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

Yutaka Kobayashi, Joe Yuichiro Wakano and Hisashi Ohtsuki

Theoretical Population Biology, 2018, vol. 123, issue C, 18-27

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 relationships. The critical behavior of the original processes M+ and M− is explained in terms of a phase transition of the branching processes. Using the results of the limiting processes in combination, we derive analytical formulae that well approximate the age–frequency spectrum and also other metrics.

Keywords: Cumulative culture; Social learning; Dual process; Backward process; Retrospective model (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0040580918300169
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:123:y:2018:i:c:p:18-27

DOI: 10.1016/j.tpb.2018.04.007

Access Statistics for this article

Theoretical Population Biology is currently edited by Jeremy Van Cleve

More articles in Theoretical Population Biology from Elsevier
Bibliographic data for series maintained by Catherine Liu ().