New robust weighted averaging‐ and model‐based methods for assessing trait–environment relationships. Issue 11 (7th October 2019) - ter Braak, Cajo J. F.
Abstract: Statistical analysis of trait–environment association is challenging owing to the lack of a common observation unit: Community‐weighted mean regression (CWMr) uses site points, multilevel models focus on 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, called MLM3, has additional site‐related random effects; they represent the unknowns in the environment that interact with the trait. The new weighted averaging method combines site‐level CWMr with a species‐level regression of Species Niche Centroids on to the trait. Because species can vary enormously in frequency and abundance giving diversity variation among sites, 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 weak evidence. In simulations, the existing multilevel model showed bias and type I error inflation, whereas MLM3 did not. Out of the weighted averaging‐based regression methods, the N 2 ‐weighted version best controlled the type I error rate. MLM3 was superior to the weighted averaging‐based methods with up to 30% more power. Both methods can be extended (a) to account for phylogeny and spatial autocorrelation and (b) to select functional traits and environmental variables from a greater set of variables.