title: Sizing up allometric scaling theory.
abstract: Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks-the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets.
authors.affiliation: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America.
authors.forename: Van M
authors.initials: VM
authors.lastname: Savage
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Deeds
authors.forename: Walter
authors.initials: W
authors.lastname: Fontana
mesh_terms: D000818:Animals; D001783:Blood Flow Velocity / Q000502:physiology; D049628:Body Size / Q000502:physiology*; D002196:Capillaries / Q000033:anatomy & histology / Q000502:physiology; D019295:Computational Biology; D003198:Computer Simulation; D016208:Databases, Factual; D008322:Mammals / Q000033:anatomy & histology / Q000502:physiology; D008433:Mathematics; D008660:Metabolism; D008954:Models, Biological; D010100:Oxygen / Q000378:metabolism
chemical_list: D010100:Oxygen
references.citation: Ecology. 2007 May;88(5):1132-41
references.pmid: 17536400
references.citation: Tree Physiol. 2001 Jan;21(1):19-26
references.pmid: 11260820
references.citation: J Physiol. 1919 May 20;52(6):409-15
references.pmid: 16993405
references.citation: Oecologia. 1978 Jan;37(2):257-272
references.pmid: 28309655
references.citation: Proc Natl Acad Sci U S A. 2007 Apr 17;104(16):6858-63
references.pmid: 17420477
references.citation: Proc Natl Acad Sci U S A. 2005 Jan 4;102(1):140-5
references.pmid: 15618408
references.citation: Tree Physiol. 2001 Jul;21(10):697-700
references.pmid: 11446999
references.citation: J Gen Physiol. 2001 Sep;118(3):267-76
references.pmid: 11524457
references.citation: Proc Natl Acad Sci U S A. 2007 Jan 16;104(3):1051-6
references.pmid: 17215372
references.citation: Science. 2002 Feb 22;295(5559):1517-20
references.pmid: 11859193
references.citation: Proc Natl Acad Sci U S A. 2002 Feb 19;99 Suppl 1:2473-8
references.pmid: 11875197
references.citation: J Exp Biol. 2006 Aug;209(Pt 16):3045-54
references.pmid: 16888053
references.citation: Am Nat. 2002 May;159(5):482-97
references.pmid: 18707431
references.citation: J Physiol. 1919 May 20;52(6):457-74
references.pmid: 16993410
references.citation: Nature. 2003 Feb 13;421(6924):713; discussion 714
references.pmid: 12610614
references.citation: Proc Natl Acad Sci U S A. 2001 Feb 27;98(5):2922-7
references.pmid: 11226342
references.citation: J Theor Biol. 1999 Apr 21;197(4):517-26
references.pmid: 10196094
references.citation: Circ Res. 1978 May;42(5):593-7
references.pmid: 639181
references.citation: Science. 1997 Apr 4;276(5309):122-6
references.pmid: 9082983
references.citation: Am Nat. 2004 Mar;163(3):429-41
references.pmid: 15026978
references.citation: Biol Rev Camb Philos Soc. 2005 Nov;80(4):611-62
references.pmid: 16221332
references.citation: J Theor Biol. 1998 Aug 21;193(4):577-92
references.pmid: 9745754
references.citation: Nature. 2001 Apr 5;410(6829):655-60
references.pmid: 11287945
references.citation: Nature. 1999 May 13;399(6732):130-2
references.pmid: 10335841
references.citation: Nature. 2007 Feb 1;445(7127):E9-10; discussion E10-1
references.pmid: 17268426
references.citation: Nature. 2006 Jan 26;439(7075):457-61
references.pmid: 16437113
references.citation: Am Nat. 2000 Aug;156(2):201-219
references.pmid: 10856202
references.citation: Proc Natl Acad Sci U S A. 2002 Aug 6;99(16):10506-9
references.pmid: 12149461
references.citation: J Physiol. 1919 May 20;52(6):391-408
references.pmid: 16993404
references.citation: J Theor Biol. 2001 Mar 7;209(1):9-27
references.pmid: 11237567
references.citation: J Exp Biol. 2007 Nov;210(Pt 21):3873-4; author reply 3875-6
references.pmid: 17951428
references.citation: Proc Natl Acad Sci U S A. 2002 Aug 6;99(16):10411-6
references.pmid: 12136124
references.citation: Proc Natl Acad Sci U S A. 2007 Aug 7;104(32):13204-9
references.pmid: 17664421
references.citation: Nature. 2002 May 9;417(6885):166-70
references.pmid: 12000958
references.citation: J Physiol. 1890 Jan;11(1-2):85-158.17
references.pmid: 16991945
references.citation: Biol Lett. 2007 Feb 22;3(1):99-102
references.pmid: 17443976
references.citation: J Comp Physiol B. 2003 Mar;173(2):87-112
references.pmid: 12624648
references.citation: Proc Natl Acad Sci U S A. 2006 Jun 13;103(24):9130-5
references.pmid: 16754845
references.citation: J Exp Biol. 2005 May;208(Pt 9):1621-5
references.pmid: 15855393
references.citation: Am J Physiol. 1993 Jul;265(1 Pt 2):H366-75
references.pmid: 8342653
references.citation: J Theor Biol. 2001 Sep 21;212(2):183-90
references.pmid: 11531384
references.citation: Magn Reson Med. 1990 Apr;14(1):68-78
references.pmid: 2161986
references.citation: Science. 1999 Jun 4;284(5420):1677-9
references.pmid: 10356399
references.citation: Am J Physiol. 1993 Jul;265(1 Pt 2):H350-65
references.pmid: 8342652
references.citation: Tree Physiol. 2000 Aug;20(14):965-7
references.pmid: 11303571
references.citation: Proc Natl Acad Sci U S A. 2003 Apr 1;100(7):4046-9
references.pmid: 12637681
references.citation: Proc Natl Acad Sci U S A. 2007 Oct 23;104(43):16998-7003
references.pmid: 17942680
references.citation: Hypertension. 2003 Jun;41(6):1180-2
references.pmid: 12756217
references.citation: Proc Natl Acad Sci U S A. 2007 Mar 13;104(11):4718-23
references.pmid: 17360590
references.citation: Proc Natl Acad Sci U S A. 1926 Mar;12(3):207-14
references.pmid: 16576980