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Probabilistic models of population evolution: scaling limits, genealogies and interactions

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 t...

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Detalles Bibliográficos
Autor principal: Pardoux, Étienne
Lenguaje:eng
Publicado: Springer 2016
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-30328-4
http://cds.cern.ch/record/2196720
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author Pardoux, Étienne
author_facet Pardoux, Étienne
author_sort Pardoux, Étienne
collection CERN
description 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.
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spelling cern-21967202021-04-21T19:38:41Zdoi:10.1007/978-3-319-30328-4http://cds.cern.ch/record/2196720engPardoux, ÉtienneProbabilistic models of population evolution: scaling limits, genealogies and interactionsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:21967202016
spellingShingle Mathematical Physics and Mathematics
Pardoux, Étienne
Probabilistic models of population evolution: scaling limits, genealogies and interactions
title Probabilistic models of population evolution: scaling limits, genealogies and interactions
title_full Probabilistic models of population evolution: scaling limits, genealogies and interactions
title_fullStr Probabilistic models of population evolution: scaling limits, genealogies and interactions
title_full_unstemmed Probabilistic models of population evolution: scaling limits, genealogies and interactions
title_short Probabilistic models of population evolution: scaling limits, genealogies and interactions
title_sort probabilistic models of population evolution: scaling limits, genealogies and interactions
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-30328-4
http://cds.cern.ch/record/2196720
work_keys_str_mv AT pardouxetienne probabilisticmodelsofpopulationevolutionscalinglimitsgenealogiesandinteractions