Spatial autocorrelation and the scaling of species-environment relationships.

Issues of residual spatial autocorrelation (RSA) and spatial scale are critical to the study of species-environment relationships, because RSA invalidates many statistical procedures, while the scale of analysis affects the quantification of these relationships. Although these issues independently are widely covered in the literature, only sparse attention is given to their integration. This paper focuses on the interplay between RSA and the spatial scaling of species-environment relationships. Using a hypothetical species in an artificial landscape, we show that a mismatch between the scale of analysis and the scale of a species' response to its environment leads to a decrease in the portion of variation explained by environmental predictors. Moreover, it results in RSA and biased regression coefficients. This bias stems from error-predictor dependencies due to the scale mismatch, the magnitude of which depends on the interaction between the scale of landscape heterogeneity and the scale of a species' response to this heterogeneity. We show that explicitly considering scale effects on RSA can reveal the characteristic scale of a species' response to its environment. This is important, because the estimation of species-environment relationships using spatial regression methods proves to be erroneous in case of a scale mismatch, leading to spurious conclusions when scaling issues are not explicitly considered. The findings presented here highlight the importance of examining the appropriateness of the spatial scales used in analyses, since scale mismatches affect the rigor of statistical analyses and thereby the ability to understand the processes underlying spatial patterning in ecological phenomena.