Testing models of biological scaling with mammalian ...

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Title Testing models of biological scaling with mammalian population densities
Author(s) F. S. Dobson, B. Zinner, Marina Silva
Journal Canadian Journal of Zoology / Revue Canadienne De Zoologie
Date 2003
Volume 81
Issue 5
Start page 844
End page 851
Abstract Two hypotheses have been suggested to explain the form of interspecific scaling of organismal characteristics to body size, such as the well-known increase in total metabolism with body mass. A hypothesis based on simple Euclidean geometry suggests that the scaling of many biological variables to body size should have a scaling exponent of 2/3, or approximate to0.667. On the other hand, according to a hypothesis based on fractal dimensions, the relationship between biological variables and body mass should have a scaling exponent of 0.750. We conducted a power analysis of the predicted exponents of scaling under the Euclidean and fractal hypotheses, using average adult body masses and population densities collected from the published literature on mammalian species. The collected data reflect 987 mammal populations from a broad variety of terrestrial habitats. Using statistical methods we determined the sample sizes required to decide between the values of the scaling exponent of the density-to-mass relationship based on the Euclidean (-0.667) and fractal (-0.750) hypotheses. Non-linearities in the dataset and insufficient power plagued our tests of the predictions. We found that mammalian species weighing less than 100 kg had a linear scaling pattern, sufficient power to reveal a difference between the scaling coefficients -0.667 and -0.750, and an actual scaling coefficient of -0.719 (barely significantly different from -0.667 but not from -0.750). Thus, our results support the fractal hypothesis, though the support was not particularly strong, which suggests that the relationship between body mass and population density should have a scaling exponent of -0.750.

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