The quantitative genetic theory of parental effects

There are many theoretical approaches for studying the evolution of parental care and parent–offspring interactions (Chapters 2, 7, 9, and 16; Mock and Parker 1997), but here I focus on theory developed in the field of quantitative genetics. The reasons for this are twofold; first, they allow tractable dynamic models for phenotypes determined by multiple genes and the environment. Second, theory and application are so entwined in quantitative genetics that the development of theory is nearly always followed, or sometimes even preceded, by methods to estimate the relevant parameters from data—a useful resource for empiricists. However, my main aim is not to champion the quantitative genetic approach over others, but to clarify how quantitative genetic models of parent–offspring interaction work, and how the key concepts fit with more familiar ideas from behavioural ecology. Traditionally, the two approaches have often focused on fundamentally different things; with behavioural ecology focusing on parent–offspring conflict and quantitative genetics focusing on parent–offspring co-adaptation (reviewed in Smiseth et al. 2008; Hinde et al. 2010). The goal of this chapter is to dispel the perception that the tension between the interests of the individual and the interests of kin does not have a natural place in the quantitative genetic approach, and to clarify that its omission from much recent theoretical and empirical work is not warranted. Its omission seems to be inadvertent and may have arisen because those applying the quantitative genetic approach have continued to associate concepts from behavioural ecology with concepts of the same name from quantitative genetics, particularly those pertaining to fitness and selection (Chapter 1). Quantitative genetic models of parental effects are designed to predict evolutionary change in suites of traits that affect traits expressed in offspring and/or are affected by traits expressed in parents. In the first section I give a detailed exposition of the Kirkpatrick–Lande model (hence forth the K–L model; Kirkpatrick and Lande 1989, 1992; Lande and Kirkpatrick 1990), a model that generalized a great deal of previous theory in which the phenotype and fitness of an individual was influenced by the phenotypes of its parents (Dickerson 1947; Willham 1963, 1972; Falconer 1965; Cheverud 1984). The model is difficult to understand and so the intention is to derive and explain it in a way that is both didactic and complementary to the original work, with special emphasis on clarifying what is meant by selection. To facilitate this, I work through a simple biological example in the second section and highlight the relationship between the selection parameters of the K–L model and concepts from behavioural ecology and life-history evolution. By doing this I argue that recent theoretical and empirical work in quantitative genetics has assumed values for these selection parameters that contradict central ideas from behavioural ecology that have wide empirical support. In the third section I describe the Willham model (Willham 1963, 1972), a special case of the K–L model widely used by empiricists, and show that by changing assumptions about the form of selection we come to very different conclusions about what types of genetic architecture act as constraints to evolutionary change. Following