Analyzing community-weighted trait means across environmental gradients: should phylogeny stay or should it go?

Functional traits mediate ecological responses of organisms to the environment, determining community structure. Community-weighted trait means (CWM) are often used to characterize communities by combining information on species traits and distribution. Relating CWM variation to environmental gradients allows for evaluating species sorting across the metacommunity, either based on correlation tests or ordinary least squares (OLS) models. Yet, it is not clear if phylogenetic signal in both traits and species distribution affect those analyses. On one hand, phylogenetic signal might indicate niche conservatism along clade evolution, reinforcing the environmental signal in trait assembly patterns. On the other hand, it might introduce phylogenetic autocorrelation to mean trait variation among communities. Under this latter scenario, phylogenetic signal might inflate type I error in analysis relating CWM variation to environmental gradients. We explore multiple ways phylogenetic history may influence analysis relating CWM to environmental gradients. We propose the concept of neutral trait diffusion, which predicts that for a functional trait x, CWM variation among local communities does not deviate from the expectation that x evolved according to a neutral evolutionary process. Based on this framework we introduce a graphical tool called neutral trait diffusion representation (NTDR) that allows for the evaluation of whether it is necessary to carry out phylogenetic correction in the trait prior to analyzing the association between CWM and environmental gradients. We illustrate the NTDR approach using simulated traits, phylogenies and metacommunities. We show that even under moderate phylogenetic signal in both the trait used to define CWM and species distribution across communities, OLS models relating CWM variation to environmental gradients lead to inflated type I error when testing the null hypothesis of no association between CWM and environmental gradient. To overcome this issue, we propose a phylogenetic correction for OLS models and evaluate its statistical performance (type I error and power). Phylogeny-corrected OLS models successfully control for type I error in analysis relating CWM variation to environmental gradients but may show decreased power. Combining the exploratory tool of NTDR and phylogenetic correction in traits, when necessary, guarantees more precise inferences about the environmental forces driving trait-mediated species sorting across metacommunities.