Probabilistic optimization of phenotype distributions: a general solution for the effects of uncertainty on natural selection?

Summary

Explorations of optimizing selection often find discrepancies between the theoretically expected and observed phenotypes. Such discrepancies are usually attributed to a variety of potential constraints. We suggest that one common constraint, environmental uncertainty, may reduce the applicability of traditional deterministic or stochastic optimization methods and that many apparent discrepancies might be artifacts of these methods. Since natural selection is essentially a statistical process, we propose that a probabilistic optimization procedure, that includes all of the variability in phenotype distributions and associated fitness potential functions might offer better results. The traditional methods define an optimal gene or genotype as that which produces a phenotype distribution with a mean or other measure of central tendency that equals the value yielding the maximum fitness potential. Our method defines the optimal gene or genotype as that which produces the phenotype distribution that maximizes fitness summed or integrated over its associated fitness potential function. Often the central tendency of the phenotype distribution yielding the probabilistic optimum will differ from the deterministic expectation. This method is an extension of utility theory to any phenotypic character. We illustrate our method using an example based on Price and Waser's (1979) notion of optimal inbreeding via optimal pollen dispersal.