Fitness Functions for Alternative Developmental Pathways in the Timing of Diapause Induction

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Abstract
We analyze five commonly occurring ontogenetic relationships between the sensitive period (SP) for diapause induction, during which environmental cues are assessed and the decision is made whether to diapause, and the diapause stage (DS), during which normal development ceases and diapause characteristics prevail. One relationship (case 1), in which both the SP and DS occur in the juvenile stages of the same generation, has previously been analyzed in detail. Here we concentrate on the remaining four developmental pathways. In case 2a, the DS is the adult preceded by a determinate SP. Since a determinate SP has a fixed end before reproduction, adults are committed to reproduction or to diapause before reproducing. In case 2b, the DS is the adult preceded by an indeterminate SP, which has no fixed end and extends into the reproductive adult stage, allowing an adult to reproduce before entering diapause. The parental generation in case 3a determines the disapausing fate of a preadult stage in the next generation, and the SP is determinate (i.e. offspring are all diapausing or all nondiapausing). Case 3b is the same as case 3a, but with an indeterminate SP, permitting females to produce nondiapausing and then diapausing offspring. Each of these four cases generates a unique fitness function. For each case, we provide formulas for the optimal time at which individuals should enter diapause or produce diapausing offspring; we also show which parameters determine the shape of the fitness functions. We review the literature on the occurrence of the alternative pathways among various arthropods and discuss the evolutionary significance of a determinate versus indeterminate SP. It is suggested that case 2b would be the best for testing the predictions of the theory.