Chemical evolutionary games

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 2×2 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 in the 2×2 examples, the behavior of our new spatial model can be predicted from that of the mean field differential equation using ideas of Durrett and Levin (1994). However, in the three species colicin model, the system with diffusion does not have the coexistence which occurs in the lattices model in which sites interact with only their nearest neighbors.