Spatio-temporal patterns of gene flow and dispersal under temperature increase

Recent data show that the Earth climate is undergoing a change at a rate which is outstanding in geologic history. Temperature is one of the major driving forces of gene flow and dispersal. In this paper the spatial dynamics of genetic dispersal is studied under the auspices of temperature increase by means of a mathematical model. The main elements genetics, competition and dispersal are combined in a coherent approach by a system of coupled partial differential equations with non-linear reaction terms describing population dynamics, genetic exchange and competition. Temperature reaction norms are conferred by a two allele system. The non-linearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. Here we show how invasion processes in form of travelling waves are initiated by a temperature rise.