Estimating density dependence, environmental variance, and long-term selection on a stage-structured life history

A method for analyzing long-term demographic data on density-dependent stage-structured populations in a stochastic environment is derived to facilitate comparison of populations and species with different life histories. We assume that a weighted sum of stage abundances, N, exerts density dependence on stage-specific vital rates of survival and reproduction and that N has a small or moderate coefficient of variation. The dynamics of N are approximated as a univariate stochastic process governed by three key parameters: the density-independent growth rate, the net density dependence, and environmental variance in the life history. We show how to estimate the relative weighs of stages in N and the key parameters. Life history evolution represents a stochastic maximization of a simple function of the key parameters. The long-term selection gradient on the life history can be expressed as a vector of sensitivities of this function with respect to density-independent, density-dependent, and stochastic components of the vital rates. To illustrate the method, we analyze 38 years of demographic data on a great tit population, estimating the key parameters, which accurately predict the observed mean, coefficient of variation, and fluctuation rate of N; we also evaluate the long-term selection gradient on the life history.