Skip to main content
Log in

Flow analysis sensitivities for models of energy or material flow

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Sensitivity analyses have been used to examine the flow structure of two hypothetical ecosystem models. These analyses have results which relate to important aspects of ecosystem theory. Cycles are shown to increase the sensitivity of the network, while increased throughflow is shown to decrease the sensitivity. Such results indicate that several factors can be modified to decrease the sensitivity of ecosystems to environmental stress.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Barber, M. C. 1978a. “A Markovian Model of Ecosystem Flow Analysis.”Ecol. Mod.,5, 193–206.

    Article  Google Scholar 

  • — 1978b. “A Retrospective Markovian Model for Ecosystem Resource Flow.Ecol. Mod.,5, 125–130.

    Article  Google Scholar 

  • —, B. C. Patten and J. T. Finn. 1980. “Review and Evaluation of Input-Output Flow Analysis for Ecological Applications.” InCompartmental Analysis of Ecosystem Models, Vol. S10, Proc. Satellite Program in Statistical Ecology, Parma, Italy. Fairland, Maryland: International Cooperative Publ. House.

    Google Scholar 

  • Bosserman, R. W. 1980. “Complexity Measures for Assessment of Environmental Impact in Ecosystem Networks.” InProceedings of the Pittsburgh Conference on Modeling and Stimulation. Pittsburgh, Pennsylvania.

  • — 1981. “Sensitivity Techniques for Examination of Input-Output flow Analyses.” InProceedings of the International Symposium on Energy and Ecological Modelling, Eds W. J. Mitsch, R. W. Bosserman and J. M. Klopatek. New York: Elsevier.

    Google Scholar 

  • Bosserman, R. W. 1982. “Structural Comparisons for Four Lake Ecosystem Models.” InProceedings of Society for General Systems Research. Washington, D.C.

  • Bosserman, R. W. 1983. “Complexity Measures for Evaluation of Ecosystem Networks.”ISEM Journal forthcoming.

  • Bosserman, R. W. and F. Harary. 1981a. “The Hierarchical Decomposition ofDigraphs into Demiarcs, Genons, and Creaons.” InProceedings of the Tenth Annual Conference of the Southeastern Region for the Society of General Systems Research. Lousville, Kentucky.

  • — and —. 1981b. Demiarcs, Genons, and Creaons.J. theor. Biol.,92, 241–254.

    Article  MathSciNet  Google Scholar 

  • Costanza, R. 1981. “Embodied Energy and Economic Valuation.”Science, N.Y. 210, 1219–1224.

    Google Scholar 

  • Faddeev, D. K. and V. N. Faddeeva 1963.Computational Methods of Linear Algebra. San Francisco: Freeman.

    Google Scholar 

  • Finn, J. T. 1976a. “Cycling Index: a General Measure of Cycling in Compartmental Models.” InEnvironmental Chemistry and Cycling Processes Symposium, Eds D. C. Adriana and I. L. Brisbin. Washington, D.C.: U.S. Energy Research and Development

    Google Scholar 

  • — 1976b. “Measure of Ecosystem Structure and Function Derived from Analysis of Flows.”J. theor. Biol.,56, 363–380.

    Article  Google Scholar 

  • — 1977. “Flow Analysis: a Method for Analyzing Flows in Ecosystems.” Ph. D. Dissertation, University of Georgia, Athens, Georgia.

    Google Scholar 

  • Gallopin, G. C., 1972. “Structural Properties of Food Webs.” InSystems Analysis and Simulation in Ecology, Vol. 2, Ed. B. C. Patten. New York: Academic Press.

    Google Scholar 

  • Gardner, M. R. and W. R. Ashby. 1970. “Connectedness of Large Dynamic (Cybernetic) Systems: Critical Value of Stability.”Nature, Lond. 228, 784.

    Article  Google Scholar 

  • Goodman, D. 1975. “The Theory of Diversity-Stability Relationships in Ecology.”Q. Rev. Biol.,50, 237–266.

    Article  Google Scholar 

  • Hannon, B. 1973. “The Structure of Ecosystems.”J. theor. Biol. 41 535–546.

    Article  Google Scholar 

  • Harary, F. 1969.Graph Theory. Reading, Massachusetts: Addison-Wesley.

    Google Scholar 

  • Jorgensen, S. E. 1981a. “Holistic Approach to Ecological Modelling by Application of Thermodynamics.” InProceedings of the International Symposium on Energy and Ecological Modelling, Eds W. J. Mitsch, R. W. Bosserman and J. M. Klopatek. New York: Elsevier.

    Google Scholar 

  • — 1981b. “Energy as Key Function in Ecological Models.” InEnergetics and Systems, Eds J. A. Dillon, Jr., W. J. Mitsch, R. K. Ragade and R. W. Bosserman. Ann Arbor, Michigan: Ann Arbor Science.

    Google Scholar 

  • Lane, P. and R. Levins. 1977. “The Dynamics of Aquatic Systems. 2. The Effects of Nutrient Enrichment on Model Plankton Communities.”Limnol. Oceanogr.,22, 454–471.

    Article  Google Scholar 

  • Leontief, W. W. 1966.Input-Output Economics. London and New York: Oxford University Press.

    Google Scholar 

  • Levins, R. 1975. “Problems of Signed Digraphs in Ecological Theory.” InEcosystem Analysis and Prediction, Ed. S. Levin, pp. 264–277. Philadelphia, Pennsylvania: Soc. Industrial Appl. Math.

    Google Scholar 

  • May, R. M. 1972. “Will a Large Complex System be Stable?”Nature, Lond. 238, 413–414.

    Article  Google Scholar 

  • — 1973.Stability and Complexity in Model Ecosystems. Princeton, New Jersey: Princeton University Press.

    Google Scholar 

  • Noble, B. 1969.Applied Linear Algebra. Englewood Cliffs New Jersey: Prentice-Hall.

    MATH  Google Scholar 

  • Odum, E. P. 1971.Fundamentals of Ecology. Philadelphia, Pennsylvania: Saunders Press.

    Google Scholar 

  • Patten, B. C. 1981. “Environs: Partition Units of Ecosystems.” InEnergetics and Systems, Eds J. A. Dillon, Jr, W. J. Mitsch, R. K. Ragade and R. W. Bosserman. Ann Arbor, Michigan: Ann Arbor Science.

    Google Scholar 

  • —, R. W. Bosserman, J. T. Finn and W. G. Gale, 1976. “Propagation of Cause in Ecosystems.” InSystems Analysis and Simulation in Ecology, Vol. 4, Ed. B. C. Patten. New York: Academic Press.

    Google Scholar 

  • Richey, J. E., R. C. Wissmar, H. T. Devol, G. E. Likens, J. S. Eaton, R. G. Wetzel, W. E. Odum, N. M. Johnson, O. L. Loucks, R. T. Prentki and P. H. Rich, 1978. “Carbon Flow in Four Lake Ecosystems: a Structural Approach.”Science, N.Y. 202, 1183–1186.

    Google Scholar 

  • Siljak, D. D. 1974. “Connective Stability of Complex Ecosystems.”Nature, Lond. 249, 280.

    Article  Google Scholar 

  • — 1976. “When is a Complex Ecosystem Stables?”Math. Biosci. 25, 25–50.

    Article  Google Scholar 

  • Siljak, D. D. 1977. “On Reachability of Dynamic Systems.”Int. J. Syst. Sci. 8.

  • — 1979. “Structure and Stability of Model Ecosystems.” InTheoretical Systems Ecology, Ed. E. Halfon New York: Academic Press.

    Google Scholar 

  • Ulanowitz, R. E. 1981. “A Unified Theory of Self-Organization.” InProceedings of the International Symposium on Energy and Ecological Modelling, Eds W. J. Mitsch, R. W. Bosserman and J. M. Klopatek, New York: Elsevier.

    Google Scholar 

  • Waide, J. B. and J. R. Webster. 1976. “Engineering Systems Analysis: Applicability to Ecosystems.” InSystems Analysis and Simulation in Ecology, Vol. 2, Ed. B. C. Patten. New York: Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bosserman, R.W. Flow analysis sensitivities for models of energy or material flow. Bltn Mathcal Biology 45, 807–826 (1983). https://doi.org/10.1007/BF02460051

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460051

Keywords

Navigation