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The evolution of frequency-dependent cultural transmission

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  • Liberman, Uri
  • Ram, Yoav
  • Altenberg, Lee
  • Feldman, Marcus W.

Abstract

In a model of vertical and oblique cultural transmission of a dichotomous trait, the rates of transmission of each form of the trait are functions of the trait frequency in the population. Sufficient conditions on these functions are derived for a stable trait polymorphism to exist. If the vertical transmission rates are monotone decreasing functions of the trait frequency, a complete global stability analysis is presented. It is also shown that a unique protected polymorphism can be globally stable even though the sufficient conditions are not met. The evolution of frequency-dependent transmission is modeled using modifier theory, and exact conditions are derived for a transmission modifier to invade a population at a stable polymorphism. Finally, the interaction between frequency-dependent selection and frequency-dependent transmission is explored.

Suggested Citation

  • Liberman, Uri & Ram, Yoav & Altenberg, Lee & Feldman, Marcus W., 2020. "The evolution of frequency-dependent cultural transmission," Theoretical Population Biology, Elsevier, vol. 132(C), pages 69-81.
    • Handle: RePEc:eee:thpobi:v:132:y:2020:i:c:p:69-81
    DOI: 10.1016/j.tpb.2019.12.004
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    References listed on IDEAS

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    5. Ram, Yoav & Liberman, Uri & Feldman, Marcus W., 2019. "Vertical and oblique cultural transmission fluctuating in time and in space," Theoretical Population Biology, Elsevier, vol. 125(C), pages 11-19.
    6. Ram, Yoav & Altenberg, Lee & Liberman, Uri & Feldman, Marcus W., 2018. "Generation of variation and a modified mean fitness principle: Necessity is the mother of genetic invention," Theoretical Population Biology, Elsevier, vol. 123(C), pages 1-8.
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