Genetic drift and selection in many-allele range expansions

Bryan T Weinstein; Maxim O Lavrentovich; Wolfram Möbius; Andrew W Murray; David R Nelson

doi:10.1371/journal.pcbi.1005866

Genetic drift and selection in many-allele range expansions

PLoS Comput Biol. 2017 Dec 1;13(12):e1005866. doi: 10.1371/journal.pcbi.1005866. eCollection 2017 Dec.

Authors

Bryan T Weinstein¹, Maxim O Lavrentovich², Wolfram Möbius^{3

4

5}, Andrew W Murray^{6

7}, David R Nelson^{1

5

6

7}

Affiliations

¹ School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, United States of America.
² Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America.
³ Living Systems Institute, University of Exeter, Exeter, United Kingdom.
⁴ Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom.
⁵ Department of Physics, Harvard University, Cambridge, Massachusetts, United States of America.
⁶ FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America.
⁷ Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts, United States of America.

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.

MeSH terms

Algorithms
Alleles*
Computational Biology
Computer Simulation
Escherichia coli / genetics
Evolution, Molecular*
Genetic Drift*
Models, Genetic*
Selection, Genetic / genetics*

Grants and funding

Research by BTW is supported by the Department of Energy Office of Science Graduate Fellowship Program (DOE SCGF), made possible in part by the American Recovery and Reinvestment Act of 2009, administered by ORISE-ORAU under contract no. DE-AC05-06OR23100, by the US Department of Energy (DOE) under Grant No. DE-FG02-87ER40328, as well as Harvard University’s Institute for Applied Computational Science (IACS) Student Fellowship. BTW, AWM, and DRN benefitted from support from the Human Frontiers Science Program Grant RGP0041/2014 and from the National Science Foundation, through grants DMR1608501 and via the Harvard Materials Science and Engineering Center, through grant DMR1435999. MOL acknowledges support from NSF grant DMR-1262047, the UPenn MRSEC under Award No. NSF-DMR-1120901, the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Grant No. DE-FG02-05ER46199, and from the Simons Foundation for the collaboration "Cracking the Glass Problem’’ (Grant No. 454945). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.