Demography is increasingly being invoked to account for features of the archaeological record, such as the technological conservatism of the Lower and Middle Pleistocene, the Middle to Upper Paleolithic transition, and cultural loss in Holocene Tasmania. Such explanations are commonly justified in relation to population dynamic models developed by Henrich [Henrich J (2004)Am Antiq69:197-214] and Powell et al. [Powell A, et al. (2009)Science324(5932):1298-1301], which appear to demonstrate that population size is the crucial determinant of cultural complexity. Here, we show that these models fail in two important respects. First, they only support a relationship between demography and culture in implausible conditions. Second, their predictions conflict with the available archaeological and ethnographic evidence. We conclude that new theoretical and empirical research is required to identify the factors that drove the changes in cultural complexity that are documented by the archaeological record.