Regional Mathematics and Statistics Conference

Plenary Lecture

Dr. Benjamin Allen
Emmanuel College

Evolution as a field of mathematics

New mathematical fields arise when fundamental patterns and structures—either from the real world or from within math itself—are abstracted and formalized into definitions and axioms. Examples include calculus for the study of continuous change, group theory for the study of symmetry, or topology for the study of deformable shapes. Evolution is a ubiquitous process: it underlies all of biology, and also occurs in other contexts such as human culture, technology, and language. So what would evolution look like as a field of mathematics? As a potential starting point, I will present a framework that formalizes the fundamental building blocks of population, heritable types, replacement, and mutation. Within this framework, I will show how key concepts like neutral drift and fixation probability can be defined and mathematically analyzed. Applying this framework to social dilemmas on networks, I will show how graph structure can be a key determinant of whether cooperative behaviors can evolve.