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Letters to Nature
Nature 264, 633 - 634 (16 December 1976); doi:10.1038/264633a0

Model of material cycling in a closed ecosystem


Department of Applied Physics, University of Strathclyde, Glasgow, G4 0NG, UK

ALTHOUGH ecosystem behaviour is ultimately determined by the combination of energy flow through the system and material cycling within it, remarkably little effort has been directed towards elucidating the effects of material cycling on ecosystem stability, noteworthy exceptions being the works of Ulanowicz1, May2, and Dudzik et al. 3. Ulanowicz1 and May2 studied a model of a linear trophic chain in which both the biomass and energy fluxes between any two levels involved bilinear sums of the biomasses of all the species present and concluded that the system was stable only if the specific energy (that is, energy content per unit biomass) increased on ascending the trophic chain. Although producers are normally found to have a lower specific energy than consumers, there seems to be little or no significant difference between the specific energy of different consumer levels (see, for example, refs 4 and 5). The implication of the Ulanowicz–May model is thus that the stability of a trophic chain is a fragile property dependent on small differences in specific energy between levels. We believe that this result is due to a neglect of the distinctive nature of the dynamics of the decomposition of biological material to inorganic material, a viewpoint consistent with the results of Dudzik et al. 3 who analysed a number of detailed models of nutrient cycles in both open and closed ecosystems. Here we propose an alternative model of a trophic chain, which suggests that the effect of material cycling is to stabilise the system.



1. Ulanowicz, R. E., J. theor. Biol., 34, 239 (1972).
2. May, R. M., J. theor. Biol., 39, 155 (1973).
3. Dudzik, M., Harte, J., Levy, D., and Sandusky, J., Lawrence Berkeley Rep. LBL-3264 (1975).
4. Morowitz, H. T., Energy Flow in Biology (Academic, New York and London, 1968).
5. Odum, E. P., Fundamentals of Ecology (Saunders, Philadelphia, 1971).
6. Whittaker, R. H., Communities and Ecosystems, 112 (Macmillan, London, 1970).
7. May, R. M., Stability and Complexity in Model Ecosystems (Princeton University, Princeton, 1973).

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