Long-term Response: Finite Populations

Genetic drift is of considerable importance in most artificial selection experiments, which tend to have very small effective population sizes. We have previously considered the short-term implications of drift in generating variance around the expected response (Chapter 6), which occurs even in the absence of major changes in allele frequencies. This chapter examines the implications for long-term response, considering how drift interacts with selection and how new mutations contribute to the selection response. Throughout, we generally restrict attention to directional selection, considering stabilizing selection in Chapter 13. Given that both initial variation and new mutation can contribute to a selection response, we will use the term long-term response to refer to that component of the response expected from the initial variation in the population at the start of selection. Eventually, all the initial variation will be exhausted and the response from this component will have reached a selection limit. The actual response, however, can continue past this limit due to the input from new mutation, eventually reaching (under constant selection) an asymptotic response, wherein the response reaches a steady-state value due to the contribution to the genetic variance from new mutation is balanced by its removal from drift and selection. This chapter covers a wide variety of topics, starting with a review of allele frequency changes under the joint actions of drift and selection. Next, we examine the subtle (but very important) effect of selection in decreasing the effective population size over that expected from the number of reproducing individuals. This reduction occurs because with selection on a heritable character, a few families (and their relatives) end up making most of the contribution to the total response. Thus, individuals that survive selection to reproduce are closer relatives than expected by change, increasing the rate of inbreeding. With the background provided by these two areas in hand, we then turn to considerations of the ultimate contribution from the initial genetic variation in a population and expected asymptotic response due to the contribution of new mutations. Historically, the theory of the expected long-term response ignored the effects of mutation by considering only the expected response that can be generated given the initial genetic variation present, and we consider long-term response