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

TL;DR

This paper introduces a class of stochastic mechanistic models for animal space use that interpolate between RSA and advection-diffusion models, providing a closed-form steady-state solution and enabling rapid simulations for complex habitats.

Contribution

The authors derive a closed-form steady-state distribution for a new class of models and develop a fast computational method for simulating animal space use in heterogeneous environments.

Findings

Steady-state distribution u* depends on preference function w and kernel width.

Rapid simulations facilitate model fitting and inverse modeling.

Behavior at habitat boundaries analyzed for discontinuities.

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.