Genetic analysis of a population of Tribolium. IX. Maximization of population size and the concept of a stochastic equilibrium

Abstract

Motivated by the genetic hypothesis that natural selection results in the maximization of the equilibrium population size, we quantified this latter equilibrium for laboratory populations of the flour beetle Tribolium castaneum, using the gamma probability density function. Gamma density functions were fitted to adult numbers for each of the experimental treatments that were started with frequencies of the corn oil sensitive (cos) allele in the range 0–1 at intervals of 0.1. The gamma density function adequately described all observed distributions. However, contrary to theory, statistical comparisons of the fitted distribution indicate that the polymorphic populations did not converge to the same identical distribution and that the polymorphic populations are intermediate in population size to the two homozygous groups. The need for a stochastic theory that combines both population size and genetic selection is discussed.Key words: natural selection, Tribolium, gamma distribution, maximum population size, stationary distribution, stochastic differential equation, stochastic population model.