How obstacles perturb population fronts and alter their genetic structure

Abstract

As populations spread into new territory, environmental heterogeneities can shape the population front and genetic composition. We study here the effect of one important building block of inhomogeneous environments, compact 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 manifested in plaque growth. The transient perturbations of the plaque boundary 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 alleles that just graze 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 latter highlight as well the effect of the obstacle on the genealogy of individuals at the front. We argue that related ideas and experimental techniques are applicable to a wide variety of more complex environments, leading to a better understanding of how environmental heterogeneities affect population range expansions.