The fourth dimension of life: Fractal geometry and allometric scaling of organisms

Science

Volumn 284, Issue 5420, 1999, Pages 1677-1679

  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

OXIDOREDUCTASE;

ALGA; ALLOMETRY; ARTICLE; BIOLOGY; CAPILLARY; ENZYME ACTIVITY; EVOLUTION; FRACTAL ANALYSIS; GEOMETRY; MAMMAL; METABOLIC CAPACITY; MITOCHONDRION; NATURAL SELECTION; PLANT LEAF; PRIORITY JOURNAL; PROTOZOON;

ANIMALS; BLOOD VESSELS; BODY CONSTITUTION; BODY SURFACE AREA; FRACTALS; HUMANS; MATHEMATICS; METABOLISM; MODELS, BIOLOGICAL; PLANTS; SELECTION (GENETICS);

EID: 0033522952     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.284.5420.1677     Document Type: Article

References (13)

1. 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); R. H. Peters, The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983); K. J. Niklas, Plant Allometry: The Scaling of Form and Process (Univ. of Chicago Press, Chicago, IL, 1994); J. H. Brown and G. B. West. Eds., Scaling in Biology (Oxford Univ. Press, Oxford, in press).
2. 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); R. H. Peters, The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983); K. J. Niklas, Plant Allometry: The Scaling of Form and Process (Univ. of Chicago Press, Chicago, IL, 1994); J. H. Brown and G. B. West. Eds., Scaling in Biology (Oxford Univ. Press, Oxford, in press).
3. 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); R. H. Peters, The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983); K. J. Niklas, Plant Allometry: The Scaling of Form and Process (Univ. of Chicago Press, Chicago, IL, 1994); J. H. Brown and G. B. West. Eds., Scaling in Biology (Oxford Univ. Press, Oxford, in press).
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); R. H. Peters, The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983); K. J. Niklas, Plant Allometry: The Scaling of Form and Process (Univ. of Chicago Press, Chicago, IL, 1994); J. H. Brown and G. B. West. Eds., Scaling in Biology (Oxford Univ. Press, Oxford, in press).
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); R. H. Peters, The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983); K. J. Niklas, Plant Allometry: The Scaling of Form and Process (Univ. of Chicago Press, Chicago, IL, 1994); J. H. Brown and G. B. West. Eds., Scaling in Biology (Oxford Univ. Press, Oxford, in press).
6. G. B. West, J. H. Brown, B. J. Enquist, Science 276, 122 (1997).
7. Rubner originally suggested that metabolic rate scales like the external Euclidean surface area, A, erroneously leading to a 2/3-power law [M. Rubner, Z. Biol. Munich 19, 535 (1883)].
8. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1977); H. Takayasu, Fractals in the Physical Sciences (Wiley, Chichester, UK, 1992).
9. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1977); H. Takayasu, Fractals in the Physical Sciences (Wiley, Chichester, UK, 1992).
10. In particular, this shows that the derivation for mammalian and plant systems presented in (2) does not depend on details of the network such as symmetric branching. This was confirmed numerically by D. L Turcotte, J. D. Pelletier, and W. I. Newman [J. Theor. Biol. 193, 577 (1998)].
11. Blum earlier noted that, in four Euclidean dimensions, the surface area of a sphere would scale as the 3/4-power of its four-dimensional volume, and that this might in some way be related to the 3/4 exponent in Kleiber's law. Hainsworth subsequently proposed that this extra dimension be identified with time. Neither of these authors, however, gave any argument to support their conjectures [J.]. Blum, J. Theor. Biol. 64, 599 (1977); F. R. Hainsworth, Animal Physiology; Adaptions in Function (Addison-Wesley, Reading, MA), p. 170.
12. Blum earlier noted that, in four Euclidean dimensions, the surface area of a sphere would scale as the 3/4-power of its four-dimensional volume, and that this might in some way be related to the 3/4 exponent in Kleiber's law. Hainsworth subsequently proposed that this extra dimension be identified with time. Neither of these authors, however, gave any argument to support their conjectures [J.]. Blum, J. Theor. Biol. 64, 599 (1977); F. R. Hainsworth, Animal Physiology; Adaptions in Function (Addison-Wesley, Reading, MA), p. 170.
13. G. B. West, J. H. Brown, B. J. Enquist, in Scaling in Biology, J. H. Brown and G. B. West, Eds. (Oxford Univ. Press, Oxford, in press).