On the quantitative genetics of correlated characters under directional selection in age-structured populations

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Abstract
The evolution of correlated characters in natural populations depends on the demographic structure of these populations. This is often considerably more complicated than the structure of populations typically addressed by quantitative genetics, involving overlapping generations, age-dependent vital rates, and large fluctuations in recruitment from year to year. It is important to know more about such evolution because human exploitation of natural populations such as fishes is selective and has the potential to cause major changes in their properties. Here the theory of quantitative genetics of correlated characters under directional selection is extended to incorporate some demographic properties of non-equilibrium age structured populations. Short-term evolution is described in terms of changes in a matrix of mean breeding values of the traits at each age, and depends on the selection differentials in operation, together with the variances and covariances of breeding and phenotypic values. Because the selection differentials depend on the current mean phenotypic values which are themselves changing as each cohort grows older, the dynamics of mean phenotypic values within cohorts are also followed. Together, the changes in mean breeding and phenotypic values are sufficient to predict the short-term transient evolutionary dynamics of correlated characters in non-equilibrium age-structured populations. The predictions are compared with the dynamics observed in some randomly generated populations, and the application of the theory to evolution in commercially exploited populations of fish is discussed.