Some Mathematical Models from Population Genetics: Ecole D'ete De Probabilites De Saint-flour Xxxix-2009

by Etheridge, Alison

• ISBN13: 9783642166310
• ISBN10: 3642166318
• Edition: 1st
• Format: Paperback
• Copyright: 2011-01-29
• Publisher: Springer Verlag

Summary

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.