Role of Depletion on the Dynamics of a Diffusing Forager

Abstract

We study the dynamics of a starving random walk in general spatial dimension $d$. This model represents an idealized description for the fate of an unaware forager whose motion is not affected by the presence or absence of resources. The forager depletes its environment by consuming resources and dies if it wanders too long without finding food. In the exactly-solvable case of one dimension, we explicitly derive the average lifetime of the walk and the distribution for the number of distinct sites visited by the walk at the instant of starvation. We also give a heuristic derivation for the averages of these two quantities. We tackle the complex but ecologically-relevant case of two dimensions by an approximation in which the depleted zone is assumed to always be circular and which grows incrementally each time the walk reaches the edge of this zone. Within this framework, we derive a lower bound for the scaling of the average lifetime and number of distinct sites visited at starvation. We also determine the asymptotic distribution of the number of distinct sites visited at starvation. Finally, we solve the case of high spatial dimensions within a mean-field approach.

References in corpus (4)

• A survey of random processes with reinforcement
• Depletion-Controlled Starvation of a Diffusing Forager
• Universality classes of foraging with resource renewal
• Diffusion-limited reactions and mortal random walkers in confined geometries

Cited by in corpus (18)

• Random walks and diffusion on networks
• Depletion of Resources by a Population of Diffusing Species
• Optimally Frugal Foraging
• Dimensionality-dependent crossover in motility of polyvalent burnt-bridges ratchets
• Universal exploration dynamics of random walks
• Does Greed Help a Forager Survive?
• Semantic Information in a model of Resource Gathering Agents
• Random Search with Memory in Patchy Media: Exploration-Exploitation Tradeoff
• First-passage properties of mortal random walks: ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs
• Analytical results for the distribution of cover times of random walks on random regular graphs
• Analytical results for the distribution of first hitting times of random walks on random regular graphs
• How Smart Should a Forager Be?
• Impact of food distribution on lifetime of a forager with or without sense of smell
• From Maximum of Intervisit Times to Starving Random Walks
• Information-theoretic description of a feedback-control Kuramoto model
• The joint distribution of first return times and of the number of distinct sites visited by a 1D random walk before returning to the origin
• Forager with intermittent rest: Better for survival?
• Evanescent random walker on networks: Hitting times, budget renewal, and survival dynamics