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

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.