  An ecological flow network is a weighted directed graph in which nodes are
species, edges are "who eats whom" relationships and weights are rates of
energy or nutrients transfer between species. Allometric scaling is a
ubiquitous feature for flow systems like river basins, vascular networks and
food webs. By "ecological network analysis" method, we can reveal the hidden
allometry directly on the original flow networks without cutting edges. On the
other hand, dissipation law, which is another significant scaling relationship
between the energy dissipation (respiration) and the throughflow of any species
is also discovered on the collected flow networks. Interestingly, the exponents
of allometric law ($\eta$) and the dissipation law ($\gamma$) have a strong
connection for both empirical and simulated flow networks. The dissipation law
exponent $\gamma$ rather than the topology of the network is the most important
ingredient to the allometric exponent $\eta$. By reinterpreting $\eta$ as the
inequality of species impacts (direct and indirect influences) to the whole
network along all energy flow pathways but not the energy transportation
efficiency, we found that as $\gamma$ increases, the relative energy loss of
large nodes (with high throughflow) increases, $\eta$ decreases, and the
inequality of the whole flow network as well as the relative importance of
large species decreases. Therefore, flow structure and thermodynamic constraint
are connected.
