J.J. Colleau, Genetics, Selection, Evolution 30: 203-204

As mentioned by the authors, recent important advances have occurred in the area of what could be called biometrical genetics. This has resulted from contemporaneous progress in developing concepts and methods in three areas, namely evolutionary biology, animal and plant breeding, and human genetics, with in this case a major emphasis put on QTL detection. However, the relevant information has remained scattered among various specialized papers and textbooks, which has made it difficult for the common reader, not a specialist but eager to learn basics, to get a correct overview of the current scientific situation in biometrical genetics.

The objective of this book has been definitely to meet this need. The authors have attempted to carry out a comprehensive approach combining a large coverage of numerous subjects (detailed hereafter) and deep insights into the genetical models and their counterparts in terms of statistical models and methods. Throughout the book, the authors have alternated fully detailed presentation from population genetics to statistical genetics, supporting the latter by displaying basic algebra results in specialized chapters and appendices. However, this theoretical machinery has been faced with empirical examples extracted from the literature. Furthermore, a dense literature referencing has made it easy to follow the relevant scientific history and to have access both to historical cornerstone papers and to the latest references. This demanding approach has cost the authors ten years of preparation and has given birth to this present impressive book (around 1000 pages and 2000 references), that is to be followed by a second book devoted to population dynamics i.e. evolution and selection of quantitative traits.

Part I (11 chapters) presents foundations of quantitative genetics i.e. the basic concepts involved when analyzing genetic variation for single loci or combinations of loci, and environmental in connection with genetic variation. Taking these models as backgrounds, the expectations of resemblance between relatives, and of differences between line crosses are given. Familiar notions already found in Falconer's classical books, such as gene effect, additivity, dominance, epistasis, inbreeding, genotype x environment interaction, maternal effect, are then revisited and discussed at length. Basic properties of distributions and matrix algebra are given. The interesting chapter 11 reminds one that simplicity can be obtained from transformed data if the original metric is not appropriate.

Part II (5 chapters) is almost exclusively devoted to detailed presentations of the statistical considerations that have to be employed when trying to detect major genes without markers or QTLs with markers. In the last case, very up-to-date chapters display the basic concepts of molecular markers and genetic maps and detail the current methodology used for QTL mapping from inbred-line crosses or from outbred populations. Part II relies heavily on maximum likelihood procedures, likelihood ratio tests and assessment of power of statistical tests, all of which are carefully presented in specialized appendices.

Part III (11 chapters) is entitled "estimation procedures ". This part is highly heterogeneous and the only common characteristic is that the genetic model underlying the statistical procedures is definitely infinitesimal. In this context, the authors present estimation procedures, accuracies of estimates and statistical tests for parent - offspring regression, sib analysis, clone analysis, cross-classified designs, correlations between traits, genotype x environment interaction, maternal effect, sexual dimorphism and threshold characters. The last two chapters provide an interesting and clear summary of the state of the art for the estimation of breeding values (BLUPs within linear mixed models) and the estimation of variance components with complex pedigrees (ML and REML estimates).

Undoubtedly, this book should be considered as useful and even a must for anyone involved in biometrical genetics. From the seasoned specialist to the less statistically sophisticated reader or the student, everyone is likely to take profit from consulting this book for a variety of subjects. As soon as data are involved, even if the major interest is on biology, the use of appropriate statistical methods cannot be passed over because, as stated by the authors, " the rewards of mathematical theory can be enormous, particularly when what looks like mind-boggling complexity collapses into a relatively simple formulation ". There is no doubt that the authors have provided the appropriate tool for reconciling biology and mathematics.