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

R. Lande* (Corresponding author), V. Grøtan, S. Engen, M. E. Visser, B.-E. Sæther

*Corresponding author for this work

Research output: Contribution to journal/periodicalArticleScientificpeer-review

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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.
Original languageEnglish
Pages (from-to)557-573
Number of pages17
JournalAmerican Naturalist
Issue number4
Publication statusPublished - 03 Feb 2023


  • demography
  • density dependence
  • environmental vari-ance
  • great tit
  • selection
  • sensitivity


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