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

School of Mathematical Sciences

Tel Aviv University

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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Ecology, Evolution, Behavior and Systematics

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10.1016/j.tpb.2019.12.004

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title = "The evolution of frequency-dependent cultural transmission",

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 = "Frequency-dependent selection, Frequency-dependent transmission, Modifier of transmission, Oblique transmission, Vertical transmission",

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T1 - The evolution of frequency-dependent cultural transmission

AU - Liberman, Uri

AU - Ram, Yoav

AU - Altenberg, Lee

AU - Feldman, Marcus W.

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N2 - 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.

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.

KW - Frequency-dependent selection

KW - Frequency-dependent transmission

KW - Modifier of transmission

KW - Oblique transmission

KW - Vertical transmission

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DO - 10.1016/j.tpb.2019.12.004

M3 - مقالة

C2 - 31866423

SN - 0040-5809

VL - 132

SP - 69

EP - 81

JO - Theoretical Population Biology

JF - Theoretical Population Biology

ER -

The evolution of frequency-dependent cultural transmission

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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