Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution

Theoretical Population Biology
Yutaka KobayashiHisashi Ohtsuki

Abstract

A finite-population, discrete-generation model of cultural evolution is described, in which multiple discrete traits are transmitted independently. In this model, each newborn may inherit a trait from multiple cultural parents. Transmission fails with a positive probability unlike in population genetics. An ancestral process simulating the cultural genealogy of a sample of individuals is derived for this model. This ancestral process, denoted by M-, is shown to be dual to a process M+ describing the change in the frequency of a trait. The age-frequency spectrum is defined as a two-dimensional array whose (i,k) element is the expected number of distinct cultural traits introduced k generations ago and now carried by i individuals in a sample of a particular size n. Numerical calculations reveal that the age-frequency spectrum and related metrics undergo a critical transition from a phase with a moderate number of young, rare traits to a phase with numerous very old, common traits when the expected number of cultural parents per individual exceeds one. It is shown that M+ and M- converge to branching or deterministic processes, depending on the way population size tends to infinity, and these limiting processes bear some duality ...Continue Reading

Citations

Nov 2, 2019·Theoretical Population Biology·Mitsuhiro NakamuraYutaka Kobayashi
Jan 23, 2021·Theoretical Population Biology·Yutaka KobayashiJoe Yuichiro Wakano

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