Phenomena like meat sharing in hunter-gatherers, self-sacrifice in intergroup conflicts, and voluntary contribution to public goods provision in laboratory experiments have led to the development of numerous theories on the evolution of altruistic in-group beneficial behavior in humans. Many of these theories abstract away from the effects of kinship on the incentives for public goods provision, though. Here, it is investigated analytically how genetic relatedness changes the incentive structure of that paradigmatic game which is conventionally used to model and experimentally (...) investigate collective action problems: the linear public goods game. Using recent anthropological data sets on relatedness in 61 contemporary hunter-gatherer and horticulturalist societies the relevant parameters of this model are then estimated. It turns out that the kinship patterns observed in these societies substantially reduce the negative effect of increasing group size on incentives for public goods provision. It is suggested, therefore, that renewed attention should be given to inclusive fitness theory in the context of public goods provision also in sizable groups, because its explanatory power with respect to this central problem in the evolution of human cooperativeness and altruism might have been substantially underrated. (shrink)