This expository book presents the mathematical description of evolutionary models of
populations subject to interactions (e.g. competition) within the population. The author
includes both models of finite populations and limiting models as the size of the population
tends to infinity. The size of the population is described as a random function of time and of
the initial population (the ancestors at time 0). The genealogical tree of such a population is
given. Most models imply that the population is bound to go extinct in finite time. It is
explained when the interaction is strong enough so that the extinction time remains finite
when the ancestral population at time 0 goes to infinity. The material could be used for
teaching stochastic processes together with their applications. Étienne Pardoux is Professor
at Aix-Marseille University working in the field of Stochastic Analysis stochastic partial
differential equations and probabilistic models in evolutionary biology and population
genetics. He obtained his PhD in 1975 at University of Paris-Sud.
