Cultural bistability and connectedness in a subdivided population

We propose a stochastic model of cultural evolution in a hunter–gatherer population that is subdivided into demes (subpopulations) of variable size and distributed over a finite or infinite number of sites. We assume a skill acquirable by either social or individual learning, such as the know how for positive niche construction, which raises the carrying capacity of a site. We further assume a positive feedback between the number of individuals in a deme with the skill and the size of that deme, which entails that, for most of the time, a deme will either be small and include few skilled individuals or large and include many skilled individuals. Our principal goal is to examine the effect of the migration rate among sites, a measure of their connectedness, on the frequency and duration of shifts to the large-deme/many-skilled-individuals condition that simultaneously involve many demes. We find that the frequency of these concerted shifts is maximized at an intermediate migration rate, whereas their mean duration is monotone increasing in the migration rate. Finally, we use these theoretical predictions to interpret the Still Bay and Howiesons Poort industries, which are believed to have had spatially-synchronous and widespread distributions of relatively short duration in southern Africa.