(Continued):(Update part 2)
Dr. Boyd responded and told me:
The metapopulation is made up of 128 populations. Payoff biased imitation tends to reduce the frequency of punishers in each population. Random variation due to sampling variation in who gets imitated causes frequencies to jiggle around randomly, but if these were the only two processes populations would all eventually evolve to all defect. However, competition between populations causes some populations to become extinct, and this is more likely to happen in populations in which have fewer punishers because such groups tend to have fewer cooperators. Sometimes these processes balance out so that the metapopulation frequency of punishers reaches an approximate steady state---only approximate because stochastic variation in which groups go extinct and who reproduces causes variation in punisher frequency around the long term means reported in the paper.
Very interesting. I emailed him back and told him a little about my MS thesis and my PhD dissertation, and he offered to send me the VB code that he used for this paper. How exciting.