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

ISBN-13: 9783319303260 / Angielski / Miękka / 2016 / 125 str.

Etienne Pardoux

Opis

Presenting the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) in the population, this book includes models of finite populations, and limiting models as the size of the population tends to infinity. The material could be used for teaching stochastic processes and their applications.

Recenzje

"This book presents the mathematical description of evolutionary models of populations subject to interactions within the population. ... For readers' convenience, the book contains an appendix summarizing the necessary backgrounds and technical results on stochastic calculus. The materials are presented with clarity, brevity and styles. ... The book provides nice supplementary material for courses in stochastic processes and stochastic calculus." (Chao Zhu, Mathematical Reviews, April, 2017)

"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)

Spis treści

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.

O autorze

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.

Blurb

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.