Keywords
reaction-diffusion equations, biological invasion, range expansion, travelling waves, temperature dependence
Start Date
1-7-2012 12:00 AM
Abstract
Due to human migration and climate change invasion of alien species has been observed in Europe. Recently, the mosquito Aedes albopictus has invaded the south of France. The spatial-temporal dynamics of invasion is studied in dependence of temperature and predation pressure of the resident ecosystem. The main elements population dynamics, predation and dispersal are combined in a coherent approach based on a system of coupled reaction diffusion equations for the aquatic and winged phase. The nonlinear reaction terms comprise a population dynamic model with temperature dependent reproduction rates and a predation term. The effect of temperature and predation pressure on travelling wave solutions is first investigated for a one dimensional model version. 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 human population density are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the invasion of species at the scale of middle Europe. The results show that invasion is enhanced in urban regions with ephemeral habitats provided by temporary water bodies.
Modelling large scale invasion of new species under temperature change by reaction-diffusion equations
Due to human migration and climate change invasion of alien species has been observed in Europe. Recently, the mosquito Aedes albopictus has invaded the south of France. The spatial-temporal dynamics of invasion is studied in dependence of temperature and predation pressure of the resident ecosystem. The main elements population dynamics, predation and dispersal are combined in a coherent approach based on a system of coupled reaction diffusion equations for the aquatic and winged phase. The nonlinear reaction terms comprise a population dynamic model with temperature dependent reproduction rates and a predation term. The effect of temperature and predation pressure on travelling wave solutions is first investigated for a one dimensional model version. 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 human population density are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the invasion of species at the scale of middle Europe. The results show that invasion is enhanced in urban regions with ephemeral habitats provided by temporary water bodies.
