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Center for Nonlinear Studies |
What is the fate of a random-walk forager that depletes its environment as it wanders? Whenever the forager lands on a food-containing site, all the food is consumed and the forager becomes fully sated. However, when the forager lands on an empty site, it moves one time unit closer to starvation. If the forager wanders S steps without encountering food, it starves to death. We show that the lifetime of this starving random walk forager scales linearly with S in one dimension by solving an underlying non-Markovian first-passage problem. In greater than two dimensions, we present evidence that the lifetime grows quasi-exponentially in S. We also investigate the role of greed, in which the forager preferentially moves towards food when faced with a choice of hopping to food or to an empty site in its local neighborhood. Paradoxically, the forager lifetime can have a non-monotonic dependence on greed, with different senses to the non-monotonicity in one and in two dimensions. In one dimension, the forager lifetime exhibits a huge peak when greed is negative, while in two dimensions the maximum lifetime occurs for positive, but not perfect, greed. Finally, we briefly discuss the role of frugality and myopia on foraging dynamics. Frugality means that the forager does not eat until it is nutritionally depleted beyond a specified level. Myopia means that the forager sometime does not "see" food at its current site and leaves the food undisturbed. Both attributes are surprisingly effective in extending the forager lifetime.
Host: Francesco Caraveilli