Journal of Mathematical Biology

, Volume 57, Issue 1, pp 139–159 | Cite as

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* ∝ 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.


Mechanistic Home range Advection–diffusion Resource selection analysis Markov Space use 

Mathematics Subject Classification (2000)

92D50 35K15 65C20 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

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

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