Diversity in a fuzzy world: a review of models and measures

This is a Preprint and has not been peer reviewed. This is version 1 of this Preprint. You must log in to post a comment. There are no comments or no comments have been made public for this article. This is a Preprint and has not been peer reviewed. This is version 1 of this Preprint. Add a Comment You must log in to post a comment. Comments There are no comments or no comments have been made public for this article. Biological diversity metrics have evolved from simple species counts to measures that incorporate increasingly complex functional information. A critical aspect is that different families of diversity indices are grounded in distinct mathematical models for representing uncertainty, including classical set theory, probability theory, and fuzzy set theory, which shape what these measures can reveal about community structure. In this paper, we propose a unified theoretical framework that links commonly used diversity indices to their underlying models of uncertainty, thereby clarifying the ecological and mathematical meaning of the information they summarize. As one of our main results, we show that Rao’s quadratic diversity, one of the best known indices of functional diversity, can be interpreted as a measure of strife or discord for a set of functionally overlapping species. We further demonstrate that Rao’s diversity can be expressed as the mathematical expectation of the fuzzy specificity (or functional distinctiveness) of the individual species in the community, thereby revealing a closer ecological and statistical connection between these two forms of uncertainty than previously recognized. Overall, our approach provides an integrated perspective on the relationship between uncertainty theory and biodiversity measurement, offering new insights for understanding ecological processes and for developing more coherent and informative biodiversity indices. https://doi.org/10.32942/X22M26 Life Sciences, Physical Sciences and Mathematics Functional distinctiveness, Fuzzy sets, Information theory, Rao quadratic diversity, Shannon entropy, Simpson diversity, Species richness, Specificity, Uncertainty Published: 2026-02-06 09:53 Last Updated: 2026-02-06 09:53 CC BY Attribution 4.0 International Conflict of interest statement: None Data and Code Availability Statement: Not applicable Language: English