Density dependence tests, are they?

Abstract

A large number of time series of abundances of insects and birds from a variety of data sets were submitted to a new density dependence test. The results varied enormously between data sets, but the relation between the frequency of statistically significant density dependence (SSDD) and the length of the series was similar to that of the power curve of the test, making the results consistent with the hypothesis of the density-dependent model being universally applicable throughout the data used. Pest and non-pest species did not differ in the incidence of SSDD. The more sampling error present in the data, the higher the percentages of SSDD. This was expected given that the power of the test increases with increasing sampling error in the data. Many of the data used here, as well as in the literature, clearly violate the basic assumption of the test that the organism concerned should be univoltine and semelparous. Yet the incidence of SSDD was the same in univoltine as in bi/polyvoltine species and the same in semelparous organisms as in birds that are reproductively active in more than one year. The seasonal migrant Autographa gamma in Britain and Czechoslovakia and even rainfall data were found to have SSDD. Statistical significance, however, does not automatically lead to the conclusion of density-dependent regulation. Any series of random variables which are in a stochastic equilibrium, such as a series of independent, identically distributed, random variables, is typically described better by the alternative (density-dependent) model than by the null (density-independent) model. Significant test results were often obtained with sloppy data, with data that clearly violate the basic assumptions of the test and with other data where an interpretation of the results in terms of densitydependent regulation was absurd. Given the fact that other explanations have to be found for significant test results for all these cases, mechanisms other than regulation may very well be applicable too where the data are entirely appropriate for the test. The test is simply a data-based choice between a model without and one with a stochastic equilibrium. A time series as such does not contain any information about the causes of the fluctuation pattern, so that one cannot expect statistics to produce such information from that time series. A significant test result using suitable data is entirely consistent with the hypothesis of density-dependent regulation, but also with any other suitable hypotheses. Because the test results were generally consistent with the hypothesis of a universal applicability of the density-dependence model, a negative test result may only mean that the time series was not long enough for the density dependence that was present to become statistically significant. Positive results are difficult to interpret, but so are negative results. A final decision needs to be based not so much on the test result as on much detailed information about the population concerned. Because the “density-dependence test” does not test for the presence of the mechanism of density-dependent regulation and because of the loaded, multiple meanings of the term “density-dependence”, calling the test a “test of statistical density dependence” may be preferable.