Quantifying diversity is of central importance for the study of structure, function and evolution of microbial communities. The estimation of microbial diversity has received renewed attention with the advent of large-scale metagenomic studies. Here, we consider what the diversity observed in a sample tells us about the diversity of the community being sampled. First, we argue that one cannot reliably estimate the absolute and relative number of microbial species present in a community without making unsupported assumptions about species abundance distributions. The reason for this is that sample data do not contain information about the number of rare species in the tail of species abundance distributions. We illustrate the difficulty in comparing species richness estimates by applying Chao's estimator of species richness to a set of in silico communities: they are ranked incorrectly in the presence of large numbers of rare species. Next, we extend our analysis to a general family of diversity metrics ('Hill diversities'), and construct lower and upper estimates of diversity values consistent with the sample data. The theory generalizes Chao's estimator, which we retrieve as the lower estimate of species richness. We show that Shannon and Simpson diversity can be robustly estimated for the in silico communities. We analyze nine metagenomic data sets from a wide range of environments, and show that our findings are relevant for empirically-sampled communities. Hence, we recommend the use of Shannon and Simpson diversity rather than species richness in efforts to quantify and compare microbial diversity.

We report two strategies toward the synthesis of 3-alkyl-4-fluorothiophenes containing straight (hexyl and octyl) and branched (2-ethylhexyl) alkyl groups. We demonstrate that treatment of the dibrominated monomer with 1 equiv of alkyl Grignard reagent leads to the formation of a single regioisomer as a result of the pronounced directing effect of the fluorine group. Polymerization of the resulting species affords highly regioregular poly(3-alkyl-4-fluoro)thiophenes. Comparison of their properties to those of the analogous non-fluorinated polymers shows that backbone fluorination leads to an increase in the polymer ionization potential without a significant change in optical band gap. Fluorination also results in an enhanced tendency to aggregate in solution, which is ascribed to a more co-planar backbone on the basis of Raman and DFT calculations. Average charge carrier mobilities in field-effect transistors are found to increase by up to a factor of 5 for the fluorinated polymers.

A general semiconductor‐independent two‐dimensional character of the carrier distribution in top‐gate polymer field‐effect transistors is revealed by analysing temperature‐dependent transfer characteristics and the sub‐bandgap absorption tails of the polymer semiconductors. A correlation between the extracted width of the density of states and the Urbach energy is presented, corroborating the 2D accumulation layer and demonstrating an intricate connection between optical measurements concerning disorder and charge transport in transistors.

The composition of planets is largely determined by the chemical and dynamical evolution of the disk during planetesimal formation and growth. To predict the diversity of exoplanet compositions, previous works modeled planetesimal composition as the equilibrium chemical composition of a protoplanetary disk at a single time. However, planetesimals form over an extended period of time, during which, elements sequentially condense out of the gas as the disk cools and are accreted onto planetesimals. To account for the evolution of the disk during planetesimal formation, we couple models of disk chemistry and dynamics with a prescription for planetesimal formation. We then follow the growth of these planetesimals into terrestrial planets with N-body simulations of late stage planet formation to evaluate the effect of sequential condensation on the bulk composition of planets. We find that our model produces results similar to those of earlier models for disks with C/O ratios close to the solar value (0.54). However, in disks with C/O ratios greater than 0.8, carbon rich planetesimals form throughout a much larger radial range of the disk. Furthermore, our model produces carbon rich planetesimals in disks with C/O ratios as low as ∼0.65, which is not possible in the static equilibrium chemistry case. These results suggest that (1) there may be a large population of short period carbon rich planets around moderately carbon enhanced stars (0.65 < C/O < 0.8) and (2) carbon rich planets can form throughout the terrestrial planet region around carbon rich stars (C/O > 0.8).

NASA's Kepler Mission uncovered a wealth of planetary systems, many with planets on short-period orbits. These short-period systems reside around 50% of Sun-like stars and are similarly prevalent around M dwarfs. Their formation and subsequent evolution is the subject of active debate. In this paper, we simulate late-stage, in situ planet formation across a grid of planetesimal disks with varying surface density profiles and total mass. We compare simulation results with observable characteristics of the Kepler sample. We identify mixture models with different primordial planetesimal disk properties that self-consistently recover the multiplicity, radius, period and period ratio, and duration ratio distributions of the Kepler planets. We draw three main conclusions. (1) We favor a "frozen-in" narrative for systems of short-period planets, in which they are stable over long timescales, as opposed to metastable. (2) The "Kepler dichotomy," an observed phenomenon of the Kepler sample wherein the architectures of planetary systems appear to either vary significantly or have multiple modes, can naturally be explained by formation within planetesimal disks with varying surface density profiles. Finally, (3) we quantify the nature of the "Kepler dichotomy" for both GK stars and M dwarfs, and find that it varies with stellar type. While the mode of planet formation that accounts for high multiplicity systems occurs in 24%±7% of planetary systems orbiting GK stars, it occurs in 63%±16% of planetary systems orbiting M dwarfs.