Short Talk: Edge effects in evolutionary dynamics of spatially structured tumors

Artem Kaznatcheev (September 17, 2014)

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A typical assumption in analytic evolutionary game theory models of cancer is that the population is inviscid: the probability of a cell with a given phenotypic strategy interacting with another depends exclusively on the respective abundance of those strategies in the population. To overcome this limitation, we show how to use the Ohtsuki-Nowak transform to approximate spatial structure and study the effect of interaction neighborhood size. In particular, we focus on the change in neighborhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane. In the case of the go vs. grow game, this edge effect allows a tumor with no invasive phenotypes expressed internally to have a polyclonal boundary with both invasive and non-invasive cells. We hope that our approach serves as a useful analytic compliment to the more common simulation based methods of modeling the effects of spatial structure on cancer dynamics.