Cumulative culture and explosive demographic transitions

A demographic transition is a change in the pattern of growth of a population. Human history records several kinds of such transitions, e.g., from stability to growth or between different kinds of growth. Culture is often implied as the main fuel of demographic transitions, but theorizing is so far limited to verbal arguments. Here we study two simple formal models in which population size and the amount of culture in a population influence each other's dynamics. The first model has two regimes: an equilibrium regime in which both population size and amount of culture reach stable values, and an explosive regime in which both variables increase exponentially without bound. A transition between these regimes is caused by changes in parameters that describe the accuracy of cultural transmission and the interaction between demography and culture. The second model suggests that a transition from extensive to intensive accumulation of culture may derive from a qualitative change in how individuals cooperate to create culture.