Accounting for the space-varying nature of the relationships between temporal community turnover and the environment.

Non-spatial regression models are rarely adequate for exploring ecological phenomena, especially in settings where the processes operate at large spatial scales and when model covariates do not explain all variation present in the outcome variable. Given the complexity of ecological processes, it is often unrealistic to assume a set of stationary regression coefficients can capture space-varying and scale-dependent relationships between covariates and an ecological response. Spatially-varying coefficients (SVC) models fit within a Bayesian inferential framework provide a statistically robust method to explore potential space-varying and scale-dependent impacts of covariates. Our study objective was to assess the utility of SVC models for capturing non-stationary relationships between temporal community dynamics in avian assemblages and variation in environmental factors. We also wanted to compare the inference drawn from SVC models to that obtained from space-varying intercept models and also models that do not acknowledge any spatial structure beyond what is introduced by the covariates. Our analysis examines the temporal turnover, expressed as a proportion, of avian communities across New York State, USA. Given the expected outcome is non-Gaussian, we detail a generalized linear model specification of the proposed model structures. Our results show the SVC model outperformed the spatially-varying intercept and non-spatial models in terms of model fit and model predictive inference. Further, by fitting these models within a Bayesian inferential framework, we were able to make inferences about the spatial impact of covariates and other process parameters, as well as obtain full posterior predictive inference about the rate of turnover at new, unobserved locations. We conclude that SVC models provide a flexible framework for exploring and accounting for non-stationary mechanisms driving ecological patterns. [ABSTRACT FROM AUTHOR]