Evolutionarily stable seasonal timing for insects with competition for renewable resource

Summary I study the evolutionarily stable seasonal patterns of hatching and pupation for herbivorous insects that engage in exploitative competition for a renewable resource. A longer larval feeding period enhances female fecundity, but also causes a higher mortality by predation and parasitism. Previously, it was shown that the evolutionarily stable population exhibits asynchronous starting and ending of the larval feeding period in a model in which larval growth rate decreases with the total larval biomass in the population due presumably to interference competition. Here I study the case in which resource availability changes not only with environmental seasonality but with the depletion by the feeding of larvae. I find that if the impact of the herbivory is strong, both hatching and pupation should occur asynchronously in the evolutionarily stable population. And if the favourable season for the host plant is short the ESS population may include synchronous timing of pupation. If the timing of hatching and pupation occurs asynchronously, in the first day of each interval some fraction of the population hatch or pupate, respectively and the rest do so gradually over the interval. In addition, if the environmental variable changes as a symmetric function of time, the length of the period in which hatching occurs tends to be much shorter than the period in which pupation occurs.