Estimating Density Dependence, Environmental Variance, and Long-Term Selection on a Stage-Structured Life History.

AbstractA 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, , exerts density dependence on stage-specific vital rates of survival and reproduction and that has a small or moderate coefficient of variation. The dynamics of 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 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 ; we also evaluate the long-term selection gradient on the life history.