Carteron, A., Jeanmougin, M., Leprieur, F., & Spatharis, S. (2012). Assessing the efficiency of clustering algorithms and goodnessoffit measures using phytoplankton field data. Ecol. Inform., 9, 64–68.
Résumé: Investigation of patterns in beta diversity has received increased attention over the last years particularly in light of new ecological theories such as the metapopulation paradigm and metacommunity theory. Traditionally, beta diversity patterns can be described by cluster analysis (i.e. dendrograms) that enables the classification of samples. Clustering algorithms define the structure of dendrograms, consequently assessing their performance is crucial. A common, although not always appropriate approach for assessing algorithm suitability is the cophenetic correlation coefficient c. Alternatively the 2norm has been recently proposed as an increasingly informative method for evaluating the distortion engendered by clustering algorithms. In the present work, the 2norm is applied for the first time on field data and is compared with the cophenetic correlation coefficient using a set of 105 pairwise combinations of 7 clustering methods (e.g. UPGMA) and 15 (dis)similarity/distance indices (e.g. Jaccard index). In contrast to the 2norm, cophenetic correlation coefficient does not provide a clear indication on the efficiency of the clustering algorithms for all combinations. The two approaches were not always in agreement in the choice of the most faithful algorithm. Additionally, the 2norm revealed that UPGMA is the most efficient clustering algorithm and Ward's the least. The present results suggest that goodnessoffit measures such as the 2norm should be applied prior to clustering analyses for reliable beta diversity measures. (C) 2012 Elsevier B.V. All rights reserved.

Maire, E., Grenouillet, G., Brosse, S., & Villeger, S. (2015). How many dimensions are needed to accurately assess functional diversity? A pragmatic approach for assessing the quality of functional spaces. Global Ecology and Biogeography, 24(6), 728–740.
Résumé: Aim Functional diversity is a key facet of biodiversity that is increasingly being measured to quantify its changes following disturbance and to understand its effects on ecosystem functioning. Assessing the functional diversity of assemblages based on species traits requires the building of a functional space (dendrogram or multidimensional space) where indices will be computed. However, there is still no consensus on the best method for measuring the quality of functional spaces. Innovation Here we propose a framework for evaluating the quality of a functional space (i.e. the extent to which it is a faithful representation of the initial functional trait values). Using simulated datasets, we analysed the influence of the number and type of functional traits used and of the number of species studied on the identity and quality of the best functional space. We also tested whether the quality of the functional space affects functional diversity patterns in local assemblages, using simulated datasets and a real study case. Main conclusions The quality of functional space strongly varied between situations. Spaces having at least four dimensions had the highest quality, while functional dendrograms and twodimensional functional spaces always had a low quality. Importantly, we showed that using a poorquality functional space could led to a biased assessment of functional diversity and false ecological conclusions. Therefore, we advise a pragmatic approach consisting of computing all the possible functional spaces and selecting the most parsimonious one.

Villeger, S., Maire, E., & Leprieur, F. (2017). On the risks of using dendrograms to measure functional diversity and multidimensional spaces to measure phylogenetic diversity: a comment on Sobral et al. (2016). Ecol. Lett., 20(4), 554–557.
Résumé: Sobral et al. (Ecology Letters, 19, 2016, 1091) reported that the loss of bird functional and phylogenetic diversity due to species extinctions was not compensated by exotic species introductions. Here, we demonstrate that the reported changes in biodiversity were underestimated because of methodological pitfalls.
