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Survie et généalogies dans quelques modèles de dynamique des populations

Abstract : This thesis presents a series of works dealing with the survival and the genealogies of populations in presence of selection in several simple models of statistical physics related to biology.

The first part focuses on the evolution of one-dimensional branching random walks in presence of an absorbing threshold which increases linearly in time. We relate the properties of these walks to travelling waves and we study the transition to extinction which occurs as the velocity of the threshold increases as well as the critical behaviour of the survival probability. We also develop a biased process which allows us to study a population of such walks conditioned on its size at a given final time. This process is used in order to study the quasi-stationary regime near the critical velocity. Finally, we present a exactly solvable model, for which several conjectures can be verified.

In the second part, we study populations with a constant size from the point of view of the genealogies and of the coalescence times. We explain how some evolutionary models with selection can be related to models of directed polymers and we present numerical results which tend to show the existence of universality classes in the genealogies. In absence of selection, we study the dynamics of the coalescence times and of the age of the most recent common ancestor of a population, as well as the correlations between this age and the genetic diversity in a simple case.
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Contributor : Damien Simon <>
Submitted on : Tuesday, June 10, 2008 - 9:49:50 AM
Last modification on : Thursday, December 10, 2020 - 12:38:35 PM
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  • HAL Id : tel-00286612, version 1


Damien Simon. Survie et généalogies dans quelques modèles de dynamique des populations. Physique mathématique [math-ph]. Université Paris-Diderot - Paris VII, 2008. Français. ⟨tel-00286612⟩



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