Summary 1.A primary goal of ecology is to understand the fundamental processes underlying the geographic distributions of species. Two major strands of ecology -habitat modelling and community ecology -approach this problem differently. Habitat modellers often use species distribution models (SDMs) to quantify the relationship between species' and their environments without considering potential biotic interactions. Community ecologists, on the other hand, tend to focus on biotic interactions and, in observational studies, use co-occurrence patterns to identify ecological processes. Here, we describe a joint species distribution model (JSDM) that integrates these distinct observational approaches by incorporating species co-occurrence data into a SDM. 2. JSDMs estimate distributions of multiple species simultaneously and allow decomposition of species co-occurrence patterns into components describing shared environmental responses and residual patterns of co-occurrence. We provide a general description of the model, a tutorial and code for fitting the model in R. We demonstrate this modelling approach using two case studies: frogs and eucalypt trees in Victoria, Australia. 3. Overall, shared environmental correlations were stronger than residual correlations for both frogs and eucalypts, but there were cases of strong residual correlation. Frog species generally had positive residual correlations, possibly due to the fact these species occurred in similar habitats that were not fully described by the environmental variables included in the JSDM. Eucalypt species that interbreed had similar environmental responses but had negative residual co-occurrence. One explanation is that interbreeding species may not form stable assemblages despite having similar environmental affinities. 4. Environmental and residual correlations estimated from JSDMs can help indicate whether co-occurrence is driven by shared environmental responses or other ecological or evolutionary process (e.g. biotic interactions), or if important predictor variables are missing. JSDMs take into account the fact that distributions of species might be related to each other and thus overcome a major limitation of modelling species distributions independently.

Quantifying how functional traits relate to environmental gradients provides insight into mechanisms governing species distributions. Here, we bring together the fields of species distribution modelling and functional trait ecology with hierarchical modelling by explicitly incorporating traits into a multi‐species distribution model. We combined traits from the leaf‐height‐seed strategy scheme (specific leaf area (SLA), plant height and seed mass) with a distribution model for 20 eucalypt taxa in Victoria, Australia. The key insight of this approach is how traits modulate species responses to environmental gradients. The strongest link was between SLA and percent rock cover (species with low SLA had positive responses to rockiness, whereas high SLA species responded negatively to rockiness). We found evidence for complex yet potentially important interactions. For instance, the probability of species occurrence increased with rainfall and solar radiation on average yet the response varied depending on species height and SLA. Tall species were predicted to increase with rainfall and solar radiation across the range of SLA values (tall species with low SLA were especially sensitive to rainfall). Short species responded positively to rainfall and solar radiation only if they had low SLA. This framework readily accounts for interactions between combinations of traits and environmental variables unlike multi‐step approaches. Further application of this concept will contribute to a generalized mechanistic understanding of how traits influence species distributions along environmental gradients, with implications for understanding the response of species to global change.

Different facets of biodiversity other than species numbers are increasingly appreciated as critical for maintaining the function of ecosystems and their services to humans. While new international policy and assessment processes such as the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) recognize the importance of an increasingly global, quantitative and comprehensive approach to biodiversity protection, most insights are still focused on a single facet of biodiversity-species. Here we broaden the focus and provide an evaluation of how much of the world's species, functional and phylogenetic diversity of birds and mammals is currently protected and the scope for improvement. We show that the large existing gaps in the coverage for each facet of diversity could be remedied by a slight expansion of protected areas: an additional 5% of the land has the potential to more than triple the protected range of species or phylogenetic or functional units. Further, the same areas are often priorities for multiple diversity facets and for both taxa. However, we find that the choice of conservation strategy has a fundamental effect on outcomes. It is more difficult (that is, requires more land) to maximize basic representation of the global biodiversity pool than to maximize local diversity. Overall, species and phylogenetic priorities are more similar to each other than they are to functional priorities, and priorities for the different bird biodiversity facets are more similar than those of mammals. Our work shows that large gains in biodiversity protection are possible, while also highlighting the need to explicitly link desired conservation objectives and biodiversity metrics. We provide a framework and quantitative tools to advance these goals for multi-faceted biodiversity conservation.

In ecology, the true causal structure for a given problem is often not known, and several plausible models and thus model predictions exist. It has been claimed that using weighted averages of these models can reduce prediction error, as well as better reflect model selection uncertainty. These claims, however, are often demonstrated by isolated examples. Analysts must better understand under which conditions model averaging can improve predictions and their uncertainty estimates. Moreover, a large range of different model averaging methods exists, raising the question of how they differ in their behaviour and performance. Here, we review the mathematical foundations of model averaging along with the diversity of approaches available. We explain that the error in model‐averaged predictions depends on each model's predictive bias and variance, as well as the covariance in predictions between models, and uncertainty about model weights. We show that model averaging is particularly useful if the predictive error of contributing model predictions is dominated by variance, and if the covariance between models is low. For noisy data, which predominate in ecology, these conditions will often be met. Many different methods to derive averaging weights exist, from Bayesian over information‐theoretical to cross‐validation optimized and resampling approaches. A general recommendation is difficult, because the performance of methods is often context dependent. Importantly, estimating weights creates some additional uncertainty. As a result, estimated model weights may not always outperform arbitrary fixed weights, such as equal weights for all models. When averaging a set of models with many inadequate models, however, estimating model weights will typically be superior to equal weights. We also investigate the quality of the confidence intervals calculated for model‐averaged predictions, showing that they differ greatly in behaviour and seldom manage to achieve nominal coverage. Our overall recommendations stress the importance of non‐parametric methods such as cross‐validation for a reliable uncertainty quantification of model‐averaged predictions.

No abstract

Aim: More than ever, ecologists seek to understand how species are distributed and have assembled into communities using the "filtering framework". This framework is based on the hypothesis that local assemblages result from a series of abiotic and biotic filters applied to regional species pools and that these filters leave predictable signals in observed diversity patterns. In theory, statistical comparisons of expected and observed patterns enable data-driven tests of assembly processes. However, so far this framework has fallen short in delivering generalizable conclusions, challenging whether (and how) diversity patterns can be used to characterize and understand underlying assembly processes better.Methods: By synthesizing the previously raised critiques and suggested solutions in a comprehensive way, we identify 10 pitfalls that can lead to flawed interpretations of α-diversity patterns, summarize solutions developed to circumvent these pitfalls and provide general guidelines. Results:We find that most issues arise from an overly simplistic view of potential processes that influence diversity patterns, which is often motivated by practical constraints on study design, focal scale and methodology. We outline solutions for each pitfall, such as methods spanning over spatial, environmental or phylogenetic scales, and suggest guidelines for best scientific practices in community ecology.

Whether species interactions influence species response to environment and species ranges has always been a central question in ecology. Joint species distribution models (JSDMs) simultaneously model the species-environment relationships of multiple species and the residual correlation between these species. These residual correlations are assumed to depict whether species co-occur less or more often than expected by the modelled species-environment relationships, which could ultimately be attributed to species interactions, or hidden environmental information. Here, we propose to specifically test the capacity of JSDMs to detect species interactions from co-occurrence data, at different scales of data aggregation. Using a recently published point-process model, we simulated equilibrium co-occurrence patterns of species pairs by varying the strength and type of interactions (e.g. competition, predator-prey, mutualism) as well as the prevalence of the interacting species in homogeneous environments (assuming the environment does not influence the species responses and co-occurrence). Then, we fitted JSDMs without environmental predictors, and compared the estimated residual correlations against the known interaction coefficients. JSDMs detected competition and mutualism well, but failed with predator-prey interactions. For the latter, JSDMs predicted both negative and positive residual correlations for these kinds of interactions, depending on the prevalence of the interacting species. Interestingly, the estimated residual correlation was strongly influenced by species' prevalence and can thus not be translated to interaction strength. At increasingly coarser data resolution, the signals of negative and positive interactions became indiscernible by JSDMs, butreassuringly -were rarely confounded. The underlying point-process model simulates the consequences rather than the mechanisms of interspecific interactions, and thus is better at corroborating rather than discrediting JSDMs. Nevertheless, our simple theoretical exercise pinpoints important limitations of JSDMs. In conclusion, we caution against interpreting residual correlations from JSDMs as interaction strength and against comparing these across different species and communities.

The extent that biotic interactions and dispersal influence species ranges and diversity patterns across scales remains an open question. Answering this question requires framing an analysis on the frontier between species distribution modelling (SDM), which ignores biotic interactions and dispersal limitation, and community ecology, which provides specific predictions on community and meta-community structure and resulting diversity patterns such as species richness and functional diversity. Using both empirical and simulated datasets, we tested whether predicted occurrences from fine-resolution SDMs provide good estimates of community structure and diversity patterns at resolutions ranging from a resolution typical of studies within reserves (250 m) to that typical of a regional biodiversity study (5 km). For both datasets, we show that the imprint of biotic interactions and dispersal limitation quickly vanishes when spatial resolution is reduced, which demonstrates the value of SDMs for tracking the imprint of community assembly processes across scales.