Probabilistic Models of Population Evolution ― Scaling Limits, Genealogies and Interactions

This expository bookpresents the mathematical description of evolutionary models of populationssubject to interactions (e.g. competition) within the population. The author includesboth models of finite populations, and limiting models as the size of thepopulation tends to infinity. The size of the population isdescribed as a random function of time and of the initial population (theancestors at time 0). The genealogical tree of such a population is given.In their typical models, the population is bound to go extinct in finitetime. It is explained when the interaction is strong enough so that theextinction time remains finite, when the ancestral population at time 0 goes toinfinity. The material could be used for teaching stochastic processes,together with their applications.

Etienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, in particular Stochastic partial differential equations. ?He obtained his PhD in 1975 at University of Paris-Sud.