Rotational distortion in conventional allometric analyses

Comparative Biochemistry and Physiology - A Molecular and Integrative Physiology

Volumn 159, Issue 4, 2011, Pages 392-400

  Packard, Gary C ^a  

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

Author keywords

Allometry; Evaporative water loss; Field metabolic rate; Kidney mass; Logarithms; Scaling

Indexed keywords

WATER;

ALLOMETRY; ARTICLE; BIVARIATE ANALYSIS; BODY MASS; BODY SIZE; EVAPORATION; NONLINEAR REGRESSION ANALYSIS;

AVES; PASSERIFORMES; PRIMATES; RODENTIA;

EID: 79957603190     PISSN: 10956433     EISSN: 15314332     Source Type: Journal    
DOI: 10.1016/j.cbpa.2011.04.005     Document Type: Article

References (63)

1. Anscombe F.J. Graphs in statistical analysis. Am. Statist. 1973, 27:17-21.
2. Bales G.S. Heterochrony in brontothere horn evolution: allometric interpretations and the effect of life history scaling. Paleobiology 1996, 22:481-495.
3. Bartholomew G.A., Cade T.J. The water economy of land birds. Auk 1963, 80:504-539.
4. Batterham A.M., Vanderburgh P.M., Mahar M.T., Jackson A.S. Modeling the influence of body size on Vo2peak: effects of model choice and body composition. J. Appl. Physiol. 1999, 87:1317-1325.
5. Behrens J.T. Principles and procedures of exploratory data analysis. Psychol. Methods 1997, 2:131-160.
6. Beuchat C.A. Structure and concentrating ability of the mammalian kidney: correlations with habitat. Am. J. Physiol. 1996, 271:R157-R179.
7. Brody S., Proctor R.C. Relation between basal metabolism and mature body weight in different species of mammals and birds. Missouri Agr. Exp. Sta. Res. Bull. 1932, 166:89-101.
8. Calder W.A., Braun E.J. Scaling of osmotic regulation in mammals and birds. Am. J. Physiol. 1983, 244:R601-R606.
9. Capellini I., Venditti C., Barton R.A. Phylogeny and metabolic scaling in mammals. Ecology 2010, 91:2783-2793.
10. Clarke A., Rothery P., Isaac N.J.B. Scaling of basal metabolic rate with body mass and temperature in mammals. J. Anim. Ecol. 2010, 79:610-619.
11. Cox N.J., Warburton J., Armstrong A., Holliday V.J. Fitting concentration and load rating curves with generalized linear models. Earth Surf. Proc. Landforms 2008, 33:25-39.
12. Dawson W.R. Evaporative losses of water by birds. Comp. Biochem. Physiol. 1982, 71A:495-509.
13. Emerson J.D., Stoto M.A. Transforming data. Understanding Robust and Exploratory Data Analysis 1983, 97-128. Wiley, New York. D.C. Hoaglin, F. Mosteller, J.W. Tukey (Eds.).
14. Finney D.J. Was this in your statistics textbook? V. Transformation data. Exp. Agric. 1989, 25:165-175.
15. Galtsoff P.S. The weight-length relationship of the shells of the Hawaiian pearl oyster, Pinctada sp. Am. Nat. 1931, 65:423-433.
16. Garland T., Bennett A.F., Rezende E.L. Phylogenetic approaches in comparative physiology. J. Exp. Biol. 2005, 208:3015-3035.
17. Gingerich P.D. Arithmetic or geometric normality of biological variation: an empirical test of theory. J. Theor. Biol. 2000, 204:201-221.
18. Glass N.R. Discussion of calculation of power function with special reference to respiratory metabolism in fish. J. Fish. Res. Bd. Canada 1969, 26:2643-2650.
19. Glazier D.S. A unifying explanation for diverse metabolic scaling in animals and plants. Biol. Rev. 2010, 85:111-138.
20. Gray J.B. On the use of regression diagnostics. Statistician 1989, 38:97-105.
21. Hayes J.P., Shonkwiler J.S. Allometry, antilog transformations, and the perils of prediction on the original scale. Physiol. Biochem. Zool. 2006, 79:665-674.
22. Huxley J.S. Problems of Relative Growth 1932, Dial Press, New York.
23. Jacoby W.G. Statistical Graphics for Univariate and Bivariate Data 1997, Sage Publications, Thousand Oaks, CA.
24. Jansson M. A comparison of detransformed logarithmic regressions and power function regressions. Geograf. Ann. 1985, 67A:61-70.
25. Kerkhoff A.J., Enquist B.J. Multiplicative by nature: why logarithmic transformation is necessary in allometry. J. Theor. Biol. 2009, 257:519-521.
26. Keys A.B. The weight-length relation in fishes. Proc. Nat. Acad. Sci. USA 1928, 14:922-925.
27. Kleiber M. Body size and metabolism. Hilgardia 1932, 6:315-353.
28. Koch A.L. The logarithm in biology. 1. Mechanisms generating the log-normal distribution exactly. J. Theor. Biol. 1966, 12:276-290.
29. Kolokotrones T., Savage V., Deeds E.J., Fontana W. Curvature in metabolic scaling. Nature 2010, 464:753-756.
30. Kutner M.H., Nachtsheim C.J., Neter J. Applied Linear Regression Models 2004, McGraw-Hill Irwin, Boston. Fourth edition.
31. Lane P.W. Generalized linear models in soil science. Europ. J. Soil Sci. 2002, 53:241-251.
32. Lasiewski R.C., Dawson W.R. Calculation and miscalculation of the equations relating avian standard metabolism to body weight. Condor 1969, 71:335-336.
33. Marquardt D.W. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Indust. Appl. Math. 1963, 11:431-441.
34. McCuen R.H., Leahy R.B., Johnson P.A. Problems with logarithmic transformations in regression. J. Hydraul. Eng. 1990, 116:414-428.
35. Motulsky H., Christopoulos A. Fitting Models to Biological Data Using Linear and Nonlinear Regression 2004, Oxford University Press, Oxford.
36. Myers R.H. Classical and Modern Regression with Applications 1990, Duxbury Press, Belmont, CA. Second edition.
37. Osborne J.W. Notes on the use of data transformations. Pract. Assess. Res. Eval. 2002, 8(6). http://PAREonline.net/getvn.asp?v=8&n=6.
38. Osborne J.W., Overbay A. The power of outliers (and why researchers should ALWAYS check for them). Pract. Assess. Res. Eval. 2004, 9(6). http://PAREonline.net/getvn.asp?v=9&n=6.
39. Packard G.C. On the use of logarithmic transformations in allometric research. J. Theor. Biol. 2009, 257:515-518.
40. Packard G.C., Birchard G.F. Traditional allometric analysis fails to provide a valid predictive model for mammalian metabolic rates. J. Exp. Biol. 2008, 211:3581-3587.
41. Packard G.C., Boardman T.J. Model selection and logarithmic transformation in allometric analysis. Physiol. Biochem. Zool. 2008, 81:496-507.
42. Packard G.C., Boardman T.J. A comparison of methods for fitting allometric equations to field metabolic rates of animals. J. Comp. Physiol. B 2009, 179:175-182.
43. Packard G.C., Boardman T.J. Bias in interspecific allometry: examples from morphological scaling in varanid lizards. Biol. J. Linn. Soc. 2009, 96:296-305.
44. Packard, G.C., Birchard, G.F., Boardman, T.J., 2011. Fitting statistical models in bivariate allometry. Biol. Rev., in press. http://doi:10.1111/j.1469-185X.2010.00160.x.
45. Prothero J. Organ scaling in mammals: the kidneys. Comp. Biochem. Physiol. 1984, 77A:133-138.
46. Sartori A.F., Ball A.D. Morphology and postlarval development of the ligament of Thracia phaseolina (Bivalvia: Thraciidae), with a discussion of model choice in allometric studies. J. Mollusc. Stud. 2009, 75:295-304.
47. Smith R.J. Rethinking allometry. J. Theor. Biol. 1980, 87:97-111.
48. Smith R.J. Allometric scaling in comparative biology: problems of concept and method. Am. J. Physiol. 1984, 246:R152-R160.
49. Smith R.J. Logarithmic transformation bias in allometry. Am. J. Phys. Anthropol. 1993, 90:215-228.
50. Smith R.J. Use and misuse of the reduced major axis for line-fitting. Am. J. Phys. Anthropol. 2009, 140:476-486.
51. Snee R.D. Validation of regression models: methods and examples. Technometrics 1977, 19:415-428.
52. Stevens J.P. Outliers and influential data points in regression analysis. Psychol. Bull. 1984, 95:334-344.
53. Tukey J.W. On the comparative anatomy of transformations. Ann. Math. Stat. 1957, 28:602-632.
54. Tukey J.W. Data analysis, computation and mathematics. Quart. Appl. Math. 1972, 30:51-65.
55. Tukey J.W. Exploratory Data Analysis 1977, Addison-Wesley, Reading, MA.
56. Verwijst T. Logarithmic transformations in biomass estimation procedures: violation of the linearity assumption in regression analysis. Biomass Bioenergy 1991, 1:175-180.
57. Warton D.I., Wright I.J., Falster D.S., Westoby M. Bivariate line-fitting methods for allometry. Biol. Rev. 2006, 81:259-291.
58. White C.R. Allometric estimation of metabolic rates in animals. Comp. Biochem. Physiol. A 2011, 158:346-357.
59. White C.R., Blackburn T.M., Seymour R.S. Phylogenetically informed analysis of the allometry of mammalian basal metabolic rate supports neither geometric nor quarter-power scaling. Evolution 2009, 63:2658-2667.
60. Williams J.B. A phylogenetic perspective of evaporative water loss in birds. Auk 1996, 113:457-472.
61. Williams J.B., Tieleman B.I. Physiological ecology and behavior of desert birds. Curr. Ornithol. 2001, 16:299-353.
62. Zar J.H. Calculation and miscalculation of the allometric equation as a model in biological data. Bioscience 1968, 18:1118-1120.
63. Zuur A.F., Ieno E.N., Elphick C.S. A protocol for data exploration to avoid common statistical problems. Meth. Ecol. Evol. 2010, 1:3-14.