Detecting variability in demographic rates: randomization with the Kullback–Leibler distance

Authors

  • KARIM AL-KHAFAJI,

    Corresponding author
    1. Stanford University – Biological Sciences, Stanford, CA 94305-5020, USA, and
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  • SHRIPAD TULJAPURKAR,

    1. Stanford University – Biological Sciences, Stanford, CA 94305-5020, USA, and
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  • CAROL HORVITZ,

    1. University of Miami – Department of Biology, 1301 Memorial Drive, Coral Gables, FL 33146, USA
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  • ANTHONY KOOP

    1. University of Miami – Department of Biology, 1301 Memorial Drive, Coral Gables, FL 33146, USA
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    • §

      Present address: Center for Plant Health Science and Technology, USDA-APHIS-PPQ, North Carolina State University – Centennial Campus, 1730 Varsity Drive, Suite 300, Raleigh, NC 27606-5202, USA.


*Author to whom correspondence should be addressed: K. Al-Khafaji. Tel. +1 650 387 1970. E-mail khafaji@stanford.edu.

Summary

  • 1Environmental stochasticity can play a major role in population dynamics with consequences for population viability and the evolution of life-history traits. However, in empirical studies it is necessary to verify that environmental stochasticity is actually present and that the observed variability is not simply a consequence of sampling variation.
  • 2We propose a non-parametric method to detect environmental variability in demographic parameters of structured populations based on data randomization using an estimated Kullback–Leibler distance as a test statistic.
  • 3The Kullback–Leibler distance is an established information-theoretic measure of the deviance between distributions and we show, with empirical and simulated data sets, that it can be adapted effectively to detect variability in demographic fates among populations.
  • 4This metric has the potential to reveal the importance of relatively rare transitions for understanding temporal variability in demography that would not be revealed by log-linear analysis.
  • 5Synthesis: Using an estimated Kullback–Leibler distance as a test statistic allows variability at the level of demographic rates to be economically assessed as an adjunct to the randomization tests that many researchers currently perform to assess variability in λ, and would provide additional and complementary insight.

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