The evolution of function-valued traits for conditional cooperation

We first analyse adaptation to homogenous environments (with constant degree of viscosity). Comparing environments characterized by different degrees of viscosity, we find that the relation between viscosity and the equilibrium type distribution is not monotone. In fact, it is possible that in fluid populations (no viscosity) there is more cooperation in equilibrium than in populations with intermediate degrees of viscosity. In a second step we analyse heterogenous environments (with varying degrees of viscosity). We find that under very weak assumptions on the distribution of the viscosity parameter strictly increasing functions are always selected and under some parameter constellations they are uniquely so.