The dynamics of a population expanding into unoccupied habitat has been
primarily studied for situations in which growth and dispersal parameters are
uniform in space or vary in one dimension. Here we study the influence of
finite-sized individual inhomogeneities and their collective effect on front
speed if randomly placed in a two-dimensional habitat. An individual-based
model allows us to investigate the front behaviour for one or a small number of
regions in which dispersal or growth of individuals is reduced to zero
(obstacles) or increased above the background (hotspots), respectively. In a
regime in which front dynamics is determined by a local front speed,
irrespective of the microscopic origin, we (i) describe the effect of multiple
inhomogeneities in the light of an event-based solution, (ii) find a slow-down
due to obstacles that is dominated by the number density and width of
obstacles, but not by their precise shape, and (iii) characterize a speedup and
its dependence on hotspot strength and density. Our findings emphasise the
importance of taking the dimensionality of the environment into account. A
simulation-driven description of the effect of individual spatial inhomogeities
on genetic diversity of the population front provides an outlook into further
research.

Spatial structure impacts microbial growth and interactions, with ecological and evolutionary consequences. It is therefore important to quantitatively understand how spatial proximity affects interactions in different environments. We tested how proximity influences colony size when either Escherichia coli or Salmonella enterica are grown on various carbon sources. The importance of colony location changed with species and carbon source. Spatially explicit, genome-scale metabolic modeling recapitulated observed colony size variation. Competitors that determine territory size, according to Voronoi diagrams, were the most important drivers of variation in colony size. However, the relative importance of different competitors changed through time. Further, the effect of location increased when colonies took up resources quickly relative to the diffusion of limiting resources. These analyses made it apparent that the importance of location was smaller than expected for experiments with S. enterica growing on glucose. The accumulation of toxic byproducts appeared to limit the growth of large colonies and reduced variation in colony size. Our work provides an experimentally and theoretically grounded understanding of how location interacts with metabolism and diffusion to influence microbial interactions.

© 2017 Weinstein et al. 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.