Conjugate Distribution Laws in Cultural Evolution via Statistical Learning

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.