On the challenge of treating various types of variables: application for improving the measurement of functional diversity

TLDR

Functional diversity is central to conservation biology, yet most diversity indices depend on variables of diverse statistical types—circular, fuzzy, ordinal—that require species‑distance matrices. The study aims to show how to compute species distances using a generalized Gower's distance that handles mixed data. This is accomplished by extending Gower's distance to include new data types and applying it to mixed data, allowing efficient treatment of missing values and variable weighting. The authors prove the extension works, illustrate its impact on an 80‑species plant dataset, and conclude that the generalized index will be crucial for functional diversity analysis at both small and large scales.

Abstract

Functional diversity is at the heart of current research in the field of conservation biology. Most of the indices that measure diversity depend on variables that have various statistical types (e.g. circular, fuzzy, ordinal) and that go through a matrix of distances among species. We show how to compute such distances from a generalization of Gower's distance, which is dedicated to the treatment of mixed data. We prove Gower's distance can be extended to include new types of data. The impact of this generalization is illustrated on a real data set containing 80 plant species and 13 various traits. Gower's distance allows an efficient treatment of missing data and the inclusion of variable weights. An evaluation of the real contribution of each variable to the mixed distance is proposed. We conclude that such a generalized index will be crucial for analyzing functional diversity at small and large scales.