A Categorical Framework for Modeling Genetic Drift

Authors

• Taylor G. Mendes, Spelman CollegeFollow

Abstract

Genetic drift describes changes in allele frequencies that arise from chance sampling in finite populations. This paper develops a categorical framework for organizing the structural features of drift. Population states are modeled as objects, evolutionary transitions as morphisms, reversible transitions as groupoid morphisms, and structure-preserving comparisons between models as functors. Group actions are used to describe deterministic evolutionary operators such as mutation and selection, while orbits and fixed points identify reachable allele-frequency states and stable absorbing outcomes. Universal properties are then used to describe drift as a coherence condition connecting stochastic transitions with deterministic evolutionary maps. The resulting framework complements classical probabilistic models by emphasizing the relational and structural organization of genetic drift.

Author Bio

Taylor Mendes is a mathematics major and computer science minor at Spelman College. This research was conducted during the summer and academic year as part of Spelman and Morehouse Colleges’ Directed Reading Program. In addition to research, she enjoys coding for outreach programs with underrepresented youth and plans to pursue a PhD in data science.

Faculty Sponsor

Yewande Olubummo

Recommended Citation

Mendes, Taylor G. (2025) "A Categorical Framework for Modeling Genetic Drift," Rose-Hulman Undergraduate Mathematics Journal: Vol. 26: Iss. 2, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol26/iss2/3