Quantitative traits—be they morphological or physiological characters, aspects of behavior, or genome-level features such as the amount of RNA or protein expression for a specific gene—usually show considerable variation within and among populations. Quantitative genetics, also referred to as the genetics of complex traits, is the study of such characters and is based on mathematical models of evolution in which many genes influence the trait and in which non-genetic factors may also be important. Evolution and Selection of Quantitative Traits presents a holistic treatment of the subject, showing the interplay between theory and data with extensive discussions on statistical issues relating to the estimation of the biologically relevant parameters for these models. Quantitative genetics is viewed as the bridge between complex mathematical models of trait evolution and real-world data, and the authors have clearly framed their treatment as such. This is the second volume in a planned trilogy that summarizes the modern field of quantitative genetics, informed by empirical observations from wide-ranging fields (agriculture, evolution, ecology, and human biology) as well as population genetics, statistical theory, mathematical modeling, genetics, and genomics. Whilst volume 1 (1998) dealt with the genetics of such traits, the main focus of volume 2 is on their evolution, with a special emphasis on detecting selection (ranging from the use of genomic and historical data through to ecological field data) and examining its consequences. This extensive work of reference is suitable for graduate level students as well as professional researchers (both empiricists and theoreticians) in the fields of evolutionary biology, genetics, and genomics. It will also be of particular relevance and use to plant and animal breeders, human geneticists, and statisticians.

Evolutionary biology has struggled to explain the coexistence of two basic observations: genetic variation is found in almost all traits in the presence of strong natural and sexual selection in natural populations. These two observations are in direct conflict as such selection should deplete genetic variation. Furthermore, the presence of genetic variation in a trait, and selection acting on that trait, is often not sufficient for the trait to respond to selection. Here, we bring together geometric perspectives on mutation, selection, and genetic variation and show how the perceived incompatibility between these two observations is a consequence of taking a trait-by-trait approach to the multivariate problem of genetic variation and selection. We conclude that the simultaneous presence of widespead genetic variation in, and strong selection on, individual traits indicates that substantial mulitvariate genetic constraints are likely to be present in natural populations.

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