Probabilistic Models of Population Evolution

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

Includes deep mathematical notions in connection with motivating applications

Suitable for graduate students and researchers in mathematical biology

Co-published jointly with Mathematical Biosciences Institute

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2016
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Mathematical Biosciences Institute Lecture Series
Inhalt:	viii 125 S. 4 s/w Illustr. 2 farbige Illustr. 125 p. 6 illus. 2 illus. in color.
ISBN-13:	9783319303260
ISBN-10:	3319303260
Sprache:	Englisch
Herstellernummer:	978-3-319-30326-0
Einband:	Kartoniert / Broschiert
Autor:	Pardoux, Étienne
Auflage:	1st edition 2016
Hersteller:	Springer Springer International Publishing AG Mathematical Biosciences Institute Lecture Series
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 8 mm
Von/Mit:	Étienne Pardoux
Erscheinungsdatum:	27.06.2016
Gewicht:	0,243 kg