New robust weighted averaging- and model-based methods for assessing trait-environment relationships.

Statistical analysis of trait-environment association is challenging owing to the lack of a common observation unit: Community weighted mean regression (CWM) uses site points, multilevel models use species points, and the fourth corner correlation uses all species-site combinations. This situation invites the development of new methods capable of using all observation-levels. To this end, new multilevel and weighted averaging-based regression methods are proposed. Compared to existing methods, the new multilevel method has additional site-related random effects that are unrelated to the observed environment; they represent the unknowns in the environment that interact with the trait. The new weighted averaging method combines site-level CWM with a species-level regression of Species Niche Centroids (SNC) on to the trait. The regressions are weighted by Hill's effective number ( N 2 ) of occurrences of each species and the N 2 -diversity of a site, and are subsequently combined in a sequential test procedure known as the max-test. Using the test statistics of these new methods, the permutation-based max test provides strong statistical evidence for trait-environment association in a plant community dataset, where existing methods show (very) weak evidence. The powers of the two new methods were similar in a simulation study based on this dataset. Both methods can be extended i) to account for phylogeny and spatial autocorrelation and ii) to select functional traits and environmental variables from a greater set of variables.