Probabilistic Models Of Population Evolution: Scaling Limits, Genealogies And Interactions by Étienne PardouxProbabilistic Models Of Population Evolution: Scaling Limits, Genealogies And Interactions by Étienne Pardoux

Probabilistic Models Of Population Evolution: Scaling Limits, Genealogies And Interactions

byÉtienne Pardoux

Paperback | June 27, 2016

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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. 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.
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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Title:Probabilistic Models Of Population Evolution: Scaling Limits, Genealogies And InteractionsFormat:PaperbackDimensions:125 pagesPublished:June 27, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319303260

ISBN - 13:9783319303260

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Table of Contents

Introduction.- Branching Processes.- Convergence to a Continuous State Branching Process.- Continuous State Branching Process (CSBP).- Genealogies.- Models of Finite Population with Interaction.- Convergence to a Continuous State Model.- Continuous Model with Interaction.- Appendix.

Editorial Reviews

"The main originality of the book is the fact that it describes the evolution of a population where the birth or death rates of the various individuals are affected by the size of the population. . The book is mainly intended to readers with some basic knowledge of stochastic processes and stochastic calculus. All in all, this is a serious piece of work." (Marius Iosifescu, zbMATH 1351.92003, 2017)