Which results of the standard test in community weighted mean approach are too optimistic?

Abstract

QuestionsCommunity weighted mean (CWM) approach analyses the relationship species attributes (like traits or Ellenberg-type indicator values) to sample attributes (environmental variables). Recently it has been shown to suffer from inflated Type I error rate if tested by standard parametric or (row-based) permutation test. Results of many published studies are likely influenced, reporting overly optimistic relationships that are in fact merely a numerical artefact. Can we evaluate results of which studies are likely to be influenced and how much?\n\nMethodsI suggest that hypotheses commonly tested by CWM approach are classified into three categories, which differ by assumption they make about the link of species composition to either species or sample attributes. I used a set of simulated and one simple real dataset to show how is the inflated Type I error rate influenced by data characteristics.\n\nResultsFor hypotheses assuming the link of species composition to species attributes, CWM approach with standard test returns correct Type I error rate. However, for the other two categories (assuming link of species composition to sample attributes or not assuming any link) it returns inflated Type I error rate and requires alternative tests to control for it (column-based and max test, respectively). Inflation index is negatively related to the beta diversity of species composition and positively to the strength of species composition-sample attributes relationship and the number of samples in the dataset. Inflation index is also influenced by modifying species composition matrix (by transformation or removal of species). The relationship of CWM with intrinsic species attributes is a case of spurious correlation and can be tested by column-based (modified) permutation test.\n\nConclusionsThe concept of three hypothesis categories offers a simple tool to evaluate whether given study reports correct or inflated Type I error rate, and how inflated the rate can be.