The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms

American Association for the Advancement of Science (AAAS) - Tập 284 Số 5420 - Trang 1677-1679 - 1999
Geoffrey B. West1,2, James H. Brown3,1, Brian J. Enquist3,1
1The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
2Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA,

Tóm tắt

Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.

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Tài liệu tham khảo

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).

10.1126/science.276.5309.122

Rubner originally suggested that metabolic rate scales like the external Euclidean surface area A erroneously leading to a 2/3-power law [

Rubner M., Z. Biol. Munich 19, 535 (1883)].

B. B. Mandelbrot The Fractal Geometry of Nature (Freeman New York 1977); H. Takayasu Fractals in the Physical Sciences (Wiley Chichester UK 1992).

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)].

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 [

Blum J. J., J. Theor. Biol. 64, 599 (1977);

; F. R. Hainsworth Animal Physiology; Adaptions in Function (Addison-Wesley Reading MA) p. 170.

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).

Supported by a University of New Mexico Faculty Research Semester (J.H.B.) by NSF grant GER- 9553623 and an NSF postdoctoral fellowship (B.J.E.) and by U.S. Department of Energy contract ERWE161 and NSF grant PHY-9873638 (G.B.W.). We also acknowledge the generous support of the Thaw Charitable Trust.

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American Association for the Advancement of Science (AAAS)

Tập 284 Số 5420

1677-1679

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