The mathematical theory of selection, recombination and mutation.

*(English)*Zbl 0959.92018
Wiley Series in Mathematical and Computational Biology. Chichester: Wiley. xi, 409 p. (2000).

The emphasis of this book is on models that have a direct bearing on evolutionary quantitative genetics. Applications concerning the maintenance of genetic variation in quantitative traits and their dynamics under selection are treated in detail. The main purpose is to provide a fairly unified and self-contained treatment of the mathematical theory of genetic multilocus systems subject to the forces of selection, mutation, and recombination.

Chapter I introduces the basic concepts of mathematical population genetics. Chapter II begins with an introduction to the classical two-locus models and then develops the general theory of multilocus models. In Chapter III, models with a finite number of alleles are treated, as well as the stepwise-mutation model. Chapter IV presents a general account of models allowing for a continuum of possible alleles. In Chapter V, a general theory for analysing both the dynamics of the distribution of an additive quantitative trait under selection and the distribution of multilocus genotypes that determines that trait is set out.

In Chapter VI, various models are investigated that have been devised to explore the potential of stabilizing selection to maintain genetic variation in an additive quantitative trait in the absence or presence of recurrent mutation.

All these chapters are focused on the analysis of mathematical models, and populations are assumed to be sufficiently large so that random genetic drift can be ignored. The emphasis in Chapter VII is more on the biological problems and the conclusions that can be drawn from the analyses of the models. Graduate students and researchers in population genetics, evolutionary theory, and biomathematics will benefit from the in-depth coverage. This text makes an excellent reference volume for the fields of quantitative genetics, population aud theoretical biology.

Chapter I introduces the basic concepts of mathematical population genetics. Chapter II begins with an introduction to the classical two-locus models and then develops the general theory of multilocus models. In Chapter III, models with a finite number of alleles are treated, as well as the stepwise-mutation model. Chapter IV presents a general account of models allowing for a continuum of possible alleles. In Chapter V, a general theory for analysing both the dynamics of the distribution of an additive quantitative trait under selection and the distribution of multilocus genotypes that determines that trait is set out.

In Chapter VI, various models are investigated that have been devised to explore the potential of stabilizing selection to maintain genetic variation in an additive quantitative trait in the absence or presence of recurrent mutation.

All these chapters are focused on the analysis of mathematical models, and populations are assumed to be sufficiently large so that random genetic drift can be ignored. The emphasis in Chapter VII is more on the biological problems and the conclusions that can be drawn from the analyses of the models. Graduate students and researchers in population genetics, evolutionary theory, and biomathematics will benefit from the in-depth coverage. This text makes an excellent reference volume for the fields of quantitative genetics, population aud theoretical biology.

Reviewer: T.Postelnicu (Bucureşti)