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The evolution of frequency-dependent cultural transmission
Uri Liberman1, Yoav Ram2, Lee Altenberg3
1School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel.
Theoretical Population Biology
|December 24, 2019
Summary
This study models cultural trait transmission, revealing how transmission rates based on trait frequency can lead to stable trait variations (polymorphisms). It explores conditions for stable evolution and the interplay between selection and transmission dynamics.
Area of Science:
- Evolutionary Biology
- Cultural Transmission Models
- Population Genetics
Background:
- Cultural traits are transmitted vertically (parent-offspring) and obliquely (non-parental adults).
- Transmission rates can depend on the frequency of the trait within a population.
- Understanding the conditions for stable trait coexistence (polymorphism) is crucial for evolutionary dynamics.
Purpose of the Study:
- To model vertical and oblique cultural transmission of dichotomous traits.
- To identify conditions for stable trait polymorphism under frequency-dependent transmission.
- To analyze the evolution of frequency-dependent transmission and its interaction with selection.
Main Methods:
- Development of a mathematical model for cultural trait transmission.
- Analysis of transmission rates as functions of trait frequency.
- Application of modifier theory to study the evolution of transmission strategies.
- Global stability analysis for specific transmission rate functions.
Main Results:
- Derived sufficient conditions for the existence of stable trait polymorphisms.
- Demonstrated that unique protected polymorphisms can be globally stable even when initial conditions are not met.
- Determined exact conditions for the invasion of transmission modifiers in a population at stable polymorphism.
- Explored the complex interactions between frequency-dependent selection and frequency-dependent transmission.
Conclusions:
- Frequency-dependent transmission plays a significant role in maintaining trait diversity.
- Stable polymorphisms can arise and persist under specific conditions of cultural transmission.
- The evolution of transmission mechanisms is influenced by both selection pressures and existing trait frequencies.
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