Inclusive fitness analysis of cumulative cultural evolution in an island-structured population

The success of humans on the globe is largely supported by our cultural excellence. Our culture is cumulative, meaning that it is improved from generation to generation. Previous works have revealed that two modes of learning, individual learning and social learning, play pivotal roles in the accumulation of culture. However, under the trade-off between learning and reproduction, one's investment into learning is easily exploited by those who copy the knowledge of skillful individuals and selfishly invest more efforts in reproduction. It has been shown that in order to prevent such a breakdown, the rate of vertical transmission (i.e. transmission from parents to their offspring) of culture must be unrealistically close to one. Here we investigate what if the population is spatially structured. In particular, we hypothesize that spatial structure should favor highly cumulative culture through endogenously arising high kinship. We employ Wright's island model and assume that cultural transmission occurs within a local island. Our inclusive fitness analysis reveals combined effects of direct fitness of the actor, indirect fitness through relatives in the current generation, and indirect fitness through relatives in future generations. The magnitude of those indirect benefits is measured by intergenerational coefficients of genetic relatedness. Our result suggests that the introduction of spatial structure raises the stationary level of culture in the population, but that the extent of its improvement compared with a well-mixed population is marginal unless spatial localization is extreme. Overall, our model implies that we need an alternative mechanism to explain highly cumulative culture of modern humans.