Abstract
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 logS 2=logn+2 logm and logS 2=logm, 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 parameterb in a biologically meaningful manner. In comparison with the power law regression, Iwao'sm *-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 arterfacts and perhaps more clearly linked to some biological mechanisms underlying spatial dispersion of populations.
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Tokeshi, M. On the mathematical basis of the variance-mean power relationship. Res Popul Ecol 37, 43–48 (1995). https://doi.org/10.1007/BF02515760
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DOI: https://doi.org/10.1007/BF02515760