title: Allometry and dissipation of ecological flow networks.
abstract: BACKGROUND
  An ecological flow network is a weighted directed graph in which the nodes are species, the edges are "who eats whom" relationships and the weights are rates of energy or nutrient transferred between species. Allometric scaling is a ubiquitous feature for flow systems such as river basins, vascular networks and food webs.
  
  
  METHODS
  The "ecological network analysis" can serve to reveal hidden allometries, the power law relationship between the throughflux and the indirect impact of node [Formula: see text], directly from the original flow networks without any need to cut edges in the network. The dissipation law, which is another significant scaling relationship between the energy dissipation (respiration) and the throughflow of any species, is also obtained from an analysis of the empirical flow networks. Interestingly, the exponents of the allometric law ([Formula: see text]) and the dissipation law ([Formula: see text]) show a strong relationship for both empirical and simulated flow networks. The dissipation law exponent [Formula: see text], rather than the topology of the network, is the most important factors that affect the allometric exponent [Formula: see text].
  
  
  CONCLUSIONS
  The exponent [Formula: see text] can be interpreted as the degree of centralization of the network, i.e., the concentration of impacts (direct and indirect influences on the entire network along all energy flow pathways) on hubs (the nodes with large throughflows). As a result, we find that as [Formula: see text] increases, the relative energy loss of large nodes increases, [Formula: see text] decreases, i.e., the relative importance of large species decreases. Moreover, the entire flow network is more decentralized. Therefore, network flow structure (allometry) and thermodynamic constraints (dissipation) are linked.
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing, China.
authors.forename: Jiang
authors.initials: J
authors.lastname: Zhang
authors.forename: Lingfei
authors.initials: L
authors.lastname: Wu
mesh_terms: D044822:Biodiversity; D017753:Ecosystem; D008962:Models, Theoretical
references.citation: Science. 1997 Apr 4;276(5309):122-6
references.pmid: 9082983
references.citation: J Theor Biol. 2004 Oct 7;230(3):351-8
references.pmid: 15302545
references.citation: Science. 2011 Jul 22;333(6041):445-8
references.pmid: 21778398
references.citation: Science. 1988 Nov 25;242(4882):1132-9
references.pmid: 17799729
references.citation: Proc Natl Acad Sci U S A. 2003 Feb 18;100(4):1467-8
references.pmid: 12578966
references.citation: Science. 1999 Jun 4;284(5420):1677-9
references.pmid: 10356399
references.citation: Phys Rev Lett. 2001 Jul 16;87(3):038101
references.pmid: 11461594
references.citation: PLoS One. 2011;6(10):e25995
references.pmid: 22046252
references.citation: J Theor Biol. 2010 Jun 7;264(3):760-70
references.pmid: 20303987
references.citation: Nature. 2003 May 8;423(6936):165-8
references.pmid: 12736684
references.citation: Nature. 1999 May 13;399(6732):130-2
references.pmid: 10335841
references.citation: Nature. 2000 Mar 9;404(6774):180-3
references.pmid: 10724169
references.citation: J Theor Biol. 1976 Feb;56(2):363-80
references.pmid: 944838
references.citation: Comput Biol Chem. 2004 Dec;28(5-6):321-39
references.pmid: 15556474
references.citation: Nature. 2005 Jun 16;435(7044):E3-4; discussion E4
references.pmid: 15959469
references.citation: J Exp Biol. 2005 May;208(Pt 9):1575-92
references.pmid: 15855389