Comparisons between model-predicted trajectories (lines) and observed SPD data (points) at Rapa Nui. Estimated (black dots) and predicted (red line) SPD values for the period 1130–1760 CE. Grey shaded area shows 95% confidence intervals of model predictions based on Ricker logistic population models: (a) model 1, (b) model 2 (palm cover effects), (c) model 3 (climatic effects; SOI) and (d) model 4 (SOI and palm cover effects). See electronic supplementary material, tables S1 and S2 for details. (d) These models support the hypothesis that the Rapa Nui experienced major demographic changes well before the arrival of European colonizers. More importantly, this trajectory was represented by a very simple population model where carrying capacity is a function of either palm tree cover and climate, and offers an alternative to the simple dichotomy of ‘ecological self-destruction’ versus the ‘idyllic equilibrium’ with nature. (Online version in colour.)