Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

Averting biodiversity collapse in tropical forest protected areas

The rapid disruption of tropical forests probably imperils global biodiversity more than any other contemporary phenomenon(1-3). With deforestation advancing quickly, protected areas are increasingly becoming final refuges for threatened species and natural ecosystem processes. However, many protected areas in the tropics are themselves vulnerable to human encroachment and other environmental stresses(4-9). As pressures mount, it is vital to know whether existing reserves can sustain their biodiversity. A critical constraint in addressing this question has been that data describing a broad array of biodiversity groups have been unavailable for a sufficiently large and representative sample of reserves. Here we present a uniquely comprehensive data set on changes over the past 20 to 30 years in 31 functional groups of species and 21 potential drivers of environmental change, for 60 protected areas stratified across the world's major tropical regions. Our analysis reveals great variation in reserve `health': about half of all reserves have been effective or performed passably, but the rest are experiencing an erosion of biodiversity that is often alarmingly widespread taxonomically and functionally. Habitat disruption, hunting and forest-product exploitation were the strongest predictors of declining reserve health. Crucially, environmental changes immediately outside reserves seemed nearly as important as those inside in determining their ecological fate, with changes inside reserves strongly mirroring those occurring around them. These findings suggest that tropical protected areas are often intimately linked ecologically to their surrounding habitats, and that a failure to stem broad-scale loss and degradation of such habitats could sharply increase the likelihood of serious biodiversity declines.

Chromium isotope variations (delta Cr-53/52) in mantle-derived sources and their weathering products: Implications for environmental studies and the evolution of delta Cr-53/52 in the Earth's mantle over geologic time

Here we report chromium isotope compositions, expressed as delta Cr-53/ 52 in per mil (&) relative to NIST 979, measured in selected Cr-rich minerals and rocks formed by the primary magmatic as well as the secondary metamorphic and weathering processes. The main objectives of this study were: (i) to further constrain the isotope composition of the Earth's mantle Cr inventory and its possible variation during geological history, based on the analysis of globally distributed and stratigraphically constrained mantle-derived chromites; and (ii) to investigate the magnitude and systematics of Cr isotope fractionation during oxidative weathering and secondary alteration (i. e., hydration, serpentinization) of the magmatic Cr sources. Specifically, we analyzed delta Cr-53/ 52 in a set of globally distributed mantle-derived chromites (FeMgCr2O4, n = 30) collected from various locations in Europe, Asia, Africa and South America, and our results confirm that a chromite-hosted Earth's mantle Cr inventory is uniform at - 0.079 +/- 0.129& (2SD), which we named here as a ` canonical' mantle d 53/ 52 Cr signature. Furthermore our dataset of stratigraphically constrained chromites, whose crystallization ages cover most of the Earth's geological history, indicate that the bulk Cr isotope composition of the chromite-hosted mantle inventory has remained uniform, within about +/- 0.100&, since at least the Early Archean times (similar to 3500 million years ago, Ma). To investigate the systematics of Cr isotope fractionation associated with alteration processes we analyzed a number of secondary Cr-rich minerals and variably altered ultramafic rocks (i. e., serpentinized harzburgites, lherzolites) that revealed large positive delta Cr-53/ 52 anomalies that are systematically shifted to higher values with an increasing degree of alteration and serpentinization. The degree of aqueous alteration and serpentinization was quantified by the abundances of fluid-mobile (Rb, K) elements, and by the Loss On Ignition (LOI) parameter, which determines the amount of structurally bound water (OH/ H2O) present in secondary hydrated minerals like serpentine. Overall, we observed that altered ultramafic rocks that yielded the highest LOI values, and the lowest amounts of fluid mobile elements, also yielded the heaviest delta Cr-53/ 52 signatures. Therefore, we conclude that secondary alteration (i.e., hydration, serpentinization) of ultramafic rocks in near-surface oxidative environments tend to shift the bulk Cr isotope composition of the weathered products to isotopically heavier values, pointing to a dynamic redox cycling of Cr in the Earth's crustal and near-surface environments. Hence, if validated by future

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher's alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between similar to 40,000 and similar to 53,000, i.e., at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of similar to 19,000-25,000 tree species. Continental Africa is relatively depauperate with a minimum of similar to 4,500-6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa.