  Understanding how cooperation can evolve in populations despite its cost to
individual cooperators is an important challenge. Models of spatially
structured populations with one individual per node of a graph have shown that
cooperation, modeled via the prisoner's dilemma, can be favored by natural
selection. These results depend on microscopic update rules, which determine
how birth, death and migration on the graph are coupled. Recently, we developed
coarse-grained models of spatially structured populations on graphs, where each
node comprises a well-mixed deme, and where migration is independent from
division and death, thus bypassing the need for update rules. Here, we study
the evolution of cooperation in these models in the rare migration regime,
within the prisoner's dilemma. We find that cooperation is not favored by
natural selection in these coarse-grained models on graphs where overall deme
fitness does not directly impact migration from a deme. This is due to a
separation of scales, whereby cooperation occurs at a local level within demes,
while spatial structure matters between demes.
