Explore the fascinating world of hybrid zones in this 44-minute lecture by Alison Etheridge, presented by the International Mathematical Union. Delve into a mathematical model of reproduction and examine deterministic approximations. Investigate examples of hybrid zones and question whether they are maintained by selection. Zoom out to study mean curvature flow and the Allen-Cahn equation, including a probabilistic proof. Analyze majority voting in historical BBM and its connection to the Allen-Cahn equation. Consider scenarios where homozygotes are not equally fit and examine sensitivity to asymmetry. Investigate invasions and blocking techniques, exploring more precise statements and effects in various domains. Conclude by examining the key arguments and the impact of noise on hybrid zone dynamics.
Overview
Syllabus
Intro
A mathematical model
Reproduction
A deterministic approximation
Examples of hybrid zones Maintained by selection?
Zooming out
(Mean) Curvature flow
The Allen-Cahn equation and curvature flow
A probabilistic proof (E. Freeman, Penington, 2017)
Majority voting in (Historical) BBM
Majority voting and the Allen-Cahn equation
Probabilistic proof of Chen's result
Some heuristics
What if homozygotes not equally fit?
Sensitivity to asymmetry (Gooding, 2018)
Invasions
Blocking (E., Gooding, Letter, 2022+)
A more precise statement
Other domains
Key argument
Effect of noise
Taught by
International Mathematical Union
