Conformity and anti-conformity in a finite population

Area of Science:

• Evolutionary Biology
• Cultural Transmission
• Population Genetics

Background:

• Conformist and anti-conformist cultural transmission are key evolutionary forces.
• Previous theoretical work relied on infinite-population models (IPMs).
• Empirical studies have investigated these phenomena across various species.

Purpose of the Study:

• To introduce and analyze finite-population models (FPMs) of cultural transmission.
• To compare FPM dynamics with established IPMs.
• To investigate the impact of population size on cultural trait evolution.

Main Methods:

• Development of finite-population models (FPMs) for conformity and anti-conformity.
• Numerical simulations of FPMs with varying numbers of role models (n=3 and n=5).
• Application of diffusion approximation to analyze FPM behavior.

Main Results:

• FPMs with n=3 role models approximate IPM short-term behavior.
• IPM stable equilibria manifest as effective equilibria in FPMs, showing persistent variation.
• FPMs with n=5 role models exhibit novel dynamics: equilibrium switching and cycling, not possible in IPMs.

Conclusions:

• Finite population size introduces complex dynamics like equilibrium switching and cycling.
• The diffusion approximation's accuracy depends on both parameter magnitudes and model qualitative behavior.
• FPMs offer a more nuanced understanding of cultural transmission compared to traditional IPMs.