Summary1. An important problem encountered by ecologists in species distribution modelling (SDM) and in multivariate analysis is that of understanding why environmental responses differ across species, and how differences are mediated by functional traits. 2. We describe a simple, generic approach to this problem -the core idea being to fit a predictive model for species abundance (or presence/absence) as a function of environmental variables, species traits and their interaction. 3. We show that this method can be understood as a model-based approach to the fourth-corner problem -the problem of studying the environment-trait association using matrices of abundance or presence/absence data across species, environmental data across sites and trait data across species. The matrix of environment-trait interaction coefficients is the fourth corner. 4. We illustrate that compared with existing approaches to the fourth-corner problem, the proposed model-based approach has advantages in interpretability and its capacity to perform model selection and make predictions. 5. To illustrate the method we used a generalized linear model with a LASSO penalty, fitted to data sets from four different studies requiring different models, illustrating the flexibility of the proposed approach. 6. Predictive performance of the model is compared with that of fitting SDMs separately to each species, and in each case, it is shown that the trait model, despite being much simpler, had comparable predictive performance, even significantly outperforming separate SDMs in some cases.

Beta diversity is an important concept used to describe turnover in species composition across a wide range of spatial and temporal scales, and it underpins much of conservation theory and practice. Although substantial progress has been made in the mathematical and terminological treatment of different measures of beta diversity, there has been little conceptual synthesis of potential scale dependence of beta diversity with increasing spatial grain and geographic extent of sampling. Here, we evaluate different conceptual approaches to the spatial scaling of beta diversity, interpreted from 'fixed' and 'varying' perspectives of spatial grain and extent. We argue that a 'sliding window' perspective, in which spatial grain and extent covary, is an informative way to conceptualize community differentiation across scales. This concept more realistically reflects the varying empirical approaches that researchers adopt in field sampling and the varying scales of landscape perception by different organisms. Scale dependence in beta diversity has broad implications for emerging fields in ecology and biogeography, such as the integration of fine-resolution ecogenomic data with large-scale macroecological studies, as well as for guiding appropriate management responses to threats to biodiversity operating at different spatial scales.

Although many taxa show a latitudinal gradient in richness, the relationship between latitude and species richness is often asymmetrical between the northern and southern hemispheres. Here we examine the latitudinal pattern of species richness across 1003 local ant assemblages. We find latitudinal asymmetry, with southern hemisphere sites being more diverse than northern hemisphere sites. Most of this asymmetry could be explained statistically by differences in contemporary climate. Local ant species richness was positively associated with temperature, but negatively (although weakly) associated with temperature range and precipitation. After contemporary climate was accounted for, a modest difference in diversity between hemispheres persisted, suggesting that factors other than contemporary climate contributed to the hemispherical asymmetry. The most parsimonious explanation for this remaining asymmetry is that greater climate change since the Eocene in the northern than in the southern hemisphere has led to more extinctions in the northern hemisphere with consequent effects on local ant species richness.

No abstract

raits, broadly speaking, are measurable attributes or characteristics of organisms. Traits related to function (for example, leaf size, body mass, tooth size or growth form) are often used to understand how organisms interact with their environment and other species via key vital rates such as survival, development and reproduction 1-5. Trait-based approaches have long been used in systematics and macroevolution to delineate taxa and reconstruct ancestral morphology and function 6-8 and to link candidate genes to phentoypes 9-11. The broad appeal of the trait concept is its ability to facilitate quantitative comparisons of biological form and function. Traits also allow us to mechanistically link organismal responses to abiotic and biotic factors with measurements that are, in principle, relatively easy to capture across large numbers of individuals. For example, appropriately chosen and defined traits can help identify lineages that share similar life-history strategies for a given environmental regime 12,13. Documenting and understanding the diversity and composition of traits in ecosystems directly contributes to our understanding of organismal and ecosystem processes, functionality, productivity and resilience in the face of environmental change 14-19. In light of the multiple applications of trait data to address challenges of global significance (Box 1), a central question remains: How can we most effectively advance the synthesis of trait data within and across disciplines? In recent decades, the collection, compilation and availability of trait data for a variety of organisms has accelerated rapidly. Substantial trait databases now exist for plants 20-23 , reptiles 24,25 , invertebrates 23,26-29 , fish 30,31 , corals 32 , birds 23,33,34 , amphibians 35 , mammals 23,36-38 and fungi 23,39 , and parallel efforts are no doubt underway for other taxa. Though considerable effort has been made to quantify traits for some groups (for example, Fig. 1), substantial work remains. To develop and test theory in biodiversity science, much greater effort is needed to fill in trait data across the Tree of Life by combining and integrating data and trait collection efforts.