Modelling the effect of temperature on the range expansion of species by reaction-diffusion equations

The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe.