Traditional allometric analysis fails to provide a valid predictive model for mammalian metabolic rates

Journal of Experimental Biology

Volumn 211, Issue 22, 2008, Pages 3581-3587

  Packard, Gary C ^a   Birchard, Geoffrey F ^b  

^a Department of Ecosystem Science and Sustainability   (United States)

^b GEORGE MASON UNIVERSITY   (United States)

Author keywords

Allometry; Logarithms; Metabolic rates; Scaling; Transformations

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BASAL METABOLIC RATE; BIOLOGICAL MODEL; BODY SIZE; BODY WEIGHT; MAMMAL; PHYSIOLOGY;

ALGORITHMS; ANIMALS; BASAL METABOLISM; BODY SIZE; BODY WEIGHT; MAMMALS; MODELS, BIOLOGICAL;

MAMMALIA;

EID: 55949133713     PISSN: 00220949     EISSN: None     Source Type: Journal    
DOI: 10.1242/jeb.023317     Document Type: Article

References (53)

1. Agutter, P. S. and Wheatley, D. N. (2004). Metabolic scaling: consensus or controversy? Theor. Biol. Med. Model. 1, 13.
2. Albrecht, G. H. (1988). Simple allometry coefficients: fact or fiction. Am. Zool. 28, 172A.
3. Albrecht, G. H. and Gelvin, B. R. (1987). The simple allometry equation reconsidered: assumptions, problems, and alternative solutions. Am. J. Phys. Anthropol. 72, 174.
4. Anscombe, F. J. (1973). Graphs in statistical analysis. Am. Stat. 27, 17-21.
5. Asselman, N. E. M. (2000). Fitting and interpretation of sediment rating curves. J. Hydrol. 234, 228-248.
6. Banavar, J. R., Maritan, A. and Rinaldo, A. (1999). Size and form in efficient transportation networks. Nature 399, 130-132.
7. Benedict, F. G. (1938). Vital Energetics. Washington, DC: Carnegie Institution of Washington.
8. Brody, S. (1945). Bioenergetics and Growth. New York: Reinhold Publishing.
9. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. and West, G. B. (2004). Response to forum commentary on "Toward a metabolic theory of ecology." Ecology 85, 1818-1821.
10. Cox, N. J., Warburton, J., Armstrong, A. and Holliday, V. J. (2008). Fitting concentration and load rating curves with generalized linear models. Earth Surf. Process. Landforms 33, 25-39.
11. Darveau, C. A., Suarez, R. K., Andrews, R. D. and Hochachka, P. W. (2002). Allometric cascade as a unifying principle of body mass effects on metabolism. Nature 417, 166-170.
12. da Silva, J. K. L., Garcia, G. J. M. and Barbosa, L. A. (2006). Allometric scaling laws of metabolism. Phys. Life Rev. 3, 229-261.
13. Dodds, P. S., Rothman, D. H. and Weitz, J. S. (2001). Re-examination of the "3/4-law" of metabolism. J. Theor. Biol. 209, 9-27.
14. Emerson, J. D. and Stoto, M. A. (1983). Transforming data. In Understanding Robust and Exploratory Data Analysis (ed. D. C. Hoaglin, F. Mosteller and J. W. Tukey), pp. 97-128. New York: Wiley.
15. Farrell-Gray, C. C. and Gotelli, N. J. (2005). Allometric exponents support a 3/4-power scaling law. Ecology 86, 2083-2087.
16. Finney, D. J. (1989). Was this in your statistics textbook? V. Transformation of data. Exp. Agric. 25, 165-175.
17. Garland, T., Jr, Bennett, A. F. and Rezende, E. L. (2005). Phylogenetic approaches in comparative physiology. J. Exp. Biol. 208, 3015-3035.
18. Glass, N. R. (1969). Discussion of calculation of power function with special reference to respiratory metabolism in fish. J. Fish. Res. Bd. Canada 26, 2643-2650.
19. Glazier, D. S. (2005). Beyond the '3/4-power law': variation in the intra- and interspecific scaling of metabolic rate in animals. Biol. Rev. Camb. Philos. Soc. 80, 611-662.
20. Glazier, D. S. (2008). Effects of metabolic level on the body size scaling of metabolic rate in birds and mammals. Proc. R. Soc. Lond., B, Biol. Sci. 275, 1405-1410.
21. Gould, S. J. (1966). Allometry and size in ontogeny and phylogeny. Biol. Rev. Camb. Philos. Soc. 41, 587-640.
22. Hayes, J. P. and Shonkwiler, J. S. (2006). Allometry, antilog transformations, and the perils of prediction on the original scale. Physiol. Biochem. Zool. 79, 665-674.
23. Heusner, A. A. (1987). What does the power function reveal about structure and function in animals of different size? Annu. Rev. Physiol. 49, 121-133.
24. Hoppeler, H. and Weibel, E. R. (2005). Scaling functions to body size: theories and facts. J. Exp. Biol. 208, 1573-1574.
25. Hui, D. and Jackson, R. B. (2007). Uncertainty in allometric exponent estimation: a case study in scaling metabolic rate with body mass. J. Theor. Biol. 249, 168-177.
26. Jansson, M. (1985). A comparison of detransformed logarithmic regressions and power function regressions. Geograf. Ann. 67A, 61-70.
27. Kleiber, M. (1932). Body size and metabolism. Hilgardia 6, 315-353.
28. Kleiber, M. (1961). The Fire of Life. New York: Wiley.
29. Kozlowski, J. and Konarzewski, M. (2005). West, Brown and Enquist's model of allometric scaling again: the same questions remain. Funct. Ecol. 19, 739-743.
30. Kutner, M. H., Nachtsheim, C. J. and Neter, J. (2004). Applied Linear Regression Models, 4th edn. Boston: McGraw-Hill Irwin.
31. Lane, P. W. (2002). Generalized linear models in soil science. European J. Soil Sci. 53, 241-251.
32. Manaster, B. J. and Manaster, S. (1975). Techniques for estimating allometric equations. J. Morphol. 147, 299-308.
33. Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Indust. Appl. Math. 11, 431-441.
34. McCuen, R. H., Leahy, R. B. and Johnson, P. A. (1990). Problems with logarithmic transformations in regression. J. Hydraul. Eng. 116, 414-428.
35. Miller, D. R. (1984). Reducing transformation bias in curve fitting. Am. Stat. 38, 124-126.
36. Motulsky, H. and Christopoulos, A. (2004). Fitting Models to Biological Data Using Linear and Nonlinear Regression. Oxford: Oxford University Press.
37. Myers, R. H. (1986). Classical and Modern Regression with Applications. Boston: Duxbury Press.
38. Osborne, J. W. (2002). Notes on the use of data transformations. Pract. Assess. Res. Eval. 8, 6.
39. Osborne, J. W. and Overbay, A. (2004). The power of outliers (and why researchers should ALWAYS check for them). Pract. Assess. Res. Eval. 9, 6.
40. Packard, G. C. and Boardman, T. J. (2008a). Model selection and logarithmic transformation in allometric analysis. Physiol. Biochem. Zool. 81, 496-507.
41. Packard, G. C. and Boardman, T. J. (2008b). A comparison of methods for fitting allometric equations to field metabolic rates of animals. J. Comp. Physiol. B (in press).
42. Packard, G. C. and Boardman, T. J. (2008c). Bias in interspecific allometry: examples from morphological scaling in varanid lizards. Biol. J. Linn. Soc. (in press).
43. Pandey, G. R. and Nguyen, V.-T.-V. (1999). A comparative study of regression based methods in regional flood frequency analysis. J. Hydrol. 225, 92-101.
44. Pattyn, F. and Van Huele, W. (1998). Power law or power flaw? Earth Surf. Process. Landforms 23, 761-767.
45. Savage, V. M., Gillooly, J. F., Woodruff, W. H., West, G. B., Allen, A. P., Enquist, B. J. and Brown, J. H. (2004). The predominance of quarter-power scaling in biology. Funct. Ecol. 18, 257-282.
46. Smith, R. J. (1984). Allometric scaling in comparative biology: problems of concept and method. Am. J. Physiol. 246, R152-R160.
47. Smith, R. J. (1993). Logarithmic transformation bias in allometry. Am. J. Phys. Anthropol. 90, 215-228.
48. Snee, R. D. (1977). Validation of regression models: methods and examples. Technometrics 19, 415-428.
49. Stevens, J. P. (1984). Outliers and influential data points in regression analysis. Psychol. Bull. 95, 334-344.
50. Warton, D. I., Wright, I. J., Falster, D. S. and Westoby, M. (2006). Bivariate line-fitting methods for allometry. Biol. Rev. Camb. Philos. Soc. 81, 259-291.
51. West, G. B. and Brown, J. H. (2005). The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. J. Exp. Biol. 208, 1575-1592.
52. West, G. B., Brown, J. H. and Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science 276, 122-126.
53. Zar, J. H. (1968). Calculation and miscalculation of the allometric equation as a model in biological data. BioScience 18, 1118-1120.