A large array of species distribution model (SDM) approaches has been developed for explaining and predicting the occurrences of individual species or species assemblages. Given the wealth of existing models, it is unclear which models perform best for interpolation or extrapolation of existing data sets, particularly when one is concerned with species assemblages. We compared the predictive performance of 33 variants of 15 widely applied and recently emerged SDMs in the context of multispecies data, including both joint SDMs that model multiple species together, and stacked SDMs that model each species individually combining the predictions afterward. We offer a comprehensive evaluation of these SDM approaches by examining their performance in predicting withheld empirical validation data of different sizes representing five different taxonomic groups, and for prediction tasks related to both interpolation and extrapolation. We measure predictive performance by 12 measures of accuracy, discrimination power, calibration, and precision of predictions, for the biological levels of species occurrence, species richness, and community composition. Our results show large variation among the models in their predictive performance, especially for communities comprising many species that are rare. The results do not reveal any major trade‐offs among measures of model performance; the same models performed generally well in terms of accuracy, discrimination, and calibration, and for the biological levels of individual species, species richness, and community composition. In contrast, the models that gave the most precise predictions were not well calibrated, suggesting that poorly performing models can make overconfident predictions. However, none of the models performed well for all prediction tasks. As a general strategy, we therefore propose that researchers fit a small set of models showing complementary performance, and then apply a cross‐validation procedure involving separate data to establish which of these models performs best for the goal of the study.

Summary1. An increasing number of studies are examining the distribution and congruence of ecosystem services, often with the goal of identifying areas that will provide multiple ecosystem service 'hotspots'. However, there is a paucity of data on most ecosystem services, so proxies (e.g. estimates of a service for a particular land cover type) are frequently used to map their distribution. To date, there has been little attempt to quantify the effects of using proxies on distribution maps of ecosystem services, despite the potentially large errors associated with such data sets. 2. Here, we provide the first study examining the effects of using proxies on ecosystem service maps and the degree of spatial congruence of these maps with primary data, using England as a case study. 3. We show that land cover based proxies provide a poor fit to primary data surfaces for biodiversity, recreation and carbon storage, and that correlations between ecosystem services change depending on whether primary or proxy data are used for the analyses. 4. The poor fit of proxies to primary data was also evident when we selected hotspots of single ecosystem services, and consistency between raw and modelled surfaces was extremely low when considering the locations that were coincident hotspots for multiple services. 5. Synthesis and applications. Proxies may be suitable for identifying broad-scale trends in ecosystem services, but even relatively good proxies are likely to be unsuitable for identifying hotspots or priority areas for multiple services.

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 smallrange 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.

We link spatially explicit climate change predictions to a dynamic metapopulation model. Predictions of species' responses to climate change, incorporating metapopulation dynamics and elements of dispersal, allow us to explore the range margin dynamics for two lagomorphs of conservation concern. Although the lagomorphs have very different distribution patterns, shifts at the edge of the range were more pronounced than shifts in the overall metapopulation. For Romerolagus diazi (volcano rabbit), the lower elevation range limit shifted upslope by approximately 700 m. This reduced the area occupied by the metapopulation, as the mountain peak currently lacks suitable vegetation. For Lepus timidus (European mountain hare), we modelled the British metapopulation. Increasing the dispersive estimate caused the metapopulation to shift faster on the northern range margin (leading edge). By contrast, it caused the metapopulation to respond to climate change slower, rather than faster, on the southern range margin (trailing edge). The differential responses of the leading and trailing range margins and the relative sensitivity of range limits to climate change compared with that of the metapopulation centroid have important implications for where conservation monitoring should be targeted. Our study demonstrates the importance and possibility of moving from simple bioclimatic envelope models to second-generation models that incorporate both dynamic climate change and metapopulation dynamics.

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