Linking trait variation to the environment: critical issues with community-weighted mean correlation resolved by the fourth-corner approach

Establishing trait-environment relationships has become routine in community ecology. Here, we demonstrate that the community weighted means correlation (CWM) and its parallel approach in linking trait variation to the environment, the species niche centroid correlation (SNC), have important shortcomings, arguing against their continuing application. Using mathematical derivations and simulations, we show that the two major issues are inconsistent parameter estimation and unacceptable significance rates when only the environment or only traits are structuring species distributions, but they themselves are not linked. We show how both CWM and SNC are related to the fourth-corner correlation and propose to replace all by the Chessel fourth-corner correlation, which is the fourth-corner correlation divided by its maximum attainable value. We propose an appropriate hypothesis testing procedure that is not only unbiased but also has much greater statistical power in detecting trait-environmental relationships. We derive an additive framework in which trait variation is partitioned among and within communities, which can be then modeled against the environment. We finish by presenting a contrast between methods and an application of our proposed framework across 85 lake-fish metacommunities.