Optimally Frugal Foraging

Abstract

We introduce the \emph{frugal foraging} model in which a forager performs a discrete-time random walk on a lattice, where each site initially contains $\mathcal{S}$ food units. The forager metabolizes one unit of food at each step and starves to death when it last ate $\mathcal{S}$ steps in the past. Whenever the forager decides to eat, it consumes all food at its current site and this site remains empty (no food replenishment). The crucial property of the forager is 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 a function of frugality threshold and show that there exists an optimal strategy, namely, a frugality threshold $k^{\ast }$ that maximizes the forager lifetime.

5 pages, 3 figures

References in corpus (3)

• Depletion-Controlled Starvation of a Diffusing Forager
• Role of Depletion on the Dynamics of a Diffusing Forager
• Random Search with Memory in Patchy Media: Exploration-Exploitation Tradeoff

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• Dimensionality-dependent crossover in motility of polyvalent burnt-bridges ratchets
• Loss of Percolation Transition in the Presence of Simple Tracer-Media Interactions
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• From Maximum of Intervisit Times to Starving Random Walks
• The Advantage of Foraging Myopically
• Covariance of the running range of a Brownian trajectory
• Optimizing a jump-diffusion model of a starving forager
• The shape of a memorised random walk
• Persistence exponents of self-interacting random walks
• Forager with intermittent rest: Better for survival?
• Active stop and go motion: a strategy to improve spatial exploration and survival
• Does Partial Consumption Help Foraging?
• Energy-constrained random walk with boundary replenishment