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Replicator dynamics with diffusion on multiplex networks

In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to account for non-linear terms when working with fractions of individuals. We also derive the transition probabilities that give rise to such macroscopic behavior, completing the bottom-up description. Finally, it shown that the usual assumption of constant population sizes induces a hidden selective pressure in the system.