Egg Distribution within Patches: An Optimality Problem for Insects

A puzzling phenomenon in insect oviposition is the variety of egg distributions over plants. A clumped distribution can cause food competition among the offspring, and consequently risky migration to other plants. On the other hand, egg clumping can initially be advantageous. To examine under which conditions egg clumping is optimal, we studied the optimal distribution of eggs within a patch. A three-step model is proposed, representing hatching and initial growth of the larvae, migration and pupation. Assuming that egg clumping is advantageous in the first step, but disadvantageous in the subsequent steps, we analyze the trade-off between these effects. Five factors are investigated to see if they can contribute towards egg clumping: (1) size of egg supply; (2) number of plants per patch; (3) number of patches; (4) competition between insects; (5) small stochastic fluctuations in patch quality. Our results show that (1), (2), and (3) can contribute towards egg clumping, but (5) cannot. As an example, the model is applied to the cinnabar moth. We show that only (2) and (3) contribute towards the clumped egg distribution of the moth.