Prestige bias in cultural evolutionary dynamics

If the traits of more successful individuals are more likely to be adopted, the resulting cultural transmission is described as success biased. In contrast, if the traits of 'prestigious' individuals - those who have already been copied many times - are more likely to be adopted, this is described as prestige-biased cultural transmission. In this case, prestige can be a convenient proxy for success. However, it is unclear how success and prestige biases interact to determine the outcome of cultural evolutionary dynamics. Here, we aim to clarify this using mathematical analysis and stochastic simulations. We find analytic approximations to the stochastic role-model choice process that 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. Our results show that success bias effectively plays the role of natural selection, whereas prestige bias effectively plays the role of genetic drift. Prestige bias, which may be strong in highly social communities, also accelerates the evolutionary dynamics, as expected in a rich-get-richer process. These results signify a step forward in understanding how different cultural transmission biases interact.