Putting Things in Order: A Critique of Detrended Correspondence Analysis

Methods of ordination are multivariate statistical techniques designed to order individual entities on the basis of the similarities or differences for variables scored for each entity. These methods, most of which are based on linear-model theory, often fail to order entities correctly because of the nonlinear relationships among the observed variables. Under simple assumptions, the joint distribution of entities viewed in multidimensional variable space results in a curved structure that is called the circumplex in psychology, the horseshoe in archaeology, and the arch in ecology. We review the reasons for the formation of this structure and point out the limitations of traditional ordination methods for resolving data with this structure. We argue that detrended correspondence analysis, although designed as a new, improved ordination method, is no better and perhaps worse than traditional methods. All methods are influenced by data curvature and scaling. Until more-effective ordination methods can be developed, we recommend reporting the arch unscaled in two dimensions, even though it is a one-dimensional form.