On the mathematical basis of the variance-mean power relationship

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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 languageEnglish
Pages (from-to)43-48
Number of pages6
JournalResearches on Population Ecology
Volume37
Issue number1
DOIs
Publication statusPublished - Jun 1 1995
Externally publishedYes

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power law
Population
Linear Models
methodology
comparison
method
Datasets
population (ecological)
parameter

All Science Journal Classification (ASJC) codes

  • Agricultural and Biological Sciences(all)

Cite this

On the mathematical basis of the variance-mean power relationship. / Tokeshi, Mutsunori.

In: Researches on Population Ecology, Vol. 37, No. 1, 01.06.1995, p. 43-48.

Research output: Contribution to journalArticle

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