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Some Mathematical Models from Population Genetics

École d'Été de Probabilités de Saint-Flour XXXIX-2009

  • Book
  • © 2011

Overview

Authors:
  1. Alison Etheridge

    1. , Department of Statistics, University of Oxford, Oxford, United Kingdom

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  • First volume aimed at mathematicians to cover a wide range of models from population genetics
  • Provides the biological motivation for models without using too much `jargon'
  • Provides the mathematical and biological background needed by a mathematician to read research papers in theoretical population genetics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2012)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

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Table of contents (6 chapters)

  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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Keywords

About this book

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.

Authors and Affiliations

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

    Alison Etheridge

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