ON THE MATHEMATICAL BASIS OF THE VARIANCE-MEAN POWER RELATIONSHIP

The mathematical basis of a widely-known variance-mean power relations hip of ecological populations was examined. It is shown that the log v ariance (S-2)-log mean (m) plot is virtually delimited by two lines lo g S-2 = log n + 2 log m and log S-2 = log m, thus increasing the chanc e that a linear regression line can be successfully fitted, without a profoundly behavioural background. This makes difficult the task of in terpreting a successful fit of the power law regression and its parame ter b in a biologically meaningful manner. In comparison with the powe r law regression, Iwao's m-m regression is structurally less constrain ed, i.e. has a wider spatial region in which data points can scatter. This suggests that a comparison between the two methods in terms of ho w good a fit is achieved for a particular data set is largely meaningl ess, since the power law regression may inherently produce a better fi t due to its constrained spatial entity. Furthermore, it could be argu ed that a successful fit in Iwao's method, when found, is less taxed w ith mathematical artefacts and perhaps