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Quantifying the impact of density, extrinsic climatic fluctuations, and demography on population fluctuations is a persistent challenge in ecology. We analyzed the effect of these processes on the irregular pattern of population crashes of Soay sheep on the St. Kilda archipelago, United Kingdom. Because the age and sex structure of the population fluctuates independently of population size, and because animals of different age and sex respond in different ways to density and weather, identical weather conditions can result in different dynamics in populations of equal size. In addition, the strength of density-dependent processes is a function of the distribution of weather events. Incorporating demographic heterogeneities into population models can influence dynamics and their response to climate change.