Date of Award

Spring 1-1-2013

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

Samuel Flaxman

Second Advisor

Anne Dougherty

Third Advisor

Juan Restrepo

Abstract

In order to model the spatial distributions of predators and prey many investigators have used a simplified three-species system where a predator species consumes a prey species that consumes a resource. One of the recurring predictions from such models is that the spatial distribution of the predator will match the spatial distribution of the resource instead of that of the prey; this is known as ``leapfrogging". While it is interesting that leapfrogging is consistently predicted by models of three species, tritrophic systems, real biological communities are more complicated, being less like chains and more like multi-dimensional food webs (i.e., multiple prey and predator species interacting with each other). I ask: Are systems with more species and more connections among them well approximated by simpler, three-species single-chain models? I construct two different five-dimensional systems (a resource consumed by two prey species consumed by two predator species) and compare them to the single-chain system to see if more complicated systems yield the same predictions as a simpler single-chain system. I discovered that, in aggregate, the dynamics of predators in a multi-species web, is very similar to the dynamics of a simpler, single-chain system; yet individualy the dynamics of predator species in a multi-species web are very different from the dynamics of a simpler, single-chain system.

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