Figure 4.

The population dynamics of mutualists and exploiters as a function of preferential allocation (b, x-axis) and the half-saturation constant of preferential allocation (α, y-axis). Exploiters dominate at low preferential allocation values (‘e’). The symbiotic service cost (z) in each plot is equal to 1. At higher values of b, mutualists go to fixation (‘m’, linear functions, α = 0.50), coexistence between mutualist and exploiters occurs (‘m & e’, saturating functions, α > 0.50), or conditional dynamics drive either mutualists or exploiters to fixation (‘m or e’, accelerating functions, α < 0.50). Increasing module occupancy results in exploiters dominating at higher values of b, while increasing nonlinearity expands the region of values associated with stable or unstable equilibrium.