Evolving genealogies in cultural evolution, the descendant process, and the number of cultural traits

Joe Yuichiro Wakano, Hisashi Ohtsuki, Yutaka Kobayashi and Ellen Baake

Theoretical Population Biology, 2026, vol. 168, issue C, 1-18

Abstract: We consider a Moran-type model of cultural evolution, which describes how traits emerge, are transmitted, and get lost in populations. Our analysis focuses on the underlying cultural genealogies; they were first described by Aguilar and Ghirlanda (2015) and are closely related to the ancestral selection graph of population genetics, wherefore we call them ancestral learning graphs. We investigate their dynamical behaviour, that is, we are concerned with evolving genealogies. In particular, we consider the total length of the genealogy of the entire population as a function of the (forward) time where we start looking back. This quantity shows a sawtooth-like dynamics with linear increase interrupted by collapses to near-zero at random times. We relate this to the metastable behaviour of the stochastic logistic model, which describes the evolution of the number of ancestors as well as the number of descendants of a given sample.

Keywords: Cultural evolution; Ancestral learning graph; Ancestral selection graph; Stochastic logistic model; Metastability; Merging of genealogies (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:168:y:2026:i:c:p:1-18

DOI: 10.1016/j.tpb.2025.12.003

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