Assessing the joint behaviour of species traits as filtered by environment

Understanding and predicting how species traits are shaped by prevailing environmental conditions is an important yet challenging task in ecology. Functional trait-based approaches can replace potentially idiosyncratic species-specific response models in learning about community behaviour across environmental gradients. Customarily, models for traits given environment consider only trait means to predict species and functional diversity, as intra-taxon variability in traits is often thought to be negligible. A growing body of literature indicates that intra-taxon trait variability is substantial and critical in structuring plant communities and assessing ecosystem function. We propose flexible joint trait distribution models given environment and across species that incorporate intra-taxon variability as well as inter-site/plot variability. Using a Bayesian framework, our joint trait distribution models allow for mixed continuous, binary and ordinal trait variables and incorporate dependence among traits enabling both joint and conditional trait prediction at unobserved sites. The models can be used to inform about the well-known fourth-corner problem, which attempts to interpret trait-by-environment matrices. We demonstrate the utility of our methodology through joint predictive trait distributions for individual species as well as joint community-weighted trait distributions for environments while incorporating intra-taxon trait variability. Explicit details on the probabilistic interpretations of the random trait-by-environment matrices obtained arising under our model are also provided to address the fourth-corner problem. Finally, our joint trait distribution model is applied to simulated and real vegetation data collected from the Greater Cape Floristic Region of South Africa. The proposed methodology places a fully model-based foundation on explaining intra-taxon trait variation given environment. It extends the utility and interpretability of commonly applied techniques for investigating community-weighted traits and illuminates randomness in the fourth-corner problem.