Gene genealogies, variation and evolution. A primer in coalescent theory.

*(English)*Zbl 1113.92048
Oxford: Oxford University Press (ISBN 0-19-852996-1/pbk; 0-19-852995-3/hbk). xiii, 276 p. (2005).

The coalescent has developed to a powerful tool in modern population genetics. Starting from the work of Kingman in the 1980s, coalescent processes have been proven to be useful for studying the ancestral history of a sample of individuals, genes or DNA sequences chosen from large populations, in order to make inferences about genealogies, relationships between populations and about the factors of evolution. This book presents a straightforward and general account of coalescent theory from the genetic, mathematical and statistical point of view.

Based on the Wright-Fisher model of the evolution of an idealized population, the basic coalescent process in discrete and continuous time is introduced first. Coalescent trees and important quantities, e.g., their height and total branch length are discussed and calculated. Different mutation models are introduced next, a mathematical framework for working with probabilities of sample configurations is discussed, and examples of quantities that can be calculated on coalescent genealogies are given. In the following chapters the basic coalescent is extended to situations with varying population size, heterogeneous population structure and various forms of selection and recombination. Moreover, there is a chapter on the usage of coalescent theory in the field of linkage disequilibrium mapping combinded with the efforts towards locating genes underlying common diseases, such as cancer or Alzheimer’s. The last chapter, finally, adresses several questions where coalescent theory helps with a better understanding of human evolution.

From the mathematical point of view, this graduate-level text deals mainly with discrete mathematics and probability theory, and a general basic knowledge of combinatorics, probability distributions and random processes is advisable. All chapters are clearly arranged, full of exciting examples and illustrations. The book also contains an appendix with a number of web based tools available through www.coalescent.dk, as well as an extensive bibliography.

Based on the Wright-Fisher model of the evolution of an idealized population, the basic coalescent process in discrete and continuous time is introduced first. Coalescent trees and important quantities, e.g., their height and total branch length are discussed and calculated. Different mutation models are introduced next, a mathematical framework for working with probabilities of sample configurations is discussed, and examples of quantities that can be calculated on coalescent genealogies are given. In the following chapters the basic coalescent is extended to situations with varying population size, heterogeneous population structure and various forms of selection and recombination. Moreover, there is a chapter on the usage of coalescent theory in the field of linkage disequilibrium mapping combinded with the efforts towards locating genes underlying common diseases, such as cancer or Alzheimer’s. The last chapter, finally, adresses several questions where coalescent theory helps with a better understanding of human evolution.

From the mathematical point of view, this graduate-level text deals mainly with discrete mathematics and probability theory, and a general basic knowledge of combinatorics, probability distributions and random processes is advisable. All chapters are clearly arranged, full of exciting examples and illustrations. The book also contains an appendix with a number of web based tools available through www.coalescent.dk, as well as an extensive bibliography.

Reviewer: Günther Karigl (Wien)

##### MSC:

92D15 | Problems related to evolution |

92D10 | Genetics and epigenetics |

92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |

92D20 | Protein sequences, DNA sequences |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

92-02 | Research exposition (monographs, survey articles) pertaining to biology |