Chemical mediated competition

Andreas C. Aristotelous and Richard Durrett

Abstract. Inspired by the use of hybrid cellular automata in modeling cancer, we introduce a generalization of evolutionary games in which cells produce and absorb chemicals, and the chemical concentrations dictate the death rates of cells and their fitnesses. Our long term aim is to understand how the details of the interactions in a system with n species and m chemicals translate into the qualitative behavior of the system. Here, we study two simple 2 x 2 games with two chemicals and revisit the two and three species versions of the one chemical colicin system studied earlier by Durrett and Levin (1997). We find that the behavior of our new spatial model can be predicted from that of the mean field differential equation, but it can have different behavior from lattices models in which sites interact with only their nearest neighbors. The figure gives a snapshot of the three species colicin system, which does not have coexistence in the new formulation.

Preprint of paper to appear in Theoretical Population Biology

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