Evaluation of relevant species in communities: Development of structuring indices for the classification of communities using a self-organizing map

Ecological data are mostly multivariate, characterizing complexity and nonlinearity and some information in the data is only interpretable indirectly (Jongman et al. 1995). Ecological interpretation and especially the explanation of the structure of several descriptors (i.e., multivariate data) can be carried out following two approaches: direct or indirect comparison schemes (Legendre and Legendre 1998) which refer to direct gradient analysis and indirect gradient analysis respectively (ter Braak 1987). The former includes principal component analysis (PCA) and correspondence analysis, whereas the latter includes canonical correspondence analysis, redundancy analysis, and canonical correlation analysis. However, these conventional multivariate methods are mainly based on the linear data matrix limiting the usages due to strong distortions with nonlinear relations in the dataset (Kenkel and Orloci 1986, Bunn et al. 1986, Ludwig and Reynolds 1988, Legendre and Legendre 1998). Due to the nonlinearity and complexity of ecological data, nonlinear analyzing methods are preferred (Blayo and Demartines 1991, Lek and Guegan 2000). One of these methods is artificial neural networks (ANNs), which are versatile tools to extract information out of complex data, and which could be effectively applicable to classification and association (i.e., presentation with fewer space dimensions). Among ANNs, recently a self-organizing map (SOM) has become more and more popular in ecological studies. The SOM approximates the probability density function of the input data, and it is a method for clustering, visualization, and abstraction, the idea of which is to show the data set in another, more usable, representation (Kohonen 2001). These characteristics have been used efficiently in various ecological areas (Lek and Guégan 1999, 2000, Recknagel 2003): classification of communities (Chon et al. 1996, Park et al. 2001a, 2003a); identification of community patterns (Brosse et al. 2001), water quality assessments (Walley et al. 2000, Aguilera et al. 2001), and prediction of population and community structure (Céréghino et al. 2001, Obach et al. 2001). Recently Park et al. (2003a) proposed a method to integrate the relationships between sampling sites (or clusters), biological attributes, and environmental variables in the SOM map. They showed the distribution gradient of each variable on the SOM map, presenting the importance of variables concerning communities. However, there are difficulties to quantify the importance of each variable in the patterns defined by the SOM. Therefore, in this study we aim to develop a method to quantify the importance of each variable in the patterns defined in the SOM map. These quantified values can be used as an index of the relative importance of the variables, and will be helpful for the interpretation of ecological data.