Journal of Mathematical Biology

, Volume 72, Issue 5, pp 1369–1400 | Cite as

Spatial Moran models, II: cancer initiation in spatially structured tissue

  • R. DurrettEmail author
  • J. Foo
  • K. Leder


We study the accumulation and spread of advantageous mutations in a spatial stochastic model of cancer initiation on a lattice. The parameters of this general model can be tuned to study a variety of cancer types and genetic progression pathways. This investigation contributes to an understanding of how the selective advantage of cancer cells together with the rates of mutations driving cancer, impact the process and timing of carcinogenesis. These results can be used to give insights into tumor heterogeneity and the “cancer field effect,” the observation that a malignancy is often surrounded by cells that have undergone premalignant transformation.


Biased voter model Shape theorem Asymptotics for waiting times Cancer field effect 

Mathematics Subject Classification

60K35 92C50 



RD is partially supported by NIH grant 5R01GM096190, JF by NSF grants DMS-1224362 and DMS-1349724, and KL by NSF Grants DMS-1224362 and CMMI-1362236. We would like to thank Marc Ryser for helpful comments on previous versions of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Deptartment of MathematicsDuke UniversityDurhamUSA
  2. 2.Deptartment of MathematicsUniversity of MinnesotaMinneapolisUSA
  3. 3.Industrial and Systems EngineeringUniversity of MinnesotaMinneapolisUSA

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