Bristol University                  Mathematical Physics Seminar                    December 11, 2023

Competition at the front of expanding populations

Daniel Swartz, Lauren Li

Hyunseok Lee, Kirill Korolev

Jordan Horowitz, Daniel Beller, David Nelson, Sherry Chu

Outline

I.      Range Expansion: Bacteria growing into new environment; models with and without a rough front

II.     Drift of boundaries on a sloped surface

III.   Competition & invasion, Fisher waves (pulled/pushed)

IV.    Morphologies of competitive growth

V.     Speed of invasion on a growing front

VI.   Cole-Hopf mapping: growth on an undulating substrate

VII.  Fitness variations: revisiting synchronous growth & DPRM

VIII. Specialization: evolution of new traits and universality classes

IX.    Summary

 

 

 

 

 

 

 

 

 

 

 

Title: Competition at the front of expanding populations

Abstract:

When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations, we present a model that  integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness, as well as fixation time upon differentiation, are shown to belong to distinct universality classes depending on limits to gain of fitness.