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Modeling the genealogy of a cultural trait

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  • Aguilar, Elliot
  • Ghirlanda, Stefano

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.

Suggested Citation

  • Aguilar, Elliot & Ghirlanda, Stefano, 2015. "Modeling the genealogy of a cultural trait," Theoretical Population Biology, Elsevier, vol. 101(C), pages 1-8.
  • Handle: RePEc:eee:thpobi:v:101:y:2015:i:c:p:1-8
    DOI: 10.1016/j.tpb.2014.12.007
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    References listed on IDEAS

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    1. Russell D. Gray & Quentin D. Atkinson, 2003. "Language-tree divergence times support the Anatolian theory of Indo-European origin," Nature, Nature, vol. 426(6965), pages 435-439, November.
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    Cited by:

    1. Kobayashi, Yutaka & Wakano, Joe Yuichiro & Ohtsuki, Hisashi, 2018. "Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution," Theoretical Population Biology, Elsevier, vol. 123(C), pages 18-27.
    2. Takahashi, Takuya & Ihara, Yasuo, 2022. "Application of a Markovian ancestral model to the temporal and spatial dynamics of cultural evolution on a population network," Theoretical Population Biology, Elsevier, vol. 143(C), pages 14-29.
    3. Kobayashi, Yutaka & Kurokawa, Shun & Ishii, Takuya & Wakano, Joe Yuichiro, 2021. "Time to extinction of a cultural trait in an overlapping generation model," Theoretical Population Biology, Elsevier, vol. 137(C), pages 32-45.

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