Second, increased data availability often leads to data dependency over space, time, or both, thus to violation of the assumptions of many statistical tests. It is still not clear whether, and to what extent, spatial or temporal autocorrelation and collinearity contribute to the inconsistency in earlier studies. In our particular case, spatial autoregressions confirm the results from multiple regressions and increase confidence in data interpretation. The OLS and SAR gave consistent results (Table S1), suggesting that the explanatory variables are also spatially autocorrelated (see Fig. S1). Thus, removing any autocorrelation among the explanatory variables would also remove most of the explanatory power of the explanatory variables. Unlike the native or exotic richness and exotic fraction, the residuals of most variables do not exhibit spatial autocorrelations (V. Jarosik, Personal Communications; see also Dormann et al. 2007, Pyšek et al. 2010). Therefore, in agreement with findings by social scientists at the state-level by Wasserman and Stack (1995), spatial autocorrelation does not seem to be a serious problem in our analyses at the state scale. However, the spatial autocorrelations of different variables over varied distance intervals do offer additional details regarding their spatial patterns and could potentially reflect the effects of underlying ecological gradients.
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