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Pattern formation through genetic drift at expanding population fronts
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Ali, Adnan and Grosskinsky, Stefan (2010) Pattern formation through genetic drift at expanding population fronts. Advances in Complex Systems, Vol.13 (No.3). pp. 349-366. doi:10.1142/S0219525910002578 ISSN 0219-5259.
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Official URL: http://dx.doi.org/10.1142/S0219525910002578
Abstract
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., 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 nontrivial 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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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Library of Congress Subject Headings (LCSH): | Evolution (Biology) -- Mathematical models, Population genetics -- Mathematical models | ||||
Journal or Publication Title: | Advances in Complex Systems | ||||
Publisher: | World Scientific Publishing Company PTE Ltd | ||||
ISSN: | 0219-5259 | ||||
Official Date: | June 2010 | ||||
Dates: |
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Volume: | Vol.13 | ||||
Number: | No.3 | ||||
Number of Pages: | 18 | ||||
Page Range: | pp. 349-366 | ||||
DOI: | 10.1142/S0219525910002578 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 3 December 2015 | ||||
Date of first compliant Open Access: | 3 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/E501311/1 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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