The forces driving cultural accumulation in human populations, both modern and ancient, are hotly debated. Did genetic, demographic, or cognitive features of behaviorally modern humans (as opposed to, say, early modern humans or Neanderthals) allow culture to accumulate to its current, unprecedented levels of complexity? Theoretical explanations for patterns of accumulation often invoke demographic factors such as population size or density, whereas statistical analyses of variation in cultural complexity often point to the importance of environmental factors such as food stability, in determining cultural complexity. Here we use both an analytical model and an agent-based simulation model to show that a full understanding of the emergence of behavioral modernity, and the cultural evolution that has followed, depends on understanding and untangling the complex relationships among culture, genetically determined cognitive ability, and demographic history. For example, we show that a small but growing population could have a different number of cultural traits from a shrinking population with the same absolute number of individuals in some circumstances. [ABSTRACT FROM AUTHOR]