Modeling Animal Movements: Current Approaches and Challenges
LOUIS J. GROSS and E. JANE COMISKEY
The Institute for Environmental Modeling
Department of Ecology and Evolutionary Biology
University of Tennessee, Knoxville, TN 37996-1610
Abstract
The ATLSS (Across Trophic Level System Simulation) hierarchy of models
is designed to utilize varying levels of detail and data availability to
assess the relative impact of alternative hydrological plans on the biotic
components of South Florida. ATLSS is being used regularly in the
ongoing planning for Everglades restoration (see http://atlss.org/). A
key segment of the ATLSS hierarchy includes models that follow the
behavior of individual organisms, and the relationship between
individuals and underlying habitat and environmental conditions. The
combination of individual-based modeling methods, advances in
telemetry information for locations of individuals, and the demands for
realistic models in application to public policy issues involving
endangered species presents new challenges to enable us to
appropriately project animal movements. Additionally, the availability
of parallel computing architectures enables us to conceptualize
movement models in new ways that serial implementations would
preclude. We here summarize the advantages and disadvantages of
classic movement models based upon diffusion assumptions, and
discuss how these models may be extended using agent-based
approaches to deal with issues such as underlying spatial
heterogeneity, barriers and corridors, and territoriality. This includes
methods to link dynamic movement models to geographic information
systems, and developing appropriate statistics to compare modeled
movement to telemetry data. Applications to the Florida panther are
shown as a case study, relative to assessing the impacts of alternative
hydrologic plans for the restoration of the Everglades of South Florida.
Limitations of Diffusion-based Models for Animal
Movement within Home Range
The Florida Panther Example
•Consider individual variations in factors such as sex, size, age, health,
social status, etc.
•Include spatially-explicit information on habitat, roads, topography, etc.
and the effects these have on individual behavior.
•Provide mechanism for interactions between individuals.
•Allow for dynamic coupling of habitat components to organisms
through direct feedback of organism behavior on appropriate habitat
conditions, such as reducing available forage due to effects of
individuals.
•Provide mechanisms to take into account detailed behavioral and
physiological information when available.
•Estimate larger-scale phenomena (e.g. population/community) from
actions of individuals
General issues associated with movement rules for
individual-based models:
Home range of panther #49, with telemetry
points connected in time sequence
Home range boundaries of a female Florida
panther (in black) and her male (blue) and female
(red) offspring.
Comparison of panther movement patterns for wet (right) and dry (left) seasons
n  f (n)    ( Dn)
t
assumes:
•Movements follow a random walk
•Probabilities for movement in particular directions depend
on current location
•Step size in the walk are repeated small steps
•Biased movement with attraction to a central location
•Probability distributions for various turning angles and step
sizes
•Turning rate driven by local resource availability
•Boundary constraints with biased movement at boundaries
•Movement biases determined by difference between local
and spatiallyaveraged factors
For application to endangered species affected by the
spatially dynamic patterns of water in South Florida, the ATLSS
project has chosen an individual-based approach.
2. How to derive from available movement data a simplified set of rules
for the model, including what environmental or habitat characteristics are
essential to include and which can be ignored, under what
circumstances movement is modified by loaction of con-specifics,
potential prey or potential predators, and what history-dependence
occurs (e.g. what memory there is in the sytem).
References
Comparison of activity ranges of male and female panthers. Male ranges seldom overlap with
those of other males, but generally include the ranges of several females. Female ranges often
overlap. The territory of dominant male #12 (border outlined with solid line) includes the
territories of five female panthers (borders outlined with dashed lines.) Overlapping female
ranges are often mother/daughter pairs, as females disperse close to their natal ranges.
Abbott, C. A., M. W. Berry, E. J. Comiskey, L. J. Gross and H.-K. Luh (1997)
Computational models of white-tailed deer in the Florida Everglades. IEEE
Computational Science and Engineering 4:60-72.
Comiskey, E. J., O. L. Bass, Jr., L. J. Gross, R. T. McBride and R. A. Salinas.
(2001) Panthers and forests in south Florida: an ecological perspective.
Conservation Ecology (submitted).
DeAngelis, D. L., L. J. Gross, M. A. Huston, W. F. Wolff, D. M. Fleming,
E. J. Comiskey, S. M. Sylvester. 1998. Landscape Modeling for Everglades
Ecosystem Restoration. Ecosystems 1:64-75.
DeAngelis, D. L., L. J. Gross, W. F. Wolff, D. M. Fleming, M. P. Nott and E. J.
Comiskey. 2000. Individual-based models on the landscape: applications
to the Everglades. P. 199-211 in J. Sanderson and L. D. Harris (eds.),
Landscape Ecology: A Top-Down Approach. Lewis Publishers, Boca Raton,
FL.
The limitations of these models are the difficulty of taking
account of:
•Local habitat features
•Differences in movement based upon age/stage/sex or
other individual characteristics
•Differences in movement due to time of day or season
•Interactions with conspecifics
•Estimating functions and parameters from telemetry data
1. How to appropriately analyze telemetry and other behavior data in
order to assess differences between individuals in movement and how
these are affected by underlying habitat, and spatio-temporal variation
in environmental conditions (e.g water depth, snow-pack, etc.)
3. How to appropriately compare modeled movements with data in order
to evaluate the reliability of the model to mimic the dynamics of
movement, the trajectories of individuals as well as the spatial patterns
that arise at a population level.
The classic diffusion equation of the form
These may be modified to include:
Major objectives of individual-based models are to:
Time series of movements of panthers #9 (mother of #10); #10 (subadult male offspring); and #12 (adult
male whose range includes that of female 9). As a kitten, #10 moves with his mother within her range,
undisturbed by the neighboring adult male #12. At about 18 months of age, #10 disperses from his
mother's range, into the heart of the range of #12, where he is killed by #12 within 2 months.
So the above data indicate movement differs with: (1) gender
and age; (2) time of year; (3) location of conspecifics; (4) habitat
characteristics.
Kerkhoff, A. J., B. T. Milne, and D. S. Maehr. 2000. Toward a panthercentered view of the forests of South Florida. Conservation Ecology 4(1):1.
[online] URL: http://www.consecol.org/vol4/iss1/art1.
Mellott, L. E., M. W. Berry, E. J. Comiskey, and L. J. Gross (1999) The
design and implementation of an individual-based predator-prey model
for a distributed computing environment. Simulation Theory and Practice
7:47-70.
Okubo, A. and L. Gross (2001) Animal movements in home range. Chapter
8 of A. Okubo and S. Levin (ed.) Diffusion and Ecological Problems (2nd
Ed.)
The ATLSS Hierarchy of Models
Movement rules for individual-based models - the Florida
panther example
Individual-Based
Models
Age/Size Structured
Models
Cape Sable
Seaside Sparrow
Snail Kite
White-tailed Deer
Wading Birds
Florida Panther
Fish Functional Groups
Alligators
Radio-telemetry
Tracking Tools
The model has different sets of movement rules for gender and status of
panthers in the population:
* movement with mother in the natal range
* dispersal from natal range
* transient sub-adult stage (males only)
* establishment of independent range
* movement within established home ranges
Reptiles and Amphibians
Linked Cell
Models
Lower Trophic Level Components
Vegetation
Process Models
Spatially-Explicit
Species Index Models
Cape Sable
Seaside Sparrow
Long-legged
Wading Birds
Short-legged
Wading Birds
White-tailed Deer
Alligators
Snail Kite
Abiotic Conditions
Models
High Resolution Topography
High Resolution Hydrology
Disturbance
Model rules must capture the requirement of panthers for large home ranges
as individuals and for large areas of contiguous, relatively undisturbed habitat
as a population, the solitary nature of their life, apart from mother/kitten
groups, their need for abundant large prey, the prevalent causes of mortality,
and likely outcomes of intra-specific encounters.
© TIEM / University of Tennessee 1999
Shown in red are the ATLSS components which are used for the Panther Model
Using telemetry data:
These data are typically not gathered continuously, but sampled at
particular times. The times of sampling may bias the locations found, as
may the accessibility of sites from which to assess movement (e.g near
roads), the ease of colaring or tagging certain individuals, and the
potential treatment effect of having a radio collar or other telemetry
device.
Deriving movement rules:
Simulated panthers move about on a simulated landscape of 500-m x 500-m
cells. When making a movement decision, panthers have access to
information about adjacent cells, and also to information about the
surrounding neighborhood of cells. A 500-m movement potential map is
created by weighting each cell with combined factors influencing movement,
drawn from multiple landscape layers. Weights are created by centering on
each cell a moving focal window of the finest scale resolution available for
each landscape layer (e.g. 30-m for habitat type, 500-m deer presence, 100m for water depth), and
assigning a value derived from information about cells within the window.
Natural land cover types are more likely to be selected; areas of human
activity are more likely to be avoided by panthers.
The factors affecting movement included in landscape layers are:
These may be limited by the geographic structure of the model (e.g. the
spatial resolution of underlying habitat data), serial implementations which
require an ordering relationship in the code as to which individuals are
treated sequentially during a simulation, the assumed percentual range of
individuals in terms of their capacity to be affected by other individuals
within some spatial neighborhood, and the assumed memory by which
individuals may either have history-dependent movement or have a proxy
(e.g. territorial marking) which provides an inherent history (when one adds
time-decay of marks) without an explicit memory.
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Comparing models to data:
This weighting map simulates knowledge that panthers have about their
environment from daily travel and from likely sensory input (sight, hearing,
smell). Dispersing animals are given less information about their immediate
environment, moving more by trial and error.
Simulations offer the potential to compare in great detail the simulated
movement of individuals to data. The simulations can include surveys
carried out in the same way as field surveys are done in order to provide
appropriate comparison samples from the model simulations. These may
then be resampled in order to provide model distributions of a wide variety
of statistics (home range size, patterns of home range use, correlations
between locations and habitat/environmental conmditions, nearest
neighbor distances, etc.) which may then be compared to observations.
Parallelization and individual-based models:
Usual arguments for the use of parallel computing methods rely on the speedups possible through the use of multiple processors. An alternative view of the
utility of paralellization is appropriate for individual-based models due to the
limitations imposed on model assumptions by serial implementations. A result of
previous research is that moving to a parallel scheme can change the
underlying model assumptions - this is not parallelizing a serial code but
rethinking the model itself. In reality, organisms do not act in parallel but
synchronously. Parallel architectures allow for concurrency in the model where
individuals handled by different processors act in synchrony. An efficient
method for this is through spatial grid-partitioning. This allows for synchronous
movement of individuals and obviates the need for randomization schemes for
order of action required in serial implementations of individual-based models.
The objective is not necessarily speedup (though that may arise and be
particularly important for the multiple simulations needed for sensitivity and
control applied to these models), but realism.
utilized habitat types present (e.g. amount of cover, hunting edge)
intensity of land use (urban/ag/grazing)
distance from urban patches
density and type of roads
barriers and impediments to movement
water depths on the landscape
proximity to other panthers
information about the gender and reproductive status of other panthers
availability of prey
Movement rules are specific to the activity being pursued (hunting, mating,
denning), account for individual differences such as gender, age, size,
reproductive status, time since last meal, etc. Rules are mediated by scent
markings recorded in cells and by a place memory that each individual
carries of past events, such as where kills have been made, where deer have
been seen. Decision-making is stochastic, based on comparison of a random
number with a set of probabilities.
Parameters such as likely dispersal distances are taken from telemetry data
which capture dispersals in the South Florida population. For example, so far
no female panthers have dispersed naturally away from the natal range
(though several have been translocated). Mean observed overlap of female
ranges with the natal range is 59%, while it is rare that male ranges overlap at
all with the range of their mother.
ATLSS models are always used in a relative
assessment framework. We do not claim these
models are able to predict the exact abundance
and distribution of panthers in the future. Rather,
they provide a relative ranking of the effects of
alternative management scenarios on the various
speces modeled, based upon the best scientific
information available.