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Title: | An Analytical Model of Microbial Interactions |
Authors: | Bauman, Daniel |
Advisors: | Tarnita, Corina |
Department: | Mathematics |
Class Year: | 2023 |
Abstract: | Interactions between bacteria which produce antibiotics and those which produce degrading enzymes to counteract the antibiotics are common in nature. They have been proposed as a mechanism enabling robust species coexistence and the stability of communities with many species. Current approaches to this rely on complex simulations, without effective mathematical treatment or insight. As a possible approach to better understand this system, I describe these bacterial interactions as a Wright-Fisher evolutionary model on a randomly colored graph. By taking an infinite-population limit, I derive a replicator equation, which is studied at varying degrees of simplicity. I show that the interaction can be captured by a three-strategy matrix game which exhibits stability. Three-strategy matrix games are then studied more generally, and I prove a theorem connecting coexistence of all species in the replicator equation to the ability of smaller sub-communities to be invaded. |
URI: | http://arks.princeton.edu/ark:/88435/dsp01nz806295z |
Type of Material: | Princeton University Senior Theses |
Language: | en |
Appears in Collections: | Mathematics, 1934-2023 |
Files in This Item:
File | Description | Size | Format | |
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BAUMAN-DANIEL-THESIS.pdf | 664.69 kB | Adobe PDF | Request a copy |
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