Yuan Lou, Ohio State University and Renmin University of China
601, Pao Yue-Kong Library
To study the evolution of conditional dispersal we extend the Perthame-Souganidis mutation-selection model and consider an integro-PDE model for a population structured by the spatial variables and one trait variable. We assume that both diffusion rate and advection rate are functions of the trait variable, which lies within a short interval I. Under proper conditions on the invasion fitness gradient, we show that in the limit of small mutation rate, the positive steady state will concentrate in the trait variable and forms a Dirac mass supported at one end of I，or a Dirac mass supported at the interior of I, or two Dirac masses supported at both ends of I. This is based on joint works with Wenrui Hao (Penn State) and King-Yeung Lam (Ohio State).