ON THE MATHEMATICAL BASIS OF THE VARIANCE-MEAN POWER RELATIONSHIP

摘要

The mathematical basis of a widely-known variance-mean power relationship of ecological populations was examined. It is shown that the log variance (S-2)-log mean (m) plot is virtually delimited by two lines log S-2 = log n + 2 log m and log S-2 = log m, thus increasing the chance that a linear regression line can be successfully fitted, without a profoundly behavioural background. This makes difficult the task of interpreting a successful fit of the power law regression and its parameter b in a biologically meaningful manner. In comparison with the power law regression, Iwao's m-m regression is structurally less constrained, 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 how good a fit is achieved for a particular data set is largely meaningless, since the power law regression may inherently produce a better fit due to its constrained spatial entity. Furthermore, it could be argued that a successful fit in Iwao's method, when found, is less taxed with mathematical artefacts and perhaps [References: 40]