THE MAINTENANCE OF PHENOTYPIC AND GENETIC-VARIATION IN THRESHOLD TRAITS BY FREQUENCY-DEPENDENT SELECTION

Many traits are phenotypically dimorphic but determined by the action of many loci, the phenotype being a result of a threshold of sensitivi ty. Quantitative genetic analysis has shown that generally there is co nsiderable additive genetic variation for the trait, the average herit ability being 0.52. In numerous cases threshold traits have been shown , or are assumed, to be under frequency-dependent selection; examples include satellite-territorial behaviour, sex-determination, wing dimor phism and trophic dimorphism. In this paper I investigate the potentia l for frequency-dependent selection to maintain both phenotypic and ad ditive genetic variation in threshold traits. The qualitative results are robust to the particular form of the frequency-dependent selection function. The equilibrium proportion is more or less independent of p opulation size but the heritability increases with population size, ty pically approaching its maximal value at a population size of 5000, wh en the mutation rate is 10(-4). A tenfold decrease in the mutation rat e requires an approximate doubling of the population size before an as ymptotic value is approached. Thus frequency-dependent selection can a ccount for both the existence of two morphs in a population and the ob served levels of heritability. It is also shown, both via simulation a nd theory, that the quantitative genetic model and a simple phenotypic analysis predict the same equilibrium morph proportion.