The Advantage of Foraging Myopically

TL;DR

This paper investigates how a myopic forager's probability of eating when encountering food affects its lifetime, revealing that an optimal level of myopia significantly extends survival, especially in higher dimensions.

Contribution

It introduces a model of a myopic forager with probabilistic eating behavior and analyzes how this affects its lifetime across different spatial dimensions.

Findings

Optimal myopia probability maximizes forager lifetime.

Lifetime scales superlinearly with the forager's food-escape capacity $\

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Abstract

We study the dynamics of a \emph{myopic} forager that randomly wanders on a lattice in which each site contains one unit of food. Upon encountering a food-containing site, the forager eats all the food at this site with probability $p<1$; otherwise, the food is left undisturbed. When the forager eats, it can wander $\mathcal{S}$ additional steps without food before starving to death. When the forager does not eat, either by not detecting food on a full site or by encountering an empty site, the forager goes hungry and comes one time unit closer to starvation. As the forager wanders, a multiply connected spatial region where food has been consumed---a desert---is created. The forager lifetime depends non-monotonically on its degree of myopia $p$, and at the optimal myopia $p=p^*(\mathcal{S})$, the forager lives much longer than a normal forager that always eats when it encounters food. This optimal lifetime grows as $\mathcal{S}^2/\ln\mathcal{S}$ in one dimension and faster than a power law in $\mathcal{S}$ in two and higher dimensions.