in each 20-m pixel was calculated from the water depth at P-34

(centrally located water gauge) and the relative elevations of each habitat (Section 2.2.2).

For model calibration, an annual water depth cycle was repeated for each year of the

simulation. This annual cycle was based on the average monthly water depth at P-34

during the collection of model calibration data (Table 4.2).

Water depth in each 60-m pixel was calculated as the mean depth of water in the

nine 20-m pixels it contained. A relative affinity score for each pixel was calculated as











[ rif depth < 8

affinity = a- (depth f) if f6 < depth < y
1 if depth > y



forj = 1, 2, 3,..., 9 and where a, P3, and y were the parameters with values determined

during the calibration process (Fig. 4.6). The relative affinity for each pixel was

standardized by converting it to a probability:

affinity
P =-- 9
L affinityj
j=1

forj = 1, 2, 3,..., 9 and where pj was the probability of moving to pixelj based solely on

water depth, and affinity was the relative affinity score for pixelj.


Table 4.2. Monthly water depths at P-34 for one annual cycle of the calibration
simulation, using average water depths for each month from April 1989 to March 1992.
Month Depth (cm) Month Depth (cm)
April -40.78 October 20.56
May -30.00 November 10.81
June -0.06 December -1.50
July 19.79 January -9.42
August 27.99 February -16.39
September 28.51 March -27.10

















0 1

0)


1 o .. .. .. ... ... ... .. . .. ...... .. ..... ................. .. .. . . ... ............. ...

P Y
Water depth



Figure 4.6. Relationship between water depth and relative affinity for moving to a
particular pixel, with the minimum affinity score set at 1. a, P3, and y were parameters
optimized in the model calibration.


4.2.2.c. Home range

Two algorithms utilizing the previous locations of a deer induce the formation and

maintenance of home ranges. A homing beacon encouraged movement towards the center

of the home range, and pixel memory encouraged deer to move to pixels visited in their

recent past (e.g., 2 months). A combination of the two algorithms was utilized because

neither performed adequately when used alone. The homing beacon produced circular

home ranges with little variation in size, and the pixel memory algorithm was not strong

enough to maintain the strong site fidelity of these deer. However, together these

algorithms produced home ranges that varied in shape and size and that maintained a

realistic degree of site fidelity in the simulated deer.

The homing beacon algorithm provided simulated deer with a stronger affinity for

pixels closer to their homing beacon, (home' y9home ) than away from their homing











beacon. The location of the homing beacon, based on k previous radio-location

coordinates (one taken every 5 days), was updated every 5 days using the moving

averages:
1
Xhome = (X, + x,-, + Xt-2+...+Xt-k+l)
1

Home = k(Y + Y,-\ + Yt-2+..+Yt-k+l)

where (x,, y,) were the coordinates of the most recent radio-location and (x,.,, y,.,) were the

coordinates of the radio-location taken 5 days earlier, etc. The window of time used to

calculate the location of the homing beacon encompassed the k prior radio-locations.

The relative affinity scores for the nine 60-m pixels to which the deer could move

were based on the direction of travel from the current location of the individual deer to

the homing beacon (Fig. 4.7). To avoid simulated deer from gradually shrinking their

home ranges due to a concentration of movements around the homing beacon, the

strength of the beacon, 6 (equal to 1, --, or 4)), was reduced exponentially as a deer

moved closer to its beacon:


. |^ if z~f
affinityij = if<
8 otherwise

z
forj = 1, 2 ,3,..., 9, and where 8 or 8 '/ was the relative affinity score, g was the

distance from the homing beacon at which relative affinity was constant, and z was the

distance from the current location to the homing beacon. The final values for 0 (>0) and

I.i (>0) were estimated through model calibration; in initial simulations, <(=3 and p=750

m.








61



(a) (b) (c)
1 1 1 1 A 1 l+2 1+
2 2 N

1 1 1 1 'A 'A 2
01+0 0

'A 'A 'A 1 'A 'A 2



Figure 4.7. Illustration of relative affinity calculations for the homing beacon, with the
homing beacon located southeast of the current location [center pixel of (a), (b), and (c)].
Affinity scores to move (a) towards the south and (b) towards the east were averaged to
give (c) 6 (equal to 1, L-, or (|) which was used to calculate the relative affinity scores of
moving to each of the nine possible pixels.

The pixel memory algorithm provided simulated deer with a stronger affinity for

previously visited pixels than for those not visited in the recent past. The relative affinity

score for pixelj was defined as

aA if pixel j visited during known memory
affinity = Ie
{ [ otherwise

forj = 1, 2, 3, ..., 9 and where I. (>1) was the relative affinity. Each simulated deer had

a map of its recent locations created with a moving window, containing all previous

locations of a deer for a given period of time (e.g., 2 months). This map was used to

assign relative affinity scores for each of the nine 60-m pixels a deer evaluated for each

step. The final value for X was estimated through model calibration; in the initial

simulations, 1=4.










The relative affinity scores for the homing beacon algorithm and for the pixel

memory algorithm for each of the nine 60-m pixels were standardized by converting them

to probabilities:

affinity
Pj- 9
L affinity j
j=1


forj = 1, 2, 3,..., 9 and where pj was the probability of moving to pixelj and affinity

was the relative affinity score for pixelj either for homing beacon or for pixel memory.

4.2.2.d. Combining movement factors

The probability of moving to each of the nine 60-m pixels was calculated, for each

of the four algorithms as described above. For each pixel, the probabilities for each factor

were averaged to give the probability of moving to each pixel:

1 4
Ir. =4-Y'.__


forj = 1, 2, 3,...., 9 and where pJ, P2j, P3j, and p4j were probabilities of moving to pixel

j based on habitat, water depth, homing beacon, and pixel memory, respectively. The deer

chose a 60-m pixel for its next location based on a random draw from the multinomial

distribution (n1, 72, 13,..., 19).

4.2.3. 20-m Movement Stage

The nine 20-m pixels contained inside the 60-m pixel of the location of the deer

were evaluated based on habitat and water depth. Relative affinity scores were used to

calculate the probabilities of moving to each 20-m pixel based habitat and based on water

depth. These probabilities were averaged to obtain the probability of moving to each of










the nine 20-m pixels:


-ID.P + P j
2 = 22ij p

forj = 1, 2, 3,..., 9 and where p '" and p were the probabilities of moving to the 20-m

pixelj based on habitat and water depth, respectively. The deer selected a 20-m pixel

based on a random draw from the multinomial distribution (nt',, it'2, 2'3t... 1t'9).

4.2.4. Simulation Initialization

The simulation began with 30 deer in a set of specified locations that were

representative of the home range centers of the deer included in the calibration data set.

Each deer started the simulation with no history or memory of previous locations. During

the time deer were building their initial memory map and homing beacon coordinates,

their movements were a function of habitat and water depth only. Once the simulation ran

for the length of the memory of a deer (e.g., 2 months), a deer began to use the home

range algorithms in its movement steps.

4.3. Model Calibration Experiments

In this section, the first two of a series of calibration experiments for females were

discussed. In these two experiments, only annual summary outcomes were evaluated;

however, data from later experiments were analyzed to explore and calibrate seasonal

patterns. These two experiments and subsequent experiments for females were described

in Appendix C, and calibration experiments for males were discussed in Appendix D.










4.3.1. First Calibration Experiment

The first experiment focused on the number of two-stage movement steps over a

5-day interval and parameter values for the home range algorithms (Table 4.3). A one-

half fraction of a 26 factorial design (i.e., 2"- fractional factorial) was used. This design

allowed estimation of all main effects and first-order interactions with 10 degrees of

freedom for experimental error, assuming higher-order interactions were negligible. Each

of the 32 EUs consisted of 30 deer with same starting coordinates, located in areas where

the majority of the study deer had resided.


Table 4.3. Factor levels for the first calibration experiment.
Factor description Symbol Low High
Maximum affinity for homing beacon 4 3 5
Distance (min) from homing beacon at which 1750
affinity is t 750 1750
Relative affinity for previously visited pixels 1 4 12
Memory length (5-day intervals) ML 12 36
Number of steps per 5-day interval STEP 100 300
Relative affinity score for tree islands and AWSA 30 50
willow/dense sawgrass.^ 3050


The movement algorithms in this experiment were those discussed in Section 4.2

with the exception of water depth. Since simulation bum-in time may have been

confounded with temporal effects of water levels, seasonally fluctuating parameters and

algorithms were not included. After several experiments were completed and a reference

value for bum-in time was estimated, water depth was included as a factor in the

simulation experiments (Table C.6). Until water depth was included in the model, the

probability of moving to each large-scale pixel was calculated as











1 1 1



forj = 1, 2, 3,..., 9 and where plj,p2j, andp3j were the probabilities of moving to pixel

j based on habitat, homing beacon, and location memory, respectively.

Simulations were run for an extended period of time to adequately estimate burn-

in time. At this stage of calibration of the simulation model, the main focus was to

simulate movement patterns of deer and understand the temporal and spatial dynamics of

the movement algorithms. Although longer than the expected life span of a white-tailed

deer, each EU was run for 15 years. Based on preliminary simulations, a simulation

length of 15 years was sufficient to determine if and when a steady-state had been reached

by the outcome measures (e.g., annual home range size and percentage of observations in

each habitat). Incorporating additional dynamics, such as recruitment and mortality,

would make the simulation more realistic, but adequate evaluation of the dynamics of the

movement algorithms would be difficult because of the potential for confounding.

Additionally, only 1 year of data (the year following experiment bum-in) from of each EU

was used for analysis of the factorial experiment, thus minimizing the effect of population

dynamics examined simulation outcomes.

For the simulated data to be comparable to observed data, 72 locations per year (1

per 5 days) were used to calculate outcome measures. Annual home range size, distance

between consecutive annual centers of activity, mean distance between consecutive

locations, and percentage of observations in each habitat were calculated and used as

outcome statistics.










A series of repeated measures ANOVAs was performed on the annual outcome

measures to estimate bum-in time. A separate analysis for each outcome for each of the

32 EUs was performed. These outcomes were annual home range size, distance between

consecutive annual centers of activity, mean distance between consecutive locations, and

percentage of radio-locations in each of the four major habitats in the study area (i.e., wet

prairie, herbaceous prairie, tree islands, and willow/dense sawgrass). Several covariance

structures were evaluated before testing specific hypotheses regarding temporal trends.

Compound symmetry assumed equal correlation among all years. An auto-correlation

structure assumed correlation among years was a function of "distance" between any pair

of years (i.e., the correlation between outcomes from year i and year was equal to p-"). A

heterogenous auto-correlation structure was similar to an auto-correlation structure, with

additional parameters to estimate variances for each year. Akaike Information Criterion

values (AICs), log-likelihood values penalized for the number of estimated parameters

(Akaike 1974), were compared to determine the most appropriate structure for each

outcome measure. For distance between consecutive annual centers of activity, mean

distance between consecutive locations, and percentage of radio-locations in each of the

four major habitats, the auto-correlation structure provided the best fit. For annual home

range size, the heterogenous auto-correlation structure provided the best fit. Tests for

linear time trends were used to estimate bum-in time for each EU for each outcome.

Based on an a-level of 0.01, the maximum burn-in time was estimated at 4 years, so

summary data from the 5th year of simulation were used to evaluate the adequacy of the

simulation model parameters (Tables 4.4 and 4.5). Data from the 6th year to the 15' year

of the simulations were not used in the following analyses.











Table 4.4. Summary outcome measures of home range size, distance between
consecutive home range centers, and distance between consecutive locations from first
calibration experiment for adult females from the 5th year of simulation.


(I) I X ML STEP


3 750 4 12
3 750 4 12
3 750 4 36
3 750 4 36
3 750 12 12
3 750 12 12
3 750 12 36
3 750 12 36
3 1750 4 12
3 1750 4 12
3 1750 4 36
3 1750 4 36
3 1750 12 12
3 1750 12 12
3 1750 12 36
3 1750 12 36
5 750 4 12
5 750 4 12
5 750 4 36
5 750 4 36
5 750 12 12
5 750 12 12
5 750 12 36
5 750 12 36
5 1750 4 12
5 1750 4 12
5 1750 4 36
5 1750 4 36
5 1750 12 12
5 1750 12 12
5 1750 12 36
5 1750 12 36


100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100
300
100


ATUWSA

30
50
50
30
50
30
30
50
50
30
30
50
30
50
50
30
50
30
30
50
30
50
50
30
30
50
50
30
50
30
30


300 50 785 536 790


II


Home range Annual center
size (ha) shift (m)
563 1134
709 1181
502 703
815 453
436 913
734 920
543 1118
539 681
792 1460
1426 1523
715 862
1044 588
698 1411
953 1292
638 1381
1058 1318
428 538
568 351
474 646
538 372
397 432
474 362
356 424
519 337
662 625
831 565
528 746
951 504
487 710
908 568
556 589


5-day
distance (mn)
486
737
503
800
458
738
465
685
499
830
524
842
482
741
470
776
496
747
509
734
499
724
481
721
530
826
493
847
487
819
502











Table 4.5. Summary outcome measures of percentage of radio-locations in each habitat
from first calibration experiment for adult females from the 5th year of simulation.
I ML STE A S Percentage of radio-locations in each habitat
*__ ML STEP ATBWSA WPR HPR TRE WSA CYP MAN


750
750
750
750
750
750
750
750
1750
1750
1750
1750
1750
1750
1750
1750
750
750
750
750
750
750
750
750
1750
1750
1750
1750
1750
1750
1750
1750


4 12 100
4 12 300
4 36 100
4 36 300
12 12 100
12 12 300
12 36 100
12 36 300
4 12 100
4 12 300
4 36 100
4 36 300
12 12 100
12 12 300
12 36 100
12 36 300
4 12 100
4 12 300
4 36 100
4 36 300
12 12 100
12 12 300
12 36 100
12 36 300
4 12 100
4 12 300
4 36 100
4 36 300
12 12 100
12 12 300
12 36 100
12 36 300


37.2 33.0 14.5
32.7 23.2 26.5
43.0 17.3 24.2
40.3 27.5 21.9
28.1 24.6 32.0
31.1 30.2 23.8
43.5 22.9 19.0
24.3 24.2 33.7
36.9 18.1 26.2
34.1 33.1 16.6
48.2 21.6 16.1
29.3 29.8 24.9
38.0 28.4 17.4
23.3 28.2 34.2
41.5 16.5 20.1
38.3 26.9 19.5
30.3 28.6 23.6
43.1 31.2 16.9
46.7 28.5 15.4
31.9 21.6 27.5
42.6 28.4 16.5
33.6 21.9 28.3
45.0 14.4 25.3
30.2 31.5 28.5
43.5 31.3 15.9
34.1 20.6 29.2
30.4 22.9 25.3
41.1 26.8 20.0
31.8 22.0 27.1
37.3 36.2 17.0
41.8 25.4 18.1
31.1 24.6 28.0


5.0
4.4
1.7
0.9
1.5
3.3
5.0
2.3
6.3
4.7
1.3
3.7
5.6
1.1
6.3
4.7
4.1
0.8
0.5
0.9
3.1
1.9
1.7
1.4
1.4
2.4
5.2
1.2
1.7
0.6
2.9
3.3


" WPR=wet prairie, HPR=herbaceous prairie, TRE--tree island, WSA=willow/dense
sawgrass, CYP=cypress/pine, MAN=mangrove/mangrove-prairie transition.


v.m








69
For each of the summary outcome measures of annual home range size, distance

between annual centers of activity, and distance between consecutive radio-locations, a

discrepancy measure (DM) was calculated. First, for each EU, the mean outcome measure

was calculated (e.g., mean home range size for 30 deer in the 6th year of the simulation for

the i"' EU). Then, for each EU and for each summary outcome, the DM was calculated as

D(x) = -P(x)-0i


for i = 1,2,3,..., 32 and where 0 was the observed summary outcome and P/x) was the

summary outcome from the /h EU based on the simulation model. On an annual basis, the

observed summary statistics for females were mean home range size of 271 ha, mean

distance between consecutive centers of 307 m, and mean distance between consecutive

locations of 686 m (Section 3.3.1).

For the summary outcome measures of percentage of observations in each habitat,

a discrepancy measure (DM) also was calculated. First, for each EU, the mean outcome

measure was calculated (e.g., mean percentage of observations in wet prairie for 30 deer

in the 6th year of the simulation for the ih EU). The DM for habitat use was calculated for

the Ith EU as

6 (i ..(X ) 0 j

j=I O1


for i = 1,2,3,..., 32 and where 0O was the mean percentage of time observed deer were

radio-located in habitat and Po(x) was the mean percentage of time simulated deer were

located in habitat. On an annual basis, the observed summary statistics for females were










50%, 17%, 17%, 9%, 2%, and 2% of radio-locations in wet prairie, herbaceous prairie,

tree islands, willow/dense sawgrass, cypress/pine, and mangrove, respectively (Section

3.3.1).

An ANOVA to test for main effects and first-order interactions of the evaluated

simulation parameters was performed for each of the four DMs (Table 4.6). Statistical

significance was determined using an a-level of 0.05; however, effect size (i.e., relative

decrease in the DMs) also was taken into account when determining the most influential

factors and the levels to be used in the subsequent simulation experiment.

All average home range sizes of the simulated females were larger than those of

females observed in the field. The DM for home range size was significantly smaller with

smaller $, smaller R, larger ., smaller STEP, and larger ATmWsA (see Table 4.3 for factor

descriptions). Distance between consecutive annual centers ranged from very close to the

observed average to more than three times the observed average. The DM for distance

between consecutive centers was reduced with larger 4, smaller iX, and a longer ML.

Average distance between consecutive locations ranged from 458 m to 847 m,

encompassing the observed value of 686 m. The DM for mean distance between

consecutive locations was significantly smaller with smaller Ii and larger STEP. Also,

there were significant interactions between X and STEP and between ATWSA and STEP.

The interaction between and STEP indicated that when STEP=-100, an increase in A

caused an increase in the DM and when STEP=300, an increase in X caused a decrease in

the DM. The interaction between ATUwsA and STEP indicated that when STEP=100, an

increase in AmwsA caused an increase in the DM, and when STEP--300, an increase in

ATmwsA caused a decrease in the DM.











Table 4.6. Summary of ANOVA results (p-values) from the first calibration experiment
for each DM from the 5h year of simulation.
r ^c *Home Annual 5-day ..,
Experiment Factor Home Annual 5y Habitat use
ExermntFctr range size center shift distance Hbau
S0.0001 0.0001 0.6471 0.2707
S0.0001 0.0030 0.0013 0.8645
S0.0020 0.5000 0.1600 0.2588
ML 0.1853 0.0277 0.8252 0.0475
STEP 0.0001 0.0708 0.0001 0.0279
ATRwsA 0.0014 0.7571 0.4403 0.4109
* t 0.1642 0.2315 0.1686 0.9795
4) *A. 0.2139 0.1823 0.4383 0.3754
S* 0.4672 0.3137 0.6073 0.7999
4) ML 0.2764 0.0274 0.8643 0.2044
ML 0.2264 0.6255 0.5227 0.4663
ML 0.3905 0.0568 0.3659 0.9218
*STEP 0.0739 0.9324 0.1663 0.5359
STEP 0.0008 0.7396 0.0001 0.6528
STEP 0.3346 0.8458 0.0005 0.1028
ML STEP 0.5827 0.2778 0.7040 0.2202
ATRE,WSA 0.3688 0.5001 0.2724 0.3010
T* ARWSA 0.4406 0.9300 0.3113 0.3871
S*AARE,WSA 0.8761 0.6816 0.7797 0.8811
ML ATwsA 0.6918 0.6783 0.9174 0.4974
STEP Al, ,pA 0.0905 0.6761 0.0217 0.9590


Habitat use patterns of the simulated female deer (Table 4.5) were not comparable

to those of the observed female deer (Table 3.2). Simulated females were observed in tree

islands and herbaceous prairie more and wet prairie less than observed females, indicating

a need for further evaluation of relative habitat affinities. An increase in ML and a

decrease in STEP caused a decrease in the DM for habitat use. ATR,wsA and its associated

interactions had no significant effect on the DM, perhaps because the overall agreement


was poor.









72

In addition to quantitative analyses of simulation results, qualitative observations

also aided in the verification and calibration processes. Movement paths of simulated and

observed female deer residing in the same area on the landscape were plotted and

compared. For example, during a 1-year interval, one simulated deer had a realistic

movement pattern when compared to an observed deer (3-year-old female) in the same

geographic area; however, the movement paths of all simulated deer were not similarly

realistic, indicating the model still needed improvement (Fig. 4.8).

The outcome measures that had the greatest disagreement with the observed

summary data were home range size and habitat use. Analysis results for each summary

outcome indicated a direction in the parameter space to move in order to minimize the

DM; however, these directions were contradictory for several of the DMs. So, for the

subsequent experiment, current parameter settings were maintained. Instead, I focused on

minimizing the habitat use discrepancies by including additional factors (e.g., relative

affinities for herbaceous prairie, willow/dense sawgrass, cypress, pine, and mangrove) in

the following experiment.

4.3.2. Second Calibration Experiment

The second experiment focused on the number of steps over a 5-day interval,

parameter values for the home range algorithms, and values for relative habitat affinities

(Table 4.7). A 2"' fractional factorial design was used, which allowed estimation of all

main effects with 20 degrees of freedom for experimental error, assuming interactions

were negligible. As in the first experiment, each of the 32 EUs consisted of 30 deer,

starting in the same locations, simulated for a 15-year time interval. The movement

algorithms were not changed from those used in the first calibration experiment.













































SWet Prairie [-- Tree Island
=" Herbaceous Prairie M Willow/dense sawgrass


Figure 4.8. Examples of observed and simulated deer movement paths over a 1-year time
period. (a) observed adult female; (b) observed adult female; (c) simulated female
exhibiting a movement path comparable to the observed females; and (d) simulated
female not exhibiting typical site fidelity of observed females.










Table 4.7. Factor levels for second calibration experiment.
Factor description Symbol Low High
Maximum relative affinity for homing beacon ( 3 5
Distance (min) from homing beacon at which 7 1
affinity is I 750 1750
Relative affinity for previously visited pixels A 4 12
Memory length (5-day interval) ML 12 36
Number of moves per 5-day interval STEP 100 300
Relative affinity for herbaceous prairie AHPR 20 30
Relative affinity for tree islands Am- 20 50
Relative affinity for willow/dense sawgrass AwSA 30 50
Relative affinity for cypress Acys 5 15
Relative affinity for pine ApN 5 15
Relative affinity for mangrove AMAN 1 10


Annual home range size, distance between consecutive annual centers of activity,

mean distance between consecutive locations, and percentage of observations in each

habitat were the calculated outcome measures. Using the outcome measures for each of

the 15 years of simulation, repeated measures ANOVA was conducted to estimate bum-in

time, with a separate analysis for each outcome for each of the 32 EUs. Correlation

structures providing the best fit to the data for each outcome were the same as in the first

experiment. For distance between consecutive annual centers of activity, mean distance

between consecutive locations, and percentage of radio-locations in each of the four

major habitats, the auto-correlation structure provided the best fit. For annual home range

size, the heterogenous auto-correlation structure provided the best fit. Tests for linear

time trends were used to estimate bum-in time for each EU for each outcome. Based on

an a-level of 0.01, the maximum bum-in time was estimated at 5 years; thus, summary








75
data from the 6th year of simulation were used to evaluate the adequacy of the simulation

model parameters (Tables 4.8 and 4.9).

DMs were calculated for annual home range size, distance between consecutive

radio-locations, distance between annual centers, and habitat use for each of the 32 EUs

as in the first experiment. In addition to the four DMs, a mean discrepancy (MD) for each

EU was also calculated:


_M = I (D :DHR + 1 D5D 5D + (DCS +cs) + (DHU ;HUJI
MD = s. ----s ---- + --- +----
4_l S S^ ) SCS I SH )


where DHR,Dcs, DjD, and DHu were the discrepancies for home range, annual center shift,

5-day distance, and habitat use (Table 4.9). D5HR, Dcs, DD, and DHU were the mean

discrepancies and SHnR, Scs, So, and SHu were the standard deviations for home range,

annual center shift, 5-day distance, and habitat use discrepancies for this experiment. This

measure provided an indication of the factors evaluated in the experiment that had the

greatest effect on lack-of-fit of the simulation model output when averaging over all

DMs.

An ANOVA testing for main effects of the evaluated simulation parameters was

performed for the each of the four DMs and MD using a significance level of 0.05 (Table

4.10). The DM for home range size was significantly smaller with smaller 4), smaller u,

larger X, smaller STEP, and larger ATRE (see Table 4.7 for factor descriptions). The DM

for distance between consecutive annual centers was reduced with larger 4), smaller p,

longer ML, and larger STEP. The DM for mean distance between consecutive radio-

locations was significantly smaller with larger STEP. The DM for habitat use was










Table 4.8. Summary outcomes of home range size, shift in annual centers, distance between consecutive locations, DM for habitat use,
and mean discrepancy (MD) from second calibration experiment for adult females for the 6th year of simulation.
SML STEP A A A A A A Home range Annual center 5-day Chi-
p A ML STP APR AT Aws Acs A A size (ha) shift (m) distance (m) square M
3 750 4 12 100 30 50 50 15 5 1 598 1217 480 40.5 0.32
3 750 4 12 300 20 20 30 5 5 1 893 1025 771 53.9 0.27
3 750 4 36 100 30 50 30 15 15 10 553 660 508 27.7 -0.37
3 750 4 36 300 20 20 50 5 15 10 885 563 822 23.9 -0.25
3 750 12 12 100 20 20 50 15 5 10 541 1378 467 23.4 0.18
3 750 12 12 300 30 50 30 5 5 10 604 861 702 73.3 -0.17
3 750 12 36 100 20 20 30 15 15 1 530 642 511 66.2 0.10
3 750 12 36 300 30 50 50 5 15 1 683 439 777 55.1 -0.32
3 1750 4 12 100 30 20 30 5 15 10 761 1663 507 78.3 1.22
3 1750 4 12 300 20 50 50 15 15 10 1098 1268 810 57.5 0.87
3 1750 4 36 100 30 20 50 5 5 1 799 864 529 29.7 0.00
3 1750 4 36 300 20 50 30 15 5 1 1094 729 846 31.0 0.29
3 1750 12 12 100 20 50 30 5 15 1 641 1539 472 16.9 0.30
3 1750 12 12 300 30 20 50 15 15 1 1107 1379 774 51.2 0.73
3 1750 12 36 100 20 50 50 5 5 10 612 765 499 29.2 -0.18
3 1750 12 36 300 30 20 30 15 5 10 1061 595 836 71.6 0.67
5 750 4 12 100 20 50 50 5 15 1 488 1026 465 19.9 -0.15
5 750 4 12 300 30 20 30 15 15 1 571 662 694 74.8 -0.35
5 750 4 36 100 20 50 30 5 5 10 407 412 489 33.9 -0.55
5 750 4 36 300 30 20 50 15 5 10 568 345 758 62.5 -0.49









Table 4.8. continued.
4 1 ML STEP AHPR AT AwsA Ac A A Home range Annual center 5-day Chi-
S ML S P AHpR ARE Aws Acs Ap A, size (ha) shift (m) distance (m) square M
5 750 12 12 100 30 20 50 5 15 10 399 911 461 48.9 0.07
5 750 12 12 300 20 50 30 15 15 10 468 714 667 49.4 -0.74
5 750 12 36 100 30 20 30 5 5 1 394 377 488 66.1 -0.15
5 750 12 36 300 20 50 50 15 5 1 471 288 710 38.4 -1.12
5 1750 4 12 100 20 20 30 15 5 10 730 1551 503 11.9 0.23
5 1750 4 12 300 30 50 50 5 5 10 872 1098 771 42.9 0.15
5 1750 4 36 100 20 20 50 15 15 1 631 817 522 36.7 -0.11
5 1750 4 36 300 30 50 30 5 15 1 879 474 812 51.6 0.01
5 1750 12 12 100 30 50 30 15 5 1 565 968 461 43.6 0.23
5 1750 12 12 300 20 20 50 5 5 1 850 1248 741 26.0 -0.12
5 1750 12 36 100 30 50 50 15 15 10 570 714 512 24.7 -0.37
5 1750 12 36 300 20 20 30 5 15 10 862 532 836 29.3 -0.18










Table 4.9. Summary outcome measures of percentage of observations in each habitat from the second calibration experiment for adult
females for the 6th year of simulation.


1A I ML STEP AHpR ATRE AwsA ACYS ApIN


750
750
750
750
750
750
750
750
1750
1750
1750
1750
1750
1750
1750
1750
750
750
750
750


Percentage of observations in each habitat"
WPR HPR TRE WSA CYP MAN

1 24.4 34.4 24.7 5.0 2.6 0.1
1 32.8 42.9 13.4 3.5 0.8 0.0
10 35.5 27.2 25.3 2.3 5.3 0.3
10 34.0 32.1 13.5 5.2 0.4 2.0
10 40.7 26.6 10.6 4.4 6.1 0.0
10 18.3 38.3 32.6 1.7 0.5 4.2
1 42.1 27.0 10.3 2.5 11.9 0.1
1 23.5 38.5 26.9 4.4 0.4 0.0
10 31.3 48.9 10.6 2.9 0.3 0.3
10 20.8 27.1 29.2 3.7 8.3 1.3
1 42.7 33.8 6.8 4.7 0.7 0.0
1 31.9 29.4 26.7 2.3 4.1 0.6
1 40.5 23.2 21.9 2.5 5.0 0.5
1 33.8 39.0 9.4 3.3 5.6 0.0
10 29.3 22.4 30.9 3.5 2.0 4.1
10 29.2 44.0 10.2 2.3 6.4 3.1
1 36.6 21.9 28.9 4.4 0.4 0.4
1 32.4 47.1 8.5 2.2 4.1 0.1
10 33.9 26.8 32.2 2.1 0.0 0.9
10 28.1 43.8 7.7 4.4 2.8 3.2


12 100 30
12 300 20
36 100 30
36 300 20
12 100 20
12 300 30
36 100 20
36 300 30
12 100 30
12 300 20
36 100 30
36 300 20
12 100 20
12 300 30
36 100 20
36 300 30
12 100 20
12 300 30
36 100 20
36 300 30










Table 4.9. continued.
Percentage of observations in each habitat
4) X ML STEP AR An AWSA ACs Ap Au WPR HPR TRE WSA CYP MAN
5 750 12 12 100 30 20 50 5 15 10 28.6 40.0 12.4 4.9 0.1 3.8
5 750 12 12 300 20 50 30 15 15 10 26.1 18.9 36.2 2.8 5.8 4.1
5 750 12 36 100 30 20 30 5 5 1 35.1 45.9 9.7 3.0 0.1 0.0
5 750 12 36 300 20 50 50 15 5 1 23.9 24.6 32.8 5.3 3.5 0.2
5 1750 4 12 100 20 20 30 15 5 10 46.9 27.0 10.9 4.0 1.5 1.3
5 1750 4 12 300 30 50 50 5 5 10 24.0 30.7 29.6 3.7 0.2 3.9
5 1750 4 36 100 20 20 50 15 15 1 35.1 26.5 13.4 4.9 8.5 0.3
5 1750 4 36 300 30 50 30 5 15 1 26.4 36.3 29.3 2.5 0.2 0.6
5 1750 12 12 100 30 50 30 15 5 1 26.5 34.2 27.5 3.1 0.9 0.0
5 1750 12 12 300 20 20 50 5 5 1 36.9 33.0 14.4 4.4 0.4 0.0
5 1750 12 36 100 30 50 50 15 15 10 34.6 30.8 22.5 2.9 0.5 1.9
5 1750 12 36 300 20 20 30 5 15 10 40.2 35.3 12.6 3.6 0.6 0.5
SWPR=wet prairie, HPR=herbaceous prairie, TRE=--tree island, WSA=willow/dense sawgrass, CYP=cypress/pine,
MAN=mangrove/mangrove-prairie transition.










significantly smaller with smaller AHPR. Overall, habitat use of the simulated deer

exhibited strong lack of fit evidenced by the large values of the chi-square DM and the

mean percentage of observations of simulated deer in each habitat. Adjustments to

relative affinity scores for the subsequent experiment were made based on the mean

percentage of radio-locations in each habitat for each of the relative affinities (Table

4.11).


Table 4.10. Summary of ANOVA results (p-values) from the second calibration
experiment for each DM and the mean discrepancy for the 6h year of simulation.
Experiment Home range Annual 5-day Habitat use Mean
Factor size center shift distance Hbtu discrepancy
4) 0.0001 0.0001 0.3439 0.4387 0.0001
11 0.0001 0.0001 0.1761 0.1647 0.0001
X 0.0024 0.1313 0.7828 0.6787 0.1625
ML 0.6581 0.0001 0.4619 0.6956 0.0005
STEP 0.0001 0.0001 0.0001 0.0367 0.3152
AHPR 0.6133 0.0504 0.5917 0.0029 0.1293
ATRB 0.0309 0.0448 0.9891 0.1876 0.0238
AwsA 0.7129 0.1430 0.8878 0.0661 0.2955
AcYs 0.7703 0.7923 0.5421 0.7149 0.9397
Apnr 0.8733 0.7072 0.8288 0.6987 0.5496
AMA^N 0.6354 0.6388 0.7003 0.8825 0.9921


MD was significantly reduced with larger 4), smaller V, and longer ML. MD was

also reduced with larger AT". This finding was misleading because with larger ATR,

home range sizes had smaller discrepancies; however, concurrently, the percentage of

locations of individuals in tree islands was much higher than was observed in the field.

When plots of simulated female deer movement paths were reviewed, some individuals











were finding and concentrating their movements in tree islands and not moving into the

prairies, indicating a need to reevaluate some of the movement algorithms and

parameters.

For the subsequent simulation experiment, 1 was increased, and ApR, AT, and

AWsA, and AmAN were decreased. Because cypress and pine habitats were a minor

component of the habitat map and not this focus of the study, Acys and Apr were

combined as Acyp in future experiments.


Table 4.11. Mean percentage of radio-locations in each habitat for each relative affinity
score from the second calibration experiment for the 6th year of simulation.
Habitat3
Factor Levels WPR HPR TRE WSA CYP MAN
20 34 28 21 4 4 1
HR 30 30 38 18 3 2 1
20 36 37 11 4 3 1
50 29 29 29 3 2 1
30 33 34 20 3 3 1
WA 50 31 32 20 4 3 1
5 32 34 20 4 1 1
S 15 32 32 19 4 5 1
5 32 34 20 4 2 1
p 15 33 33 19 3 4 1
1 33 34 19 4 3 0
10 32 32 20 3 3 2
SWPR=wet prairie, HPR=herbaceous prairie, TRE--=tree island, WSA=willow/dense
sawgrass, CYP=--cypress/pine, MAN=mangrove/mangrove-prairie transition.











4.4. Final Movement Model

The model for adult females and for adult males was finalized after calibration

with the observed field data through a series of simulation experiments. The final

algorithms, parameter values, and factor weights used in the movement decisions were

determined through experimentation during the model calibration (Appendices C and D).

Several algorithms were changed from the initial description in Section 4.2, so all

movement algorithms were described in the following sections for completeness.

Because deer could not move off the map, the habitat map was considered a

closed environment. Initial locations of simulated deer were located randomly in the

study area at least 1.5 km from the perimeter of the habitat map (Fig. 4.9); however, there

was no 'repelling force' to prevent them from moving towards the edge of the map.

Simulated deer made multiple movements over a 5-day interval, the interval over

which simulated 'radio-locations' were taken. Each movement was a two-stage process.

In the first stage of each movement iteration, the deer moved a maximum of one pixel in

any direction, using 60-m pixels (Fig. 4.5). During this stage, the deer evaluated its

surroundings and determined the probability of moving to each pixel based on habitat,

water depth, and relative location in its home range. The second stage consisted of

selecting a 20-m pixel inside the 60-m pixel and was based solely on habitat and water

depth. Females made 200 two-stage moves per 5-day interval, and males made 250 two-

stage moves per 5-day interval.












-I

I--

II


I~.













8 0 8 16 Kilometers


S'BCNP I ENP boundary
aitat Classifications N
SWet Prairie
Herbaceous Prairie
Tree island
I Willowldense sawgrass
[] Dwarf cypress prairie
Cypress strand
SPine S
Mangrove/prairie transition
Mangrove


Figure 4.9. Starting locations of simulated deer were located randomly within the solid
black line (approximately 1.5 km from edge of habitat map).










4.4.1. 60-mn Movement Stage

Each 20-m pixel was assigned a relative affinity score based on habitat contained

within the pixel (Table 4.12). A habitat relative affinity score for a 60-m pixel was

determined using the mean relative affinity of the nine 20-m pixels contained within it.


Table 4.12. Habitat relative affinity scores for the final simulation model.
Habitat Relative affinity
Habitat
Female Male
Wet prairie 10 10
Herbaceous prairie 10 35
Tree island 35 100
Willow/dense sawgrass 40 150
Cypress prairie/strand 7.5 5
Pine 7.5 5
Mangrove 10 5


Water depth in each 60-m pixel was calculated as the mean water depth of the

nine 20-m pixels contained within it. A relative affinity score for each 60-m pixel was

calculated as

a if depth < 8

affinity= a (depth ) iff,# depth < y

1 if depth > y



forj = 1, 2, 3,.... 9 and where a=20, 3=10 cm, and y=40 cm for females and a=10,

13=30 cm, and y=60 cm for males (see Fig 4.6).

In addition to evaluating habitat and water depth in the current and the adjacent

pixels, deer used information on habitat and water depth from pixels in the vicinity of its










current location, but not adjacent to its current location (Fig. 4.10). The simulated deer

used the information regarding 'long-distance habitat' and 'long-distance water depth' in

these pixels to influence movement to the adjacent pixels.




60m-|












___*---*-__* ------ -9 ^^^^^^^^ *...-- --- -- ----- mll--- ------- --...
2 i







........ 4k ..... ..... .....
I -

















Figure 4.10. Calculation of relative affinities using pixels farther than the pixels adjacent
to the current location of a hypothetical deer (center 60-m pixel marked with a large X).
Each small square is a 60-m pixel, and the colors represent relative affinity scores
assigned to each 60-m pixel (based on either habitat or water depth). A deer could move
to any of the eight immediately surrounding 60-m pixels or stay in its current pixel. For
each of these neighboring pixels, the 'long-distance' relative affinity was the mean
affinity of the nine 60-m pixels associated with it. For example, the long-distance relative
affinity for the pixel southwest of the current location of the deer (horizontal hatch marks)
was the mean affinity score of the nine pixels further southwest (diagonal hatch marks).








86
The homing beacon algorithm provided simulated deer with an affinity for pixels

closer to their homing beacon, (Xome ,Yhome) The location of the homing beacon, based

on 24 previous radio-location coordinates, was updated every 5 days using the moving

averages:


Home = 2(XI + X-I + X-2+.""+X-23)
1
Yhome = -2(Y + Yt-l + Yt-2 +. Y-23)

where (x,, y,) were coordinates of the most recent radio-location, and (x,.-, y,._) were

coordinates of the radio-location taken 5 days earlier, etc. This window of time used to

calculate the location of the homing beacon encompassed the 24 previous radio-locations.

The relative affinity scores for the nine pixels to which the deer could move were

based on the direction of travel from the current location of the deer to the homing beacon

(Fig. 4.11). The strength of the beacon, 6 (equal to 1, 4, or <2), was reduced exponentially

as a deer moved closer to its homing beacon:


1f/ J if z affinity =
8 otherwise


forj = 1, 2, 3,..., 9, and where or 6" was the relative affinity score, |i was the

distance from homing beacon at which the relative affinity was constant, and z was the

distance from current location to homing beacon. For females and males, I=500 m.

By altering the value of (0 over the course of an annual cycle, seasonal changes in

movement patterns were simulated. For females, (=4 when water depth at P-34 (the

gauging station) was >0 cm, and 4<=3 when water depth at P-34 was <0 cm, enabling










them to travel farther during the dry season to simulate an expanding search for forage.

For males, the value of 4) decreased during rut to simulate the search for females. From

November through May, 4=3. During June, as males came into the rutting season, ;0=2.5.

During the peak of rut, from July to September, 4)=2. During October, as the rutting

season concluded, 4)=2.5.



(a) (b) (c)

1 1 1 1 4) 4) 1 N

4 ( 0 1 )) i) 2

4 ) 4) 1 ) 4) 4) (02 (02


Figure 4.11. Illustration of homing beacon relative affinity calculations, with the homing
beacon located southeast of current location [center pixel of (a), (b), and (c)]. Affinity
scores to move (a) towards the south and (b) towards the east are multiplied to give (c) 6
(equal to 1, 4), g02) which was used to calculate the relative affinity scores of moving to
each of nine possible pixels.


The pixel memory algorithm gave simulated deer a stronger affinity for previously

visited pixels than for unfamiliar pixels. Pixels visited in the immediate past were

avoided to prevent deer from moving to habitat with a high affinity (e.g., tree island) and

not venturing out of that habitat patch. For females, the relative affinity score for pixelj

was defined as

0.5 visited in previous 40 steps
affinity = 5.0 visited in previous 30 days (but not in previous 40 steps)
1.0 not visited in previous 30 days










forj = 1, 2, 3,..., 9. For males, the relative affinity score for pixelj was defined as

0.5 visited in previous 125 steps
affinity = 5.0 visited in previous 30 days (but not in previous 125 steps)
1.0 not visited in previous 30 days


for = 1,2,3,...,9.

The relative affinity scores for each pixel for each of the six factors (i.e., habitat,

long-distance habitat, water depth, long-distance water depth, homing beacon, and pixel

memory) were standardized by converting them to probabilities:

affinity,
Pij = 9
Z affinityij
j=1

forj = 1, 2, 3,..., 9 and where p. was the probability of moving to pixel j for factor i and

affinity, was the relative affinity score for pixelj for factor i.

For each of the nine pixels to which the deer could move, the probabilities for

moving to a pixel based on habitat (i.e., habitat inside the pixel under consideration and

habitat in the nine 'long-distance' pixels) or water depth were combined using a weighted

average. For females, the weighted averages for habitat and water depth were


Phabita = (0.8 x Padjacent habitat) + (0.2 x Plong.distanc habitat)

Pwa = (0.8 x padjact water) + (0.2 x plog1isa water)


Because males have a stronger affinity for wooded areas than females and tend to travel

farther, 'long-distance habitat' and 'long-distance water' were weighted more heavily








when calculating the probability of moving to a given pixel based on habitat or water
depth:

Habitat = (0-6 X Padjacent habitat) + (0.4 X Plong-ditance habitat)
Water= (0.6 X Pdjacent water )+ (0.4 x plong-distane water )


During the first 4 months of the simulation, deer initialized their memories for the
homing beacon and pixel memory algorithms. The probability of moving to' (/ = 1,2, 3,
.., 9) pixel was calculated as

I = (0.45 X phabitt ) + (0.45 x pwater) + (0.10 x Phoming beacon)

for females, and as

J = (0.45 x Phabitat) + (0.45 x Pwate) + (o.05x Phoning beacon) + (0.05 x Ppi, memory)

for males. Throughout the remainder of the simulation the probability of moving to theft
( = 1, 2, 3, ..., 9) pixel was calculated as

= (O.25 x Phabitat ) + (0.25 x Pwater) + (0.25 x Phomingbeacon) + (0.25X Ppixel memory)

for females. For males, the weights of the four factors depended on biological season. For
most of the year, the four factors were weighted as

j = +(0.35X ph + (0.15X pwater ) + (0.25 x Phomingbeacon) + (0.25x Ppixemmemory)

However, during rut (July, August, and September), simulated males had a reduced
weighting of habitat and an increased weighting of pixel memory on their movement










decisions; therefore, the four factors were weighted as

r = (0.23X Phabitat) + (0.12 X Pwatr)+ (0.25 X Phoming beacon) + (0.40X Ppxe memory)


Each deer chose a 60-m pixel for its next location based on a random draw from the

multinomial distribution (n,, n2, T3,..., T9).

4.4.2. 20-m Movement Stage

The nine 20-m pixels contained inside the 60-m pixel were evaluated based on

habitat and water depth. For females and males, probabilities of moving to each 20-m

pixel were calculated from relative affinity scores for habitat and water depth, and the

probabilities of moving to each pixel were calculated as


l(P )
= (p1+ p;j)


where p ', andp were the probabilities of moving to theft' 20-m pixel based on habitat

and water depth, respectively. The deer selected a 20-m pixel based on a random draw

from the multinomial distribution (t',, i'2, T'3,. .., t'9).

4.5. Evaluation Approach for the Final Movement Model

To evaluate performance of the final model, 50 runs of the simulation for females

and 50 runs of the simulation for males (each consisting of 30 individuals) were

conducted using the final model parameterization detailed in Section 4.4. Analyses of the

final models were done separately for each gender.

For bum-in evaluation, the annual outcome measures of home range size, distance

between consecutive home range centers, mean distance between consecutive locations,

and percentage of locations in each of the four major habitats (wet prairie, herbaceous










prairie, tree islands, and willow/dense sawgrass) were used. For each run of the

simulation, bum-in time was estimated, and based on these results, a bum-in time for the

simulation model was determined.

Once bum-in time was established for the final model, performance was evaluated

using data from the 1" year after completion of simulation bum-in. The mean annual

outcome measures of home range size, distance between consecutive home range centers,

mean distance between consecutive locations, and percentage of locations in each of the

habitats (wet prairie, herbaceous prairie, tree islands, willow/dense sawgrass,

cypress/pine, and mangrove) from the simulation were compared to the observed mean

annual outcome measures from the field data. Also, comparisons were made on a

hydrologic season basis, using the seasonal outcomes of home range size, distance

between consecutive locations, and percentage of locations in each of the four major

habitats (wet prairie, herbaceous prairie, tree islands, and willow/dense sawgrass).

Simulated deer that were radio-located in the cypress/pine or mangrove habitats were not

included in calculation of mean percentage of locations in the four major habitats. These

comparisons were performed using a predictive p-value analysis (Section 4.1.6) in which

the likelihood of the value of the observed outcome (i.e., mean from the field data) arising

as an outcome of the simulation was assessed.

4.6. Evaluation of the Final Movement Model for Females

Variability in outcome measures was high both among individuals (Figs. 4.12 and

4.13) and among simulation runs (Figs. 4.14 and 4.15). However, the variation in

outcomes was much larger among individuals within a simulation than among means for

each simulation run. Because of heterogeneity in habitat across the study site, a simulated










deer placed in one area of the map may have different habitat-use patterns than a deer

placed several kilometers away. The impact of habitat heterogeneity on the variance of

the outcome measures was minimized as the number of simulation runs increased.

Of the 50 simulation runs, 56% required no bum-in period (i.e., no significant

linear trend over time), 24% had a bum-in time of 1 year, 10% had a bum-in time of 2

years, 6% had a burn-in time of 3 years, and 4% had a bum-in time of>4 years. Based on

these results, data from the 4th year of simulation were used to evaluate the final model.

Home range size and distance between consecutive measurements initially

decreased from the 1 year to the 2" year and then stabilized for the remainder of the

simulation. This was due primarily to the fact that the home range algorithms had less

weight in the movement decision during the first 4 months of the simulation then they did

during the rest of the simulation run. The outcome measures that required the most time

to stabilize were the percentages of observations in wet prairie and in tree islands. On

average, percentage of observations in the tree islands tended to increase and percentage

of observations in wet prairie tended to decrease for the first several years of the

simulation. This trend was not present in all runs of the simulation (e.g., the simulation

run depicted in Fig. 4.12 and 4.13). For this randomly selected run, several individual

deer showed an increase in percentage of observations in tree islands, and one showed an

increase in percentage of locations in the herbaceous prairie; but most deer appeared to

exhibit consistent habitat-use patterns over time. For this particular experimental run,

there was no significant linear trend over time (i.e., no bum-in period) for any of the

outcome measures.




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