Conjugate Distribution Laws in Cultural Evolution via Statistical Learning

Abstract: Many cultural traits characterizing intelligent behaviors are now thought to be transmitted through statistical learning, motivating us to study its effects on cultural evolution. We conduct a large-scale music data analysis and observe that various statistical parameters of musical products approximately follow the beta distribution and other conjugate distributions. We construct a simple model of cultural evolution incorporating statistical learning and analytically show that conjugate distributions emerge at equilibrium in the presence of oblique transmission. The results demonstrate that the distribution of a cultural trait within a population depends on the individual's model for cultural production (the conjugate distribution law), and reveal interesting possibilities for theoretical and experimental studies on cultural evolution and social learning.