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Models of Evolutionary Games: Cyclic Dominance, Public Goods and Heterogeneous Tumors

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Abstract

In this dissertation we consider several applications of evolutionary game theory. Using the replicator equation as a starting point we explore broadly the question of how interactions between agents in heterogeneous populations influence how the demographics of the population change over time. We explore in depth how mutation mechanisms can lead to oscillatory population dynamics (via Hopf bifurcations) in systems with natural cyclicity. Building on previous work examining the evolutionary dynamics of the game Rock-Paper-Scissors with one mutation mechanism, we obtain similar results using a more biologically inspired model of mutation. The evolutionary dynamics of the class of social dilemmas known as public goods games are analyzed in detail. In particular, we study these games in cases where a continuum of possible strategies is available to players. A strategy in this context is simply the amount that a player contributes to the creation of a public good. Many questions arise here: What effect do mutations have on the dynamics? What happens when the value of the public good doesn't depend linearly on the sum of the contributions to its creation? What happens if an ecological component is included, so that growth rates are partly determined by available space and resources? We answer each of these questions as well as several others and see what implications can be drawn from such models regarding the persistence of pro-social behaviour. An analysis of evolutionary game assay experiments is presented also. In these experiments heterogeneous populations of cancer cells are monitored during their evolution. At regular intervals during each trial the numbers of cells of each type are estimated by photographic means. Important characteristics of the population's state are inferred from the resulting data. However, mutational effects may be obscuring the true counts of different types of cells during the experiment, leading to errors in the conclusions that are drawn. We present a speculative population model of the experiment and show, under the assumption of its correctness, that mutation need not be worried about very much when interpreting the experimental results.

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151 pages

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Date Issued

2022-05

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Keywords

Applied Dynamical Systems; Evolutionary Game Assay; Evolutionary Game Theory; Hopf Bifurcations; Integro-Differential Equations; Public Goods Games

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Strogatz, Steven H.

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Pizarro, David A.
Rand, Richard Herbert
Kleinberg, Jon M.

Degree Discipline

Applied Mathematics

Degree Name

Ph. D., Applied Mathematics

Degree Level

Doctor of Philosophy

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Government Document

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Attribution 4.0 International

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dissertation or thesis

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