Several equations have been proposed to describe ontogenetic growth trajectories for organisms justified primarily on the goodness of fit rather than on any biological mechanism1,2,3,4,5,6. Here, we derive a general quantitative model based on fundamental principles7,8,9 for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass. We thus predict the parameters governing growth curves from basic cellular properties10 and derive a single parameterless universal curve that describes the growth of many diverse species. The model provides the basis for deriving allometric relationships for growth rates and the timing of life history events2,11,12.
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Brody, S. Bioenergetics and Growth (Hafner Press, Darien, Connecticut, 1964).
Charnov, E. L. Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology (Oxford Univ. Press, Oxford, 1993).
Stearns, S. C. The Evolution of Life Histories (Oxford Univ. Press, Oxford, 1992).
Reiss, M. J. The Allometry of Growth and Reproduction (Cambridge Univ. Press, Cambridge, 1989).
Ricker, W. E. Growth rates and models. Fish Physiol. 8, 677–743 (1979).
von Bertalanffy, L. Quantitative laws in metabolism and growth. Q. Rev. Biol. 32, 217–231 (1957).
West, G. B., Brown, J. H. & Enquist, B. J. A general model for the origin of allometric scaling laws in biology. Science 276, 122–126 (1997).
Brown, J. H. & West, G. B. Scaling in Biology (Oxford Univ. Press, Oxford, 2000).
West, G. B., Brown, J. H. & Enquist, B. J. The fourth dimension of life; fractal geometry and allometric scaling of organisms. Science 284, 1677–1679 (1999).
Alberts, M. Molecular Biology of the Cell (Garland, New York, 1994).
Peters, R. H. The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983).
Calder III, W. A. Size, Function and Life History (Harvard Univ. Press, Cambridge, Massachusetts, 1984).
Rogers, D. M., Olson, B. L. & Wilmore, J. H. Scaling for the V ˙ O 2 -to-body size relationship among children and adults. J. Appl. Physiol. 79(3), 958–967 (1995).
Weathers, W. W. & Siegel, R. B. Body size establishes the scaling of avian postnatal metabolic rate: an interspecific analysis using phylogenetically independent contrasts. Ibis 137, 532–542 (1995).
Xiaojun, X. & Ruyung, S. The bioenergetics of the southern catfish (Silurus meridionalis chen). I. Resting metabolic rate as a function of body weight and temperature. Physiol. Zool. 63, 1181–1195 (1990).
Brett, J. R. The relation of size to rate of oxygen consumption and sustained swimming speed of Sockeye Salmon (Oncorhynchus nerka). J. Fish Res. Bd Can. 22, 1491–1501 (1989).
Hamburger, K. et al. Size, oxygen consumption and growth in the mussel Mytilus edulis. Mar. Biol. 75, 303–306 (1983).
Enquist, B. J., Brown, J. H. & West, G. B. Scaling of plant energetics and population density. Nature 395, 163–165 (1998).
Cummins, K. W. & Wuycheck, J. C. Caloric equivalents for investigations in ecological energetics. Mitt. Int. Verein. Theor. Angew. Limnol. 18, 1–158 (1971).
Kohler, A. C. Variations in the growth of Atlantic Cod (Gadus morhua L.). J. Fish. Res. Bd Can. 21(1), 57–100 (1964).
Blueweiss, L. et al. Relationships between body size and some life history parameters. Oecologia 37, 257–272 (1978).
Kozlowski, J. Optimal allocations of resources explains interspecific life-history patterns in animals with indeterminate growth. Proc. R. Soc. Lond. B 263, 559–566 (1996).
Day, T. & Taylor, P. D. von Bertalanffy's growth equation should not be used to model age and size at maturity. Am. Nat. 149, 381–393 (1997).
Enquist, B. J., West, G. B., Charnov, E. L. & Brown, J. H. Allometric scaling of production and life-history variation in vascular plants. Nature 401, 907–911 (1999).
We thank E. Charnov for discussing the role of reproduction in our formalism, L. Thomson for supplying data on salmon and P. Taylor for comments. Support from the National Science Foundation and the National Center for Ecological Analysis and Synthesis are gratefully acknowledged. J.H.B. and G.B.W. also acknowledge the support of the Thaw Charitable Trust and a Packard Interdisciplinary Science Grant.
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West, G., Brown, J. & Enquist, B. A general model for ontogenetic growth. Nature 413, 628–631 (2001). https://doi.org/10.1038/35098076
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