THE TIGHT-BINDING APPROACH TO THE DIELECTRIC RESPONSE IN THE MULTIBAND SYSTEMS

Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with respect to the usual plane-wave decomposition are pointed out. The analysis becomes particularly transparent in the long wavelength limit, after performing the multipole expansion of bare Coulomb matrix elements. For illustration, the collective modes and the macroscopic dielectric function for a general cubic lattice are derived. It is shown that the dielectric instability in conducting narrow band systems proceeds by a common softening of one transverse and one longitudinal mode. Furthermore, the self-polarization corrections which appear in the macroscopic dielectric function for finite band systems, are identified as a combined effect of intra-atomic exchange interactions between electrons sitting in different orbitals and a finite inter-atomic tunneling.Comment: 20 pages, LaTeX, no figure

A function-based typology for Earth’s ecosystems

As the United Nations develops a post-2020 global biodiversity framework for the Convention on Biological Diversity, attention is focusing on how new goals and targets for ecosystem conservation might serve its vision of ‘living in harmony with nature’1,2. Advancing dual imperatives to conserve biodiversity and sustain ecosystem services requires reliable and resilient generalizations and predictions about ecosystem responses to environmental change and management3. Ecosystems vary in their biota4, service provision5 and relative exposure to risks6, yet there is no globally consistent classification of ecosystems that reflects functional responses to change and management. This hampers progress on developing conservation targets and sustainability goals. Here we present the International Union for Conservation of Nature (IUCN) Global Ecosystem Typology, a conceptually robust, scalable, spatially explicit approach for generalizations and predictions about functions, biota, risks and management remedies across the entire biosphere. The outcome of a major cross-disciplinary collaboration, this novel framework places all of Earth’s ecosystems into a unifying theoretical context to guide the transformation of ecosystem policy and management from global to local scales. This new information infrastructure will support knowledge transfer for ecosystem-specific management and restoration, globally standardized ecosystem risk assessments, natural capital accounting and progress on the post-2020 global biodiversity framework

Global patterns and environmental drivers of forest functional composition

Aim To determine the relationships between the functional trait composition of forest communities and environmental gradients across scales and biomes and the role of species relative abundances in these relationships. Location Global. Time period Recent. Major taxa studied Trees. Methods We integrated species abundance records from worldwide forest inventories and associated functional traits (wood density, specific leaf area and seed mass) to obtain a data set of 99,953 to 149,285 plots (depending on the trait) spanning all forested continents. We computed community-weighted and unweighted means of trait values for each plot and related them to three broad environmental gradients and their interactions (energy availability, precipitation and soil properties) at two scales (global and biomes). Results Our models explained up to 60% of the variance in trait distribution. At global scale, the energy gradient had the strongest influence on traits. However, within-biome models revealed different relationships among biomes. Notably, the functional composition of tropical forests was more influenced by precipitation and soil properties than energy availability, whereas temperate forests showed the opposite pattern. Depending on the trait studied, response to gradients was more variable and proportionally weaker in boreal forests. Community unweighted means were better predicted than weighted means for almost all models. Main conclusions Worldwide, trees require a large amount of energy (following latitude) to produce dense wood and seeds, while leaves with large surface to weight ratios are concentrated in temperate forests. However, patterns of functional composition within-biome differ from global patterns due to biome specificities such as the presence of conifers or unique combinations of climatic and soil properties. We recommend assessing the sensitivity of tree functional traits to environmental changes in their geographic context. Furthermore, at a given site, the distribution of tree functional traits appears to be driven more by species presence than species abundance

Integrated global assessment of the natural forest carbon potential

Forests are a substantial terrestrial carbon sink, but anthropogenic changes in land use and climate have considerably reduced the scale of this system1. Remote-sensing estimates to quantify carbon losses from global forests2,3,4,5 are characterized by considerable uncertainty and we lack a comprehensive ground-sourced evaluation to benchmark these estimates. Here we combine several ground-sourced6 and satellite-derived approaches2,7,8 to evaluate the scale of the global forest carbon potential outside agricultural and urban lands. Despite regional variation, the predictions demonstrated remarkable consistency at a global scale, with only a 12% difference between the ground-sourced and satellite-derived estimates. At present, global forest carbon storage is markedly under the natural potential, with a total deficit of 226 Gt (model range = 151–363 Gt) in areas with low human footprint. Most (61%, 139 Gt C) of this potential is in areas with existing forests, in which ecosystem protection can allow forests to recover to maturity. The remaining 39% (87 Gt C) of potential lies in regions in which forests have been removed or fragmented. Although forests cannot be a substitute for emissions reductions, our results support the idea2,3,9 that the conservation, restoration and sustainable management of diverse forests offer valuable contributions to meeting global climate and biodiversity targets

Co-limitation towards lower latitudes shapes global forest diversity gradients

The latitudinal diversity gradient (LDG) is one of the most recognized global patterns of species richness exhibited across a wide range of taxa. Numerous hypotheses have been proposed in the past two centuries to explain LDG, but rigorous tests of the drivers of LDGs have been limited by a lack of high-quality global species richness data. Here we produce a high-resolution (0.025° × 0.025°) map of local tree species richness using a global forest inventory database with individual tree information and local biophysical characteristics from ~1.3 million sample plots. We then quantify drivers of local tree species richness patterns across latitudes. Generally, annual mean temperature was a dominant predictor of tree species richness, which is most consistent with the metabolic theory of biodiversity (MTB). However, MTB underestimated LDG in the tropics, where high species richness was also moderated by topographic, soil and anthropogenic factors operating at local scales. Given that local landscape variables operate synergistically with bioclimatic factors in shaping the global LDG pattern, we suggest that MTB be extended to account for co-limitation by subordinate drivers