Model selection and logarithmic transformation in allometric analysis

Physiological and Biochemical Zoology

Volumn 81, Issue 4, 2008, Pages 496-507

  Packard, Gary C ^a,b   Boardman, Thomas J ^a  

^a Department of Environmental and Radiological Health Sciences   (United States)

^b NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALLOMETRY; BODY SIZE; MODELING;

ANIMAL; ARTICLE; ARTIODACTYLA; BIOLOGICAL MODEL; BODY SIZE; HISTOLOGY; LIZARD; METABOLISM; SONGBIRD; STATISTICAL ANALYSIS; STATISTICAL MODEL;

ANIMALS; ARTIODACTYLA; BODY SIZE; DATA INTERPRETATION, STATISTICAL; LIZARDS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; PASSERIFORMES;

EID: 46449090644     PISSN: 15222152     EISSN: None     Source Type: Journal    
DOI: 10.1086/589110     Document Type: Article

References (49)

1. Agutter P.S. and D.N. Wheatley. 2004. Metabolic scaling: consensus or controversy? Theor Biol Med Model 1:13.
2. Allen D.M. 1971. Mean square error of prediction as a criterion for selecting variables. Technometrics 13:469-475.
3. Anscombe F.J. 1973. Graphs in statistical analysis. Am Stat 27:17-21.
4. Bartlett M.S. 1947. The use of transformations. Biometrics 3:39-52.
5. Brown J.H., J.F. Gillooly, A.P. Allen, V.M. Savage, and G.B.West. 2004. Toward a metabolic theory of ecology. Ecology 85:1771-1789.
6. Calder W.A., III. 1984. Size, Function, and Life History. Harvard University Press, Cambridge, MA.
7. da Silva J.K.L., G.J.M. Garcia, and L.A. Barbosa. 2006. Allometric scaling laws of metabolism. Phys Life Rev 3:229-261.
8. Finney D.J. 1989. Was this in your statistics textbook? V. Transformation of data. Exp Agric 25:165-175.
9. Glass N.R. 1967. A technique for fitting nonlinear models to biological data. Ecology 48:1010-1013.
10. _. 1969. Discussion of calculation of power function with special reference to respiratory metabolism in fish. J Fish Res Board Can 26:2643-2650.
11. Glazier D.S. 2005. Beyond the "3/4-power law": variation in the intra- and interspecific scaling of metabolic rate in animals. Biol Rev 80:611-662.
12. Gould S.J. 1966. Allometry and size in ontogeny and phylogeny. Biol Rev 41:587-640.
13. Greer A.E. 1989. The Biology and Evolution of Australian Lizards. Surrey Beatty, Chipping Norton.
14. Hartley H.O. 1961. The modified Gauss-Newton method for the fitting of non-linear regression functions by least squares. Technometrics 3:269-280.
15. Hayes J.P. and J.S. Shonkwiler. 2001. Morphometric indicators of body condition: worthwhile or wishful thinking? Pp. 8-38 in J.R. Speakman, ed. Body Composition Analysis of Animals: A Handbook of Non-Destructive Methods. Cambridge University Press, Cambridge.
16. _. 2006. Allometry, antilog transformations, and the perils of prediction on the original scale. Physiol Biochem Zool 79:665-674.
17. Hoppeler H. and E.R. Weibel. 2005. Scaling functions to body size: theories and facts. J Exp Biol 208:1573-1574.
18. Hoyle M.H. 1973. Transformations: an introduction and a bibliography. Int Stat Rev 41:203-223.
19. Jansson M. 1985. A comparison of detransformed logarithmic regressions and power function regressions. Geogr Ann Ser A Phys Geogr 67:61-70.
20. Kleiber M. 1961. The Fire of Life. Wiley, New York.
21. Kutner M.H., C.J. Nachtsheim, and J. Neter. 2004. Applied Linear Regression Models. 4th ed. McGraw-Hill Irwin, Boston.
22. Lasiewski R.C. and W.R. Dawson. 1967. A re-examination of the relation between standard metabolic rate and body weight in birds. Condor 69:13-23.
23. _. 1969. Calculation and miscalculation of the equations relating avian standard metabolism to body weight. Condor 71:335-336.
24. Manaster B.J. and S. Manaster. 1975. Techniques for estimating allometric equations. J Morphol 147:299-308.
25. Marquardt D.W. 1963. An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11:431-441.
26. Martin R.D., M. Genoud, and C.K. Hemelrijk. 2005. Problems of allometric scaling analysis: examples from mammalian reproductive biology. J Exp Biol 208:1731-1747.
27. McCuen R.H., R.B. Leahy, and P.A. Johnson. 1990. Problems with logarithmic transformations in regression. J Hydraul Eng 116:414-428.
28. Miller D.R. 1984. Reducing transformation bias in curve fitting. Am Stat 38:124-126.
29. Osborne J.W. 2002. Notes on the use of data transformations. Pract Assess Res Eval 8:6.
30. Osborne J.W. and A. Overbay. 2004. The power of outliers (and why researchers should ALWAYS check for them). Pract Assess Res Eval 9:6.
31. Packard G.C. and T.J. Boardman. 1988. The misuse of ratios, indices, and percentages in ecophysiological research. Physiol Zool 61:1-9.
32. Pandey G.R. and V.-T.-V. Nguyen. 1999. A comparative study of regression based methods in regional flood frequency analysis. J Hydrol (Amst) 225:92-101.
33. Peters R.H. 1983. The Ecological Implications of Body Size. Cambridge University Press, Cambridge.
34. Pianka E.R. 1995. Evolution of body size: varanid lizards as a model system. Am Nat 146:398-414.
35. Savage V.M., J.F. Gillooly, W.H. Woodruff, G.B. West, A.P. Allen, B.J. Enquist, and J.H. Brown. 2004. The predominance of quarter-power scaling in biology. Funct Ecol 18:257-282.
36. Schmidt-Nielsen K. 1984. Scaling: Why Is Animal Size So Important? Cambridge University Press, Cambridge.
37. Smith R.J. 1980. Rethinking allometry. J Theor Biol 87:97-111.
38. _. 1984. Allometric scaling in comparative biology: problems of concept and method. Am J Physiol 246:R152-R160.
39. _. 1993. Logarithmic transformation bias in allometry. Am J Phys Anthropol 90:215-228.
40. Stevens J.P. 1984. Outliers and influential data points in regression analysis. Psychol Bull 95:334-344.
41. Thompson G.G. and P.C. Withers. 1997. Comparative morphology of Western Australian varanid lizards (Squamata: Varanidae). J Morphol 233:127-152.
42. Tufte E.R. 1983. The Visual Display of Quantitative Information. Graphics Press, Cheshire, CT.
43. Tukey J.W. 1977. Exploratory Data Analysis. Addison-Wesley, Reading, MA.
44. Warton D.I., I.J. Wright, D.S. Falster, and M. Westoby. 2006. Bivariate line-fitting methods for allometry. Biol Rev 81:259-291.
45. West G.B. and J.H. Brown. 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.
46. White C.R. and R.S. Seymour. 2005a. Allometric scaling of mammalian metabolism. J Exp Biol 208:1611-1619.
47. _. 2005b. Sample size and mass range effects on the allometric exponent of basal metabolic rate. Comp Biochem Physiol A 142:74-78.
48. Zar J.H. 1968. Calculation and miscalculation of the allometric equation as a model in biological data. BioScience 18:1118-1120.
49. _. 1970. On the fitting of equations relating avian standard metabolism to body weight. Condor 72:247.