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This thesis contributes to the field of cultural evolution by presenting two experimental and two theoretical models of cultural evolution. Prior to presenting these I survey existing experimental and theoretical models of cultural evolution. In the first experiment, I test the hypothesis that increasing group size speeds up cultural accumulation, using a novel puzzle-solving task and within a transmission chain design. I find support for this hypothesis, in contrast with previous experiments. In the second experiment, also using a transmission chain design, I examine perceptual errors in recreating Acheulean handaxes and ask whether such errors can account for the variability of Acheulean technology over time. Using the accumulated copying error model to compare the experimental data to archaeological records, I conclude that perceptual errors alone were likely not the driving force behind Acheulean evolution. In the first theoretical chapter, I present models of cultural differences between populations and of cumulative culture, which build on existing models and accord with empirical data. I then show that the models, when combined, have two qualitative regimes which may correspond to human and nonhuman culture. In the second theoretical chapter, I present a ‘fundamental theorem of cultural selection’, an equivalent of Fisher’s Fundamental Theorem of Natural Selection for cultural evolution. I discuss how this theorem formalizes and sheds light on cultural evolutionary theory. Finally I conclude and discuss future research directions.