Optimal Dispersal Rates in Meta-Population Models


  Shlomit Weissman  ,  David A. Kessler  
Bar Ilan University

A central question in ecology is how species determine their migration rate. In this work we study the optimal migration rate in a system that includes reaction diffusion processes together with evolution of dispersal rates. The life cycle includes three stages: reproduction, competition and dispersal. In this model there is a probability of death during migration. We compared the optimal migration rate of this model to the optimal migration rate from an identical model except for the dispersal which occurs before the competition. The optimal diffusion rate is calculated both in the limit of low probability to survive migration and for a large number of individuals per site after competition. When the dispersal occurs after competition the model has an optimal hopping rate that vanishes in the limit of vanishing survival probability in contradistinction to the other model. The optimal hopping rate is equal to one when the survival probability is one in the two models