### 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 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 arterfacts and perhaps more clearly linked to some biological mechanisms underlying spatial dispersion of populations.

Original language | English |
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Pages (from-to) | 43-48 |

Number of pages | 6 |

Journal | Researches on Population Ecology |

Volume | 37 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 1 1995 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Agricultural and Biological Sciences(all)