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Probabilistic Models of Population Evolution

Scaling Limits, Genealogies and Interactions

Étienne Pardoux (Autor)

Buch | Softcover

VIII, 125 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-30326-0 (ISBN)

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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.

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.

"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)

Erscheinungsdatum	11.05.2016
Reihe/Serie	Mathematical Biosciences Institute Lecture Series
Reihe/Serie	Stochastics in Biological Systems
Zusatzinfo	VIII, 125 p. 6 illus., 2 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Weitere Themen ► Bioinformatik
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Bienaymé-Galton-Watson Processes • Continuous state branching processes • Evolutionary Models • markov chains • Mathematical and Computational Biology • mathematics and statistics • Population models • Populations with Interactions • Probability theory and stochastic processes • Theoretical Ecology/Statistics
ISBN-10	3-319-30326-0 / 3319303260
ISBN-13	978-3-319-30326-0 / 9783319303260
Zustand	Neuware