Network integration of ecological extremal principles: exergy, emergy, power, ascendency, and indirect effects

Self organization in ecosystems has been postulated to be directed by a number of seemingly unrelated goal functions or extremal principles. These include exergy, the useful work content of energy, which measures distance from thermodynamic ground; emergy, which increases in proportion to the number of steps energy has taken away from its point of input to a system; power, which is work per unit time, and can be measured as the total energy flow in an ecosystem; ascendency, which combines a mutual information measure of the distribution of flows in a system network with the total flow; and indirect effects, which concern relationships at a distance in energy networks. S.E. Jّrgensen recently obtained high correlations between exergy, emergy, ascendency, and the ratio of indirect to direct effects, in a set of ecosystem models. These results suggest that these optimality criteria may be formally related. This paper shows, for systems at macroscopic steady states, that they are. Exergy, emergy, power, ascendency, and indirect effects all have common origins in the path structure and associated microscopic dynamics of energy and matter flows and storages in ecosystem networks. Thus, these organizational measures, originally derived from different perspectives on ecosystems, are in fact related through a common basis.