Assessing the efficiency of clustering algorithms and goodness-of-fit measures using phytoplankton field data

a r t i c l e i n f o Keywords: 2-norm Cophenetic correlation coefficient Beta diversity Dendrogram UPGMA Ward's algorithm 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 suit-ability is the cophenetic correlation coefficient c. Alternatively the 2-norm has been recently proposed as an increasingly informative method for evaluating the distortion engendered by clustering algorithms. In the present work, the 2-norm 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 2-norm, 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 2-norm revealed that UPGMA is the most efficient clustering algorithm and Ward's the least. The present results suggest that goodness-of-fit measures such as the 2-norm should be applied prior to clustering analyses for reliable beta diversity measures. Enhancing our knowledge of the processes that shape variability in community structure (beta diversity) remains one of the fundamental challenges in contemporary community ecology (Condit et al., 2002; Gaston et al., 2007; Tuomisto et al., 2003). To meet this challenge , applications of multivariate statistics in community ecology have expanded significantly during the last two decades (Dray and Among multivariate statistical methods, ordination and clustering are now routinely applied by ecologists to explore the spatial or temporal turnover of field communities (e.g. Among clustering methods, those based on a hierarchy of clusters have been used in many research fields (e.g. Torrente-Vilara et al., 2011). Hierarchical clustering analysis is subdivided into agglomerative and divisive methods, the former being most common in ecological studies (Clarke and Warwick, 2001). All ag-glomerative procedures begin with an initial matrix (I) which is then transformed in inter-objects/samples matrix (D) using a relevant distance measure whose selection depends on the scientific question (see Fig. 1). …