Stochastic Models for Structured Populations

In this contribution, several probabilistic tools to study population dynamics are developed. The focus isonscaling limits of qualitatively different stochastic individual based modelsand the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processesdescribing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations.Biologically relevant questions are considered, such as extinction criteria,the effect of large birth events, the impact of environmental catastrophes,the mutation-selection trade-off, recovery criteria in parasite infections,genealogical properties of a sample ofindividuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie MéléardareProfessors at Ecole Polytechnique (France). They are aspecialists ofbranching processes andrandom particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.