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 proportional, variant w, whereas when it is narrow relative to variation in w, u proportional, variant 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.
Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA. ahb@math.dartmouth.edu
Alex H
AH
Barnett
Paul R
PR
Moorcroft
D025041:Animal Migration; D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D006702:Homing Behavior; D015233:Models, Statistical; D011156:Population Density; D011157:Population Dynamics; D013037:Spatial Behavior