A meta-analysis shows that species are shifting their distributions in response to climate change at an accelerating rate.

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 spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix.

Many factors, including climate, resource availability, and habitat diversity, have been proposed as determinants of global diversity, but the links among them have rarely been studied. Using structural equation modeling (SEM), we investigated direct and indirect effects of climate variables, host‐plant richness, and habitat diversity on butterfly species richness across Britain, at 20‐km grid resolution. These factors were all important determinants of butterfly diversity, but their relative contributions differed between habitat generalists and specialists, and whether the effects were direct or indirect. Climate variables had strong effects on habitat generalists, whereas host‐plant richness and habitat diversity contributed relatively more for habitat specialists. Considering total effects (direct and indirect together), climate variables had the strongest link to butterfly species richness for all groups of species. The results suggest that different mechanistic hypotheses to explain species richness may be more appropriate for habitat generalists and specialists, with generalists hypothesized to show direct physiological limitations and specialists additionally being constrained by trophic interactions (climate affecting host‐plant richness).

Why do areas with high numbers of small-range species occur where they do? We found that, for butterfly and plant species in Europe, and for bird species in the Western Hemisphere, such areas coincide with regions that have rare climates, and are higher and colder areas than surrounding regions. Species with small range sizes also tend to occur in climatically diverse regions, where species are likely to have been buffered from extinction in the past. We suggest that the centres of high small-range species richness we examined predominantly represent interglacial relict areas where cold-adapted species have been able to survive unusually warm periods in the last ca 10 000 years. We show that the rare climates that occur in current centres of species rarity will shrink disproportionately under future climate change, potentially leading to high vulnerability for many of the species they contain.