Beyond branch lengths: a fuzzy theory of evolutionary distinctiveness

In the face of accelerating biodiversity loss, conservation strategies require effective tools to identify species of high conservation priority. In this context, the index of evolutionary distinctiveness (ED), which quantifies the unique contribution of individual species to the overall phylogenetic diversity of a given assemblage, has played a pivotal role. In this paper, we propose a general mathematical framework for ED based on the notion of specificity, a type of non-probabilistic uncertainty derived from fuzzy set theory. This new perspective allows ED to be extended to other forms of distinctiveness, such as functional distinctiveness, provided that an appropriate pairwise (dis)similarity matrix between species is available. It also enables the development of new measures that capture aspects of species distinctiveness not accounted for by the ED index. Our formulation further connects species-level distinctiveness with traditional community-level metrics, such as alpha and beta diversity. We demonstrate how beta diversity, traditionally used to measure species turnover among sites, can be reframed as the average specificity of the sampled sites. Overall, linking ED to fuzzy specificity opens new directions for biodiversity measurement and conservation planning.