OPTIMIZATION MODELS, QUANTITATIVE GENETICS, AND MUTATION.

The process of selection on a multivariate set of characters subject to functional constraints is considered from the points of view of both evolutionary optimization theory and quantitative genetics. Special attention is given to life-history characteristics. It is shown that, under suitable conditions (including weak selection), useful approximate formulas for the relations between the functional constraints and the additive genetic variance-covariance matrix can be derived. These can be used to show that the conditions for equilibrium under selection according to the two different approaches are approximately equivalent. Although large negative genetic correlations are to be expected between some pairs of life-history traits in populations at equilibrium under selection, in general some small negative genetic correlations and some positive genetic correlations will also be present. Thus, the observation of a positive genetic correlation between a pair of life-history traits does not necessarily refute the possibility of trade-offs among a multivariate set of traits that contains the pair in question. The relation between the pattern of functional constraints and the genetic correlations is often complex, and little insight into the former can be derived from the latter. The effects of mutations that lower the overall efficiency of resource utilization, thereby creating a positive component to the genetic covariances among life-history traits, are also considered for a specific model. Although such mutations can have a substantial effect on the form of the life history, extreme conditions seem to be needed for them to produce a large effect on the pattern of genetic correlations in a random-mating population. They can, however, cause the appearance of positive correlations following inbreeding, due to the exposure of deleterious recessive or partially recessive mutations. The analysis also suggests that the population means of individual components of a constrained multivariate system may often equilibrate at values that are far from the optima that would be attained if they were selected in isolation from the other members of the system.