We model growth of a density-dependent stage-structured population undergoing small or moderate fluctuations around a deterministically stable equilibrium in a stochastic environment, assuming that a weighted sum of stage abundances, N, exerts density dependence on the stage-specific vital rates of survival and reproduction. We approximate the dynamics of N as a onedimensional stochastic process with three key parameters: the density-independent growth rate and the net density dependence and environmental variance in the life history. Comparisons of populations and species with different life histories are facilitated using the key parameters, which we show how to estimate from long-term demographic data on fluctuations in the vital rates. We also show that life history evolution is a stochastic maximization of a simple function of the key parameters. Elements in the long-term selection gradient acting on the life history can be expressed as sensitivities of this function with respect to density-independent, density-dependent, and stochastic components of the vital rates. Using years of demographic data on a great tit population, we estimate the key demographic parameters, which accurately predict the observed mean, coefficient of variation, and fluctuation rate of N, and also evaluate the long-term selection gradient on the population.

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