Evolutionary dynamics on sequential temporal networks
Fig 3
Fixation probabilities by the mean-field approximation.
a, We consider a sequential temporal network with two snapshots. The fixation probabilities and
are identical under neutral drift, i.e.,
(the black dashed line in b). b, We compare these two probabilities
and
under weak selection. We provide numerical simulations for the sequential temporal network (red solid line) and the static network (red dashed line) in the left panel. The probability
is higher than the probability
when the benefit-to-cost ratio b/c is larger than 1. We also calculate the difference between the two probabilities by our mean-field approximation (green dashed line), and the results can well predict the simulations (red diamonds). Furthermore, we calculate the critical benefit-to-cost ratio (b/c)* of the sequential temporal network (solid arrows) and the static network (dashed arrows) by the theoretical formula (red arrows) and approximation (green arrows). The sequential temporal network has a lower positive critical ratio, which shows a better potential to promote cooperation. Parameter values are c = 1, δ = 0.025.