Conjugate Distribution Laws in Cultural Evolution via Statistical Learning

TL;DR

This paper investigates how statistical learning influences cultural evolution, showing that conjugate distributions like the beta distribution naturally emerge in cultural traits through a simple analytical model.

Contribution

It introduces a model demonstrating the emergence of conjugate distributions in cultural evolution due to statistical learning and oblique transmission.

Findings

Conjugate distributions approximate cultural trait distributions.

Statistical learning shapes cultural evolution dynamics.

Analytical model predicts equilibrium distributions.

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.