Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

We introduce a general theory for a consensus-based combination of estimations of probability measures. Potential applications include parallelized or distributed sampling schemes as well as variations on aggregation from resampling techniques like boosting or bagging. Taking into account the possibility of very discrepant estimations, instead of a full consensus we consider a "wide consensus" procedure. The approach is based on the consideration of trimmed barycenters in the Wasserstein space of probability measures. We provide general existence and consistency results as well as suitable properties of these robustified Fréchet means. In order to get quick applicability, we also include characterizations of barycenters of probabilities that belong to (non necessarily elliptical) location and scatter families. For these families, we provide an iterative algorithm for the effective computation of trimmed barycenters, based on a consistent algorithm for computing barycenters, guarantying applicability in a wide setting of statistical problems

Global patterns and environmental drivers of forest functional composition

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. 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). 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, withinbiome 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. 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.Fil: Bouchard, Elise. Université du Québec a Montreal; CanadáFil: Searle, Eric B.. Université du Québec a Montreal; CanadáFil: Drapeau, Pierre. Université du Québec a Montreal; CanadáFil: Liang, Jingjing. Purdue University; Estados UnidosFil: Gamarra, Javier G. P.. Food and Agriculture Organization of the United Nations; ItaliaFil: Abegg, Meinrad. No especifíca;Fil: Alberti, Giorgio. No especifíca;Fil: Zambrano, Angelica Almeyda. No especifíca;Fil: Alvarez Davila, Esteban. No especifíca;Fil: Alves, Luciana F.. No especifíca;Fil: Avitabile, Valerio. No especifíca;Fil: Aymard, Gerardo. No especifíca;Fil: Bastin, Jean François. No especifíca;Fil: Birnbaum, Philippe. No especifíca;Fil: Bongers, Frans. No especifíca;Fil: Bouriaud, Olivier. No especifíca;Fil: Brancalion, Pedro. No especifíca;Fil: Broadbent, Eben. No especifíca;Fil: Bussotti, Filippo. No especifíca;Fil: Gatti, Roberto Cazzolla. No especifíca;Fil: Češljar, Goran. No especifíca;Fil: Chisholm, Chelsea. No especifíca;Fil: Cienciala, Emil. No especifíca;Fil: Clark, Connie J.. No especifíca;Fil: Peri, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Santa Cruz. Universidad Tecnológica Nacional. Facultad Regional Santa Cruz. Centro de Investigaciones y Transferencia de Santa Cruz. Universidad Nacional de la Patagonia Austral. Centro de Investigaciones y Transferencia de Santa Cruz; ArgentinaFil: Zawiła Niedźwiecki, Tomasz. No especifíca;Fil: Zhou, Mo. No especifíca;Fil: Zhu, Zhi Xin. No especifíca;Fil: Zo Bi, Irié C.. No especifíca;Fil: Paquette, Alain. Université du Québec a Montreal; Canad

Evenness mediates the global relationship between forest productivity and richness

1. Biodiversity is an important component of natural ecosystems, with higher species richness often correlating with an increase in ecosystem productivity. Yet, this relationship varies substantially across environments, typically becoming less pronounced at high levels of species richness. However, species richness alone cannot reflect all important properties of a community, including community evenness, which may mediate the relationship between biodiversity and productivity. If the evenness of a community correlates negatively with richness across forests globally, then a greater number of species may not always increase overall diversity and productivity of the system. Theoretical work and local empirical studies have shown that the effect of evenness on ecosystem functioning may be especially strong at high richness levels, yet the consistency of this remains untested at a global scale. 2. Here, we used a dataset of forests from across the globe, which includes composition, biomass accumulation and net primary productivity, to explore whether productivity correlates with community evenness and richness in a way that evenness appears to buffer the effect of richness. Specifically, we evaluated whether low levels of evenness in speciose communities correlate with the attenuation of the richness–productivity relationship. 3. We found that tree species richness and evenness are negatively correlated across forests globally, with highly speciose forests typically comprising a few dominant and many rare species. Furthermore, we found that the correlation between diversity and productivity changes with evenness: at low richness, uneven communities are more productive, while at high richness, even communities are more productive. 4. Synthesis. Collectively, these results demonstrate that evenness is an integral component of the relationship between biodiversity and productivity, and that the attenuating effect of richness on forest productivity might be partly explained by low evenness in speciose communities. Productivity generally increases with species richness, until reduced evenness limits the overall increases in community diversity. Our research suggests that evenness is a fundamental component of biodiversity– ecosystem function relationships, and is of critical importance for guiding conservation and sustainable ecosystem management decisions

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Native diversity buffers against severity of non-native tree invasions

Determining the drivers of non-native plant invasions is critical for managing native ecosystems and limiting the spread of invasive species. Tree invasions in particular have been relatively overlooked, even though they have the potential to transform ecosystems and economies. Here, leveraging global tree databases, we explore how the phylogenetic and functional diversity of native tree communities, human pressure and the environment influence the establishment of non-native tree species and the subsequent invasion severity. We find that anthropogenic factors are key to predicting whether a location is invaded, but that invasion severity is underpinned by native diversity, with higher diversity predicting lower invasion severity. Temperature and precipitation emerge as strong predictors of invasion strategy, with non-native species invading successfully when they are similar to the native community in cold or dry extremes. Yet, despite the influence of these ecological forces in determining invasion strategy, we find evidence that these patterns can be obscured by human activity, with lower ecological signal in areas with higher proximity to shipping ports. Our global perspective of non-native tree invasion highlights that human drivers influence non-native tree presence, and that native phylogenetic and functional diversity have a critical role in the establishment and spread of subsequent invasions

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file