Figure 5

Simulation results for the multilevel selection model with voluntary participation. The average propensity for cooperation concerning the two kinds of group actions, the public goods game and the voluntary group competition action as a function of the two costs of cooperation (C(x) and C(a)) and the initial ratio of cooperators (x _i ) in the Public Goods Game. (a) For high cost values the tendency of cooperating in both of group actions is low, (b) or there is a full cooperation in the Public Goods Game, but full defection in the group defense action. (c) If the costs of cooperation are not high, every individual cooperates in both of the group actions (x = ~1, a = ~1). (d) At the boundaries of these regions, for intermediate cost values division of labour evolves in the population (h). On graphs e.-h. each bubble illustrates the results of an individual based simulation, the size representing the average a in the population (large bubbles represent a = 1 and vice versa), and the colouring depicting the average value of x (red bubbles denote x = 1, while yellow ones denote x = 0). For the simulations we either used no initial incentive in the populations for participating in the group competition (a _i = 0) (e, g), or the simulation was started with full participation (a _i = 1) (f, h). The 5 group members were either picked randomly from the population in the well-mixed model (e, f), or from the same site in the spatially explicit model (g, h). ((a) C(x) = 0.5, C(a) = 0.5, x _i = 0, a _i = 0; (b) C(x) = 0, C(a) = 0.6, x _i = 0, a _i = 0.5; (c) C(x) = 0.2, C(a) = 0.05, x _i = 0.05, a _i = 0.2; (d) C(x) = 0.6, C(a) = 0.2, x _i = 0.6, a _i = 0.5).