Modelling dispersal of populations and genetic information by finite element methods

Abstract

This paper shows how biological population dynamic models in the form of partial differential equations can be applied to heterogeneous landscapes. The systems of coupled partial differential equations presented combine dispersal, growth, competition and genetic interactions. The equations belong to the class of reaction diffusion equations and are strongly non-linear. Realistic biological dispersal behaviour is introduced by density dependent diffusion coefficients and chemotaxis terms, which model the active movement along gradients of environmental variables. The resulting non-linear initial boundary value problems are solved for geometries of heterogeneous landscapes, which determine model parameters such as diffusion coefficients, habitat suitability and land use. Geometry models are imported from a geographical information system into a general purpose finite element solver for systems of coupled PDEs. The importance of spatial heterogeneity is demonstrated for management of biological control by sterile males and for risk management of GMO crops.