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Spatial autocorrelation is the lack of independence between pairs of observations at given distances within a geographical space, a phenomenon commonly found in ecological data. Taking into account spatial autocorrelation when evaluating problems in geographical ecology, including gradients in species richness, is important to describe both the spatial structure in data and to correct the bias in Type I errors of standard statistical analyses. However, to effectively solve these problems it is necessary to establish the best way to incorporate the spatial structure to be used in the models. In this paper, we applied autoregressive models based on different types of connections and distances between 181 cells covering the Cerrado region of Central Brazil to study the spatial variation in mammal and bird species richness across the biome. Spatial structure was stronger for birds than for mammals, with R(2) values ranging from 0.77 to 0.94 for mammals and from 0.77 to 0.97 for birds, for models based on different definitions of spatial structures. According to the Akaike Information Criterion (AIC), the best autoregressive model was obtained by using the rook connection. In general, these results furnish guidelines for future modelling of species richness patterns in relation to environmental predictors and other variables expressing human occupation in the biome.

Recently, the hypothesis that the geographic distribution of species could be influenced by the shape of the domain edges, the so-called Mid-Domain Effect (MDE), has been included as one of the five credible hypotheses for explaining spatial gradients in species richness, despite all the unsuccessful current attempts to prove empirically the validity of MDE. We used data on spatial worldwide distributions of Falconiformes to evaluate the validity of MDE assumptions, incorporated into two different sorts of null models at a global level and separately across five domains/landmasses. Species richness values predicted by the null models of the MDE and those values predicted by Net Primary Productivity, a surrogate variable expressing the effect of available energy, were compared in order to evaluate which hypothesis better predicts the observed values. Our tests showed that MDE continues to lack empirical support, regardless of its current acceptability, and so, does not deserve to be classified as one possible explanation of species richness gradients.