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

• Published in: Landscape ecology Vol. 34; no. 12; pp. 2735 - 2742
• Main Author: Camargo, Julio A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2019; Springer Nature B.V
• Subjects: Biomedical and Life Sciences; Compatibility; Composition; Dominance; Ecology; Entropy (Information theory); Environmental Management; Land cover; Landscape Ecology; Landscape/Regional and Urban Planning; Life Sciences; Lorenz Curve; Mathematical analysis; Nature Conservation; Perspective; Sustainable Development; Patch evenness; Lorenz-compatible indices; Patch diversity; based indices; Patch dominance
• ISSN: 0921-2973; 1572-9761
• DOI: 10.1007/s10980-019-00926-4

Context 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 ). Objectives 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. Methods 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. Results 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. Conclusions 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.