Probabilistic models of population evolution [electronic resource] : scaling limits, genealogies and interactions / Étienne Pardoux.
2016
QA274.76
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Title
Probabilistic models of population evolution [electronic resource] : scaling limits, genealogies and interactions / Étienne Pardoux.
ISBN
9783319303284 (electronic book)
3319303287 (electronic book)
9783319303260
3319303287 (electronic book)
9783319303260
Published
Switzerland : Springer, 2016.
Language
English
Description
1 online resource (viii, 125 pages) : illustrations.
Item Number
10.1007/978-3-319-30328-4 doi
Call Number
QA274.76
Dewey Decimal Classification
519.2/34
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 29, 2016).
Series
Mathematical Biosciences Institute lecture series. Stochastics in biological systems.
Available in Other Form
Print version: 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.
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.