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Analytical and numerical tools for diffusion-based movement models

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  • Ovaskainen, Otso

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.

Suggested Citation

  • Ovaskainen, Otso, 2008. "Analytical and numerical tools for diffusion-based movement models," Theoretical Population Biology, Elsevier, vol. 73(2), pages 198-211.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:2:p:198-211
    DOI: 10.1016/j.tpb.2007.11.002
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    Citations

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    Cited by:

    1. Potgieter, L. & van Vuuren, J.H. & Conlong, D.E., 2013. "A reaction–diffusion model for the control of Eldana saccharina Walker in sugarcane using the sterile insect technique," Ecological Modelling, Elsevier, vol. 250(C), pages 319-328.
    2. Juan Manuel Morales & Agustina Virgilio & María Delgado & Otso Ovaskainen, 2017. "A General Approach to Model Movement in (Highly) Fragmented Patch Networks," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 393-412, September.
    3. Potgieter, L. & van Vuuren, J.H. & Conlong, D.E., 2015. "The role of heterogeneous agricultural landscapes in the suppression of pest species following random walk dispersal patterns," Ecological Modelling, Elsevier, vol. 306(C), pages 240-246.
    4. Ma, Brian O. & Davis, Brad H. & Gillespie, David R. & VanLaerhoven, Sherah L., 2009. "Incorporating behaviour into simple models of dispersal using the biological control agent Dicyphus hesperus," Ecological Modelling, Elsevier, vol. 220(23), pages 3271-3279.
    5. Zheng, Chaozhi & Pennanen, Juho & Ovaskainen, Otso, 2009. "Modelling dispersal with diffusion and habitat selection: Analytical results for highly fragmented landscapes," Ecological Modelling, Elsevier, vol. 220(12), pages 1495-1505.

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