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