title: Analytical and numerical tools for diffusion-based movement models.
abstract: I present a general diffusion-based modeling framework for the analysis of animal movements in heterogeneous landscapes, including terms representing advection, mortality, and edge-mediated behavior. I use adjoint operator theory to develop mathematical machinery for the assessment of a number of biologically relevant quantities, such as occupancy times, hitting probabilities, quasi-stationary distributions, the backwards equation, and conditional probability densities. I derive finite-element approximations, which can be used to obtain numerical solutions in domains which do not allow for an analytical treatment. As an example, I model the movements of the butterfly Melitaea cinxia in an island consisting of a set of habitat patches and the intervening matrix habitat. I illustrate the behavior of the model and the mathematical theory by examining the effects of a hypothetical movement barrier and advection caused by prevailing wind conditions.
authors.affiliation: Department of Biological and Environmental Sciences, PO Box 65, Viikinkaari 1, FI-00014 University of Helsinki, Finland. otso.ovaskainen@helsinki.fi
authors.forename: Otso
authors.initials: O
authors.lastname: Ovaskainen
mesh_terms: D025041:Animal Migration; D000818:Animals; D002080:Butterflies; D017753:Ecosystem; D020342:Finite Element Analysis; D005387:Finland; D015233:Models, Statistical; D011157:Population Dynamics