title: A paradox of cumulative culture.
abstract: Culture can grow cumulatively if socially learnt behaviors are improved by individual learning before being passed on to the next generation. Previous authors showed that this kind of learning strategy is unlikely to be evolutionarily stable in the presence of a trade-off between learning and reproduction. This is because culture is a public good that is freely exploited by any member of the population in their model (cultural social dilemma). In this paper, we investigate the effect of vertical transmission (transmission from parents to offspring), which decreases the publicness of culture, on the evolution of cumulative culture in both infinite and finite population models. In the infinite population model, we confirm that culture accumulates largely as long as transmission is purely vertical. It turns out, however, that introduction of even slight oblique transmission drastically reduces the equilibrium level of culture. Even more surprisingly, if the population size is finite, culture hardly accumulates even under purely vertical transmission. This occurs because stochastic extinction due to random genetic drift prevents a learning strategy from accumulating enough culture. Overall, our theoretical results suggest that introducing vertical transmission alone does not really help solve the cultural social dilemma problem.
authors.affiliation: Research Center for Social Design Engineering, Kochi University of Technology, Kochi 782-8502, Japan; Department of Management, Kochi University of Technology, Kochi 782-8502, Japan. Electronic address: kobayashi.yutaka@kochi-tech.ac.jp.
authors.forename: Yutaka
authors.initials: Y
authors.lastname: Kobayashi
authors.affiliation: Meiji Institute for Advanced Study of Mathematical Sciences, Nakano, Tokyo 164-8525, Japan.
authors.forename: Joe Yuichiro
authors.initials: JY
authors.lastname: Wakano
authors.affiliation: The Graduate University for Advanced Studies, Shonan Village, Hayama, Kanagawa 240-0193, Japan.
authors.forename: Hisashi
authors.initials: H
authors.lastname: Ohtsuki
mesh_terms: D000818:Animals; D003469:Culture; D006801:Humans; D008962:Models, Theoretical
keywords: Cultural evolution; Cultural social dilemma; Dual inheritance theory; Gene culture coevolution; Social learning