Universality classes of foraging with resource renewal

TL;DR

This paper explores how resource renewal rates affect the lifespan of foragers in a minimal model, revealing three universal behavioral classes based on renewal speed, including conditions for immortality and finite lifetime.

Contribution

It introduces a classification of foraging behavior into three universal regimes based on resource renewal times within a minimal starving random walk model.

Findings

For rapid renewal, foragers are immortal.

In slower renewal regimes, foragers have finite lifetimes.

In one dimension, a regime exists where lifetime is independent of renewal time.

Abstract

We determine the impact of resource renewal on the lifetime of a forager that depletes its environment and starves if it wanders too long without eating. In the framework of the minimal starving random walk model with resource renewal, there are three universal classes of behavior as a function of the renewal time. For sufficiently rapid renewal, foragers are immortal, while foragers have a finite lifetime otherwise. In one dimension, there is a third regime, for sufficiently slow renewal, in which the lifetime of the forager is independent of the renewal time. We outline an enumeration method to determine the mean lifetime of the forager in the mortal regime.