Summary
A formal approach to the analysis of ecosystem stability has resulted in a theoretically important finding; the stability of an ecosystem can be enhanced by increasing the number of non-linear interactions that exist between the ecosystem components.
The stability analysis presented in this paper does not depend upon differential equations which have been postulated to describe an ecosystem on theoretical grounds. The analysis employs a power-law approximation and requires that experimental data be obtained only for the species of interest, not for all the components of the ecosystem. The proposed stability analysis makes it possible for one to predict the consequences of removing one or more species or combinations of species from an ecosystem. Some systems will possess steady state solutions even after one or more species or combinations of species have become extinct; other systems are unable to achieve any subsequent steady state and will suffer further collapse. The stability analysis presented in this paper allows one to predict each and every possible combination of system components whose extinction will result in further disruption of the ecosystem. The stability analysis described here permits one to predict the number of steady state solutions possessed by the ecosystem and the values of the system variables in each of those steady states.
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References
Carlucci, A. F., Bowes, P. G.: Vitamin production and utilization by phytoplankton in mixed culture. J. Phycol. 6, 393–400 (1970)
Hohn, F. E.: Elementary matrix algebra, 2nd ed., 395 pp. New York: Macmillan 1965
May, R. M.: Stability in multispecies community models. Mathematical Biosciences 12, 59–79 (1971)
May, R. M.: Stability and complexity in model ecosystems. Princeton: Princeton University Press 1973
Roberts, A.: The stability of a feasible random ecosystem. Nature (Lond.) 251, 607–608 (1974)
Savageau, M. A.: Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J. theor. Biol. 25, 365–369 (1969a)
Savageau, M. A.: Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. J. theor. Biol. 25, 370–379 (1969b)
Smith, D. F.: Quantitative analysis of the functional relationships existing between ecosystem components. I. Analysis of the linear intercomponent mass transfers. Oecologia (Berl.) 16, 97–106 (1974a)
Smith, D. F.: Quantitative analysis of the functional relationships existing between ecosystem components. II. Analysis of non-linear relationships. Oecologia (Berl.) 16, 107–117 (1974b)
Smith, D. F.: Ecosystem model extraction, an alternative to model building. Proceedings of the Second International Symposium on Coral Reefs, vol. 2. Brisbane: The Great Barrier Reef Committee 1974c
Systems Analysis in Ecology: K. E. F. Watt, ed. New York: Academic Press 1966
Systems Analysis and Simulation in Ecology: B. C. Patten, ed., vol. 1. New York: Academic Press 1971
Systems Analysis and Simulation in Ecology: B. C. Patten, ed., vol. 2. New York: Academic Press 1972
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Smith, D.F. Quantitative analysis of the functional relationships existing between ecosystem components. Oecologia 21, 17–29 (1975). https://doi.org/10.1007/BF00345890
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DOI: https://doi.org/10.1007/BF00345890