Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species' distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing

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We examine the advantages and disadvantages of a methodological framework designed to analyze the poorly understood relationships between the ecosystem properties of large portions of land, and their capacities (stocks) to provide goods and services (flows). These capacities (stocks) are referred to as landscape functions. The core of our assessment is a set of expert-and literaturedriven binary links, expressing whether specific land uses or other environmental properties have a supportive or neutral role for given landscape functions. The binary links were applied to the environmental properties of 581 administrative units of Europe with widely differing environmental conditions and this resulted in a spatially explicit landscape function assessment. To check under what circumstances the binary links are able to replace complex interrelations, we compared the landscape function maps with independently generated continent-wide assessments (maps of ecosystem services or environmental parameters/ indicators). This rigorous testing revealed that for 9 out of 15 functions the straightforward binary links work satisfactorily and generate plausible geographical patterns. This conclusion holds primarily for production functions. The sensitivity of the nine landscape functions to changes in land use was assessed with four land use scenarios (IPCC SRES). It was found that most European regions maintain their capacity to provide the selected services under any of the four scenarios, although in some cases at other locations within the region. At the proposed continental scale, the selected input parameters are thus valid proxies which can be used to assess the mid-term potential of landscapes to provide goods and services.

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