Fig. 7

Schematic explanation of the two different effects of spatial constraints in the spatially explicit and implicit models (lattice and CF models, respectively). A The effect of viscosity. Cooperators benefit from slow mixing (viscosity) during the cooperation phase, as their perceived local cooperator density exceeds the population average. Fragmented cooperators fail to achieve the local quorum of cooperation, despite the same global density of cooperators on the lattice. B The effects of local and global competition in well-mixed populations. Local competition between cooperators and parasites (left panel) benefits the parasite because their overlapping cooperation neighborhoods (including themselves) contain an equal expected number of cooperators, but the parasite carries a smaller cost. The cooperator in a distant cooperator-parasite pair (right panel) represents an extra cooperator in its own (otherwise statistically identical) neighborhood compared to its parasitic opponent. This advantage may (over-)compensate its handicap in cooperation cost