Collapses of food producer societies are recurrent events in prehistory and have triggered a growing concern for identifying the underlying causes of convergences/divergences across cultures around the world. One of the most studied and used as a paradigmatic case is the population collapse of the Rapa Nui society. Here, we test different hypotheses about it by developing explicit population dynamic models that integrate feedbacks between climatic, demographic and ecological factors that underpinned the socio-cultural trajectory of these people. We evaluate our model outputs against a reconstruction of past population size based on archaeological radiocarbon dates from the island. The resulting estimated demographic declines of the Rapa Nui people are linked to the long-term effects of climate change on the island's carrying capacity and, in turn, on the ‘per-capita food supply’.