Fig. 6

Evolutionary dynamics of cooperation, conditional defection, and defection by mathematical modeling. Mathematical models are conducted under the two scenarios where cooperators are able (a and b) and unable (c and d) to exclude defectors, respectively. Panels a and c depict the time series of frequencies of cooperator (black line), defector (red line), and conditional defector (blue line). Panels b and d depict the evolutionary trajectories in the simplex, where filled circle represents stable fixed point and open circles represent unstable fixed points. The evolutionary trajectories were obtained through numerical integrations based on the replicator equations in the mathematical model and drawn by using the MATLAB software package (R2014a). Parameters: group size N = 5, multiplication factor r = 3, contribution cost c = 0.3, cost of exclusion δ = 0.3, probability of exclusion p = 1, transfer rate of conditional defectors q = 0, and observation cost ∆ = 0.35. When cooperators are able to exclude defectors, the three strategists can form the periodic oscillations during evolution (a and b), where the three strategists coexist. In contrast, when cooperators cannot exclude defectors, cooperator and conditional defector are both extinct and defector dominates the whole population finally (c and d). C, cooperator; CD, conditional defector; D, defector