Edge effects in game theoretic dynamics of spatially structured tumours

 Edge effects in game theoretic dynamics of spatially structured tumours

Authors: +Artem Kaznatcheev , +Jacob Scott and +David Basanta

Abstract:
Evolutionary game theory has been used to model many situations in ecology
where different species, or different phenotypes within one species, compete
against one another. Of late, this has extended to cancer biology to understand
the dynamics of disease progression as a game between competing cellular
phenotypes. A major assumption in this modeling paradigm is that the population
is inviscid: the probability of a player with a given phenotypic strategy
interacting with another depends exclusively on the respective abundance of
those strategies in the population. While there are scenarios where this
assumption might be useful, in solid tumours, where the populations have
spatial structure, this assumption can yield misleading results. In this study
we use a recently developed mathematical tool, the Ohtsuki-Nowak transform, to
study the effect of interaction neighborhood size on a canonical evolutionary
cancer game: go vs. grow. We show that spatial structure promotes invasive (go)
strategy. By considering the change in neighbourhood size at a boundary we show
an edge effect in solid tumours. This edge effect allows a tumour with no
invasive phenotypes expressed internally to have a polyclonal boundary with
both invasive and non-invasive cells. We focus on evolutionary game dynamics
between competing cancer cells, but we anticipate that our approach can be
extended to games between other types of players where interaction
neighborhoods change at the system boundary.

Manuscript in arXiv [link].