How Obstacles Perturb Population Fronts and Alter Their Genetic Structure
PLOS Computational Biology
Public Library of Science
© 2015 Möbius et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
As populations spread into new territory, environmental heterogeneities can shape the population front and genetic composition. We focus here on the effects of an important building block of heterogeneous environments, isolated obstacles. With a combination of experiments, theory, and simulation, we show how isolated obstacles both create long-lived distortions of the front shape and amplify the effect of genetic drift. A system of bacteriophage T7 spreading on a spatially heterogeneous Escherichia coli lawn serves as an experimental model system to study population expansions. Using an inkjet printer, we create well-defined replicates of the lawn and quantitatively study the population expansion of phage T7. The transient perturbations of the population front found in the experiments are well described by a model in which the front moves with constant speed. Independent of the precise details of the expansion, we show that obstacles create a kink in the front that persists over large distances and is insensitive to the details of the obstacle’s shape. The small deviations between experimental findings and the predictions of the constant speed model can be understood with a more general reaction-diffusion model, which reduces to the constant speed model when the obstacle size is large compared to the front width. Using this framework, we demonstrate that frontier genotypes just grazing the side of an isolated obstacle increase in abundance, a phenomenon we call ‘geometry-enhanced genetic drift’, complementary to the founder effect associated with spatial bottlenecks. Bacterial range expansions around nutrient-poor barriers and stochastic simulations confirm this prediction. The effect of the obstacle on the genealogy of individuals at the front is characterized by simulations and rationalized using the constant speed model. Lastly, we consider the effect of two obstacles on front shape and genetic composition of the population illuminating the effects expected from complex environments with many obstacles.
Support for this work was provided by the National Institute of General Medical Sciences Grant P50GM068763 of the National Centers for Systems Biology (www.nih.gov, awarded to AWM), by the National Science Foundation through grant DMR1306367 and through the Harvard Materials Research and Engineering Center through Grant DMR-1420570 (www.nsf.gov/div/index.jsp?div=DMR, awarded to DRN). WM was supported by the Leopoldina Postdoc Scholarship LPDS 2009-51 (www.leopoldina.org) and by grants from the National Philanthropic Trust Grant RFP-12-15 (www.templeton.org, awarded to AWM), and from the Human Frontiers Science Program Grant RGP0041/2014 (www.hfsp.org, awarded to AWM). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
This is the final version of the article. Available from Public Library of Science via the DOI in this record.
Vol. 11 (12), article e1004615