Mass and Energy Flow in Closed Ecosystems: Do Ecological or Mathematical Constraints Prevail?

Hirata & Fukao (1977, Math. Biosci.33, 321-334) showed that the model of mass and energy flow in closed ecosystems presented by Ulanowicz (1972, J. theor. Biol.34, 239-253) and May (1973, J. theor. Biol.39, 155-163) was physically inconsistent and proposed an improved version of it. It is shown here that the model of Hirata and Fukao is also physically and ecologically inconsistent, and that the problem lies in the very methodology followed by these authors, which consists in letting the flows be determined by mathematical constraints on the allocation of mass and energy within the recipient traphic levels. A brief comparison between ecological and economic models is made in this respect. ernative framework to account consistently for coupled mass and energy flows in ecosystems is proposed, based on the principle that the allocation of mass and energy within the recipient trophic levels is subject to the constraints of coupling between mass and energy.