Euclidean geometry explains why lengths allow precise body mass estimates in terrestrial invertebrates: The case of oribatid mites

T. Caruso*, M. Migliorini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Indirect measures of soil invertebrate body mass M based on equations relating the latter to body length (l) are becoming increasingly used due to the required painstaking laboratory work and the technical difficulties involved in obtaining some thousands of reliable weight estimates for animals that can be very small. The implicit assumption of such equations is that dM/dV=δ, where V is body volume and δ is a constant density value. Classical Euclidean scaling implies that V∝l3∝M. One may thus derive M from l when the latter can provide a good estimate of V and the assumption of a constant δ is respected. In invertebrates, equations relating weight to length indicate that the power model always provides the best fit. However, authors only focused on the empirical estimation of slopes linking the body mass to the length measure variables, sometimes fitting exponential and linear models that are not theoretically grounded. This paper explicates how power laws derive from fundamental Euclidean scaling and describes the expected allometric exponents under the above assumptions. Based on the classical Euclidean scaling theory, an equivalent sphere is defined as a theoretical sphere with a volume equal to that of the organism whose body mass must be estimated. The illustrated application to a data set on soil oribatid mites helps clarify all these issues. Lastly, a general procedure for more precise estimation of M from V and δ is suggested.

Original languageEnglish
Pages (from-to)436-440
Number of pages5
JournalJournal of Theoretical Biology
Issue number3
Publication statusPublished - 07 Feb 2009
Externally publishedYes


  • Density
  • Indirect estimate
  • Scaling
  • Soil invertebrates
  • Volume
  • Weight

ASJC Scopus subject areas

  • General Medicine
  • General Immunology and Microbiology
  • General Biochemistry,Genetics and Molecular Biology
  • General Agricultural and Biological Sciences
  • Modelling and Simulation
  • Statistics and Probability
  • Applied Mathematics


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