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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/ behavior of individual organisms, and the relationship between realistic models in application to public policy issues involving endangered species presents new challenges to enable us to of parallel computing architectures enables us to conceptualize discuss how these models may be extended using agent-based approaches to deal with issues such as underlying spatial ). A key segment of the ATLSS hierarchy includes models that follow the 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 appropriately project animal movements. Additionally, the availability 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 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 classic diffusion equation of the form
t n
f
(
n
) (
D
n
)
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
These may be modified to include:
•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 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
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.
The Florida Panther Example
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 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.
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.
Major objectives of individual-based models are to:
•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:
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.) 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). 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.
References
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. Kerkhoff, A. J., B. T. Milne, and D. S. Maehr. 2000. Toward a panther centered 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
Individual-Based Models Cape Sable Seaside Sparrow Snail Kite Wading Birds White-tailed Deer Florida Panther Radio-telemetry Tracking Tools Age/Size Structured Models Linked Cell Models Process Models Fish Functional Groups Alligators Lower Trophic Level Components Reptiles and Amphibians Vegetation Spatially-Explicit Species Index Models Cape Sable Seaside Sparrow Snail Kite Long-legged Wading Birds Short-legged Wading Birds White-tailed Deer Alligators Abiotic Conditions Models High Resolution Topography High Resolution Hydrology Disturbance © 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:
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.
Comparing models to data:
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 speed ups 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.
Movement rules for individual-based models - the Florida panther example
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 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.
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, 100 m 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:
•
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
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.
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.