  Cancer cells obtain mutations which rely on the production of diffusible
growth factors to confer a fitness benefit. These mutations can be considered
cooperative, and studied as public goods games within the framework of
evolutionary game theory. The population structure, benefit function and update
rule all influence the evolutionary success of cooperators. We model the
evolution of cooperation in epithelial cells using the Voronoi tessellation
model. Unlike traditional evolutionary graph theory, this allows us to
implement global updating, for which birth and death events are spatially
decoupled. We compare, for a sigmoid benefit function, the conditions for
cooperation to be favoured and/or beneficial for well mixed and structured
populations. We find that when population structure is combined with global
updating, cooperation is more successful than if there were local updating or
the population were well-mixed. Interestingly, the qualitative behaviour for
the well-mixed population and the Voronoi tessellation model is remarkably
similar, but the latter case requires significantly lower incentives to ensure
cooperation.
