Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

Abstract

A model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or longestablished cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.

Genetic Constraints on the Evolution of Mate Recognition under Natural Selection

“…Although such dramatic increases in genetic variance as a consequence of selection have been predicted by theory, they have rarely been observed (Barton and Turelli 1987), if at all (Keightley and Hill 1989). Large increases in genetic variance are more likely to occur if the traits in question have been under strong stabilizing selection before the advent of directional selection (Keightley and Hill 1989;Burger and Lande 1994). This is because the distribution of allele frequencies under strong stabilizing selection will be U-shaped, with few loci having alleles at intermediate frequencies (Keightley and Hill 1989).…”

“…Large increases in genetic variance are more likely to occur if the traits in question have been under strong stabilizing selection before the advent of directional selection (Keightley and Hill 1989;Burger and Lande 1994). This is because the distribution of allele frequencies under strong stabilizing selection will be U-shaped, with few loci having alleles at intermediate frequencies (Keightley and Hill 1989). Mate recognition has been considered to be under strong stabilizing selection as a consequence of the requirement of coordination between male and female components to maintain effective communication (Butlin and Ritchie 1989;Ritchie 1996), particularly in relation to traits involved in species recognition (Butlin et al 1985;Paterson 1985).…”

“…While this discrepancy between theory and experiment may in part be a consequence of low statistical power in experimental studies (Shaw et al 1995), our experiment suggested that a real difference may exist between the stability of G in short-term experiments and comparative studies investigating longer-term changes. For example, under some conditions, selection will change the genetic variances and covariances over the short term, but the new equilibrium values reached in the long term may sometimes be very similar to those before selection (Keightley and Hill 1989;Reeve 2000;Agrawal et al 2001). Alternatively, there may be the opportunity for mutation to restore variation over the long term (Lande 1980).…”

Stability of the G-Matrix in a Population Experiencing Pleiotropic Mutation, Stabilizing Selection, and Genetic Drift

“…For comparison of the dynamics of the genetic variance of our traits determined by pleiotropic loci with those expected of a single, completely independent trait experiencing stabilizing selection, genetic drift, and mutation, we also calculated the stochastic house-of-cards approximation for the expected genetic variance of a single trait (Barton 1989;Bürger et al 1989;Houle 1989;Keightley and Hill 1989). Under this model, the formula for the expected genetic variance is…”

“…Such a modeling approach has led to useful insights in quantitative genetic studies involving single traits. For example, stochastic models have been used to address the maintenance of genetic variance for quantitative traits in finite populations (Bulmer 1972;Barton 1989;Bü rger et al 1989;Keightley and Hill 1989;Foley 1992;Bü rger and Lande 1994) and the risk of extinction due to quantitative trait evolution in response to environmental change (Bü rger and Lynch 1995). So far, few studies have attempted to extend these stochastic models to problems involving a phenotype comprising multiple traits (Wagner 1989;Baatz and Wagner 1997;Wagner et al 1997;Reeve 2000), and none has investigated the stability of G in detail.…”