Allometry and dissipation of ecological flow networks.

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. METHODOLOGY: 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.

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