Spatial expansions have shaped the evolutionary history of many organisms, from microbes to humans. These expansions are usually described by two types of reaction-diffusion waves: pulled waves, which are driven by growth at the edge of the expansion, and pushed waves, which are driven by the bulk. We investigated how demographic fluctuations affect fluctuations in genetic composition and population density when waves transition from pulled to pushed. We showed that the variance of the fluctuations decreases with the population size, following a logarithmic dependence for pulled waves or a power law dependence for pushed waves. However, for weakly pushed waves the exponent is small and the fluctuations large, while for strongly pushed waves, the variance of the fluctuations decreases inversely proportional to the population size. Regarding fluctuations in the genetic composition, the change in scaling is a result of the genealogical structure of the population transitioning from a Bolthausen-Sznitman to a Kingman coalescent as the wave changes from pulled to pushed. Importantly, we found that all of these results are independent of the dispersal and growth models and are controlled by a universal parameter: the ratio of the expansion velocity to the geometric mean of the dispersal and growth rates at low density. Thus, we predict that cooperative dispersal and growth could have a large impact on evolutionary dynamics, even when their contributions to the expansion velocity is small.
Special ICMT/Theoretical Biophysics Seminar: Universality classes of evolutionary dynamics in expanding populations
(sign-up)Gabriel Birzu (Boston University)
|Sponsor:||Sergei Maslov (BioE & Physics)|
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