The Detection of Density‐Dependence from a Series of Annual Censuses

TLDR

Caution is urged in using tests for density‑dependence in census data because they rely on assumptions about population processes and measurement errors can spuriously indicate dependence. The study proposes a distribution‑free method to detect density‑dependence from annual census data. The method employs the correlation between population change and size, using a randomization procedure to define a rejection region for density‑independence and compares this test to two recent alternatives. The randomization test is shown to be equivalent to a likelihood‑ratio test for a specific time‑series family, performs reliably regardless of trend presence, and offers a way to improve one of the competing tests.

Abstract

We report a distribution—free approach to the detection of density—dependence in the variation of population abundance, measured by a series of annual censuses. The method uses the correlation coefficient between the observed population changes and population size and proposes a randomization procedure to define a rejection region for the hypothesis of density—independence. It is shown that the use of the proposed statistic under the randomization approach is equivalent to the likelihood ratio test for a particular family of time series models. The randomization test is compared with two other recently proposed tests. Using computer—generated density—independent and density—dependent data, it is shown that, unlike the other tests, the randomization test is effective whether or not there is a marked trend in the observed data. Arguments are presented showing how one of the other two tests can be further improved. Caution is urged in the use and interpretation of any test for detecting density—dependence in census data because (a) the tests depend on assumptions about population processes, (b) errors of measurement may lead to spurious detection of density—dependence.