Evaluating the Predictive Power of Ordination Methods in Ecological Context

When striving for the ordination methods best predicting independently measured site factors, the following questions arise: does the optimal choice depend on the kind of biological community analysed? Are there different ordination methods needed to address different site factors? Simultaneously, I explore alternative similarity approaches of entire ordinations, as well as the role of the transformations applied to the scale used in measuring species performance. The combination of methods and data transformations results in 96 alternative solutions for any one data set. These are compared by a graphical display, that is, an ordination of ordinations. The goodness-of-fit of independently measured site factors is assessed by two alternative methods. The resulting 96 performance values serve as independent variables in trend surfaces overlaid to the ordination of ordinations. The results from two real-world data sets indicate that some ordination methods greatly vary with data transformation. Scores close to a binary scale perform best in almost all ordination methods. Methods that intrinsically constrain the range of species scores, such as principal components analysis based on correlation, correspondence analysis (including its detrended version), nonmetric multidimensional scaling, as well as principal coordinates analysis based on the Bray-Curtis distance, always figure among the most successful methods, irrespective of data used.