Consequences of shifting species distributions: Climate change is causing geographical redistribution of plant and animal species globally. These distributional shifts are leading to new ecosystems and ecological communities, changes that will affect human society. Pecl et al. review these current and future impacts and assess their implications for sustainable development goals. Science , this issue p. eaai9214

Mountains contribute disproportionately to the terrestrial biodiversity of Earth, especially in the tropics, where they host hotspots of extraordinary and puzzling richness. With about 25% of all land area, mountain regions are home to more than 85% of the world’s species of amphibians, birds, and mammals, many entirely restricted to mountains. Biodiversity varies markedly among these regions. Together with the extreme species richness of some tropical mountains, this variation has proven challenging to explain under traditional climatic hypotheses. However, the complex climatic characteristics of rugged mountain regions differ fundamentally from those of lowland regions, likely playing a key role in generating and maintaining diversity. With ongoing global changes in climate and land use, the role of mountains as refugia for biodiversity may well come under threat.

Mountain regions are unusually biodiverse, with rich aggregations of small-ranged species that form centers of endemism. Mountains play an array of roles for Earth’s biodiversity and affect neighboring lowlands through biotic interchange, changes in regional climate, and nutrient runoff. The high biodiversity of certain mountains reflects the interplay of multiple evolutionary mechanisms: enhanced speciation rates with distinct opportunities for coexistence and persistence of lineages, shaped by long-term climatic changes interacting with topographically dynamic landscapes. High diversity in most tropical mountains is tightly linked to bedrock geology—notably, areas comprising mafic and ultramafic lithologies, rock types rich in magnesium and poor in phosphate that present special requirements for plant physiology. Mountain biodiversity bears the signature of deep-time evolutionary and ecological processes, a history well worth preserving.

We develop a novel class of measures to quantify sample completeness of a biological survey. The class of measures is parameterized by an order q ≥ 0 to control for sensitivity to species relative abundances. When q = 0, species abundances are disregarded and our measure reduces to the conventional measure of completeness, that is, the ratio of the observed species richness to the true richness (observed plus undetected). When q = 1, our measure reduces to the sample coverage (the proportion of the total number of individuals in the entire assemblage that belongs to detected species), a concept developed by Alan Turing in his cryptographic analysis. The sample completeness of a general order q ≥ 0 extends Turing's sample coverage and quantifies the proportion of the assemblage's individuals belonging to detected species, with each individual being proportionally weighted by the ( q − 1)th power of its abundance. We propose the use of a continuous profile depicting our proposed measures with respect to q ≥ 0 to characterize the sample completeness of a survey. An analytic estimator of the diversity profile and its sampling uncertainty based on a bootstrap method are derived and tested by simulations. To compare diversity across multiple assemblages, we propose an integrated approach based on the framework of Hill numbers to assess (a) the sample completeness profile, (b) asymptotic diversity estimates to infer true diversities of entire assemblages, (c) non‐asymptotic standardization via rarefaction and extrapolation, and (d) an evenness profile. Our framework can be extended to incidence data. Empirical data sets from several research fields are used for illustration.

Simulating South American biodiversity: The emergence, distribution, and extinction of species are driven by interacting factors—spatial, temporal, physical, and biotic. Rangel et al. simulated the past 800,000 years of evolution in South America, incorporating these factors into a spatially explicit dynamic model to explore the geographical generation of diversity. Their simulations, based on a paleoclimate model on a 5° latitude-longitude scale, result in shifting maps of speciation, persistence, and extinction (or cradles, museums, and graves). The simulations culminate in a striking resemblance to contemporary distribution patterns across the continent for birds, mammals, and plants—despite having no target patterns and no empirical data parameterizing them. Science , this issue p. eaar5452

Based on sampling data, we propose a rigorous standardization method to measure and compare beta diversity across datasets. Here beta diversity, which quantifies the extent of among‐assemblage differentiation, relies on Whittaker's original multiplicative decomposition scheme, but we use Hill numbers for any diversity order q ≥ 0. Richness‐based beta diversity (q = 0) quantifies the extent of species identity shift, whereas abundance‐based (q > 0) beta diversity also quantifies the extent of difference among assemblages in species abundance. We adopt and define the assumptions of a statistical sampling model as the foundation for our approach, treating sampling data as a representative sample taken from an assemblage. The approach makes a clear distinction between the theoretical assemblage level (unknown properties/parameters of the assemblage) and the sampling data level (empirical/observed statistics computed from data). At the assemblage level, beta diversity for N assemblages reflects the interacting effect of the species abundance distribution and spatial/temporal aggregation of individuals in the assemblage. Under independent sampling, observed beta (= gamma/alpha) diversity depends not only on among‐assemblage differentiation but also on sampling effort/completeness, which in turn induces dependence of beta on alpha and gamma diversity. How to remove the dependence of richness‐based beta diversity on its gamma component (species pool) has been intensely debated. Our approach is to standardize gamma and alpha based on sample coverage (an objective measure of sample completeness). For a single assemblage, the iNEXT method was developed, through interpolation (rarefaction) and extrapolation with Hill numbers, to standardize samples by sampling effort/completeness. Here we adapt the iNEXT standardization to alpha and gamma diversity, that is, alpha and gamma diversity are both assessed at the same level of sample coverage, to formulate standardized, coverage‐based beta diversity. This extension of iNEXT to beta diversity required the development of novel concepts and theories, including a formal proof and simulation‐based demonstration that the resulting standardized beta diversity removes the dependence of beta diversity on both gamma and alpha values, and thus reflects the pure among‐assemblage differentiation. The proposed standardization is illustrated with spatial, temporal, and spatiotemporal datasets, while the freeware iNEXT.beta3D facilitates all computations and graphics.