Bet-hedging when targets may disappear: Optimal mate-seeking or prey-catching trajectories and the stability of leks and herds

When a female frog moves towards a calling male, the male may suddenly stop calling and the female have to switch to another male. Analogous situation s where "hunters" move towards "targets" that can disappear unpredictably i nclude predators stalking prey and plants growing towards gaps in the canop y. I use dynamic programming to show that when the hunter has a choice of s uch targets it is optimal to take a curved bet-hedging trajectory, initiall y heading between two targets so that if one target disappears the other is closer. Also hunters should prefer groups of targets, even if a solitary t arget is somewhat closer, because it is unlikely that all targets in a grou p will disappear. Assuming that hunters follow these optimal trajectories I then ask whether it will pay targets to form herds or leks. The extra attr activeness of groups in this model turns out not to be sufficient to outwei gh the advantages of herding, but the net benefits of herding are considera bly reduced. (C) 1999 Academic Press.