Figure 2
Bifurcation plots illustrating the evolutionary dynamics of pool rewarding in spatially structured populations. The scaled relatedness coefficient serves as a control parameter. Arrows show the direction of evolution for the probability of playing prosocial rewarding. Solid (dashed) lines correspond to convergence stable (unstable) equilibria. In the left column panels (a,d,g), rewards are absent (i.e., r 2 = 1). In the middle column panels (b,e,h), r 2 = 2.5. In the right column panels (c,f,i), r 2 = 4.5. In the top row panels (a–c), r 1 = 1.25. In the middle row panels (d–f), r 1 = 2.5. In the bottom row panels (g–i), r 1 = 4.5. In all panels, n = 5. A value of κ = 0 could correspond to an infinitely large well-mixed population (Eq. (8)); a value of κ = 0.25 could correspond to an evolutionary graph updated with a death-birth Moran model with \({N}_{{\rm{T}}}\gg k\) and k = 4 (Eq. (10)); a value of κ ≈ 0.167 could correspond to an infinite island model with deme size N = 5 and \(m\ll 1\) (Eq. (9)).
