Functional traits and community composition: multilevel models outperform community-weighted means

1. Plant functional traits are increasingly being used to infer mechanisms about community assembly and predict global change impacts. Of the several approaches that are used to analyze trait-environment relationships, one of the most popular is community-weighted means (CWM), in which species trait values are averaged at the site level. Other approaches that do not require averaging are being developed, including multilevel models (MLM, also called generalized linear mixed models). However, relative strengths and weaknesses of these methods have not been extensively compared. 2. We investigated three statistical models for trait-environment associations: CWM, a MLM in which traits were not included as fixed effects (MLM1), and a MLM with traits as fixed effects (MLM2). We analyzed a real plant community dataset to investigate associations between two traits and one environmental variable. We then analyzed permutations of the dataset to investigate sources of type I errors, and performed a simulation study to compare the statistical power of the methods. 3. In the analysis of real data, CWM gave highly significant associations for both traits, while MLM1 and MLM2 did not. Using P-values derived by simulating the data using the fitted MLM2, none of the models gave significant associations, showing that CWM had inflated type I errors (false positives). In the permutation tests, MLM2 performed the best of the three approaches. MLM2 still had inflated type I error rates in some situations, but this could be corrected using bootstrapping. The simulation study showed that MLM2 always had as good or better power than CWM. These simulations also confirmed the causes of type I errors from the permutation study. 4. The MLM that includes main effects of traits (MLM2) is the best method for identifying trait-environmental association in community assembly, with better type I error control and greater power. Analyses that regress CWMs on continuous environmental variables are not reliable because they are likely to produce type I errors.