Paper short abstract:

Assuming that culture can be represented by a vector of 1’s and 0’s, as is often done in empirical studies of cultural evolution among pre-contact peoples, we obtain theoretical predictions for the cultural evolutionary rate and cultural diversity under various modes of social learning.

Paper long abstract:

Cultural evolution occurs when innovations produced by individual learning (e.g. by trial-and-error) are propagated in a population by social learning (e.g. by imitation). Empirical studies of cultural evolution among pre-contact peoples often represent the cultural traits of a society by a vector of 1's (presence) and 0's (absence). To study the cultural evolution of such 0, 1-vectors, we assign a possibly different 0, 1-vector to each individual in a finite population and calculate the changes in their frequencies. Then, assuming the infinite sites model of innovation, we obtain predictions, by mathematical analysis and by agent-based simulation, for the cultural evolutionary rate and within-population cultural diversity under various modes of social learning. We argue that the emphasis placed on demography (e.g. population size) by many theoretically-minded archaeologists should be regarded with caution. Instead, we point out that innovativeness (i.e. individual learning ability) is an equally, if not more, important determinant of the cultural evolutionary rate and within-population cultural diversity, and discuss the conditions that favor the biological evolution of innovativeness. An additional question of interest is to identify the conditions under which a serial founder effect may operate on cultural traits, resulting in a decrease of within-population cultural diversity with distance from the geographical origin of range expansion or of cultural diffusion.