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Radial Domany-Kinzel models with mutation and selection

Author(s)
Davidson, James West; Korolev, Kirill Sergeevich; Nelson, David R.
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Abstract
We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, and so on. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimizes otherwise persistent lattice artifacts. With both simulations and analytical techniques, we study the survival probability of advantageous mutants, the spatial correlations between domains of neutral strains, and the dynamics of populations with deleterious mutations. “Inflation” at the frontier leads to striking differences between radial and linear expansions. For a colony with initial radius R[subscript 0] expanding at velocity v, significant genetic demixing, caused by local genetic drift, occurs only up to a finite time t[superscript *]=R[subscript 0]/v, after which portions of the colony become causally disconnected due to the inflating perimeter of the expanding front. As a result, the effect of a selective advantage is amplified relative to genetic drift, increasing the survival probability of advantageous mutants. Inflation also modifies the underlying directed percolation transition, introducing novel scaling functions and modifications similar to a finite-size effect. Finally, we consider radial range expansions with deflating perimeters, as might arise from colonization initiated along the shores of an island.
Date issued
2013-01
URI
http://hdl.handle.net/1721.1/78318
Department
Massachusetts Institute of Technology. Department of Physics
Journal
Physical Review E
Publisher
American Physical Society
Citation
Lavrentovich, Maxim O., Kirill S. Korolev, and David R. Nelson. “Radial Domany-Kinzel Models with Mutation and Selection.” Physical Review E 87.1 (2013). ©2013 American Physical Society
Version: Final published version
ISSN
1539-3755
1550-2376

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