Predicting long-term response to selection

Abstract

Lande's equation for predicting the response of trait means to a shift in optimal trait values is tested using a stochastic simulation model. The simulated population is finite, and each individual has a finite number of loci. Therefore, selection may cause allele frequencies and distributions to change over time. Since the equation assumes constant genetic parameters, the degree to which such allelic changes affect predictions can be examined. Predictions are based only on information available at generation zero of directional selection. The quality of the predictions depends on the nature of allelic distributions in the original population. If allelic effects are approximately normally distributed, as assumed in Lande's Gaussian approximation to the continuum-of-alleles model, the predictions are very accurate, despite small changes in the G matrix. If allelic effects have a leptokurtic distribution, as is likely in Turelli's ‘house-of-cards’ approximation, the equation underestimates the rate of response and correlated response, and overestimates the time required for the trait means to reach their equilibrium values. Models with biallelic loci have limits as to the amount of trait divergence possible, since only two allelic values are available at each of a finite set of loci. If the new optimal trait values lie within these limits, predictions are good. if not, singularity in the G matrix results in suboptimal equilibria, despite the presence of genetic variance for each individual trait.