Functional traits and community composition: A comparison among community‐weighted means, weighted correlations, and multilevel models. Issue 3 (9th December 2018) - Miller, Jesse E. D.; Damschen, Ellen I.; Ives, Anthony R.
Abstract: Of the several approaches that are used to analyse functional trait–environment relationships, the most popular is community‐weighted mean regressions (CWMr) in which species trait values are averaged at the site level and then regressed against environmental variables. Other approaches include model‐based methods and weighted correlations of different metrics of trait–environment associations, the best known of which is the fourth‐corner correlation method. We investigated these three general statistical approaches for trait–environment associations: CWMr, five weighted correlation metrics (Peres‐Neto, Dray, & ter Braak, Ecography, 40, 806–816, 2017), and two multilevel models (MLM) using four different methods for computing p ‐values. We first compared the methods applied to a plant community dataset. To determine the validity of the statistical conclusions, we then performed a simulation study. CWMr gave highly significant associations for both traits, whereas the other methods gave a mix of support. CWMr had inflated type I errors for some simulation scenarios, implying that the significant results for the data could be spurious. The weighted correlation methods had generally good type I error control but had low power. One of the multilevel models, that from Jamil, Ozinga, Kleyer, and ter Braak ( Journal of Vegetation Science, 24, 988–1000, 2013) had both good type I error control and high power when an appropriate method was used to obtain p ‐values. In particular, if there was no correlation among species in their abundances among sites, a parametric bootstrap likelihood ratio test (LRT) gave the best power. When there was correlation among species in their abundances, a conditional parametric LRT had correct type I errors but had lower power. There is no overall best method for identifying trait–environment associations. For the simple task of testing associations between single environmental variables and single traits, the weighted correlations with permutation tests all had good type I error control, and their ease of implementation is an advantage. For the more complex task of multivariate analyses and model fitting, and when high statistical power is needed, we recommend MLM2 (Jamil et al., 2013). However, care must be taken to ensure against inflated type I errors for both weighted correlations and MLM2. Because CWMr exhibited highly inflated type I error rates, it should always be avoided.