Decomposing environmental, spatial, and spatiotemporal components of species distributions
- Species distribution models are an important tool to predict the impact of global change on species distributional ranges and community assemblages. Although considerable progress has been made in the statistical modeling during the last decade, many approaches still ignore important features of species distributions, such as nonlinearity and interactions between predictors, spatial autocorrelation, and nonstationarity, or at most incorporate only some of these features. Ecologists, however, require a modeling framework that simultaneously addresses all these features flexibly and consistently. Here we describe such an approach that allows the estimation of the global effects of environmental variables in addition to local components dealing with spatiotemporal autocorrelation as well as nonstationary effects. The local components can be used to infer unknown spatiotemporal processes; the global component describes how the species is influenced by the environment and can be used for predictions, allowing the fitting of many well-knownSpecies distribution models are an important tool to predict the impact of global change on species distributional ranges and community assemblages. Although considerable progress has been made in the statistical modeling during the last decade, many approaches still ignore important features of species distributions, such as nonlinearity and interactions between predictors, spatial autocorrelation, and nonstationarity, or at most incorporate only some of these features. Ecologists, however, require a modeling framework that simultaneously addresses all these features flexibly and consistently. Here we describe such an approach that allows the estimation of the global effects of environmental variables in addition to local components dealing with spatiotemporal autocorrelation as well as nonstationary effects. The local components can be used to infer unknown spatiotemporal processes; the global component describes how the species is influenced by the environment and can be used for predictions, allowing the fitting of many well-known regression relationships, ranging from simple linear models to complex decision trees or from additive models to models inspired by machine learning procedures. The reliability of spatiotemporal predictions can be qualitatively predicted by separately evaluating the importance of local and global effects. We demonstrate the potential of the new approach by modeling the breeding distribution of the Red Kite (Milvus milvus), a bird of prey occurring predominantly in Western Europe, based on presence/absence data from two mapping campaigns using grids of 40 km 2 in Bavaria. The global component of the model selected seven environmental variables extracted from the CORINE and WorldClim databases to predict Red Kite breeding. The effect of altitude was found to be nonstationary in space, and in addition, the data were spatially autocorrelated, which suggests that a species distribution model that does not allow for spatially varying effects and spatial autocorrelation would have ignored important processes determining the distribution of Red Kite breeding across Bavaria. Thus, predictions from standard species distribution models that do not allow for real-world complexities may be considerably erroneous. Our analysis of Red Kite breeding exemplifies the potential of the innovative approach for species distribution models. The method is also applicable to modeling count data.…
