Skip to main content

Meaningful and Meaningless Statements in Landscape Ecology and Environmental Sustainability

  • Chapter
  • First Online:
Clusters, Orders, and Trees: Methods and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 92))

  • 1135 Accesses

Abstract

The growing population and increasing pressures for development lead to challenges to life on our planet. Increasingly, we are seeing how human activities affect the natural environment, including systems that sustain life: climate, healthy air and water, arable land to grow food, etc. There is growing interest (and urgency) in understanding how changes in human activities might lead to long-term sustainability of critical environmental systems. Of particular interest are large ecological systems that affect climate, air and water, etc. Landscape Ecology is concerned with such systems. Understanding the challenges facing our planet requires us to summarize data, understand claims, and investigate hypotheses. To be useful, these summaries, claims, and hypotheses are often stated using metrics of various kinds, using a variety of scales of measurement. The modern theory of measurement shows us that we have to be careful using scales of measurement and that sometimes statements using such scales can be meaningless—in a very precise sense. This paper summarizes the theory of meaningful and meaningless statements in measurement and applies it to statements in landscape ecology and environmental sustainability.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dalton, H.: The measurement of inequality of incomes. Econ. J. 30, 348–361 (1920)

    Article  Google Scholar 

  2. Fleming, P.J., Wallace, J.J.: How not to lie with statistics: the correct way to summarize benchmark results. Commun. ACM 29, 218–221 (1986)

    Article  Google Scholar 

  3. Gini, C.: Il diverso accrescimento delle classi sociali e la concentrazione della richezza. Giornale degli Economist, serie II, 2 (1909)

    Google Scholar 

  4. Gini, C.: Variabilite mutabilita. Studi Economicoaguridic della Facotta di Giurisprudenza dell Univ. di Cagliari III. Parte II. (1912)

    Google Scholar 

  5. Goldman, A.J.: Discrete mathematics in government. Lecture presented at SIAM Symposium on Applications of Discrete Mathematics, Troy, NY, June 1981

    Google Scholar 

  6. Heath, J.L.: Re-evaluation of RISC I. Comput. Archit. News 12, 3–10 (1984)

    Article  Google Scholar 

  7. Jackson, R.D., Huete, A.R.: Interpreting vegetation indices. Prev. Vet. Med. 11, 185–200 (1991)

    Article  Google Scholar 

  8. Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A.: Foundations of Measurement, vol. I. Academic, New York (1971)

    MATH  Google Scholar 

  9. Kruskal, J.B.: On the shortest spanning tree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7, 48–50 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  10. Luce, R.D., Krantz, D.H., Suppes, P., Tversky, A.: Foundations of Measurement, vol. III. Academic, New York (1990)

    MATH  Google Scholar 

  11. Magurran, A.E.: Ecological Diversity and its Measurement. Chapman & Hall, London (1991)

    Google Scholar 

  12. Mahadev, N.V.R., Pekeč, A., Roberts, F.S.: On the meaningfulness of optimal solutions to scheduling problems: can an optimal solution be non-optimal? Oper. Res. 46(Suppl.), S120–S134 (1998)

    Google Scholar 

  13. Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs (1982)

    MATH  Google Scholar 

  14. PekeÄŤ, A.: Limitations on conclusions from combinatorial optimization. Ph.D. thesis, Department of Mathematics, Rutgers University (1996)

    Google Scholar 

  15. PekeÄŤ, A.: Scalings in linear programming: necessary and sufficient conditions for invariance. Center for Basic Research in Computer Science (BRICS), Technical report RS-96-50 (1996)

    Google Scholar 

  16. Pfanzagl, J.: Theory of Measurement. Wiley, New York (1968)

    MATH  Google Scholar 

  17. Roberts, F.S.: Building an energy demand signed digraph I: choosing the nodes. Rept. \(927/1 - NSF\). April. The RAND Corporation, Santa Monica (1972)

    Google Scholar 

  18. Roberts, F.S.: Building and analyzing an energy demand signed digraph. Environ. Plan. 5, 199–221 (1973)

    Article  Google Scholar 

  19. Roberts, F.S.: Measurement Theory, with Applications to Decisionmaking, Utility, and the Social Sciences. Addison-Wesley, Reading (1979). Digital Reprinting (2009). Cambridge University Press, Cambridge

    Google Scholar 

  20. Roberts, F.S.: Meaningfulness of conclusions from combinatorial optimization. Discrete Appl. Math. 29, 221–241 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  21. Roberts, F.S.: Limitations on conclusions using scales of measurement. In: Pollock, S.M., Rothkopf, M.H., Barnett, A. (eds.) Operations Research and the Public Sector. Handbooks in Operations Research and Management Science, vol. 6, pp. 621–671. North-Holland, Amsterdam (1994)

    Chapter  Google Scholar 

  22. Roberts, F.S.: Meaningless statements. In: Contemporary Trends in Discrete Mathematics. DIMACS Series, vol. 49, pp. 257–274. American Mathematical Society, Providence (1999)

    Google Scholar 

  23. Roberts, F.S.: Meaningful and meaningless statements in epidemiology and public health. In: Berglund, B., Rossi, G.B., Townsend, J., Pendrills, L. (eds.) Measurements with Persons, pp. 75–95. Taylor and Francis, New York (2012)

    Google Scholar 

  24. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    Article  MATH  MathSciNet  Google Scholar 

  25. Simpson, E.H.: Measurement of diversity. Nature 163, 688 (1949)

    MATH  Google Scholar 

  26. Stevens, S.S.: On the theory of scales of measurement. Science 103, 677–680 (1946)

    Article  MATH  Google Scholar 

  27. Stevens, S.S.: Mathematics, measurement, and psychophysics. In: Stevens, S.S. (ed.) Handbook of Experimental Psychology, pp. 1–49. Wiley, New York (1951)

    Google Scholar 

  28. Stevens, S.S.: Measurement, psychophysics, and utility. In: Churchman, C.W., Ratoosh, P. (eds.) Measurement: Definitions and Theories, pp. 18–63. Wiley, New York (1959)

    Google Scholar 

  29. Stevens, S.S.: Ratio scales of opinion. In: Whitla, D.K. (ed.) Handbook of Measurement and Assessment in Behavioral Sciences. Addison-Wesley, Reading (1968)

    Google Scholar 

  30. Suppes, P.: Measurement, empirical meaningfulness and three-valued logic. In: Churchman, C.W., Ratoosh, P. (eds.) Measurement: Definitions and Theories, pp. 129–143. Wiley, New York (1959)

    Google Scholar 

  31. Suppes, P.: Replies. In: Bogdan, R.J. (ed.) Patrick Suppes, pp. 207–232. Reidel, Dordrecht (1979)

    Chapter  Google Scholar 

  32. Suppes, P., Zinnes, J.: Basic measurement theory. In: Luce, R.D., Bush, R.R., Galanter, E. (eds.) Handbook of Mathematical Psychology, vol. 1, pp. 1–76. Wiley, New York (1963)

    Google Scholar 

  33. Suppes, P., Krantz, D.H., Luce, R.D., Tversky, A.: Foundations of Measurement, vol. II. Academic, New York (1989)

    Google Scholar 

  34. UNEP: Report of the Sixth Meeting of the Conference of the Parties to the Convention on Biological Diversity (UNEP/CBD/COP/6/20) (2002)

    Google Scholar 

  35. Urban, D., Keitt, T.: Landscape connectivity: a graph-theoretic perspective. Ecology 82, 1205–1218 (2001)

    Article  Google Scholar 

  36. van Wijk, M.T., Williams, M.: Optical instruments for measuring leaf area index in low vegetation: application in Arctic ecosystems. Ecol. Appl. 15, 1462–1470 (2005)

    Article  Google Scholar 

  37. Zettenberg, A.: Network based tools and indicators for landscape ecological assessments, planning, and design. Licentiate Thesis, KTH-Environmental Management and Assessment Research Group, Department of Land and Water Resources Engineering, Royal Institute of Technology (KTH), Stockholm, Sweden (2009)

    Google Scholar 

Download references

Acknowledgments

The author gratefully acknowledges the support of the National Science Foundation under grant number DMS-0829652 to Rutgers University. A number of ideas and some of the examples and language in this paper are borrowed from my papers Roberts [21, 23], which explore meaningful and meaningless statements in operations research and in epidemiology and public health, respectively. The author gratefully and thankfully acknowledges the many stimulating and fruitful scientific interchanges with Boris Mirkin over a period of many years, and wishes him many years of continued good health and success.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fred S. Roberts .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Roberts, F.S. (2014). Meaningful and Meaningless Statements in Landscape Ecology and Environmental Sustainability. In: Aleskerov, F., Goldengorin, B., Pardalos, P. (eds) Clusters, Orders, and Trees: Methods and Applications. Springer Optimization and Its Applications, vol 92. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0742-7_18

Download citation

Publish with us

Policies and ethics