Hutchinson's n‐dimensional hypervolume concept underlies many applications in contemporary ecology and evolutionary biology. Estimating hypervolumes from sampled data has been an ongoing challenge due to conceptual and computational issues. We present new algorithms for delineating the boundaries and probability density within n‐dimensional hypervolumes. The methods produce smooth boundaries that can fit data either more loosely (Gaussian kernel density estimation) or more tightly (one‐classification via support vector machine). Further, the algorithms can accept abundance‐weighted data, and the resulting hypervolumes can be given a probabilistic interpretation and projected into geographic space. We demonstrate the properties of these methods on a large dataset that characterises the functional traits and geographic distribution of thousands of plants. The methods are available in version ≥2.0.7 of the hypervolume r package. These new algorithms provide: (i) a more robust approach for delineating the shape and density of n‐dimensional hypervolumes; (ii) more efficient performance on large and high‐dimensional datasets; and (iii) improved measures of functional diversity and environmental niche breadth.

Abstract1. There is an urgent need for large-scale botanical data to improve our understanding of community assembly, coexistence, biogeography, evolution, and many other fundamental biological processes. Understanding these processes is critical for predicting and handling human-biodiversity interactions and global change dynamics such as food and energy security, ecosystem services, climate change, and species invasions.2. The Botanical Information and Ecology Network (BIEN) database comprises an unprecedented wealth of cleaned and standardised botanical data, containing roughly 81 million occurrence records from c. 375,000 species, c. 915,000 trait observations across 28 traits from c. 93,000 species, and co-occurrence records from 110,000 ecological plots globally, as well as 100,000 range maps and 100 replicated phylogenies (each containing 81,274 species) for New World species. Here, we describe an r package that provides easy access to these data. K E Y W O R D S

A key feature of life’s diversity is that some species are common but many more are rare. Nonetheless, at global scales, we do not know what fraction of biodiversity consists of rare species. Here, we present the largest compilation of global plant diversity to quantify the fraction of Earth’s plant biodiversity that are rare. A large fraction, ~36.5% of Earth’s ~435,000 plant species, are exceedingly rare. Sampling biases and prominent models, such as neutral theory and the k-niche model, cannot account for the observed prevalence of rarity. Our results indicate that (i) climatically more stable regions have harbored rare species and hence a large fraction of Earth’s plant species via reduced extinction risk but that (ii) climate change and human land use are now disproportionately impacting rare species. Estimates of global species abundance distributions have important implications for risk assessments and conservation planning in this era of rapid global change.

In a rapidly changing climate, alpine plants may persist by adapting to new conditions. However, the rate at which the climate is changing might exceed the rate of adaptation through evolutionary processes in long-lived plants. Persistence may depend on phenotypic plasticity in morphology and physiology. Here we investigated patterns of leaf trait variation including leaf area, leaf thickness, specific leaf area, leaf dry matter content, leaf nutrients (C, N, P) and isotopes (δ13C and δ15N) across an elevation gradient on Gongga Mountain, Sichuan Province, China. We quantified inter- and intra-specific trait variation and the plasticity in leaf traits of selected species to experimental warming and cooling by using a reciprocal transplantation approach. We found substantial phenotypic plasticity in most functional traits where δ15N, leaf area, and leaf P showed greatest plasticity. These traits did not correspond with traits with the largest amount of intraspecific variation. Plasticity in leaf functional traits tended to enable plant populations to shift their trait values toward the mean values of a transplanted plants’ destination community, but only if that population started with very different trait values. These results suggest that leaf trait plasticity is an important mechanism for enabling plants to persist within communities and to better tolerate changing environmental conditions under climate change.

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.