Mutation timing in a spatial model of evolution

Jasmine Foo, Kevin Leder, Jason Schweinsberg

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)6388-6413
Number of pages26
JournalStochastic Processes and their Applications
Issue number10
StatePublished - Oct 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Cancer
  • Mutations
  • Spatial population model


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