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Abstract The proton-cyclotron (PC) instability operates in various space plasma environments. In the literature, the so-called velocity moment-based quasi-linear theory is employed to investigate the physical process of PC instability that takes place after the onset of early linear exponential growth. In this method, the proton velocity distribution function (VDF) is assumed to maintain a bi-Maxwellian form for all time, which substantially simplifies the analysis, but its validity has not been rigorously examined by comparing against the actual solution of the kinetic equation. The present paper relaxes the assumption of the velocity moment-based quasi-linear theory by actually solving for the velocity space diffusion equation under the assumption of separable perpendicular and parallel VDFs, and upon comparison with the simplified velocity moment theory, it demonstrates that the simplified method is largely valid, despite the fact that the method slightly overemphasizes the relaxation of temperature anisotropy when the system is close to the marginally stable state. The overall validation is further confirmed with the results of particle-in-cell and hybrid-code simulations. The present paper thus provides a justification for making use of the velocity moment-based quasi-linear theory as an efficient first-cut theoretical tool for the PC instability. 

Abstract Earthworms are an important soil taxon as ecosystem engineers, providing a variety of crucial ecosystem functions and services. Little is known about their diversity and distribution at large spatial scales, despite the availability of considerable amounts of local-scale data. Earthworm diversity data, obtained from the primary literature or provided directly by authors, were collated with information on site locations, including coordinates, habitat cover, and soil properties. Datasets were required, at a minimum, to include abundance or biomass of earthworms at a site. Where possible, site-level species lists were included, as well as the abundance and biomass of individual species and ecological groups. This global dataset contains 10,840 sites, with 184 species, from 60 countries and all continents except Antarctica. The data were obtained from 182 published articles, published between 1973 and 2017, and 17 unpublished datasets. Amalgamating data into a single global database will assist researchers in investigating and answering a wide variety of pressing questions, for example, jointly assessing aboveground and belowground biodiversity distributions and drivers of biodiversity change.