Extending the CWM approach to intraspecific trait variation: how to deal with overly optimistic standard tests?

Community weighted means (CWMs) are widely used to study the relationship between community-level functional traits and environment. For certain null hypotheses, CWM-environment relationships assessed by linear regression or ANOVA and tested by standard parametric tests are prone to inflated Type I error rates. Previous research has found that this problem can be solved by permutation tests (i.e., the max test). A recent extension of the CWM approach allows the inclusion of intraspecific trait variation (ITV) by the separate calculation of fixed, site-specific, and intraspecific CWMs. The question is whether the same Type I error rate inflation exists for the relationship between environment and site-specific or intraspecific CWM. Using simulated and real-world community datasets, we show that site-specific CWM-environment relationships have also inflated Type I error rate, and this rate is negatively related to the relative ITV magnitude. In contrast, for intraspecific CWM-environment relationships, standard parametric tests have the correct Type I error rate, although somewhat reduced statistical power. We introduce an ITV-extended version of the max test, which can solve the inflation problem for site-specific CWM-environment relationships and, without considering ITV, becomes equivalent to the "original" max test used for the CWM approach. We show that this new ITV-extended max test works well across the full possible magnitude of ITV on both simulated and real-world data. Most real datasets probably do not have intraspecific trait variation large enough to alleviate the problem of inflated Type I error rate, and published studies possibly report overly optimistic significance results.