Affiliation - Ohio State University
Title of Talk - Some PDEs in Evolution of Dispersal
In the first part of the talk, we discuss the multi-species competition in a spatial domain, particularly the result of A. Hastings and some recent progress on the conjecture by Dockery et al. concerning the evolution of slow dispersal, i.e. when other things are equal, the slowest diffuser can competitively exclude other competitors. We then discuss the effect of adding passive drift and how it changes the evolutionary dynamics so that fast/intermediate diffuser is selected. In the second part, we will discuss the effect of mutation, and the associated moving Dirac solutions in a nonlocal PDE model proposed by Perthame and Souganidis. This latter equation describes a population structured by space and a phenotypic trait, and can be understood as competition of infinitely many species with different rate of dispersal.