Abstract Trying to explain the increase in cultural complexity over the long term of human history has long been an interest of anthropology and of historical social sciences more generally. In recent years, interest has grown rapidly in the idea that a key factor in accounting for it might be the size of the human population itself and the extent of interaction between people, because of the effect these have on the innovation rates in populations and on the success with which innovations are transmitted. An important driver of this growth of interest has been the emergence of the new interdisciplinary field of cultural evolution, which makes extensive use of mathematical techniques, especially methods derived from population genetics. The result has been the development of a range of analytical and computer simulation models that make various predictions about the way in which population size influences cultural change, and in particular the growth of cumulative culture, including the processes that have led from the very simple forms of culture possessed by other great apes to those characteristic of Homo sapiens . The aim of this review is to distinguish them, so that future work can focus on evaluating their strengths and weaknesses and the circumstances in which they are useful.
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