Some Mathematical Models from Population Genetics

1. Front Matter

   Pages i-viii

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2. Introduction

   • Alison Etheridge

   Pages 1-3

3. Mutation and Random Genetic Drift

   • Alison Etheridge

   Pages 5-32

4. One Dimensional Diffusions

   • Alison Etheridge

   Pages 33-51

5. More than Two Types

   • Alison Etheridge

   Pages 53-64

6. Selection

   • Alison Etheridge

   Pages 65-87

7. Spatial Structure

   • Alison Etheridge

   Pages 89-107

8. Back Matter

   Pages 109-119

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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.

• 60-02;92D10;92D15;60J70;60J75
• Coalescent models
• Population genetics
• stochastic models
• partial differential equations

• , Department of Statistics, University of Oxford, Oxford, United Kingdom

  Alison Etheridge

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