A wavelet-based method to remove spatial autocorrelation in the analysis of species distributional data

Accepted 4 April 2008 Copyright © EEF ISSN 1399-1183 Species distributional models based on lattice data often display spatial autocorrelation. Spatial autocorrelation means that observations from nearby locations are often more similar than would be expected on a random basis (Legendre and Legendre 1998). Spatial autocorrelation can arise in both species distributions and environmental variables. Note that statistical analyses of such data need not be seen as problematic in principle. However, a chosen method is inconsistent with its application, if and only if (1) these autocorrelated variables lead to autocorrelated errors and (2) independently and identically distributed (i.i.d.) errors are assumed in the used statistical model. In that case results of the method are not reliable (Kühn 2007). There are several reasons for autocorrelated errors in linear regressions (Kissling and Carl 2008). (1) Response variables, e.g. species distributions are spatially structured due to endogenous properties such as, e.g. dispersal, speciation, and extinction. Because structure is only inherent in the response variable, it can not be explained by explanatory environmental variables. Therefore, it leaves its mark on the regression errors. (2) Response variables are spatially structured due to exogenous properties such as specific environmental variables, e.g. wind or other climatic constraints. In the model, however, the very same variables are either not included or improperly used due to neglected non-linear transformations. Here the spatial structure, in turn, affects the errors. A wavelet-based method to remove spatial autocorrelation in the analysis of species distributional data