Landscape Ecology

, Volume 34, Issue 12, pp 2735–2742 | Cite as

The Lorenz curve: a suitable framework to define satisfactory indices of landscape composition

  • Julio A. CamargoEmail author



Patch diversity, evenness and dominance are important metrics of landscape composition. They have been traditionally measured using indices based on Shannon’s information entropy (H) and Simpson’s concentration statistic (λ).


The main objectives of this study are: (1) to show that the Lorenz curve is an appropriate framework to understand and measure patch dominance, evenness and diversity; (2) to show that Lorenz-compatible indices have better mathematical behavior than H-based and λ-based indices.


Thirteen different hypothetical landscapes were created to assess landscape composition with the Lorenz curve and to compare the mathematical behavior of Lorenz-compatible indices with that of H-based and λ-based indices.


The Lorenz curve is a suitable framework to understand and measure patch dominance, evenness and diversity due to four relevant equivalences: (1) patch dominance = the separation of the Lorenz curve from the 45-degree line of perfect patch evenness; (2) patch evenness = 1 − patch dominance; (3) patch diversity (eliminated by patch dominance) = patch richness × patch dominance; (4) patch diversity (preserved by patch evenness) = patch richness × patch evenness. Accordingly, patch diversity/patch richness = 1 − patch dominance and land-cover concentration = 1/patch diversity.


Lorenz-compatible indices have better mathematical behavior than H-based and λ-based indices, exhibiting greater coherence and objectivity when measuring patch dominance, evenness and diversity.


Patch dominance Patch evenness Patch diversity Lorenz-compatible indices H-based indices λ-based indices 



The study was financially supported by the Spanish Ministry of Science and Innovation (research project CGL2011-28585) and the University of Alcala (research budget MC-100). I would like to thank Professors J. Wu and K. McGarigal, and also an anonymous reviewer, for their valuable comments and suggestions.


  1. Barr LM, Pressey RL, Fuller RA, Segan DB, McDonald-Madden E, Possingham HP (2011) A new way to measure the world’s protected area coverage. PLoS ONE 6(9):e24707CrossRefGoogle Scholar
  2. Camargo JA (1992a) Temporal and spatial variations in dominance, diversity and biotic indices along a limestone stream receiving a trout farm effluent. Water Air Soil Pollut 63:343–359CrossRefGoogle Scholar
  3. Camargo JA (1992b) New diversity index for assessing structural alterations in aquatic communities. Bull Environ Contam Toxicol 48:428–434CrossRefGoogle Scholar
  4. Camargo JA (1993) Must dominance increase with the number of subordinate species in competitive interactions? J Theor Biol 161:537–542CrossRefGoogle Scholar
  5. Camargo JA (1995) On measuring species evenness and other associated parameters of community structure. Oikos 74:538–542CrossRefGoogle Scholar
  6. Camargo JA (2008) Revisiting the relation between species diversity and information theory. Acta Biotheor 56:275–283CrossRefGoogle Scholar
  7. Fellman J (2018) Income inequality measures. Theor Econ Lett 8:557–574CrossRefGoogle Scholar
  8. Garrabou J, Riera J, Zabala M (1998) Landscape pattern indices applied to Mediterranean subtidal rocky benthic communities. Landsc Ecol 13:225–247CrossRefGoogle Scholar
  9. Hill MO (1973) Diversity and evenness: a unifying notation and its consequences. Ecology 54:427–432CrossRefGoogle Scholar
  10. Hulshoff RM (1995) Landscape indices describing a Dutch landscape. Landsc Ecol 10:101–111CrossRefGoogle Scholar
  11. Jost L (2006) Entropy and diversity. Oikos 113:363–375CrossRefGoogle Scholar
  12. Krebs CJ (1999) Ecological methodology, 2nd edn. Harper & Row, New YorkGoogle Scholar
  13. Lorenz MO (1905) Methods of measuring the concentration of wealth. J Am Stat Assoc 9:209–219Google Scholar
  14. Magurran AE (2004) Measuring biological diversity. Blackwell, OxfordGoogle Scholar
  15. McGarigal K, Cushman SA, Ene E (2012) FRAGSTATS (version 4): spatial pattern analysis program for categorical and continuous maps.
  16. McNaughton SJ, Wolf LL (1970) Dominance and the niche in ecological systems. Science 167:131–139CrossRefGoogle Scholar
  17. O’Neill RV, Krummel JR, Gardner RH, Sugihara G, Jackson B, DeAngelis DL, Milne BT, Turner MG, Zygmunt B, Christensen SW, Dale VH, Graham RL (1988) Indices of landscape pattern. Landsc Ecol 1:153–162CrossRefGoogle Scholar
  18. Peng J, Wang Y, Zhang Y, Wu J, Li W, Li Y (2010) Evaluating the effectiveness of landscape metrics in quantifying spatial patterns. Ecol Indic 10:217–223CrossRefGoogle Scholar
  19. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(379–423):623–656CrossRefGoogle Scholar
  20. Simpson EH (1949) Measurement of diversity. Nature 163:688CrossRefGoogle Scholar
  21. Turner MG, Gardner RH (2015) Landscape ecology in theory and practice: pattern and process, 2nd edn. Springer, New YorkGoogle Scholar
  22. Whittaker RH (1972) Evolution and measurement of species diversity. Taxon 21:213–251CrossRefGoogle Scholar
  23. Wu J, Shen W, Sun W, Tueller PT (2002) Empirical patterns of the effects of changing scale on landscape metrics. Landsc Ecol 17:761–782CrossRefGoogle Scholar
  24. Zheng X, Xia T, Yang X, Yuan T, Hu Y (2013) The land Gini coefficient and its application for land use structure analysis in China. PLoS ONE 8(10):e76165CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Unidad Docente de Ecología, Departamento de Ciencias de la VidaUniversidad de AlcaláAlcalá De Henares (Madrid)Spain

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