The Structure of Cycling in the Ythan Estuary

  • Robert E. Ulanowicz
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 54)


A method for identifying all the simple, directed cycles in a network of ecosystems flows is described. Furthermore, the cycles may be divided into distinct groups, or nexuses, distinguished by certain critical links. These groupings may also be used to analytically separate the network into two constituent graphs — one graph containing only cycled flow and the other consisting of only once-through pathways.

The analysis, when applied to the carbon flow in the Ythan estuary, graphically portrays both the importance and the vulnerability of the higher trophic level transfers.


Carbon Flow Simple Cycle Fundamental Cycle Cycling Index Backtrack Search Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Literature Cited

  1. Baird, D. and Milne, H. (1981). Energy flow in the Ythan estuary, Aberdeenshire, Scotland. Estuarine. Coastal and Shelf Science 13 455–472.Google Scholar
  2. Finn, J. T. (1976). Measures of ecosystem structure and function derived from analysis of flows. J. theor. Biol. 56: 363–380.CrossRefGoogle Scholar
  3. Hutchinson, G.E. (1948). Circular causal systems in ecology. Ann. N.Y. Acad. Sci. 50: 221–246.CrossRefGoogle Scholar
  4. Jaynes, E.T. (1958). Probability Theory in Science and Engineering. Colloquium Lectures in Pure and Applied Science No. 4. Socony Mobil Oil Company, Dallas, TX. 189 pp.Google Scholar
  5. Johnson, D.B. (1975). Finding all the the elementary circuits of a directed graph. SIAM J. Comput. 4: 77–84.MathSciNetMATHCrossRefGoogle Scholar
  6. Mateti, P. and Deo, N. (1976). On algorithms for enumerating all circuits of a graph. SIAM I, Comput. 5: 90–99.Google Scholar
  7. Mateti, P. and Deo, N. (1976). On algorithms for enumerating all circuits of a graph. SIAM I, Comput. 5: 90–99.MathSciNetMATHCrossRefGoogle Scholar
  8. May, R.M. (1973). Stability and Complexity in Model Ecosystems. Princeton Univ. Press, Princeton, NJ. 235 pp.Google Scholar
  9. Odum, E.P. (1969).The strategy of ecosystem development. Science 164:262–270.CrossRefGoogle Scholar
  10. Read, R.C. and Tarjan, R.E. (1975). Bounds on backtrack algorithms for listing cycles, paths, and spanning trees. Networks 5237–252.Google Scholar
  11. Richey, J.E., Wissmar, R.C., Devol, A.H., Likens, G.E., Eaton, J.S., Wetzel, R.G., Odum, W.E., Johnson, N.M., Loucks, O.L., Prentki, R.T., and Rich, P.H. (1978). Carbon flow in four lake ecosystems: a structural approach. Science 202: 1183–1186.CrossRefGoogle Scholar
  12. Ulanowicz, R.E. (1980). An hypothesis on the development of natural communities. J. theor. Biol. 85: 223–245.CrossRefGoogle Scholar
  13. Ulanowicz, R.E. (1982). Community measures of Marine food networks and their possible applications. In M.J.R. Fasham (ed.) Measurement of Fluxes in Marine Ecosystems. UNESCO Press, Paris. (in press)Google Scholar
  14. Yan, C.S. (1969). Introduction to Input-Output Economics. Holt, Rinehart and Winston, NY.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Robert E. Ulanowicz
    • 1
  1. 1.Chesapeake Biological LaboratoryUniversity of MarylandSolomonsUSA

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