Archaeological accounts of cultural change reveal a fundamental conflict: Some suggest that change is gradual, accelerating over time, whereas others indicate that it is punctuated, with long periods of stasis interspersed by sudden gains or losses of multiple traits. Existing models of cultural evolution, inspired by models of genetic evolution, lend support to the former and do not generate trajectories that include large-scale punctuated change. We propose a simple model that can give rise to both exponential and punctuated patterns of gain and loss of cultural traits. In it, cultural innovation comprises several realistic interdependent processes that occur at different rates. The model also takes into account two properties intrinsic to cultural evolution: the differential distribution of traits among social groups and the impact of environmental change. In our model, a population may be subdivided into groups with different cultural repertoires leading to increased susceptibility to cultural loss, whereas environmental change may lead to rapid loss of traits that are not useful in a new environment. Taken together, our results suggest the usefulness of a concept of an effective cultural population size.T he breadth and diversity of cultural traits and their rates of accumulation have received a great deal of scholarly attention. Scientific knowledge in many fields appears to accumulate exponentially (1, 2). However, although the number of tool types in the archaeological record also seems to fit this pattern of exponential increase broadly (3), the number of tools and other cultural traits does not increase steadily and monotonically over time. Depending on the timescale studied, change in tool repertoire may appear punctuated and stepwise. Long, seemingly static, periods are interspersed between "cultural explosions," periods of sudden cultural accumulation (3-13). Further, in some populations, there is evidence that whole suites of cultural traits, such as the ability to make tools, clothing, and fire (14-16), may be lost, defying the general trend of cultural accumulation over time (4,7,8).Reasons for the sudden changes in hominid material culture in the archaeological record continue to be debated; they could be related to demographic factors (17), rapid cognitive change (18-21), relatively sudden changes in hand morphology (22, 23), or dramatic climatic shifts (10,(24)(25)(26)(27)(28). Further, intermediate-scale environmental change or migration to a new environment also could affect the accumulation and loss of traits that are primarily useful in specific environments (29-33). In addition, the relationship between the number of cultural traits in a population and population size has been debated (4,14,29,(34)(35)(36)(37)(38)(39)(40)(41); this relationship also might depend on the social learning strategies of the population (42, 43). Further, there could be a feedback process between the number of tools in a population and the population size: A larger population might be able to invent and retain m...