Pattern formation through genetic drift at expanding population fronts

Details Pattern formation through genetic drift at expanding population fronts Pattern formation through genetic drift at expanding population fronts

2009-12-11

arxiv.org/abs/0912.2241v2

Adv. Compl. Sys. 13(3), 349-366 (2010)

Biology

Quantitative Biology

Populations and Evolution

17 pages with 9 figures

Scientific paper

10.1142/S0219525910002578

We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two fluorescently labeled microbial species is grown in a circular geometry. As the population expands, a coarsening process driven by genetic drift gives rise to sectoring patterns with fractal boundaries, which show a non-trivial asymptotic distribution. Using simplified lattice based Monte Carlo simulations as a generic caricature of the above experiment, we present detailed numerical results to establish a model for sector boundaries as time changed Brownian motions. This is used to derive a general one-to-one mapping of sector statistics between circular and linear geometries, which leads to a full understanding of the sectoring patterns in terms of annihilating diffusions.

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