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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dalton, H.: The measurement of inequality of incomes. Econ. J. 30, 348–361 (1920)
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)
Gini, C.: Il diverso accrescimento delle classi sociali e la concentrazione della richezza. Giornale degli Economist, serie II, 2 (1909)
Gini, C.: Variabilite mutabilita. Studi Economicoaguridic della Facotta di Giurisprudenza dell Univ. di Cagliari III. Parte II. (1912)
Goldman, A.J.: Discrete mathematics in government. Lecture presented at SIAM Symposium on Applications of Discrete Mathematics, Troy, NY, June 1981
Heath, J.L.: Re-evaluation of RISC I. Comput. Archit. News 12, 3–10 (1984)
Jackson, R.D., Huete, A.R.: Interpreting vegetation indices. Prev. Vet. Med. 11, 185–200 (1991)
Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A.: Foundations of Measurement, vol. I. Academic, New York (1971)
Kruskal, J.B.: On the shortest spanning tree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7, 48–50 (1956)
Luce, R.D., Krantz, D.H., Suppes, P., Tversky, A.: Foundations of Measurement, vol. III. Academic, New York (1990)
Magurran, A.E.: Ecological Diversity and its Measurement. Chapman & Hall, London (1991)
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)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs (1982)
PekeÄŤ, A.: Limitations on conclusions from combinatorial optimization. Ph.D. thesis, Department of Mathematics, Rutgers University (1996)
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)
Pfanzagl, J.: Theory of Measurement. Wiley, New York (1968)
Roberts, F.S.: Building an energy demand signed digraph I: choosing the nodes. Rept. \(927/1 - NSF\). April. The RAND Corporation, Santa Monica (1972)
Roberts, F.S.: Building and analyzing an energy demand signed digraph. Environ. Plan. 5, 199–221 (1973)
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
Roberts, F.S.: Meaningfulness of conclusions from combinatorial optimization. Discrete Appl. Math. 29, 221–241 (1990)
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)
Roberts, F.S.: Meaningless statements. In: Contemporary Trends in Discrete Mathematics. DIMACS Series, vol. 49, pp. 257–274. American Mathematical Society, Providence (1999)
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)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)
Simpson, E.H.: Measurement of diversity. Nature 163, 688 (1949)
Stevens, S.S.: On the theory of scales of measurement. Science 103, 677–680 (1946)
Stevens, S.S.: Mathematics, measurement, and psychophysics. In: Stevens, S.S. (ed.) Handbook of Experimental Psychology, pp. 1–49. Wiley, New York (1951)
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)
Stevens, S.S.: Ratio scales of opinion. In: Whitla, D.K. (ed.) Handbook of Measurement and Assessment in Behavioral Sciences. Addison-Wesley, Reading (1968)
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)
Suppes, P.: Replies. In: Bogdan, R.J. (ed.) Patrick Suppes, pp. 207–232. Reidel, Dordrecht (1979)
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)
Suppes, P., Krantz, D.H., Luce, R.D., Tversky, A.: Foundations of Measurement, vol. II. Academic, New York (1989)
UNEP: Report of the Sixth Meeting of the Conference of the Parties to the Convention on Biological Diversity (UNEP/CBD/COP/6/20) (2002)
Urban, D., Keitt, T.: Landscape connectivity: a graph-theoretic perspective. Ecology 82, 1205–1218 (2001)
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)
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)
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
Corresponding author
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-1-4939-0742-7_18
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-0741-0
Online ISBN: 978-1-4939-0742-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)