Stronger Evidence for Trait–Environment Association by Pre-processing of Abundance Tables

Cajo ter Braak 

Understanding trait–environment relationships is central to predicting community responses to environmental change, yet statistical evidence for such relationships is often weak in observational datasets. Here, I introduce an N2-processing method for abundance tables, grounded in the observation that the precision of community weighted means (CWMs) and species niche centroids (SNCs) is proportional to Hill’s effective number N2. I refine this concept by defining informativeness, which down weights ubiquitous species whose abundances provide little environmental information. The resulting species and site weights are implemented through iterative proportional fitting (IPF), which preserves the species–site interaction structure while aligning totals with informativeness and effective numbers.
The performance of N2-processing was evaluated using simulations and 80 published trait–environment datasets from the CESTES global database, analyzed with fourth corner correlation analysis (FC), RLQ, and double constrained correspondence analysis (dc CA). In simulations, N2-processing substantially increased the power of the max test, especially when abundances were untransformed. In the CESTES analyses, the proportion of datasets exhibiting at least weak trait–environment association increased from 13% when using FC with multiple testing adjustment to 68% when using dc CA with N2 processing. The improvement was largest when associations were weak and diminished when strong prior abundance transformations (such as the logarithmic transformation) had already down weighted dominant species.
A square root abundance transformation followed by N2 processing is recommended as an effective and robust approach to strengthening inference on trait–environment relationships. The N2 processing is essential because it removes arbitrary, data analytic choices and ensures that dc CA operates under conditions that match the assumptions of the model it is testing.