title: Modeling the genealogy of a cultural trait.
abstract: The mathematical study of genealogies has yielded important insights in population biology, such as the ability to estimate the time to the most recent common ancestor (MRCA) of a sample of genetic sequences or of a group of individuals. Here we introduce a model of cultural genealogies that is a step toward answering similar questions for cultural traits. In our model individuals can inherit from a variable, potentially large number of ancestors, rather than from a fixed, small number of ancestors (one or two) as is typical of genetic evolution. We first show that, given a sample of individuals, a cultural common ancestor does not necessarily exist. We then introduce a related concept: the most recent unique ancestor (MRUA), i.e., the most recent single individual who is the earliest cultural ancestor of the sample. We show that, under neutral evolution, the time to the MRUA can be staggeringly larger than the time to MRCA in a single ancestor model, except when the average number of learning opportunities per individuals is small. Our results point out that the properties of cultural genealogies may be very different from those of genetic genealogies, with potential implications for reconstructing the histories of cultural traits.
authors.affiliation: Biology Department, Graduate Center of the City University of New York, 365 5th Ave., New York, NY 10016, United States; Centre for the Study of Cultural Evolution, Lillafrescativägen 7B, 106 91 Stockholm, Sweden. Electronic address: elliot.g.aguilar@gmail.com.
authors.forename: Elliot
authors.initials: E
authors.lastname: Aguilar
authors.affiliation: Biology Department, Graduate Center of the City University of New York, 365 5th Ave., New York, NY 10016, United States; Centre for the Study of Cultural Evolution, Lillafrescativägen 7B, 106 91 Stockholm, Sweden; Psychology Department, Brooklyn College, 2900 Bedford Ave., Brooklyn, NY 11217, United States. Electronic address: drghirlanda@gmail.com.
authors.forename: Stefano
authors.initials: S
authors.lastname: Ghirlanda
mesh_terms: D000465:Algorithms; D003468:Cultural Evolution; D019143:Evolution, Molecular; D005789:Genealogy and Heraldry; D005828:Genetics, Population / Q000379:methods*; D006801:Humans; D008957:Models, Genetic; D011157:Population Dynamics
keywords: Cultural evolution; Genealogical processes; Most recent common ancestor; Most recent unique ancestor