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Many cultural traits characterizing intelligent behaviors are now thought tobe transmitted through statistical learning, motivating us to study its effectson cultural evolution. We conduct a large-scale music data analysis and observethat various statistical parameters of musical products approximately followthe beta distribution and other conjugate distributions. We construct a simplemodel of cultural evolution incorporating statistical learning and analyticallyshow that conjugate distributions emerge at equilibrium in the presence ofoblique transmission. The results demonstrate that the distribution of acultural trait within a population depends on the individual's model forcultural production (the conjugate distribution law), and reveal interestingpossibilities for theoretical and experimental studies on cultural evolutionand social learning.

Conjugate Distribution Laws in Cultural Evolution via Statistical Learning