Friday, August 6, 2010 - 10:30 AM

COS 117-8: Does the Hellinger transformation make PCA a viable method for community ordination?

Peter R. Minchin and Lauren D. Rennie. Southern Illinois University Edwardsville


Principal Components Analysis (PCA) was one of the earliest methods used for the ordination of community data.  It fell out of favor when studies using simulated data showed that the linear model of PCA leads to curvilinear representation of community gradients in ordination space, a phenomenon known as the "horseshoe effect".  The degree of curvature increases with the beta diversity of the data, making it difficult or impossible to interpret PCA ordinations.  Nevertheless, the use of PCA on community data still has its advocates.  Recently, it has been suggested that the use of a data adjustment, the Hellinger transformation, makes PCA a viable method for community ordination.  To test this hypothesis, we simulated community data over a range of beta diversities and other data properties, with 20 replicate models of each type, and ordinated the data using PCA with and without the Hellinger transformation.  Performance was assessed by rotating the ordinations to best fit with the simulated ecological configuration, using Procrustes analysis.  For comparison, the data were also ordinated using non-metric multidimensional scaling (NMDS) with the Bray-Curtis dissimilarity index and data standardized by species maximum (SMAX), a combination of techniques currently considered to be a robust approach to community ordination. 


As expected, PCA performed poorly without standardization, though performance was better at lower beta diversities.  The Hellinger transformation did improve the ability of PCA to recover the simulated gradients but curvature was still apparent. Even at the lowest beta diversities PCA with the Hellinger transformation was unable to effectively represent all the gradients. NMDS with SMAX consistently outperformed PCA over all beta diversities and other data properties, irrespective of the data standardization employed in PCA.  We conclude that PCA is not appropriate for the ordination of community data, even with the Hellinger transformation.