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

By: Language: English Series: Mathematical biosciences institute lecture series; 1.6 [v.1: Stochastics in biological systems] | / edited by Michael Reed and Richard DurrettPublication details: Switzerland Springer 2016Description: viii,125pISBN:
  • 9783319303260
Subject(s): DDC classification:
  • 519.234 P214p
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. Etienne 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
List(s) this item appears in: New arrival August 20-26, 2018
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Item type Current library Collection Call number Status Date due Barcode Item holds
Books Books PK Kelkar Library, IIT Kanpur General Stacks 519.234 P214p (Browse shelf(Opens below)) Available A183712
Total holds: 0

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. Etienne 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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