Biodiversity measures based on species-level dissimilarities: A methodology for assessment

Biodiversity is widely recognized as a valuable natural asset to conserve. Yet biodiversity is often reported to be declining worldwide. Biodiversity measures can help evaluating it and conserving it, but need to be clearly defined and assessed. In this paper, I review several biodiversity measures and develop a new one, all based on a matrix of species-level dissimilarity data. The data can be used in its raw form, regardless of its origin (e.g. studies of morphological traits, DNA hybridization experiments…) or of any graphical representation. Then, I propose a two-step assessment of the measures. First, I assess them in terms of their deviation from a strict additive law determining the contribution of each species to the diversity of the set in an ideal setting. This setting refers to a case where the data exactly determines the hierarchical ordering of the species. Second, I assess the measures based on their compliance with a list of axioms. These axioms reflect basic mathematical properties regarded as desirable for diversity measures, such as their monotonicity in species and dissimilarities. Finally, I show the importance of applying the new quantitative assessment and the axiomatic approach together when selecting a dissimilarity-based diversity measure.