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 variation. When relationships between CWM traits and environmental variables are directly assessed using linear regression or ANOVA and tested by standard parametric tests, results are prone to inflated Type I error rates, thus producing overly optimistic results. Previous research has found that this problem can be solved by permutation tests (i.e. the max test). A recent extension of this CWM approach, that allows the inclusion of intraspecific trait variation (ITV) by partitioning information in fixed, site-specific and intraspecific CWMs, has proven popular. However, this raises the question whether the same kind of Type I error rate inflation also exists for site-specific CWM or intraspecific CWM-environment relationships. Using simulated community datasets and a real-world dataset from a subtropical montane cloud forest in Taiwan, we show that site-specific CWM-environment relationships also suffer from Type I error rate inflation, and that the severity of this inflation 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, while being somewhat conservative, with reduced statistical power. We introduce an ITV-extended version of the max test for the ITV-extended CWM approach, which can solve the inflation problem for site-specific CWM-environment relationships, and which, without considering ITV, becomes equivalent to the "original" max test used for the CWM approach. On both simulated and real-world data, we show that this new ITV-extended max test works well across the full possible magnitude of ITV. We also provide guidelines and R codes of max test solutions for each CWM type and situation. Finally, we suggest recommendations on how to handle the results of previously published studies using the CWM approach without controlling for Type I error rate inflation.