Asynchronous pupation of univoltine insects as evolutionarily stable phenology

Evolutionarily stable seasonal timing of larval feeding stages is studied theoretically for univoltine insects. In the evolutionarily stable (or ESS) population, each individual maximizes its own lifetime reproductive success by choosing the hatching and pupation dates, given the resource availability curve with a peak in the middle of a year, a higher daily mortality in the feeding stages, and the growth rate decreasing with the larval biomass in the population. If growth rate is proportional to the body size, the population at the ESS is composed of a mixture of phenotypes differing in hatching and pupation, but pupation interval over which some popation occur every day is much longer than hatching interval. If growth rate increases with the body size at a speed slower than linearly, large sized larvae should pupate earlier than small ones.