Population size has long been considered an important driver of cultural change. Results from population genetics, however, demonstrate that it is not the census population size, N, but the effective size of a population, N_e, that determines important evolutionary parameters. This effective population size governs the rate of change in a population due to drift and affects genetic variability both within and between populations. Here, we systematically examine effective population sizes for traits that evolve culturally, i.e. through processes of innovation and social learning, rather than genetically. We use different modeling approaches to investigate how cultural N_e and levels of diversity depend on the way traits are learned, population connectedness and social network structure. We show that one-to-many and frequency-dependent transmission can temporally or permanently lower effective population size compared to census numbers. Contrary to expectations in the literature, migration does not increase N_e and a process of cultural exchange among groups increases only the less meaningful inbreeding effective number but not the variance effective number. While network density in random networks leaves N_e unchanged, scale-free networks tend to decrease and small-world networks tend to increase N_e compared to census numbers. Finally, for one-to-many transmission and different network structures, effective size and cultural diversity are closely associated. For connectedness, however, small amounts of migration and cultural exchange result in highest diversity independently of N_e. Our results highlight the importance of effective population size for cultural evolution and show that inferring N_e requires detailed knowledge about underlying cultural and demographic processes.

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Effective population size for culturally evolving traits

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