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The spreading of discrete entities occurs in many complex systems, and controls for instance the speed of chemical reactions, species invasions, epidemic outbreaks or biological adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on reaction rates but also on the dispersal behavior of the species. Spreading at a constant speed is generally predicted when dispersal is sufficiently short-ranged. I present a recent exactly solvable model for this wave-like spread and the associated genealogical trees, which are generated by a  coalescent process with frequent multiple mergers. Spreading in the presence of rare long-range dispersal (e.g. triggered by aviation) has been unresolved so far: While it is clear that even rare long-range jumps can lead to a drastic speedup, it has been difficult to quantify the ensuing stochastic growth process. I present a simple self-consistent argument supported by simulations that accurately predicts the asymptotic spreading dynamics for fat-tailed jump distributions.  I discuss our results in the light of population genetics, and show how they can be used to predict evolutionary change in simple microbial experiments. 

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Dr. Oskar Hallatschek, MPI for Dynamics and Self-Organization
Seminarraum Theoretische Physik
Contact: not specified