Allometric equations for predicting body mass of dinosaurs

Journal of Zoology

Volumn 279, Issue 1, 2009, Pages 102-110

  Packard, G C ^a,c   Boardman, T J ^a   Birchard, G F ^b  

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

^b GEORGE MASON UNIVERSITY   (United States)

^c NONE   (United States)

Author keywords

Allometry; Dinosaurs; Logarithms; Scaling

Indexed keywords

ALLOMETRY; BODY MASS; COMPARATIVE STUDY; DINOSAUR; EQUATION;

ANIMALIA; DINOSAURIA; MAMMALIA;

EID: 69249097079     PISSN: 09528369     EISSN: 14697998     Source Type: Journal    
DOI: 10.1111/j.1469-7998.2009.00594.x     Document Type: Article

References (40)

1. Alexander, R.M. (1989). Dynamics of dinosaurs and other extinct giants. New York : Columbia University Press.
2. Anderson, J.F., Hall-Martin, A. Russell, D.A. (1985). Long-bone circumference and weight in mammals, birds and dinosaurs. J. Zool. (Lond.) 207, 53 61.
3. Anscombe, F.J. (1973). Graphs in statistical analysis. Am. Stat. 27, 17 21.
4. Asselman, N.E.M. (2000). Fitting and interpretation of sediment rating curves. J. Hydrol. 234, 228 248.
5. Bybee, P.J., Lee, A.H. Lamm, E.-T. (2006). Sizing the Jurassic theropod dinosaur Allosaurus: assessing growth strategy and evolution of ontogenetic scaling of limbs. J. Morphol. 267, 347 359.
6. Cox, N.J., Warburton, J., Armstrong, A. Holliday, V.J. (2008). Fitting concentration and load rating curves with generalized linear models. Earth Surf. Process. Landforms 33, 25 39.
7. Emerson, J.D. Stoto, M.A. (1983). Transforming data. In Understanding robust and exploratory data analysis : 97 128. Hoaglin, D.C., Mosteller, F. Tukey, J.W. (Eds). New York : Wiley.
8. Erickson, G.M. (2005). Assessing dinosaur growth patterns: a microscopic revolution. Trends Ecol. Evol. 20, 677 684.
9. Erickson, G.M., Makovicky, P.J., Currie, P.J., Norell, M.A., Yerby, S.A. Brochu, C.A. (2004). Gigantism and comparative life-history parameters of tyrannosaurid dinosaurs. Nature 430, 772 775.
10. Farlow, J.O., Dodson, P. Chinsamy, A. (1995). Dinosaur biology. Annu. Rev. Ecol. Syst. 26, 445 471.
11. Finney, D.J. (1989). Was this in your statistics textbook? V. Transformation of data. Exp. Agric. 25, 165 175.
12. Glass, N.R. (1969). Discussion of calculation of power function with special reference to respiratory metabolism in fish. J. Fish. Res. Board Can. 26, 2643 2650.
13. Gunga, H.-C., Suthau, T., Bellmann, A., Friedrich, A., Schwanebeck, T., Stoinski, S., Trippel, T., Kirsch, K. Hellwich, O. (2007). Body mass estimations for Plateosaurus engelhardti using laser scanning and 3D reconstruction methods. Naturwissenschaften 94, 623 630.
14. Hayes, J.P. Shonkwiler, J.S. (2006). Allometry, antilog transformations, and the perils of prediction on the original scale. Physiol. Biochem. Zool. 79, 665 674.
15. Henderson, D.M. (1999). Estimating the masses and centers of mass of extinct animals by 3-D mathematical slicing. Paleobiology 25, 88 106.
16. Hui, D. 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.
17. Jansson, M. (1985). A comparison of detransformed logarithmic regressions and power function regressions. Geograf. Ann. 67A, 61 70.
18. Kutner, M.H., Nachtsheim, C.J. Neter, J. (2004). Applied linear regression models, 4th edn. Boston : McGraw-Hill Irwin.
19. Lane, P.W. (2002). Generalized linear models in soil science. Eur. J. Soil Sci. 53, 241 251.
20. Lee, A.H. Werning, S. (2008). Sexual maturity in growing dinosaurs does not fit reptilian growth models. Proc. Natl. Acad. Sci. USA 105, 582 587.
21. Lehman, T.M. Woodward, H.N. (2008). Modeling growth rates for sauropod dinosaurs. Paleobiology 34, 264 281.
22. Marquardt, D.W. (1963). An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11, 431 441.
23. McCuen, R.H., Leahy, R.B. Johnson, P.A. (1990). Problems with logarithmic transformations in regression. J. Hydraul. Eng. 116, 414 428.
24. Motulsky, H. Christopoulos, A. (2004). Fitting models to biological data using linear and nonlinear regression. Oxford : Oxford University Press.
25. Myers, R.H. (1986). Classical and modern regression with applications. Boston : Duxbury Press.
26. Osborne, J.W. (2002). Notes on the use of data transformations. Pract. Assess. Res. Eval. 8
27. Osborne, J.W. Overbay, A. (2004). The power of outliers (and why researchers should ALWAYS check for them). Pract. Assess. Res. Eval. 9
28. Packard, G.C. (2009). On the use of logarithmic transformations in allometric analyses. J. Theor. Biol. 257, 515 518.
29. Packard, G.C. Birchard, G.F. (2008). Traditional allometric analysis fails to provide a valid predictive model for mammalian metabolic rates. J. Exp. Biol. 211, 3581 3587.
30. Packard, G.C. Boardman, T.J. (2008). Model selection and logarithmic transformation in allometric analysis. Physiol. Biochem. Zool. 81, 496 507.
31. Packard, G.C. Boardman, T.J. (2009a). A comparison of methods for fitting allometric equations to field metabolic rates of animals. J. Comp. Physiol. B 179, 175 182.
32. Packard, G.C. Boardman, T.J. (2009b). Bias in interspecific allometry: examples from morphological scaling in varanid lizards. Biol. J. Linn. Soc. 96, 296 305.
33. Pandey, G.R. Nguyen, V.-T.-V. (1999). A comparative study of regression based methods in regional flood frequency analysis. J. Hydrol. 225, 92 101.
34. Seebacher, F. (2001). A new method to calculate allometric length-mass relationships of dinosaurs. J. Vertebr. Paleontol. 21, 51 60.
35. Smith, R.J. (1984). Allometric scaling in comparative biology: problems of concept and method. Am. J. Physiol. 246, R152 R160.
36. Smith, R.J. (1993). Logarithmic transformation bias in allometry. Am. J. Phys. Anthropol. 90, 215 228.
37. Smith, R.J. (2002). Estimation of body mass in paleontology. J. Human Evol. 43, 271 287.
38. Snee, R.D. (1977). Validation of regression models: methods and examples. Technometrics 19, 415 428.
39. Stevens, J.P. (1984). Outliers and influential data points in regression analysis. Psychol. Bull. 95, 334 344.
40. Zar, J.H. (1968). Calculation and miscalculation of the allometric equation as a model in biological data. BioScience 18, 1118 1120.