Probabilistic Models Of Population Evolution: Scaling Limits, Genealogies And Interactions (mathematical Biosciences Institute Lecture Series)
by Étienne Pardoux /
2016 / English / PDF
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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.
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, stochastic partial
differential equations, and probabilistic models in evolutionary
biology and population genetics. He obtained his PhD in 1975 at
University of Paris-Sud.