le CATS regression – a model - based approach to study - ing trait - based community assembly

1. Shipley et al. (2006) proposed a maximum entropy approach to studying how species relative abundance is mediated by their traits, “community assembly via trait selection” (CATS). 2. In this paper we build on recent equivalences between the maximum entropy formalism and Poisson regression to show that CATS is equivalent to a generalised linear model for abundance, with species traits as predictor variables. 3. Main advantages gained by access to the machinery of generalised linear models can be summarised as advantages in interpretation, model-checking, extensions and inference. 4. 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 multi-site data using design-based inference. 5. 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 multi-site 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.