TY - JOUR
T1 - The evolution of frequency-dependent cultural transmission
AU - Liberman, Uri
AU - Ram, Yoav
AU - Altenberg, Lee
AU - Feldman, Marcus W.
N1 - Publisher Copyright:
© 2019 The Authors
PY - 2020/4
Y1 - 2020/4
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
UR - http://www.scopus.com/inward/record.url?scp=85077322169&partnerID=8YFLogxK
U2 - 10.1016/j.tpb.2019.12.004
DO - 10.1016/j.tpb.2019.12.004
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C2 - 31866423
AN - SCOPUS:85077322169
SN - 0040-5809
VL - 132
SP - 69
EP - 81
JO - Theoretical Population Biology
JF - Theoretical Population Biology
ER -