THEORY OF FITNESS IN A HETEROGENEOUS ENVIRONMENT. V. OPTIMAL GENETIC SYSTEMS

Abstract

In the optimum quadratic deviation model in an unstable environment, an increase in the phenotypic effect of a locus reduces fitness by increasing the variance of the mean phenotype and the average variance within the population. It also can increase fitness by increasing the correlation between the mean phenotype and the optimum, which is an environmental variable, provided the auto. correlation of the environment exceeds about 0.8. There is an optimal phenotypic effect a, different from zero, if the environment is sufficiently predictable. This optimum increases with the autocorrelation of the environment and with its variance but decreases with the homeostasis (environmental tolerance) of the individual. Thus species which are very sensitive to environmental change will depend more on genetic change to adapt. In any case, the average phenotypic variance of an optimal population is roughly 2 to 10 % of the environmental variance. The response to selection may restore a significant proportion of the fitness lost due to environmental fluctuation. For a normal random environment, the proportion of fitness restored is smaller than for environments that alternate periodically between discrete alternatives. Even a restoration of 2% would create enough selection pressure to move the population toward optimum on a time scale which is still short compared to the life of the species. Linkage reduces the response to selection and the average variance because there is an excess of repulsion over coupling gametes. Thus tight linkage is advantageous when the total phenotypic effects of the loci are above optimum, and disadvantageous when they are below optimum. Testable predictions are made relating the response to selection to other aspects of the adaptive system and species structure.