  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.
