Detection of density-dependent effects on caribou numbers from a series of census data
Keywords:caribou number, population density, density dependence, census, randomization test, permutation test
AbstractThe main objective of this paper is to review and discuss the applicability of statistical procedures for the detection of density dependence based on a series of annual or multi-annual censuses. Regression models for which the statistic value under the null hypothesis of density independence is set a priori (slope = 0 or 1), generate spurious indications of density dependence. These tests are inappropriate because low sample sizes, high variance, and sampling error consistently bias the slope when applied to a finite number of population estimates. Two distribution-free tests are reviewed for which the rejection region for the hypothesis of density independence is derived intrinsically from the data through a computer-assisted permutation process. The "randomization test" gives the best results as the presence of a pronounced trend in the sequence of population estimates does not affect test results. The other non-parametric test, the "permutation test", gives reliable results only if the population fluctuates around a long-term equilibrium density. Both procedures are applied to three sets of data (Pukaskwa herd, Avalon herd, and a hypothetical example) that represent quite divergent population trajectories over time.
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