  Evolutionary experiments with microbes are a powerful tool to study mutations
and natural selection. These experiments, however, are often limited to the
well-mixed environments of a test tube or a chemostat. Since spatial
organization can significantly affect evolutionary dynamics, the need is
growing for evolutionary experiments in spatially structured environments. The
surface of a Petri dish provides such an environment, but a more detailed
understanding of microbial growth on Petri dishes is necessary to interpret
such experiments. We formulate a simple deterministic reaction-diffusion model,
which successfully predicts the spatial patterns created by two competing
species during colony expansion. We also derive the shape of these patterns
analytically without relying on microscopic details of the model. In
particular, we find that the relative fitness of two microbial strains can be
estimated from the logarithmic spirals created by selective sweeps. The theory
is tested with strains of the budding yeast Saccharomyces cerevisiae, for
spatial competitions with different initial conditions and for a range of
relative fitnesses. The reaction-diffusion model also connects the microscopic
parameters like growth rates and diffusion constants with macroscopic spatial
patterns and predicts the relationship between fitness in liquid cultures and
on Petri dishes, which we confirmed experimentally. Spatial sector patterns
therefore provide an alternative fitness assay to the commonly used liquid
culture fitness assays.
