Document Type



Doctor of Philosophy



Date of Defense


Graduate Advisor

Sonya Bahar


Thomas Vojta

Nevena Maric

Ricardo Flores

Paul Parris


Presented here is an interdisciplinary study that draws connections between the fields of physics, mathematics, and evolutionary biology. Importantly, as we move through the Anthropocene Epoch, where human-driven climate change threatens biodiversity, understanding how an evolving population responds to extinction stress could be key to saving endangered ecosystems. With a neutral, agent-based model that incorporates the main principles of Darwinian evolution, such as heritability, variability, and competition, the dynamics of speciation and extinction is investigated. The simulated organisms evolve according to the reaction-diffusion rules of the 2D directed percolation universality class. Offspring are generated according to one of three reproduction schemes. Mate choice dictates offspring placement, and it defines a species based on reproductive isolation (known as the biological species concept), while a globally enforced death process ensues within each generation. This system is shown to exhibit nonequilibrium, continuous phase transitions as a function of the individual death probability. The dynamical rules that enable phase transition and clustering behavior to transpire behavior is discussed, and a connection is drawn to another type of phase transition that arises by mate choice alone. Coalescent theory is then used to explore common descent in evolved phylogenetic tree structures at both the individual and cluster level. Finally, an extinction scenario is implemented where, after reaching a steady-state, a large population percentage is killed. Historical contingency is shown to play a major role in recovery from mass extinction at criticality.

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