Revisiting the Effect of Population Size on Cumulative Cultural Evolution

Previous models of cultural evolution found that larger populations can better maintain complex technologies because they contain more highly skilled people whom others can imitate. These models, however, do not distinguish the effects of population size from population density or network size; a learner's social network includes the entire population. Does population size remain important when populations are subdivided and networks are realistically small? I use a mathematical model to show that population size has little effect on equilibrium levels of mean skill under a wide range of conditions. The effects of network size and transmission error rate usually overshadow that of population size. Population size can, however, affect the rate at which a population approaches equilibrium, by increasing the rate at which innovations arise. This effect is small unless innovation is very rare. Population size should predict technological complexity in the real world, then, only if technological evolution is a slow, innovation-limited process. Population density and connectedness have similar affects to population size, though density can also affect equilibrium skill. I discuss the results of this analysis in light of the current empirical debate.