The evolution of frequency-dependent cultural transmission

Uri Liberman; Yoav Ram; Lee Altenberg; Marcus W. Feldman

doi:10.1016/j.tpb.2019.12.004

The evolution of frequency-dependent cultural transmission

Uri Liberman, Yoav Ram, Lee Altenberg, Marcus W. Feldman^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	69-81
Number of pages	13
Journal	Theoretical Population Biology
Volume	132
DOIs	https://doi.org/10.1016/j.tpb.2019.12.004
State	Published - Apr 2020

Funding

Funders	Funder number
Morrison Institute for Population and Resource Studies
Stanford Center for Computational
John Templeton Foundation
Stanford University
Center for Computational, Evolutionary and Human Genomics, Stanford University

Keywords

Frequency-dependent selection
Frequency-dependent transmission
Modifier of transmission
Oblique transmission
Vertical transmission

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10.1016/j.tpb.2019.12.004

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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.",

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AU - Feldman, Marcus W.

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AB - 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.

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The evolution of frequency-dependent cultural transmission

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