Journal of Mathematical Biology

, Volume 57, Issue 1, pp 139–159

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


DOI: 10.1007/s00285-007-0149-8

Cite this article as:
Barnett, A.H. & Moorcroft, P.R. J. Math. Biol. (2008) 57: 139. doi:10.1007/s00285-007-0149-8


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* ∝ w2. 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.


MechanisticHome rangeAdvection–diffusionResource selection analysisMarkovSpace use

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA
  2. 2.OEB DepartmentHarvard UniversityCambridgeUSA