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

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 habitat preference function w depends on the characteristic width of the animals' redistribution kernel: when the redistribution kernel is wide relative to variation in w, u*. w, whereas when it is narrow relative to variation in w, u* alpha w(2). In addition, we analyze the behavior at discontinuities in w which occur at habitat type boundaries, and simulate the dynamics of space use given two-dimensional prey-availability data, exploring 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.