CPM Seminar

Brownian motion, diffusion equation, and human genetic history

Simon Gravel

Department of Human Genetics
McGill University

The amount of genetic differences between human individuals and populations depends on three factors: mutation, selection, and demography. Modeling present-day diversity can help us unravel questions about the history and biology of our species. The classical models of genetic diversity have close ties to Brownian motion and diffusion equations, and the recent surge in DNA sequencing capacity has led to a renewed interest in the theory and application of these models.

I will review the analogy between Brownian motion, diffusion, and evolution, and what these models tell us about the spread of modern humans since our common African origins, the human mutation rate, and the impact of selection in human evolution.