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Mutation timing in a spatial model of evolution

Author

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  • Foo, Jasmine
  • Leder, Kevin
  • Schweinsberg, Jason

Abstract

Motivated by models of cancer formation in which cells need to acquire k mutations to become cancerous, we consider a spatial population model in which the population is represented by the d-dimensional torus of side length L. Initially, no sites have mutations, but sites with i−1 mutations acquire an ith mutation at rate μi per unit area. Mutations spread to neighboring sites at rate α, so that t time units after a mutation, the region of individuals that have acquired the mutation will be a ball of radius αt. We calculate, for some ranges of the parameter values, the asymptotic distribution of the time required for some individual to acquire k mutations. Our results, which build on previous work of Durrett, Foo, and Leder, are essentially complete when k=2 and when μi=μ for all i.

Suggested Citation

  • Foo, Jasmine & Leder, Kevin & Schweinsberg, Jason, 2020. "Mutation timing in a spatial model of evolution," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6388-6413.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6388-6413
    DOI: 10.1016/j.spa.2020.05.015
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    References listed on IDEAS

    as
    1. Durrett, Rick & Foo, Jasmine & Leder, Kevin & Mayberry, John & Michor, Franziska, 2010. "Evolutionary dynamics of tumor progression with random fitness values," Theoretical Population Biology, Elsevier, vol. 78(1), pages 54-66.
    2. Durrett, Richard & Moseley, Stephen, 2010. "Evolution of resistance and progression to disease during clonal expansion of cancer," Theoretical Population Biology, Elsevier, vol. 77(1), pages 42-48.
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