Reproduction time statistics and segregation patterns in growing populations

TL;DR

This paper investigates how reproduction time variability influences pattern formation in microbial colonies, introducing a generalized growth model that accounts for different reproduction time distributions and analyzing their effects on sectoring patterns.

Contribution

The study introduces a one-parameter family of reproduction time distributions in a growth model, demonstrating their impact on pattern formation and confirming the model's universality class.

Findings

Reproduction time variability significantly affects sectoring patterns.

The generalized model remains in the KPZ universality class.

The approach applies to realistic biological reproduction time distributions.

Abstract

Pattern formation in microbial colonies of competing strains under purely space-limited population growth has recently attracted considerable research interest. We show that the reproduction time statistics of individuals has a significant impact on the sectoring patterns. Generalizing the standard Eden growth model, we introduce a simple one-parameter family of reproduction time distributions indexed by the variation coefficient {\delta} \in [0, 1], which includes deterministic ({\delta} = 0) and memoryless exponential distribution ({\delta} = 1) as extreme cases. We present convincing numerical evidence and heuristic arguments that the generalized model is still in the KPZ universality class, and the changes in patterns are due to changing prefactors in the scaling relations, which we are able to predict quantitatively. At the example of Saccharomyces cerevisiae, we show that our approach using the variation coefficient also works for more realistic reproduction time distributions.