Genetic drift and selection in many-allele range expansions.

Bryan T Weinstein,Wolfram Möbius,Andrew W Murray,David R Nelson,Maxim O Lavrentovich,Jeff Gore

doi:10.1371/journal.pcbi.1005866

Bryan T Weinstein, Wolfram Möbius + Show 4 more

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https://doi.org/10.1371/journal.pcbi.1005866

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Abstract

We experimentally and numerically investigate the evolutionary dynamics of four competing strains of E. coli with differing expansion velocities in radially expanding colonies. We compare experimental measurements of the average fraction, correlation functions between strains, and the relative rates of genetic domain wall annihilations and coalescences to simulations modeling the population as a one-dimensional ring of annihilating and coalescing random walkers with deterministic biases due to selection. The simulations reveal that the evolutionary dynamics can be collapsed onto master curves governed by three essential parameters: (1) an expansion length beyond which selection dominates over genetic drift; (2) a characteristic angular correlation describing the size of genetic domains; and (3) a dimensionless constant quantifying the interplay between a colony’s curvature at the frontier and its selection length scale. We measure these parameters with a new technique that precisely measures small selective differences between spatially competing strains and show that our simulations accurately predict the dynamics without additional fitting. Our results suggest that the random walk model can act as a useful predictive tool for describing the evolutionary dynamics of range expansions composed of an arbitrary number of genotypes with different fitnesses.

Highlights

A competition between stochastic and deterministic effects underlies evolution
We begin by reporting our measurements of the average fraction of each strain, the two-point correlation functions between strains, and the relative rates of annihilations and coalescences as a function of length expanded for our four competing strains of E. coli
We show how to predict the average fraction, two-point correlation functions, and relative rates of annihilation and coalescences using our random-walk model and simulation

Summary

Introduction

A competition between stochastic and deterministic effects underlies evolution. In a wellmixed system such as a shaken culture of the yeast microorganism Saccharomyces cerevisiae, stochastic competition between individuals, mutations, and selection dictate the dynamics of the population [1]. A model laboratory system that can be used to explore the coupling between local “wellmixed” effects and spatial deterministic and stochastic dynamics is a microbial range expansion [8], in which a population expands into an unoccupied region of a hard agar Petri dish. Spatial structure is present in the frozen genetic patterns because the microbes at the expanding frontier produce daughter cells of the same color that migrate only a small fraction of the front circumference within a generation. Hallatschek et al [8] identified the key role of genetic drift in producing these sectored patterns; the small population size at the front of an expanding population [9, 10] enhances number fluctuations (i.e. genetic drift), eventually leading to the local fixation of one strain past a critical expansion radius R0. The decrease in genetic diversity as the small number of individuals at the frontier expands is referred to as the “Founder effect” [11]

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