Date of Award

Spring 5-9-2019

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

Zachary Kilpatrick

Second Advisor

Nancy Rodriguez

Third Advisor

Juan Restrepo

Abstract

For many organisms, foraging for food and resources is integral to survival. Mathematical models of foraging can provide insight into the benefits and drawbacks of different foraging strategies. We begin by considering the movement of a memoryless starving forager on a one-dimensional periodic lattice, where each location contains one unit of food. As the forager lands on sites with food, it consumes the food leaving the sites empty. If the forager lands consecutively on a certain number of empty sites, then it starves. The forager has two modes of movement: it can either diffuse by moving with equal probability to adjacent lattice sites, or it can jump uniformly randomly amongst the lattice sites. The lifetime of the forager can be approximated in either paradigm by the sum of the cover time plus the number of empty sites it can visit before starving. The lifetime of the forager varies nonmontonically according to the probability of jumping. The tradeoff between jumps and diffusion is explored using simpler systems as well as numerical simulation, and we demonstrate that the best strategy is one that incorporates both jumps and diffusion. When long range jumps are time-penalized, counterintuitively, this shifts the optimal strategy to pure jumping. We next consider optimal strategies for a group of foragers to search for a target (such as food in an environment where it is sparsely located). There is a single target in one of several patches, with a greater penalty if the foragers decide to switch their positions among the patches. Both in the case of a single searcher, and in the case of a group of searchers, efficient deterministic strategies can be found to locate the target.

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