Optimally Frugal Foraging

摘要

We introduce the \emph{frugal foraging} model in which a forager performs adiscrete-time random walk on a lattice, where each site initially contains$\mathcal{S}$ food units. The forager metabolizes one unit of food at each stepand starves to death when it last ate $\mathcal{S}$ steps in the past. Wheneverthe forager decides to eat, it consumes all food at its current site and thissite remains empty (no food replenishment). The crucial property of the forageris that it is \emph{frugal} and eats only when encountering food within at most$k$ steps of starvation. We compute the average lifetime analytically as afunction of frugality threshold and show that there exists an optimal strategy,namely, a frugality threshold $k^*$ that maximizes the forager lifetime.