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arXiv · 1804.08045

The Advantage of Foraging Myopically

C. L. Rager·U. Bhat·O. Bénichou·S. Redner
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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.

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C. L. Rager, U. Bhat, O. Bénichou, S. Redner. 2018-04-21. The Advantage of Foraging Myopically. https://doi.org/10.1088/1742-5468/aace2d

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