Seminar: "Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution" by Prof. Joe Yuichi Wakano (Meiji University)
- Date: September 26 (Tuesday)
- Time: 14:00-14:30
- Speaker: Joe Yuichiro Wakano, Professor, School of Interdisciplinary Mathematical Sciences (IMS), Meiji University, Japan
Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution
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 is shown to be dual to a process describing the change in the frequency of a trait. The age–frequency spectrum is defined as the expected number of distinct cultural traits introduced generations ago and now carried by individuals in a sample of a particular size. 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 1. Using branching process theory or deterministic approximation, we obtain analytic formulae that well approximate some metrics.
Kobayashi Y, Wakano JY & Ohtsuki H (2018). Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution. Theoretical Population Biology 123:18-27.
This paper has won the 2020 Marcus W. Feldman Prize for outstanding articles published in the journal Theoretical Population Biology, as announced in Theoretical Population Biology 131: 1.
Joe Yuichiro Wakano received his Ph.D. in Science from Kyoto University in 2001. After working as Technical Officer/COE Research Fellow in the University of Tokyo and JSPS Research Fellow, he has been hired by Meiji University as Specially Appointed Associate Professor in 2007, as Associate Professor in 2013, and as Professor in 2018. His main research topics are mathematical modelling of cultural evolution, Adaptive Dynamics, and Inclusive Fitness.