Mass and energy flow in closed ecosystems: A comment

Recently Ulanowicz (1972) has proposed a formal framework in which, for a closed ecosystem, the parameters in the equations of population dynamics are related to the parameters of energy flow. In general these relations are not determinate, but Ulanowicz illustrates the method by deriving a sufficient stability condition for the simple three-species straight-chain closed system.We consider a much wider class of special webs for which Ulanowicz's relations are effectively determinate, namely webs which may be articulated into N trophic levels, with the species in any one level being linked in an arbitrary way to those in the levels immediately above and below, and with all species within any one level having a common respiration rate and energy content per unit biomass. The necessary and sufficient condition for ecosystem stability is shown to be that energy content per unit biomass increase in a hierarchical fashion as one climbs the trophic ladder. Some more fragile results are given, and discussed, for the equilibrium biomass ratios between various trophic levels.