The emergence of human societies with complex language and cumulative culture is considered a major evolutionary transition. Why such a high degree of cumulative culture is unique to humans is perplexing given the potential fitness advantages of cultural accumulation. Here, Boyd & Richerson's (1996 Why culture is common, but cultural evolution is rare. Proc. Br. Acad. 88, 77-93) discrete-cultural-trait model is extended to incorporate arbitrarily strong selection; conformist, anti-conformist and unbiased frequency-dependent transmission; random and periodic environmental variation; finite population size; and multiple 'skill levels.' From their infinite-population-size model with success bias and a single skill level, Boyd and Richerson concluded that social learning is favoured over individual learning under a wider range of conditions when social learning is initially common than initially rare. We find that this holds only if the number n of individuals observed by a social learner is sufficiently small, but with a finite population and/or a combination of success-biased and conformist or unbiased transmission, this result holds with larger n. Assuming social learning has reached fixation, the increase in a population's mean skill level is lower if cumulative culture is initially absent than initially present, if population size is finite, or if cultural transmission has a frequency-dependent component. Hence, multiple barriers to cultural accumulation may explain its rarity. This article is part of the theme issue 'Human socio-cultural evolution in light of evolutionary transitions'.
Keywords: conformity; cumulative culture; environmental change; finite population; pay-off bias; success bias.