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Probabilistic Models of Population Evolution
Scaling Limits, Genealogies and Interactions
Engels
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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.§In their typical models, 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, in particular Stochastic partial differential equations. He obtained his PhD in 1975 at University of Paris-Sud.§
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