PATTERN FORMATION THROUGH GENETIC DRIFT AT EXPANDING POPULATION FRONTS

Adnan Ali () and Stefan Grosskinsky ()
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Adnan Ali: Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, UK
Stefan Grosskinsky: Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, UK

Advances in Complex Systems (ACS), 2010, vol. 13, issue 03, 349-366

Abstract: We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatscheket al.,Proc. Natl. Acad. Sci.,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.

Keywords: Genetic drift; range expansion; domain coarsening; time-changed Brownian motion; annihilating random walks (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219525910002578

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