Archaeological and ethnohistorical evidence suggests a link between a population's size and structure, and the diversity or sophistication of its toolkits or technologies. Addressing these patterns, several evolutionary models predict that both the size and social interconnectedness of populations can contribute to the complexity of its cultural repertoire. Some models also predict that a sudden loss of sociality or of population will result in subsequent losses of useful kills/technologies. Here, we test these predictions with two experiments that permit learners to access either one or five models (teachers). Experiment 1 demonstrates that naive participants who could observe five models, integrate this information and generate increasingly effective skills (using an image editing tool) over 10 laboratory generations, whereas those with access to only one model show no improvement. Experiment 2, which began with a generation of trained experts, shows how learners with access to only one model lose skills (in knot-tying) more rapidly than those with access to five models. In the final generation of both experiments, all participants with access to five models demonstrate superior skills to those with access to only one model. These results support theoretical predictions linking sociality to cumulative cultural evolution.