Strong influence of variable treatment on the performance of numerically defined ecological regions

Numerical clustering has frequently been used to define hierarchically organized ecological regionalizations, but there has been little robust evaluation of their performance (i.e., the degree to which regions discriminate areas with similar ecological character). In this study we investigated the effect of the weighting and treatment of input variables on the performance of regionalizations defined by agglomerative clustering across a range of hierarchical levels. For this purpose, we developed three ecological regionalizations of Switzerland of increasing complexity using agglomerative clustering. Environmental data for our analysis were drawn from a 400 m grid and consisted of estimates of 11 environmental variables for each grid cell describing climate, topography and lithology. Regionalization 1 was defined from the environmental variables which were given equal weights. We used the same variables in Regionalization 2 but weighted and transformed them on the basis of a dissimilarity model that was fitted to land cover composition data derived for a random sample of cells from interpretation of aerial photographs. Regionalization 3 was a further two-stage development of Regionalization 2 where specific classifications, also weighted and transformed using dissimilarity models, were applied to 25 small scale "sub-domains" defined by Regionalization 2. Performance was assessed in terms of the discrimination of land cover composition for an independent set of sites using classification strength (CS), which measured the similarity of land cover composition within classes and the dissimilarity between classes. Regionalization 2 performed significantly better than Regionalization 1, but the largest gains in performance, compared to Regionalization 1, occurred at coarse hierarchical levels (i.e., CS did not increase significantly beyond the 25-region level). Regionalization 3 performed better than Regionalization 2 beyond the 25-region level and CS values continued to increase to the 95-region level. The results show that the performance of regionalizations defined by agglomerative clustering are sensitive to variable weighting and transformation. We conclude that large gains in performance can be achieved by training classifications using dissimilarity models. However, these gains are restricted to a narrow range of hierarchical levels because agglomerative clustering is unable to represent the variation in importance of variables at different spatial scales. We suggest that further advances in the numerical definition of hierarchically organized ecological regionalizations will be possible with techniques developed in the field of statistical modeling of the distribution of community composition.