Population Ecology

, Volume 48, Issue 1, pp 79–89 | Cite as

Modeling vital rates improves estimation of population projection matrices

  • Kevin Gross
  • William F. Morris
  • Michael S. Wolosin
  • Daniel F. Doak
Original Article


Population projection matrices are commonly used by ecologists and managers to analyze the dynamics of stage-structured populations. Building projection matrices from data requires estimating transition rates among stages, a task that often entails estimating many parameters with few data. Consequently, large sampling variability in the estimated transition rates increases the uncertainty in the estimated matrix and quantities derived from it, such as the population multiplication rate and sensitivities of matrix elements. Here, we propose a strategy to avoid overparameterized matrix models. This strategy involves fitting models to the vital rates that determine matrix elements, evaluating both these models and ones that estimate matrix elements individually with model selection via information criteria, and averaging competing models with multimodel averaging. We illustrate this idea with data from a population of Silene acaulis (Caryophyllaceae), and conduct a simulation to investigate the statistical properties of the matrices estimated in this way. The simulation shows that compared with estimating matrix elements individually, building population projection matrices by fitting and averaging models of vital-rate estimates can reduce the statistical error in the population projection matrix and quantities derived from it.


Information criteria Model selection Multimodel averaging Vital rates 



We thank Hal Caswell, Massa Nakaoka, and an anonymous reviewer for helpful comments and discussion. This work was supported by NSF grant DEB-0087096 to WFM and DFD.


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Copyright information

© The Society of Population Ecology and Springer-Verlag Tokyo 2005

Authors and Affiliations

  • Kevin Gross
    • 1
  • William F. Morris
    • 2
  • Michael S. Wolosin
    • 2
  • Daniel F. Doak
    • 3
  1. 1.Biomathematics ProgramNorth Carolina State UniversityRaleighUSA
  2. 2.Department of Biology and Program in EcologyDuke UniversityDurhamUSA
  3. 3.Department of Ecology and Evolutionary BiologyUniversity of California at Santa CruzSanta CruzUSA

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