Short - term Changes in the Mean : 1 . The Breeder ’ s Equation

Selection on quantitative traits, and its consequences, comprises the remainder of this book. We start by discussing the simplest situation — the expected change in the mean of a single character following a single generation of selection. This response is reasonably predictable in a wide variety of settings, using a regression framework and the appropriate covariances between relatives. By contrast, the response after a number of generations is much more unpredictable, as allele-frequency change alters the genetic covariances (and hence the resemblance between relatives) from their initial values. Provided that each locus has only a small effect on the trait, only minor allele-frequency change is expected over the first several generations. In the extreme under the infinitesimal model (the limit of a very large number of loci, each with vanishingly small effect), the additive genic variance (that part of the additive variance independent of any disequilibrium effects) remains essentially unchanged during selection (Chapters 16, 24). The short-term response of a trait refers to these early generations where allele-frequency change has a negligible effect on the initial additive variance. Over longer time scales, allele-frequency evolution results in substantial changes in the variance that are extremely difficult to predict. This is the setting for longterm response, examined in Chapters 25 28. Selection can occur in any matter of fashions. Our focus in this chapter is individual (or mass) selection under random mating, wherein individuals are chosen solely on the basis of their phenotypic value (i.e., information from relatives, other characters, etc. is ignored). Family selection, where individuals are chosen based on either their family mean or their ranking within a family is discussed in Chapter 21. Chapter 22 discusses the setting where individuals interact in groups (kin selection if they are related) and selection may be either on the individual and/or at the group level (group selection), while Chapter 23 and 24 examines response in inbred populations. Using additional information, such as the trait value in other relatives and/or the values of other traits in the focal individual, can improve our accuracy in predicting an individual’s breeding value and hence increase the response relative to individual selection. This can be done through index selection, which leads to BLUP-based selection (Chapters 19, 20, 22; LW Chapter 26), both of which are more fully developed in our final volume. A number of other important selection schemes (such as marker-assisted and genomic selection, selection for outcross performance, and in age-structured populations) are also deferred until our final volume. There is a huge literature on schemes exploiting special features of specific organisms (such as artificial insemination in animals or complex crosses in selfing plants). See Turner and Young (1969), Pirchner (1983), Ollivier (1988), Weller (1994), Cameron (1997), Simm (1998), and Kinghorn et al. (2000) for applications in animal breeding and Namkoong (1979), Wricke and Weber (1986), Mayo (1987), Hallauer et al. (1988), Stoskopf et al. (1993), Bos and Caligari (1995), Gallais (2003), and Bernardo (2010) for applications in plant breeding.