Modern evolutionary theory is based on a set of sophisticated mathematical models that describe how populations change over time and diverge from one another. While this collection of models has been very successful, it has not produced a unified mathematical evolutionary theory, since each model is based on different simplifying assumptions. It is thus not clear how the different models relate to one another, and some real evolutionary processes are invisible to this body of theory because they are not addressed by any particular model. The goal of this project is to develop a single body of mathematical evolutionary theory that is based only on assumptions that we know to be true, and that will both unify the existing models and allow study of evolutionary processes that current theory fails to address.
This project will have two important consequences. First, the work will provide tools for investigating evolutionary dynamics in cases that have previously been hard to study, such as very small populations, those in highly unstable environments, and those living in patchy environments with variable migration rates. These populations are most likely to experience either speciation or extinction. Second, this work will illuminate the underlying mathematical unity of evolutionary theory, both deepening our understanding of how evolution works, and solidifying evolutionary biology as a science grounded in universal mathematical rules. Graduate students and postdoctoral researchers will be trained in mathematical evolutionary biology, and particularly in presenting their research to non-mathematical audiences. Results will be published in open access journals and the PI plans a webpage that links all publications with a non-technical summary of the project.
