A foraging problem: Sit-and-wait versus active predation

The literature on foraging shows that some predators use a combination of ambush and active search to locate a prey. Let us suppose that a prey must go every day to some determined places to feed, and to another place, 0, to drink. A predator can stay at zone 0 waiting for the prey (sit-and-wait strategy) or it can move between the different places where the prey will go to eat (search strategy). If predator and prey meet each other in the same place, prey will be caught with a probability depending on the place. We study this problem in different situations, modelling them as two-person zero-sum games. We solve them in closed form, giving optimal strategies for prey and for predator and the value of the games.Game theory Two-person games Search games Search problems Predator-prey interactions

Annexes from The coupon collector urn model with unequal probabilities in ecology and evolution

This supplementary electronic material contains the Annexes of the paper: The coupon collector urn model with unequal probabilities in ecology and evolution. Zoroa, N., Lesigne, E., Fernández-Sáez, M.J., Zoroa, P. & Casas, J. Published in Journal of the Royal Society Interface

A proof of the Kikuta–Ruckle Conjecture on cyclic caching of resources

Suppose that a hider possesses a continuously divisible resource that he may distribute around a circle. The resources on a random arc in the circle are lost. The hider has a priori information on the length of the arc and he wants to maximize the probability that the retrieved portion exceeds a critical quantity, which is enough to survive on. We show that there exists an optimal resource distribution, which uses a finite number of point caches of equal size, establishing a conjecture of Kikuta and Ruckle. Our result is related to a conjecture of Samuels' on-tail probabilities