 Mutation timing in a spatial model of evolutionJasmine Foo, Kevin Leder and Jason Schweinsberg Stochastic Processes and their Applications, 2020, vol. 130, issue 10, 6388-6413 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. Keywords: Cancer; Mutations; Spatial population model (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:10:p:6388-6413 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2020.05.015 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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