On the mathematical basis of the variance-mean power relationship |
| |
Authors: | Mutsunori Tokeshi |
| |
Institution: | (1) School of Biological Sciences, Queen Mary and Westfield College, University of London, Mile End Road, E1 4NS London, UK |
| |
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. |
| |
Keywords: | variance-mean power law m *-m regression method |
本文献已被 SpringerLink 等数据库收录! |
|