Journal
THEORETICAL POPULATION BIOLOGY
Volume 132, Issue -, Pages 69-81Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.tpb.2019.12.004
Keywords
Vertical transmission; Oblique transmission; Frequency-dependent transmission; Frequency-dependent selection; Modifier of transmission
Funding
- John Templeton Foundation, United States of America
- Stanford Center for Computational, Evolutionary and Human Genomics, United States of America
- Morrison institute for Population and Resource Studies at Stanford University, United States of America
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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. (C) 2019 The Authors. Published by Elsevier Inc.
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