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. Unconstrained ordination is commonly used in ecology to visualize multivariate data, in particular, to visualize the main trends between different sites in terms of their species composition or relative abundance. 2. Methods of unconstrained ordination currently used, such as non-metric multidimensional scaling, are algorithm-based techniques developed and implemented without directly accommodating the statistical properties of the data at hand. Failure to account for these key data properties can lead to misleading results. 3. A model-based approach to unconstrained ordination can address this issue, and in this study, two types of models for ordination are proposed based on finite mixture models and latent variable models. Each method is capable of handling different data types and different forms of species response to latent gradients. Further strengths of the models are demonstrated via example and simulation. 4. Advantages of model-based approaches to ordination include the following: residual analysis tools for checking assumptions to ensure the fitted model is appropriate for the data; model selection tools to choose the most appropriate model for ordination; methods for formal statistical inference to draw conclusions from the ordination; and improved efficiency, that is model-based ordination better recovers true relationships between sites, when used appropriately.

The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW space-time is analysed in detail using a dynamical systems approach which may readily be generalised to more complicated space-times. It is shown that for a very large and natural class of models a simple and regular past asymptotic structure exists. More specifically, there exists a family of solutions which is in continuous 1-1 correspondence with the exactly integrable massless scalar field cosmologies, this correspondence being realised by a unique asymptotic approximation. The set of solutions which do not fall into this class has measure zero. The significance of this result to the cosmological initial value problem is briefly discussed.

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Tropical tuna fisheries are central to food security and economic development of many regions of the world. Contemporary population assessment and management generally assume these fisheries exploit a single mixed spawning population, within ocean basins. To date population genetics has lacked the required power to conclusively test this assumption. Here we demonstrate heterogeneous population structure among yellowfin tuna sampled at three locations across the Pacific Ocean (western, central, and eastern) via analysis of double digest restriction-site associated DNA using Next Generation Sequencing technology. The differences among locations are such that individuals sampled from one of the three regions examined can be assigned with close to 100% accuracy demonstrating the power of this approach for providing practical markers for fishery independent verification of catch provenance in a way not achieved by previous techniques. Given these results, an extended pan-tropical survey of yellowfin tuna using this approach will not only help combat the largest threat to sustainable fisheries (i.e. illegal, unreported, and unregulated fishing) but will also provide a basis to transform current monitoring, assessment, and management approaches for this globally significant species.

Abstract. Species distribution models (SDMs) are an important tool for studying the patterns of species across environmental and geographic space. For community data, a common approach involves fitting an SDM to each species separately, although the large number of models makes interpretation difficult and fails to exploit any similarities between individual species responses. A recently proposed alternative that can potentially overcome these difficulties is species archetype models (SAMs), a model-based approach that clusters species based on their environmental response. In this paper, we compare the predictive performance of SAMs against separate SDMs using a number of multi-species data sets. Results show that SAMs improve model accuracy and discriminatory capacity compared to separate SDMs. This is achieved by borrowing strength from common species having higher information content. Moreover, the improvement increases as the species become rarer.

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