Trait-environment association in ecology: from CWM/SNC to fourth corner correlation and double constrained correspondence analysis and a new model-based multi-level model.

This is a slightly edited version of the invited presentation at the CARME 2019 conference in Stellenbosch, South Africa. https://carmesa2019.wixsite.com/conferenceIt summarizes six papers that present new properties of the fourth-corner correlation and (constrained) correspondence analysis in terms of model-based (loglinear GLM & GLMMM) approaches to trait-environment association. The presentation starts with the Community weighted means approach and why it needs to be complemented with a species-level approach, e.g. using Species Niche Centroids. The presentation also shows why the current model-based approaches can give invalid outcomes. A new, more symmetric model is proposed (GLMM3 aka MLM3) and compared with fourth-corner and double constrained correspondence analysis.