Integrating vital rate variability into perturbation analysis: an evaluation for matrix population models of six plant species


  • Pieter A. Zuidema,

    Corresponding author
    1. Department of Plant Ecology, Utrecht University, PO Box 80084, 3508 TB Utrecht, The Netherlands and Programa Manejo de Bosques de la Amazonía Boliviana (PROMAB), Casilla 107, Riberalta, Beni, Bolivia; and
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  • Miguel Franco

    1. Instituto de Ecologia, Universidad Nacional Autónoma de México, Apartado Postal 70–275, 04510 Coyoacán, D.F., México
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    • §

      Present address: Department of Biological Sciences, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK.

*Correspondence and present address: Pieter Zuidema, Plant Production Systems Group, Wageningen University, PO Box 430, 6700 AK Wageningen, The Netherlands (fax + 31 317484892; e-mail


  • 1Matrix population models are usually constructed by employing average values of vital rates (survival, growth and reproduction) for each size category. Perturbation analyses of matrix models assess the influence of vital rates or matrix elements on population growth rate. They consider the impact of either an unstandardized (sensitivity analysis) or a mean-standardized (elasticity analysis) change in a model component. Certain vital rates are intrinsically more variable than others. This variation can be taken into account in variance-standardized perturbation analysis, which applies changes to vital rates in proportion to their variability.
  • 2We applied variance-standardized perturbation analysis to six plant species with different life histories (a forest understorey herb, two tropical forest palms and three tropical forest trees). 1500 random values were drawn from observed frequency distributions of each vital rate in each size category, and population growth rates (λ) were calculated for each of the simulations.
  • 3Variability differed widely between vital rates, being particularly high for growth and reproduction. Vital rate variation was negatively correlated with its effect on λ (measured by either sensitivity or elasticity). The variation in λ resulting from the sampling procedure differed between species (with higher values in shorter-lived plants) and vital rates (with particularly high values due to variation in growth rates).
  • 4The relationships between λ and vital rates were close to linear. Therefore, the product of sensitivity (or elasticity) and degree of variability of a vital rate was a good estimator of the variation in λ, explaining 95% of the variation in λ in the six study species.
  • 5Thus, a reliable estimation of the 95% confidence interval of λ due to variation in one of the vital rates can be calculated as the product of the 95% confidence interval of the vital rate and its sensitivity.
  • 6Our results suggest that variance-standardized perturbation analyses are a useful tool to determine the impact of vital rate variation on population growth rate.