Sharing a resource with randomly arriving foragers

•We consider foragers arriving as a Poisson process on a resource patch.•We give effective formulas allowing one to compute the expected gain of each forager.•We provide formulas for a finite horizon or infinite with a random death process.•We give applications in foraging theory with functional responses of types 1 and 2.•We give one example of application for the evolution of fungal plant parasites.

We consider a problem of foraging where identical foragers, or predators, arrive as a stochastic Poisson process on the same patch of resource. We provide effective formulas for the expected resource intake of any of the agents, as a function of its rank, given their common functional response. We give a general theory, both in finite and infinite horizon, and show two examples of applications to harvesting a common under different assumptions about the resource dynamics and the functional response, and an example of application on a model that fits, among others, a problem of evolution of fungal plant parasites.