A Theoretical Model for the Optimal Timing of Diapause

A theoretical model is developed to predict the optimal timing of diapause in polycyclic insects as a function of seasonal changes in survival and reproduction of diapausing and nondiapausing individuals, respectively. For a uniform population in a uniform environment, in which maturation is spread over a long time, a relatively sharp transition between 0%-100% diapause is optimal at the time when the expectation of reproduction becomes less than the expectation of survival. On the other hand, when maturation is restricted to a short interval, the optimal diapausing fraction will take an intermediate value during an extended period. Several cases of correlations between conditions on successive days are considered, and the results are discussed with reference to observed diapausing behavior.