Simple parametric tests for trait–environment association

Question: The CWM approach is an easy way of analysing trait–environment association by regressing (or correlating) the mean trait per plot against an environmental variable and assessing the statistical significance of the slope or the associated correlation coefficient. However, the CWM approach does not yield valid tests, as random traits (or random indicator values) are far too often judged significantly related to the environmental variable, even when the trait and environmental variable are extrinsic to (not derived from) the community data. Existing solutions are the ZS-modified test (Zelený & Schaffers,) and the max (or sequential) test based on the fourth-corner correlation. Both tests are based on permutations which become cumbersome when many tests need to be carried out and many permutations are required, as in methods that correct for multiple testing. The main goal of this study was to compare these existing permutation-based solutions and to develop a quick and easy parametric test that can replace them. Methods: This study decomposes the fourth-corner correlation in two ways, which suggests a simple parametric approach consisting of assessing the significances of two linear regressions, one plot-level test as in the CWM approach and one species-level test, the reverse of the CWM approach, that regresses the environmental mean per species (i.e. the species niche centroid) on to the trait. The tests are combined by taking the maximum p-value. The type I error rates and power of this parametric max test are examined by simulation of one- and two-dimensional Gaussian models and log-linear models. Results: The ZS-modified test and the fourth-corner max test are conservative in different scenarios, the ZS-modified test being even more conservative than the fourth-corner. The new parametric max test is shown to control the type I error and has equal or even higher power than permutation tests based on the fourth-corner, the ZS-modified test and variants thereof. A weighted version of the new test showed inflated type I error. Conclusion: The combination of two simple regressions is a good alternative to the fourth-corner and the ZS-modified test. This combination is also applicable when multiple trait measurements are made per plot.