Mini curso

Resumen

This mini-course explores the concept of emerging neutrality in population genetics. In neutral evolution, the fate of genetic variants is governed solely by genetic drift — the random fluctuations in offspring number from one generation to the next — rather than by natural selection. While neutrality is often regarded as a simplifying assumption, a remarkable phenomenon occurs in complex population models: neutral dynamics can emerge spontaneously in appropriate limits, even when the underlying model is far from simple.
As a guiding example, we consider the Fisher-KPP equation with Allee effect, which models range expansions with a demographic threshold. A central question is the genetic diversity at the edge of the expanding front. This setting gives rise to a rich phenomenology, including genetic bottlenecks, founder effects, and anomalous coalescence timescales, whose mathematical explanation sits at the interface of PDE analysis and probability theory.
The course will be organized around two complementary directions. We begin by reviewing classical population genetics models — branching processes, Cannings models, and their associated genealogical structures — and show that, despite their apparent simplicity, these models emerge as universal limits of a broad class of complex population dynamics. We then leverage this universality to address questions about genetic diversity in spatially structured and expanding populations, with emphasis on how analytic properties of the front (speed, shape, fluctuations) determine the genealogical structure of a complex populations.

This mini-course is designed to be accessible to a broad mathematical audience — probabilists and analysts alike — and assumes no prior knowledge of population genetics.

Ponente

Emmanuel Schertzer

Universidad de Vienna