Life at the front of an expanding population

TL;DR

This paper models genetic patterns at the expanding frontiers of populations, explaining sector formation, effects of natural selection, and the impact of deleterious mutations, with implications for understanding genetic drift and mutation thresholds during range expansions.

Contribution

It introduces a simple, predictive model linking sector boundary dynamics to natural selection and mutation effects during population range expansions.

Findings

Beneficial mutations are more likely to establish sectors with larger opening angles.

Deleterious mutations can temporarily reach high frequencies through surfing.

The model predicts a different error threshold for genetic meltdown compared to well-mixed populations.

Abstract

Recent microbial experiments suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries. Here, we propose and analyze a simple model of asexual biological evolution at expanding frontiers to explain these neutral patterns and predict the effect of natural selection. Our model attributes the observed gradual decrease in the number of sectors at the leading edge to an unbiased random walk of sector boundaries. Natural selection introduces a deterministic bias in the wandering of domain boundaries that renders beneficial mutations more likely to escape genetic drift and become established in a sector. We find that the opening angle of those sectors and the rate at which they become established depend sensitively on the selective advantage of the mutants. Deleterious mutations, on the other hand, are not able to establish a sector permanently. They can, however, temporarily "surf" on the population front, and thereby reach unusual high frequencies. As a consequence, expanding frontiers are susceptible to deleterious mutations as revealed by the high fraction of mutants at mutation-selection balance. Numerically, we also determine the condition at which the wild type is lost in favor of deleterious mutants (genetic meltdown) at a growing front. Our prediction for this error threshold differs qualitatively from existing well-mixed theories, and sets tight constraints on sustainable mutation rates for populations that undergo frequent range expansions.