Some Mathematical Models from Population Genetics
Etheridge, Alison.
Some Mathematical Models from Population Genetics École d'Été de Probabilités de Saint-Flour XXXIX-2009 / [electronic resource] : by Alison Etheridge. - VIII, 119 p. 15 illus. online resource. - École d'Été de Probabilités de Saint-Flour, 2012 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 2012 .
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.
9783642166327
10.1007/978-3-642-16632-7 doi
Genetics--Mathematics.
Differential equations, partial.
Statistics.
Genetics and Population Dynamics.
Mathematical and Computational Biology.
Mathematical Modeling and Industrial Mathematics.
Partial Differential Equations.
Statistics for Life Sciences, Medicine, Health Sciences.
QH323.5 QH455
576.58 577.88
Some Mathematical Models from Population Genetics École d'Été de Probabilités de Saint-Flour XXXIX-2009 / [electronic resource] : by Alison Etheridge. - VIII, 119 p. 15 illus. online resource. - École d'Été de Probabilités de Saint-Flour, 2012 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 2012 .
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.
9783642166327
10.1007/978-3-642-16632-7 doi
Genetics--Mathematics.
Differential equations, partial.
Statistics.
Genetics and Population Dynamics.
Mathematical and Computational Biology.
Mathematical Modeling and Industrial Mathematics.
Partial Differential Equations.
Statistics for Life Sciences, Medicine, Health Sciences.
QH323.5 QH455
576.58 577.88