Christopher J. Basten, (2000) Theoretical Population Biology 57: 307.

In quantitative genetics, we seek to understand the basis of traits that differ in degree, that is, traits that are influenced by many genes rather than by a single locus. An important goal is to identify and characterize the genes that influence a trait, thereby reducing continuous variation to a set of discrete components. The theoretical underpinnings of quantitative genetics date back to the 1920s, with the work of R. A. Fisher, S. Wright, and J. B. S. Haldane. Since then, there has been extensive experimental work in plant and animal breeding, with a golden age in the 1950s and 1960s. The 1970s saw a resurgence of interest in the field due to some important papers by Russell Lande: His work especially popularized the field to evolutionary biologists. Quantitative traits are important for evolutionary biology because they are the target of natural selection. It now becomes important to understand the spectrum of variation in natural populations as well as the underlying genetic architecture. The advent of new molecular techniques and statistical methods are leading to what may be a new golden age: Our ability to map and understand the basis of genetic traits has expanded greatly in recent time. Lynch and Walsh have produced a timely work which should advance and aid the people in the field.

The book is divided into three main sections. The first part gives an overview of the foundations of quantitative genetics. Topics include an overview of quantitative genetics, properties of a single locus, a review of genetic and environmental variation, resemblance between relatives, and the analysis of various breeding designs.

The second section treats quantitative trait loci. This is one of the hotter areas in quantitative genetics. Many of the traits of economic and biomedical import are polygenic in nature, and elucidating the genetic architecture is an important step in understanding them. Since the literature in this area is still being written and evolving qulckly, it is a section that will soon be out of date. In spite of that, the methods are important first steps in understanding the genetic architecture of polygenic traits. The theory to treat inbred lines is well developed and presented here. That pertaining to outbred populations is necessarily a bit more sketchy.

The final section delves into the procedures for estimating the parameters in our models. The sections contained therein begin from the experimental designs and proceed to the theoretical models. We learn how to analyze parent-offspring, sibs, twins, and clones and proceed to cross-classified designs such as North Carolina II and III. The main method of analysis in these cases is analysis of variance, but maximum likelihood methods are addressed later in the section. The authors clearly explain the methods for estimating the components of variation as well as their meanings. Other important areas are correlations between characters, genotype-by-environment interactions, maternal effects, and threshold traits. These methods lead to estimating breeding values. The final chapter delves into maximum likelihood methods for the estimation of variance components, especially in complex pedigrees.

One good feature of this book is the overview of the mathematical tools required for the analysis. The authors provide a background for all the statistical and mathematical methods required for the analysis of models and the estimation of parameters. For example, chapter 2 gives a brief overview of basic probability theory and statistics. We are reminded of how to calculate the moments of distributions and from them quantities such as the mean, variance, and skew. This blends immediately into ways of estimating these quantities and from there to using them with the normal distribution all-important for quantitative characters. We find this pattern repeated with a treatment of matrix algebra in Chapter 8, transformations in Chapter 11, and many other topics in the Appendixes. These chapters may not give exhaustive coverage to the mathematical techniques, but they do provide a useful summary to orient the reader.

This important and useful book will have a permanent place on my desktop. I really wish it could have been published several years ago, about the time that I began work on a computer program package to analyze QTL (quantitative trait locus) mapping data. Over the years, I have had to respond to queries from users wanting to understand specific parameters, experimental designs, or analysis methods. This book will be a useful source of answers for such questions, both for me and for the users of my programs. From now on, I can simply reference pages from Lynch and Walsh thus: LW (pages). For example, LW (395-396) would answer the question "What is the Kosambi mapping function?" and LW (242-243) would explain "What is a doubled haploid?" The consolidation of this material would have been a real timesaver as well as a source of new ideas for features in the programs.

The authors' stated aim was to "bring together the diverse array of theoretical and empirical applications of quantitative genetics..." The job turned out to be greater than expected. This book constitutes the first half of that goal, which has been achieved with great success thus far. It is well organized, lucidly written, and quite comprehensive. It opens with a historical development of the study of quantitative traits that aids in the intuitive understanding of the field. There are a wealth of examples from real experimental systems that at once illustrate the theoretical concepts and remind the reader of the continuity of theory and experiment. The highly mathematical sections refer to the theory of quantitative genetics, and the theoretical quantitative genetics sections refer to the experimental sections. Not only is this an essential reference book, but it is also an excellent textbook. The only thing I would add in this regard is a set of exercises for the students. Presently, these would have to be supplied by the instructor. I think this an important area in that, as in any theoretical science, one does not really learn the material until forced to work out problems.

As with any work of this magnitude, small errors will go by unnoticed. Rather than list them here, I direct the reader to a web page devoted to cataloging them:

With a goal of covering the depth and breadth of theoretical and empirical quantitative genetics in mind, the authors are halfway there with this first of two volumes. This is an impressive work in progress and I eagerly await the next volume.

Christopher J. Basten,
Department of Statistics,
North Carolina State University,