CATS regression - a model-based approach to studying trait-based community assembly

Shipley, Vile & Garnier (Science 2006; 314: 812) proposed a maximum entropy approach to studying how species relative abundance is mediated by their traits, community assembly via trait selection' (CATS). In this paper, we build on recent equivalences between the maximum entropy formalism and Poisson regression to show that CATS is equivalent to a generalized linear model for abundance, with species traits as predictor variables. Main advantages gained by access to the machinery of generalized linear models can be summarized as advantages in interpretation, model checking, extensions and inference. A more difficult issue, however, is the development of valid methods of inference for single-site data, as species correlation in abundance is not accounted for in CATS (whether specified as a regression or via maximum entropy). This issue can be circumvented for multisite data using design-based inference. These points are illustrated by example - our plant abundances were found to violate the implicit Poisson assumption of CATS, but a negative binomial regression had much improved fit, and our model was extended to multisite data in order to directly model the environment-trait interaction. Violations of the Poisson assumption were strong and accounting for them qualitatively changed results, presumably because larger counts had undue influence when overdispersion had not been accounted for. We advise that future CATS analysts routinely check for overdispersion and account for it if present.