Some Mathematical Models from Population Genetics: École D'Été de Probabilités de Saint-Flour XXXIX-2009, Issue 2012

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Springer Science & Business Media, Jan 7, 2011 - Mathematics - 119 pages
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This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.
 

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Contents

1 Introduction
2
2 Mutation and Random Genetic Drift
5
3 One Dimensional Diffusions
33
4 More than Two Types
52
5 Selection
65
6 Spatial Structure
89
References
108
List of Participants
113
Index
117
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