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

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.

Checklist of climbing plants in an Araucaria forest of Rio Grande do Sul State, Brazil

“…To analyze sites relationship according to species composition and traits proportion (dispersal syndromes and climbing mechanisms) we performed separate cluster analyses, using Ward's clustering criterion and evaluating groups partition sharpness through 10,000 bootstrap resampling (Pillar 1999). As resemblance measurements between sites, we used the complement of Jaccard's similarity for species composition, and a modification of Gower's distance (Pavoine et al 2009) for traits proportion. We also performed Fisher's exact tests with 10,000 Monte Carlo test replicates to evaluate whether there was a difference in the frequency of dispersal syndromes and climbing mechanisms between all sites.…”

Spatial variation of mammal richness, functional and phylogenetic diversity in the Mexican transition zone

“…FD measures the functional diversity of species traits, so that functionally different species account for higher values in FD. We used Gower distance (Pavoine et al 2009), which is an adequate multivariate distance to use with both quantitative and qualitative variables (Podani and Schmera 2006) and average linkage was used in the analysis to maximize cophenetic relationships and maintain the structure of the original dissimilarity Gaston 2002, 2006). Functional traits were obtained from published literature Oliva 2005, Aranda 2012) and databases such as PanTheria (Jones et al 2009) and Animal Diversity Web (Myers et al 2015).…”

Fish complementarity is associated to forests in Amazonian streams

“…To obtain the functional dendrogram we assembled a standardized matrix of ecomorphological traits (with zero mean and unit variance) by species and used the function "dist.ktab" in the software R (R Development Core Team, 2011), based on the distance matrix obtained by the generalization of Gower's distance. We used the unweighted pair-group method using arithmetic averages (UPGMA) clustering method (Pavoine et al, 2009). NRI and NTI were originally described by Webb (2000) for phylogenetic diversity and are considered relevant to represent the functional structure (Hidasi-Neto et al, 2012).…”