Isaac Newton Institute         Building a bridge .between non-equilibrium statistical physics and biology         July 5, 2023

Competition at the front of expanding populations

Daniel Swartz, 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

IX.    Summary

 

 

 

 

 

 

 

 

 

 

 

 

When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends of the reproductive advantage (fitness), as well as ability to colonize new domains. 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.