Experimental plant communities develop phylogenetically overdispersed abundance distributions during assembly

The importance of competition between similar species in driving community assembly is much debated. Recently, phylogenetic patterns in species composition have been investigated to help resolve this question: phylogenetic clustering is taken to imply environmental filtering, and phylogenetic overdispersion to indicate limiting similarity between species. We used experimental plant communities with random species compositions and initially even abundance distributions to examine the development of phylogenetic pattern in species abundance distributions. Where composition was held constant by weeding, abundance distributions became overdispersed through time, but only in communities that contained distantly related clades, some with several species (i.e., a mix of closely and distantly related species). Phylogenetic pattern in composition therefore constrained the development of overdispersed abundance distributions, and this might indicate limiting similarity between close relatives and facilitation/complementarity between distant relatives. Comparing the phylogenetic patterns in these communities with those expected from the monoculture abundances of the constituent species revealed that interspecific competition caused the phylogenetic patterns. Opening experimental communities to colonization by all species in the species pool led to convergence in phylogenetic diversity. At convergence, communities were composed of several distantly related but species-rich clades and had overdispersed abundance distributions. This suggests that limiting similarity processes determine which species dominate a community but not which species occur in a community. Crucially, as our study was carried out in experimental communities, we could rule out local evolutionary or dispersal explanations for the patterns and identify ecological processes as the driving force, underlining the advantages of studying these processes in experimental communities. Our results show that phylogenetic relations between species provide a good guide to understanding community structure and add a new perspective to the evidence that niche complementarity is critical in driving community assembly.

On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

Statistical inference for the optimal approximating model

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ2-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.

Multiasset Derivatives and Joint Distributions of Asset Prices

Several of multiasset derivatives like basket options or options on the weighted maximum of assets exhibit the property that their prices determine uniquely the underlying asset distribution. Related to that the question how to retrieve this distributions from the corresponding derivatives quotes will be discussed. On the contrary, the prices of exchange options do not uniquely determine the underlying distributions of asset prices and the extent of this non-uniqueness can be characterised. The discussion is related to a geometric interpretation of multiasset derivatives as support functions of convex sets. Following this, various symmetry properties for basket, maximum and exchange options are discussed alongside with their geometric interpretations and some decomposition results for more general payoff functions.

Groundwater age distributions at a public drinking water supply well field derived from multiple age tracers (⁸⁵Kr, ³H/³He, and ³⁹Ar)

Groundwater age is a key aspect of production well vulnerability. Public drinking water supply wells typically have long screens and are expected to produce a mixture of groundwater ages. The groundwater age distributions of seven production wells of the Holten well field (Netherlands) were estimated from tritium-helium (3H/3He), krypton-85 (85Kr), and argon-39 (39Ar), using a new application of a discrete age distribution model and existing mathematical models, by minimizing the uncertainty-weighted squared differences of modeled and measured tracer concentrations. The observed tracer concentrations fitted well to a 4-bin discrete age distribution model or a dispersion model with a fraction of old groundwater. Our results show that more than 75 of the water pumped by four shallow production wells has a groundwater age of less than 20 years and these wells are very vulnerable to recent surface contamination. More than 50 of the water pumped by three deep production wells is older than 60 years. 3H/3He samples from short screened monitoring wells surrounding the well field constrained the age stratification in the aquifer. The discrepancy between the age stratification with depth and the groundwater age distribution of the production wells showed that the well field preferentially pumps from the shallow part of the aquifer. The discrete groundwater age distribution model appears to be a suitable approach in settings where the shape of the age distribution cannot be assumed to follow a simple mathematical model, such as a production well field where wells compete for capture area.

Measurement of the distributions of event-by-event flow harmonics in lead-lead collisions at = 2.76 TeV with the ATLAS detector at the LHC

The distributions of event-by-event harmonic flow coefficients v_n for n=2-4 are measured in sqrt(s_NN)=2.76 TeV Pb+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using charged particles with transverse momentum pT> 0.5 GeV and in the pseudorapidity range |eta|<2.5 in a dataset of approximately 7 ub^-1 recorded in 2010. The shapes of the v_n distributions are described by a two-dimensional Gaussian function for the underlying flow vector in central collisions for v_2 and over most of the measured centrality range for v_3 and v_4. Significant deviations from this function are observed for v_2 in mid-central and peripheral collisions, and a small deviation is observed for v_3 in mid-central collisions. It is shown that the commonly used multi-particle cumulants are insensitive to the deviations for v_2. The v_n distributions are also measured independently for charged particles with 0.51 GeV. When these distributions are rescaled to the same mean values, the adjusted shapes are found to be nearly the same for these two pT ranges. The v_n distributions are compared with the eccentricity distributions from two models for the initial collision geometry: a Glauber model and a model that includes corrections to the initial geometry due to gluon saturation effects. Both models fail to describe the experimental data consistently over most of the measured centrality range.