**Selected Highlights:**

.. I have nothing but the highest praise for this book, which will surely stand as the definite treatment for many years to come. The content is comprehensive, the writing clear and concise, indeed elegant, and the overall impression is of a masterly * tour de force*. And, at the price, is a wonderful bargain as well.

At the beginning of the book, Lynch and Walsh indicate two anomalies. The first is that R. A. Fisher and S. Wright, who between them more or less founded both the theory of evolutionary population genetics and the theory of quantitative genetics, did very little work combining these two fields, namely, the theory of the evolutionary properties of a quantitative trait. Lynch and Walsh thus set themselves the aim of bring these two themes together and of writing the definitive book on evolutionary quantitative genetics. This leads to the second anomaly. There is so much background material in quantitative genetics to get through that they do not even make a start, in this book, on the evolutionary theory. Rather, the book is devoted entirely to a description of the background quantitative genetics material necessary for such a book, and a second book, to appear soon, that promised to give us the full story about evolutionary quantitative genetics.

Thus, the book must be judged on whether it fulfills what in fact (as the authors themselves state) became its aim, namely to describe the theory of quantitative genetics as it stands now. It is a pleasure to report that it succeeds admirably in this task. It is as good a book on quantitative genetics as I have seen. The presentation is both comprehensive and definitive, and the book will become an immediate classic. A particular strength is that it brings together work by human geneticists (no doubt the primary interest to readers of this journal) and evolutionary biologists, work which in the past has too often proceeded on parallel nonconverging tracks.

The book intertwines throughout themes from mathematics and statistics, on the one hand, and from genetics on the other, and these themes are increasingly brought together as the book progresses. A further strength of the book is the admirable statistical and mathematical exposition and, more important, the description of the successful application of mathematics and statistics in resolving real and important genetical problems.

The opening chapter considers historical aspects of the subject, and in particular discusses the properties of the preservation of genetic variance under a Mendelian hereditary process. This leads to discussion of topics such as inbreeding and selection for extreme values of a metrical trait.

Chapter 2 gives as good an introduction as you will get, even in a specialized statistics book, to properties of random variables and their probability distributions. In particular, properties of the truncated normal distribution, relevant for the later discussion of selection on extreme phenotypes, are presented with great clarity. This material leads naturally into the subject matter of Chapter 3, which describes bivariate distributions with the associated concepts of correlation, regression, and covariation. A feature of the material is the careful distinction between population parameters and their estimates from samples, a distinction often made badly, if at all, in similar books. Again, it would be hard to imagine a better introduction to these topics than that given in this book.

Chapter 4 introduces Mendelian genetics in a systematic way, using the material of the previous two chapters to introduce central quantities such as the average effect of a gene, a breeding value, and the additive genetic variance. The discussion is greatly simplified by the assumption of random mating, a simplification removed in later chapters.

The correlation between relatives for some metrical trait, the basis for so much important work in animal breeding (and so much dubious speculation in other areas) is taken up in Chapter 7. All the standard coefficients of kinship are described fully. Formula for correlations are established for traits depending on two gene loci, although these are not yet fully general, in that random mating continues to be assumed. The important concepts of heritability and evolvability are fully and completely discussed.

In line with the policy of interspersing the mathematical and genetical development, Chapter 8 considers pure matrix theory. Again, the presentation is masterly, and even mathematical textbooks could take a lesson from the presentation. In particular, variance-covariance matrices are discussed in detail, and the least-squares theory of multiple regression is presented fully.

Chapter 9 will perhaps be of lesser interest to students in human biology, treating as it does the theory of the crosses that are available with laboratory animals. But again the treatment is definitive. In particular, an excellent discussion of heterosis is presented. The following chapter treats the complementary topic of inbreeding depression, again definitively.

So far the book has presented the background material needed for the major topics of the book. Chapters 12 through 16 take up a major theme of the book, namely a description of properties of quantitative trait loci (QTLs). The authors discuss in full detail the genetic aspects of quantitative traits determined by a number, perhaps a large number, of different loci. By now this comment must becoming repetitious, but their is no alternative. It is difficult to imagine a more thorough and definitive presentation of QTLs than is given in this book. All relevant areas are covered, and the statistical theory built up in previous chapters plays a full part in the analysis of QTLs presented.

The final major section of the book, comprising Chapters 17 through 27, concerns estimation of genetic characteristics from sample data. Here the theory of optimal statistical estimation is used to estimation crucial quantities such as the components of variance, heritability, the correlation in some character between relatives, breeding value, and the like. There is an excellent description of the problems with twin studies along the way, and an excellent exposition of the analysis of variance technique and its application in quantitative genetics. The assumptions made earlier in the book are to a large extent removed in a chapter treating genotype by environment interactions, and a very clear exposition of the recent technique of best linear unbiased prediction. The book concludes with several excellent appendices on advanced statistical methods and mathematical theory.

Having said all this, I would like to make two minor quibbles. The description of the "Fundamental Theorem of Natural Selection" is, in my view, out of date, with a different interpretation of this theorem now being broadly accepted. Second, while the authors are quite clear on the difference between parameters and their estimates, I dislike the notation "Var" that they adopt for a variance estimate, with the associated "Covar" for a covariance estimate and "Var(Var)" for the estimate of the variance of a variance estimate. Most books using the "Var" notation use it for the actual variance itself, and this seems a more natural usage.

But, as noted, these are minor points, and it is obvious that I have nothing but the highest praise for this book, which will surely stand as the definite treatment for many years to come. The content is comprehensive, the writing clear and concise, indeed elegant, and the overall impression is of a masterly * tour de force*. And, at the price, is a wonderful bargain as well.