The evolution of frequency-dependent cultural transmission

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

Theoretical Population Biology, 2020, vol. 132, issue C, 69-81

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.

Keywords: Vertical transmission; Oblique transmission; Frequency-dependent transmission; Frequency-dependent selection; Modifier of transmission (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:132:y:2020:i:c:p:69-81

DOI: 10.1016/j.tpb.2019.12.004

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