Figure 6.

Fixation probabilities for the Prisoner’s Dilemma game in the VT model with c = 1 and δ = 0.025. Points show simulation results for a decoupled update rule (blue, circles) and a death–birth update rule (red, squares). For the decoupled update rule, the approximate fixation probabilities given by equation (3.13) are plotted (blue, solid line) and for the death–birth update we plot a best fit line (red, dashed line). Fixation probabilities, given by equation (2.5), for an HL with death–birth update in the EGT model (green, solid line) are also shown for comparison. The grey dotted line shows the fixation probability for a neutral mutant. It is clear that cooperation is significantly favoured in the VT model with decoupled update rule when compared with the EGT results, in particular, the critical benefit-to-cost ratio is more than halved. However, when a death–birth update is introduced on the VT model this effect is suppressed and the critical benefit-to-cost ratio is very close to the EGT case. (Online version in colour.)