On the stabilization of animal numbers. Problems of testing : I. Power estimates and estimation errors

It is tried to remove some misunderstandings about the "regulation" of animal numbers by density-dependent processes. Staying between limits is called "stabilization", and only when this results from density-dependent processes it is considered "regulation". We discuss two tests that may be used to detect the existence of regulation: the parametric tests of Bulmer and a nonparametric "permutation" test. The powers of these tests are compared. The first test of Bulmer and the permutation test do not differ very much in power, but the second test of Bulmer has hardly any power and therefore cannot be used in cases where densities were only estimated. The arguments from which Bulmer's second test is derived are critically discussed and found not to be very convincing. We propose, rather than using Bulmer's second test, to correct the test statistic of his first test for estimation error, and present a possible solution for this. In a following paper this method will be applied to some long series of population counts of univoltine insects, for, a basic assumption of all regulation-tests is, that the sequence of population counts is a realization of a piece of first-order Markov chain. This highly restricts the usefulness of regulation-tests. Some other recent attempts to construct such tests are discussed within the present context.