In this talk, we survey the qualitative conclusions of several recent studies concerning spatial heterogeneity in population dynamics. Using the heterogeneous logistic-diffusive equation as a paradigmatic model, we investigate the optimal location of resources in a domain: how should resources be spread inside a domain in order to optimise certain criteria, in particular the total biomass? Motivating our analysis by a study of the optimal survival ability, we shall present some qualitative properties recently obtained that show surprising phenomena. The talk will be mostly descriptive, and is based on collaborations with Grégoire Nadin, Yannick Privat and Domènec Ruiz-i-Balet.
