On the stabilization of animal numbers. Problems of testing

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Abstract
When testing for regulation of population numbers, rather than using Bulmer's second test in cases where population numbers are estimated instead of measured, we prefer to correct Bulmer's first test for estimation error. A correction method is expounded, discussed, and applied to two series of census data: the pine looper of Klomp and the garden chafer of Milne. In neither case the tentative conclusion from using the uncorrected test was changed after correction. Therefore, in practice Bulmer's first test without correction can be used well as a first orientation. Twelve long series (more than 10 years) of census data of both univoltine and semelparous (a necessary condition) insects were tested for significant density dependence in the fluctuations of numbers with the randomization test of Pollard et al. None of the series, all we could find to meet the necessary condition as well as being longer than 10 years, showed significant density dependence at the 0.05 level, though the pine looper of Klomp did so at the 0.1 level. Next, the same series were tested for regulation in the sense of “keeping density within limits” with both the first test of Bulmer and the permutation test of Reddingius and Den Boer. Onky Klomp's pine looper population at “Hoge Veluwe” scored significantly. In a following paper this population will be considered more closely, in order to enable understanding of this test result.