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

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.