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Mechanistic home range models are important tools in modeling animal dynamicsin spatially-complex environments. We introduce a class of stochastic modelsfor animal movement in a habitat of varying preference. Such models interpolatebetween spatially-implicit resource selection analysis (RSA) andadvection-diffusion models, possessing these two models as limiting cases. Wefind a closed-form solution for the steady-state (equilibrium) probabilitydistribution u* using a factorization of the redistribution operator intosymmetric and diagonal parts. How space use is controlled by the preferencefunction w then depends on the characteristic width of the redistributionkernel: when w changes rapidly compared to this width, u* ~ w, whereas onglobal scales large compared to this width, u* ~ w^2. We analyse the behaviorat discontinuities in w which occur at habitat type boundaries. We simulate thedynamics of space use given two-dimensional prey-availability data and explorethe effect of the redistribution kernel width. Our factorization allows suchnumerical simulations to be done extremely fast; we expect this to aid thecomputationally-intensive task of model parameter fitting and inverse modeling.

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