Analytic steady-state space use patterns and rapid computations in mechanistic home range analysis

A. H. Barnett; P. R. Moorcroft

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arXiv · 0705.3473

Analytic steady-state space use patterns and rapid computations in mechanistic home range analysis

A. H. Barnett·P. R. Moorcroft

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Abstract

Mechanistic home range models are important tools in modeling animal dynamics in spatially-complex environments. We introduce a class of stochastic models for animal movement in a habitat of varying preference. Such models interpolate between spatially-implicit resource selection analysis (RSA) and advection-diffusion models, possessing these two models as limiting cases. We find a closed-form solution for the steady-state (equilibrium) probability distribution u* using a factorization of the redistribution operator into symmetric and diagonal parts. How space use is controlled by the preference function w then depends on the characteristic width of the redistribution kernel: when w changes rapidly compared to this width, u* ~ w, whereas on global scales large compared to this width, u* ~ w^2. We analyse the behavior at discontinuities in w which occur at habitat type boundaries. We simulate the dynamics of space use given two-dimensional prey-availability data and explore the effect of the redistribution kernel width. Our factorization allows such numerical simulations to be done extremely fast; we expect this to aid the computationally-intensive task of model parameter fitting and inverse modeling.

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A. H. Barnett, P. R. Moorcroft. 2007-05-23. Analytic steady-state space use patterns and rapid computations in mechanistic home range analysis. https://arxiv.org/abs/0705.3473

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