Saar Egozi, Yoav Ram

If the traits of more successful individuals are more likely to be adopted, the resulting cultural transmission is described as being success-biased. Prestige may be used as a proxy for success.
Here, we model prestige bias as a combination of indirect success bias and influence bias, the latter meaning that the choice of a role-model depends on the number of individuals that have already copied that role-model.
The effect of prestige on cultural evolutionary dynamics is analyzed using mathematical analysis and stochastic simulations.
Analytic approximations to the stochastic role-model choice process facilitate the mathematical analysis and reduce the computational complexity of simulations. Approximations are given to the fixation probability and the fixation time of an invading cultural trait in different environments.
We show that indirect success bias effectively plays the role of natural selection, whereas influence bias effectively plays the role of genetic drift.
Influence bias, which may be strong in communities where social media are prevalent, also accelerates the evolutionary dynamics, as can be expected in a rich-get-richer process.