Nitrogen (N) is a major ingredient of the atmosphere, but a trace component in the silicate Earth. Its initial inventory in these reservoirs during Earth's early differentiation requires knowledge of N speciation in magmas, for example, whether it outgasses as N 2 or is sequestered in silicate melts as N 3− , which remains largely unconstrained over the entire mantle regime. Here we examine N species in anhydrous and hydrous pyrolitic melts at varying P‐T‐redox conditions by ab‐initio calculations, and find N‐N bonding under oxidizing conditions from ambient to lower mantle pressures. Under reducing conditions, N interacts with the silicate network or forms N‐H bonds, depending on the availability of hydrogen. Redox control of N speciation is demonstrated valid over a P‐T space encompassing probable magma ocean depths. Finally, if the Earth accreted from increasingly oxidized materials toward the end of its accretion, an N‐enriched secondary atmosphere might be produced and persist until later impacts.
Quantile regression is a method of fundamental importance. How to efficiently conduct quantile regression for a large dataset on a distributed system is of great importance. We show that the popularly used one-shot estimation is statistically inefficient if data are not randomly distributed across different workers. To fix the problem, a novel one-step estimation method is developed with the following nice properties. First, the algorithm is communication efficient. That is the communication cost demanded is practically acceptable. Second, the resulting estimator is statistically efficient. That is its asymptotic covariance is the same as that of the global estimator. Third, the estimator is robust against data distribution. That is its consistency is guaranteed even if data are not randomly distributed across different workers. Numerical experiments are provided to corroborate our findings. A real example is also presented for illustration.
Nutrient scarcity is pervasive for natural microbial communities, affecting species reproduction and co-existence. However, it remains unclear whether there are general rules of how microbial species abundances are shaped by biotic and abiotic factors. Here we show that the ribosomal RNA gene operon (rrn) copy number, a genomic trait related to bacterial growth rate and nutrient demand, decreases from the abundant to the rare biosphere in the nutrient-rich coastal sediment but exhibits the opposite pattern in the nutrient-scarce pelagic zone of the global ocean. Both patterns are underlain by positive correlations between community-level rrn copy number and nutrients. Furthermore, inter-species co-exclusion inferred by negative network associations is observed more in coastal sediment than in ocean water samples. Nutrient manipulation experiments yield effects of nutrient availability on rrn copy numbers and network associations that are consistent with our field observations. Based on these results, we propose a “hunger games” hypothesis to define microbial species abundance rules using the rrn copy number, ecological interaction, and nutrient availability.