Impact of food distribution on lifetime of a forager with or without sense of smell

TL;DR

This paper investigates how different spatial distributions of food influence the lifetime of foragers, analyzing models with and without sense of smell in one and two dimensions, revealing key scaling laws and conditions for immortality.

Contribution

It provides analytical insights into forager lifetime based on food distribution patterns and introduces conditions under which foragers with smell can become immortal.

Findings

Analytical expression for forager lifetime without smell in 1D.

Condition for immortality of smelling foragers in 1D.

Lifetime scales as $T o S^4f^{3/2}$ in 2D.

Abstract

Modeling foraging via basic models is a problem that has been recently investigated from several points of view. However, understanding the effect of the spatial distribution of food on the lifetime of a forager has not been achieved yet. We explore here how the distribution of food in space affects the forager's lifetime in several different scenarios. We analyze a random forager and a smelling forager in both one and two dimensions. We first consider a general food distribution, and then analyze in detail specific distributions including constant distance between food, certain probability of existence of food at each site, and power-law distribution of distances between food. For a forager in one dimension without smell we find analytically the lifetime, and for a forager with smell we find the condition for immortality. In two dimensions we find based on analytical considerations that the lifetime ($T$) scales with the starving time ($S$) and food density ($f$) as $T\sim S^4f^{3/2}$.