Statistical characteristics of the density‐independent population fluctuation and the evaluation of density‐dependence and regulation in animal populations

Summary In this study it was proved that the “density‐independent population” shows the following characteristics if the analysis is made using time‐series samples: The slope b in the density‐on‐density regression between successive developmental stages has a general tendency to become smaller than 1, though the bias approaches zero if one or more of the following three conditions are satisfied: (a) the data cover a large number of generations, (b) the variance of the rate of population change for the period concerned is small relative to that for the residual period in a whole generation, and (c) the population has a distinct trend to either increase or decrease over generations. The variance for the generation‐to‐generation population fluctuation increases continually as the number of generations is increased, even if the population has no inherent trend to increase or decrease. For a fixed number of generations, however, the variance remains constant among different developmental stages. On the basis of these theoretical results, a modified method for detecting density‐dependence from time‐series samples was presented, together with a new, tentative technique of variance analysis to evaluate the regulation of numbers directly. The results of applying these methods to some sets of data from both hypothetical and actual populations illustrated their validity for use in population studies.