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.

arXiv comment14 pages, 15 figures, supplemental materials merged, some materials added

References in corpus (11)

• Zipf's Law in Gene Expression
• The Minor Fall, the Major Lift: Inferring Emotional Valence of Musical Chords through Lyrics
• The Evolution of Popular Music: USA 1960-2010
• Evolvability is a Selectable Trait
• Interacting Individuals Leading to Zipf's Law
• AI Methods in Algorithmic Composition: A Comprehensive Survey
• Utterance Selection Model of Language Change
• Scaling breakdown in flow fluctuations on complex networks
• Music transcription modelling and composition using deep learning
• A mathematical model of social group competition with application to the growth of religious non-affiliation
• Statistical Evolutionary Laws in Music Styles