Detecting variability in demographic rates: Randomization with the Kullback-Leibler distance

Karim Al-Khafaji, Shripad Tuljapurkar, Carol Horvitz, Anthony Koop

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


1. Environmental 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. 2. We 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. 3. The 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. 4. This 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. 5. Synthesis: 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.

Original languageEnglish (US)
Pages (from-to)1370-1380
Number of pages11
JournalJournal of Ecology
Issue number6
StatePublished - Nov 2007


  • Demographic census
  • Environmental stochasticity
  • Kullback-Leibler
  • Matrix models
  • Randomization tests

ASJC Scopus subject areas

  • Ecology


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