Researcher ORCID Identifier

https://orcid.org/0009-0008-6417-7514

Graduation Year

2025

Date of Submission

12-2024

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Physics

Second Department

Economics

Reader 1

Sarah Marzen

Reader 2

Yaron Raviv

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2024 Ann Mahé

Abstract

Games of cooperation are commonly observed in biological systems and can be used to understand their evolution. An example of these dynamics is found in yeast cells, which exhibit cooperative behavior during their growth. Yeast population dynamics can be modeled with three types of cooperation games: the Prisoner’s Dilemma (PD), the Mutual Benefit Game (MB), and the Snowdrift Game (SD). Previous studies have primarily focused on fixed strains of yeast cells that consistently cooperate or defect. Here, we extend those methods to non-fixed strains capable of switching strategies with each iteration. Using a simple “RSTP” mathematical model based on relative payoffs, a linear model that introduces cost and efficiency parameters, and a non-linear model with the same parameters, we extrapolate the games onto a spatial structure and analyze the evolutionary dynamics. We find that the “RSTP” model mirrors the patterns observed in fixed-strain populations, with cooperators forming cross-like structures. The linear model also aligns with the findings for fixed strains, with the steady state showing the effects of a Prisoner’s Dilemma or a Mutual Benefit Game. However, while the non-linear spatial model exhibits the expected dynamics of a Snowdrift Game, it also reveals that cooperators in non-fixed strains can form robust square structures in the steady state.

This thesis is restricted to the Claremont Colleges current faculty, students, and staff.

Share

COinS