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Population fluctuations are caused by demographic and environmental stochasticity, time lags due to life history, and density dependence. We model a general life history allowing density dependence within and among age or stage classes in a population undergoing small or moderate fluctuations around a stable equilibrium. We develop a method for estimating the overall strength of density dependence measured by the rate of return toward equilibrium, and we also consider a simplified population description and forecasting using the density-dependent reproductive value. This generality comes at the cost of requiring a time series of the population age or stage structure instead of a univariate time series of adult or total population size. The method is illustrated by analyzing the dynamics of a fully censused population of red deer (Cervus elaphus) based on annual fluctuations of age structure through 21 years.

Original publication




Journal article


Am Nat

Publication Date





76 - 87


Age Distribution, Animals, Deer, Female, Models, Biological, Population Density, Reproduction, Time Factors