A general model for the origin of allometric scaling laws in biology

Science

Volumn 276, Issue 5309, 1997, Pages 122-126

  West, Geoffrey B ^a,b   Brown, James H ^b,c   Enquist, Brian J ^b,c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b SANTA FE INSTITUTE   (United States)

^c UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BODY SIZE; CARDIOVASCULAR SYSTEM; MATHEMATICAL MODEL; PRIORITY JOURNAL; RESPIRATORY SYSTEM;

ANIMALS; BODY CONSTITUTION; BODY WEIGHT; CARDIOVASCULAR PHYSIOLOGY; CARDIOVASCULAR SYSTEM; FRACTALS; HEMODYNAMIC PROCESSES; HUMANS; METABOLISM; MODELS, ANATOMIC; MODELS, BIOLOGICAL; MODELS, CARDIOVASCULAR; PULSATILE FLOW; RESPIRATORY PHYSIOLOGY;

INSECTA; MAMMALIA; VERTEBRATA;

EID: 0030932272     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.276.5309.122     Document Type: Article

References (41)

1. T. A. McMahon and J. T. Bonner, On Size and Life (Scientific American Library, New York, 1983); J. T. Bonner, The Evolution of Complexity by Means of Natural Selection (Princeton Univ. Press, Princeton, NJ, 1983); J. H. Brown, Macroecology (Univ. of Chicago Press, Chicago, 1995).
2. T. A. McMahon and J. T. Bonner, On Size and Life (Scientific American Library, New York, 1983); J. T. Bonner, The Evolution of Complexity by Means of Natural Selection (Princeton Univ. Press, Princeton, NJ, 1983); J. H. Brown, Macroecology (Univ. of Chicago Press, Chicago, 1995).
3. T. A. McMahon and J. T. Bonner, On Size and Life (Scientific American Library, New York, 1983); J. T. Bonner, The Evolution of Complexity by Means of Natural Selection (Princeton Univ. Press, Princeton, NJ, 1983); J. H. Brown, Macroecology (Univ. of Chicago Press, Chicago, 1995).
4. K. Schmidt-Nielsen, Scaling: Why Is Animal Size so Important? (Cambridge Univ. Press, Cambridge, 1984); W. A. Calder III, Size, Function and Life History (Harvard Univ. Press, Cambridge, MA, 1984).
5. K. Schmidt-Nielsen, Scaling: Why Is Animal Size so Important? (Cambridge Univ. Press, Cambridge, 1984); W. A. Calder III, Size, Function and Life History (Harvard Univ. Press, Cambridge, MA, 1984).
6. R. H. Peters, The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983).
7. H. A. Feldman and T. A. McMahon, Respir. Physiol. 52, 149 (1983).
8. T. A. McMahon, Science 179, 1201 (1973).
9. M. R. Patterson, ibid. 255, 1421 (1992).
10. K. J. Niklas, Plant Allometry: The Scaling of Form and Process (Univ. of Chicago Press, Chicago, 1994); Am. J. Bot. 81, 134 (1994).
11. K. J. Niklas, Plant Allometry: The Scaling of Form and Process (Univ. of Chicago Press, Chicago, 1994); Am. J. Bot. 81, 134 (1994).
12. A. M. Hemmingsen, Rep. Steno Mem. Hosp. (Copenhagen) 4, 1 (1950); ibid. 9, 1 (1960).
13. A. M. Hemmingsen, Rep. Steno Mem. Hosp. (Copenhagen) 4, 1 (1950); ibid. 9, 1 (1960).
14. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1977).
15. D'A. W. Thompson, On Growth and Form (Cambridge Univ. Press, Cambridge, 1942).
16. K. Shinozaki et al., Jpn. J. Ecol. 14, 97 (1964); ibid., p. 133; see also M. H. Zimmerman, Xylem Structure and the Ascent of Sap (Springer-Verlag, Berlin, 1983); M. T. Tyree and F. W. Ewers. New Phytol. 119, 345 (1991).
17. K. Shinozaki et al., Jpn. J. Ecol. 14, 97 (1964); ibid., p. 133; see also M. H. Zimmerman, Xylem Structure and the Ascent of Sap (Springer-Verlag, Berlin, 1983); M. T. Tyree and F. W. Ewers. New Phytol. 119, 345 (1991).
18. K. Shinozaki et al., Jpn. J. Ecol. 14, 97 (1964); ibid., p. 133; see also M. H. Zimmerman, Xylem Structure and the Ascent of Sap (Springer-Verlag, Berlin, 1983); M. T. Tyree and F. W. Ewers. New Phytol. 119, 345 (1991).
19. K. Shinozaki et al., Jpn. J. Ecol. 14, 97 (1964); ibid., p. 133; see also M. H. Zimmerman, Xylem Structure and the Ascent of Sap (Springer-Verlag, Berlin, 1983); M. T. Tyree and F. W. Ewers. New Phytol. 119, 345 (1991).
20. k+1. This relation is similar to that assumed in the Strahler method [A. N. Strahler, Trans. Am. Geophys. Union 34, 345 (1953); (11, 21)]. A generalization to nonuniform branching, where the radii and lengths at a given level may vary, is straightforward.
21. 1/4.
22. c is their total number.
23. This relation holds for plant vessels from the roots to the leaves, but not within leaves [M. J. Canney, Philos. Trans. R. Soc. London Ser. B 341, 87 (1993)].
24. A. Krogh, Pfluegers Arch. Gesamte Physiol. Menschen Tiere 179, 95 (1920).
25. C. D. Murray, Proc. Natl. Acad. Sci. U.S.A. 12, 207 (1926).
26. C. G. Caro et al., The Mechanics of Circulation (Oxford Univ. Press, Oxford, 1978).
27. J. R. Womersley, Philos. Mag. 46, 199 (1955); J. Physiol. (London) 127, 553 (1955).
28. J. R. Womersley, Philos. Mag. 46, 199 (1955); J. Physiol. (London) 127, 553 (1955).
29. 3 as evidence for cubic rather than area-preserving branching. For small vessels, where k > k̄, convincing evidence for the cubic law can be found in the analysis of the arteriolar system by M. L. Ellsworth et al., Microvasc. Res. 34, 168 (1987).
30. 3 as evidence for cubic rather than area-preserving branching. For small vessels, where k > k̄, convincing evidence for the cubic law can be found in the analysis of the arteriolar system by M. L. Ellsworth et al., Microvasc. Res. 34, 168 (1987).
31. 3 as evidence for cubic rather than area-preserving branching. For small vessels, where k > k̄, convincing evidence for the cubic law can be found in the analysis of the arteriolar system by M. L. Ellsworth et al., Microvasc. Res. 34, 168 (1987).
32. 3 as evidence for cubic rather than area-preserving branching. For small vessels, where k > k̄, convincing evidence for the cubic law can be found in the analysis of the arteriolar system by M. L. Ellsworth et al., Microvasc. Res. 34, 168 (1987).
33. 3 as evidence for cubic rather than area-preserving branching. For small vessels, where k > k̄, convincing evidence for the cubic law can be found in the analysis of the arteriolar system by M. L. Ellsworth et al., Microvasc. Res. 34, 168 (1987).
34. 3 as evidence for cubic rather than area-preserving branching. For small vessels, where k > k̄, convincing evidence for the cubic law can be found in the analysis of the arteriolar system by M. L. Ellsworth et al., Microvasc. Res. 34, 168 (1987).
35. Y. C. Fung, Biodynamics (Springer-Verlag, New York, 1984).
36. P. Gehr et al., Respir. Physiol. 44, 61 (1981).
37. P. M. Bennett and P. H. Harvey, J. Zool. 213, 327 (1987); A. F. Bennett, Am. Zool. 28, 699 (1988); P. H. Harvey and M. D. Pagel, The Comparative Method in Evolutionary Biology (Oxford Univ. Press, Oxford, 1991).
38. P. M. Bennett and P. H. Harvey, J. Zool. 213, 327 (1987); A. F. Bennett, Am. Zool. 28, 699 (1988); P. H. Harvey and M. D. Pagel, The Comparative Method in Evolutionary Biology (Oxford Univ. Press, Oxford, 1991).
39. P. M. Bennett and P. H. Harvey, J. Zool. 213, 327 (1987); A. F. Bennett, Am. Zool. 28, 699 (1988); P. H. Harvey and M. D. Pagel, The Comparative Method in Evolutionary Biology (Oxford Univ. Press, Oxford, 1991).
40. This is reminiscent of the invariance of scaling exponents to details of the model that follow from renormalization group analyses, which can be viewed as a generalization of classical dimensional analysis.
41. J.H.B. is supported by NSF grant DEB-9318096, B.J.E. by NSF grant GER-9553623 and a Fulbright Fellowship, and G.B.W. by the Department of Energy.