Selection in Age‐Structured Populations

RESPONSE WITH OVERLAPPING GENERATIONS Many natural population display age structure, with adults surviving and reproducing over several breeding periods. When generations overlap like this, during any breeding period parents of different ages are likely to have different mean breeding values, and the breeders' equation must be modified. Consider a population under constant directional selection to increase the character. Younger parents are the result of more generations of selection and are thus expected to produce larger offspring than older parents. Thus, while the genotypic value of an individual remains constant over its lifespan, at any given time younger parents have large genotypic values than older parents. This tendency arises from the population structure, and should not be confused with environmental age effects. If such age effects are present, we assume they are either small relative to the genetic change or are predictable enough to be removed before analysis (e.g., Cassuto et al. 1970). We continue to assume that epistasis and genotype × environment interactions or correlations are negligible. Asymptotic Response With overlapping generations, one measure of response to selection is ∆ r , the amount of response seen in newborn offspring per unit time interval (typically years). We use ∆ r to distinguish this rate of response from R, the response under a single discrete generation. For compartive purposes, note that the rate of response in unit time intervals for a population with a discrete generation of length τ is ∆ r = R/τ. The rate of response with overlapping generations was obtained by Dickerson and Hazel (1944) and generalized by Rendel and Robertson (1950), whose derivation we follow. The major assumption is that the amount of genetic gain per unit time interval is constant, leading Hill (1974b) to refer to these as asymptotic responses. To reach such a state, a constant amount of selection has to act on an age-structured population for a sufficient amount of time to generate a 147