Adiabatic Evolution of Low-Temperature Many-Body Systems.

We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows us to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. As a corollary, we also establish the validity of linear response. Our strategy is based on a rigorous version of the Wick rotation, which allows us to represent the Duhamel expansion for the real-time dynamics in terms of Euclidean correlation functions, for which precise decay estimates are proved using fermionic cluster expansion.

Responses of rhizosphere fungi to the root economics space in grassland monocultures of different age.

Recent studies on root traits have shown that there are two axes explaining trait variation belowground: the collaboration axis with mycorrhizal partners and the conservation ('fast - slow') axis. However, it is yet unknown whether these trait axes affect the assembly of soilborne fungi. We expect saprotrophic fungi to link to the conservation axis of root traits, whereas pathogenic and arbuscular mycorrhizal fungi link to the collaboration axis, but in opposite directions, as arbuscular mycorrhizal fungi might provide pathogen protection. To test these hypotheses, we sequenced rhizosphere fungal communities and measured root traits in monocultures of 25 grassland plant species, differing in age. Within the fungal guilds, we evaluated fungal species richness, relative abundance and community composition. Contrary to our hypotheses, fungal diversity and relative abundance were not strongly related to the root trait axes. However, saprotrophic fungal community composition was affected by the conservation gradient and pathogenic community composition by the collaboration gradient. The rhizosphere AMF community composition did not change along the collaboration gradient, even though the root trait axis was in line with the root mycorrhizal colonization rate. Overall, our results indicate that in the long term, the root trait axes are linked with fungal community composition.

Increased soil carbon storage through plant diversity strengthens with time and extends into the subsoil.

Soils are important for ecosystem functioning and service provisioning. Soil communities and their functions, in turn, are strongly promoted by plant diversity, and such positive effects strengthen with time. However, plant diversity effects on soil organic matter have mostly been investigated in the topsoil, and there are only very few long-term studies. Thus, it remains unclear if plant diversity effects strengthen with time and to which depth these effects extend. Here, we repeatedly sampled soil to 1 m depth in a long-term grassland biodiversity experiment. We investigated how plant diversity impacted soil organic carbon and nitrogen concentrations and stocks and their stable isotopes 13 C and 15 N, as well as how these effects changed after 5, 10, and 14 years. We found that higher plant diversity increased carbon and nitrogen storage in the topsoil since the establishment of the experiment. Stable isotopes revealed that these increases were associated with new plant-derived inputs, resulting in less processed and less decomposed soil organic matter. In subsoils, mainly the presence of specific plant functional groups drove organic matter dynamics. For example, the presence of deep-rooting tall herbs decreased carbon concentrations, most probably through stimulating soil organic matter decomposition. Moreover, plant diversity effects on soil organic matter became stronger in topsoil over time and reached subsoil layers, while the effects of specific plant functional groups in subsoil progressively diminished over time. Our results indicate that after changing the soil system the pathways of organic matter transfer to the subsoil need time to establish. In our grassland system, organic matter storage in subsoils was driven by the redistribution of already stored soil organic matter from the topsoil to deeper soil layers, for example, via bioturbation or dissolved organic matter. Therefore, managing plant diversity may, thus, have significant implications for subsoil carbon storage and other critical ecosystem services.

Latent Pronucleophiles in Lewis Base Catalysis: Enantioselective Allylation of Silyl Enol Ethers with Allylic Fluorides.

Lewis base catalyzed allylations of C-centered nucleophiles have been largely limited to the niche substrates with acidic C-H substituted for C-F bonds at the stabilized carbanionic carbon. Herein we report that the concept of latent pronucleophiles serves to overcome these limitations and allow for a variety of common stabilized C-nucleophiles, when they are introduced as the corresponding silylated compounds, to undergo enantioselective allylations using allylic fluorides. The reactions of silyl enol ethers afford the allylation products in good yields and with high degree of regio/stereoselectivity as well as diastereoselectivity when cyclic silyl enol ethers are used. Further examples of silylated stabilized carbon nucleophiles that undergo efficient allylation speak in favor of the general applicability of this concept to C-centered nucleophiles.

Land-use intensification causes multitrophic homogenization of grassland communities.

Land-use intensification is a major driver of biodiversity loss. Alongside reductions in local species diversity, biotic homogenization at larger spatial scales is of great concern for conservation. Biotic homogenization means a decrease in ß-diversity (the compositional dissimilarity between sites). Most studies have investigated losses in local (α)-diversity and neglected biodiversity loss at larger spatial scales. Studies addressing ß-diversity have focused on single or a few organism groups (for example, ref. 4), and it is thus unknown whether land-use intensification homogenizes communities at different trophic levels, above- and belowground. Here we show that even moderate increases in local land-use intensity (LUI) cause biotic homogenization across microbial, plant and animal groups, both above- and belowground, and that this is largely independent of changes in α-diversity. We analysed a unique grassland biodiversity dataset, with abundances of more than 4,000 species belonging to 12 trophic groups. LUI, and, in particular, high mowing intensity, had consistent effects on ß-diversity across groups, causing a homogenization of soil microbial, fungal pathogen, plant and arthropod communities. These effects were nonlinear and the strongest declines in ß-diversity occurred in the transition from extensively managed to intermediate intensity grassland. LUI tended to reduce local α-diversity in aboveground groups, whereas the α-diversity increased in belowground groups. Correlations between the ß-diversity of different groups, particularly between plants and their consumers, became weaker at high LUI. This suggests a loss of specialist species and is further evidence for biotic homogenization. The consistently negative effects of LUI on landscape-scale biodiversity underscore the high value of extensively managed grasslands for conserving multitrophic biodiversity and ecosystem service provision. Indeed, biotic homogenization rather than local diversity loss could prove to be the most substantial consequence of land-use intensification.

Biodiversity at multiple trophic levels is needed for ecosystem multifunctionality.

Many experiments have shown that loss of biodiversity reduces the capacity of ecosystems to provide the multiple services on which humans depend. However, experiments necessarily simplify the complexity of natural ecosystems and will normally control for other important drivers of ecosystem functioning, such as the environment or land use. In addition, existing studies typically focus on the diversity of single trophic groups, neglecting the fact that biodiversity loss occurs across many taxa and that the functional effects of any trophic group may depend on the abundance and diversity of others. Here we report analysis of the relationships between the species richness and abundance of nine trophic groups, including 4,600 above- and below-ground taxa, and 14 ecosystem services and functions and with their simultaneous provision (or multifunctionality) in 150 grasslands. We show that high species richness in multiple trophic groups (multitrophic richness) had stronger positive effects on ecosystem services than richness in any individual trophic group; this includes plant species richness, the most widely used measure of biodiversity. On average, three trophic groups influenced each ecosystem service, with each trophic group influencing at least one service. Multitrophic richness was particularly beneficial for 'regulating' and 'cultural' services, and for multifunctionality, whereas a change in the total abundance of species or biomass in multiple trophic groups (the multitrophic abundance) positively affected supporting services. Multitrophic richness and abundance drove ecosystem functioning as strongly as abiotic conditions and land-use intensity, extending previous experimental results to real-world ecosystems. Primary producers, herbivorous insects and microbial decomposers seem to be particularly important drivers of ecosystem functioning, as shown by the strong and frequent positive associations of their richness or abundance with multiple ecosystem services. Our results show that multitrophic richness and abundance support ecosystem functioning, and demonstrate that a focus on single groups has led to researchers to greatly underestimate the functional importance of biodiversity.

Improving the assessment of the probability of success in late stage drug development.

There are several steps to confirming the safety and efficacy of a new medicine. A sequence of trials, each with its own objectives, is usually required. Quantitative risk metrics can be useful for informing decisions about whether a medicine should transition from one stage of development to the next. To obtain an estimate of the probability of regulatory approval, pharmaceutical companies may start with industry-wide success rates and then apply to these subjective adjustments to reflect program-specific information. However, this approach lacks transparency and fails to make full use of data from previous clinical trials. We describe a quantitative Bayesian approach for calculating the probability of success (PoS) at the end of phase II which incorporates internal clinical data from one or more phase IIb studies, industry-wide success rates, and expert opinion or external data if needed. Using an example, we illustrate how PoS can be calculated accounting for differences between the phase II data and future phase III trials, and discuss how the methods can be extended to accommodate accelerated drug development pathways.

Eliciting judgements about dependent quantities of interest: The SHeffield ELicitation Framework extension and copula methods illustrated using an asthma case study.

Pharmaceutical companies regularly need to make decisions about drug development programs based on the limited knowledge from early stage clinical trials. In this situation, eliciting the judgements of experts is an attractive approach for synthesising evidence on the unknown quantities of interest. When calculating the probability of success for a drug development program, multiple quantities of interest-such as the effect of a drug on different endpoints-should not be treated as unrelated. We discuss two approaches for establishing a multivariate distribution for several related quantities within the SHeffield ELicitation Framework (SHELF). The first approach elicits experts' judgements about a quantity of interest conditional on knowledge about another one. For the second approach, we first elicit marginal distributions for each quantity of interest. Then, for each pair of quantities, we elicit the concordance probability that both lie on the same side of their respective elicited medians. This allows us to specify a copula to obtain the joint distribution of the quantities of interest. We show how these approaches were used in an elicitation workshop that was performed to assess the probability of success of the registrational program of an asthma drug. The judgements of the experts, which were obtained prior to completion of the pivotal studies, were well aligned with the final trial results.

Trotter Product Formulae for ∗ -Automorphisms of Quantum Lattice Systems.

We consider the dynamics t ↦ τ t of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that τ t can be efficiently approximated by a product of n automorphisms, each of them being an alternating product generated by the individual terms. For any integer m, we construct a product formula (in the spirit of Trotter) such that the approximation error scales as n - m . Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.

Enantioselective Synthesis of Pyrrolizin-1-ones via Lewis Base Catalyzed N-Allylation of N-Silyl Pyrrole Latent Nucleophiles.

Pyrrolizidine alkaloids and their derivatives often feature interesting biological activities. A class of substituted 2,3-dihydro-1H-pyrrolizin-1-one derivatives has been explored as a potential treatment for Alzheimer's disease, but enantioselective synthesis of these molecules is still elusive. We report that enantioselective N-allylation of N-silyl pyrrole latent nucleophiles with allylic fluorides followed by hydrogenation and diastereoselective Friedel-Crafts cyclization constitute an efficient synthetic route to access enantioenriched substituted 2,3-dihydro-1H-pyrrolizin-1-ones.

Predicting risk of secondary progression in multiple sclerosis: A nomogram.

OBJECTIVES: We aimed at designing a nomogram, a prediction tool, to predict the individual's risk of conversion to secondary progressive multiple sclerosis (SPMS) at the time of multiple sclerosis (MS) onset. METHODS: One derivation and three validation cohorts were established. The derivation cohort included 8825 relapsing-onset MS patients in Sweden. A nomogram was built based on a survival model with the best statistical fit and prediction accuracy. The nomogram was validated using data from 3967 patients in the British Columbia cohort, 176 patients in the ACROSS and 2355 patients in FREEDOMS/FREEDOMS II extension studies. RESULTS: Sex, calendar year of birth, first-recorded Expanded Disability Status Scale (EDSS) score, age at the first EDSS and age at disease onset showed significant predictive ability to estimate the risk of SPMS conversion at 10, 15 and 20 years. The nomogram reached 84% (95% confidence intervals (CIs): 83-85) internal and 77% (95% CI: 76-78), 77% (95% CI: 70-85) and 87% (95% CI: 84-89) external accuracy. CONCLUSIONS: The SPMS nomogram represents a much-needed complementary tool designed to assist in decision-making and patient counselling in the early phase of MS. The SPMS nomogram may improve outcomes by prompting timely and more efficacious treatment for those with a worse prognosis.

Latent Nucleophiles in Lewis Base Catalyzed Enantioselective N-Allylations of N-Heterocycles.

Latent nucleophiles are compounds that are themselves not nucleophilic but can produce a strong nucleophile when activated. Such nucleophiles can expand the scope of Lewis base catalyzed reactions. As a proof of concept, we report that N-silyl pyrroles, indoles, and carbazoles serve as latent N-centered nucleophiles in substitution reactions of allylic fluorides catalyzed by Lewis bases. The reactions feature broad scopes for both reaction partners, excellent regioselectivities, and produce enantioenriched N-allyl pyrroles, indoles, and carbazoles when chiral cinchona alkaloid catalysts are used.

Local Ras activation, PTEN pattern, and global actin flow in the chemotactic responses of oversized cells.

Chemotactic responses of eukaryotic cells require a signal processing system that translates an external gradient of attractant into directed motion. To challenge the response system to its limits, we increased the size of Dictyostelium discoideum cells by using electric-pulse-induced fusion. Large cells formed multiple protrusions at different sites along the gradient of chemoattractant, independently turned towards the gradient and competed with each other. Finally, these cells succeeded to re-establish polarity by coordinating front and tail activities. To analyse the responses, we combined two approaches, one aimed at local responses by visualising the dynamics of Ras activation at the front regions of reorientating cells, the other at global changes of polarity by monitoring front-to-tail-directed actin flow. Asymmetric Ras activation in turning protrusions underscores that gradients can be sensed locally and translated into orientation. Different to cells of normal size, the polarity of large cells is not linked to an increasing front-to-tail gradient of the PIP3-phosphatase PTEN. But even in large cells, the front communicates with the tail through an actin flow that might act as carrier of a protrusion inhibitor.

Gut shuttle service: endozoochory of dispersal-limited soil fauna by gastropods.

Numerous important ecosystem functions and services depend on soil biodiversity. However, little is known about the mechanisms which maintain the vast belowground biodiversity and about the filters shaping soil community composition. Yet, biotic interactions like facilitation and dispersal by animals are assumed to play a crucial role, particularly as most soil animal taxa are strongly limited in their active dispersal abilities. Here, we report on a newfound interaction of potentially high ubiquity and importance in soil communities: the endozoochorous dispersal of soil fauna by gastropods. We focus on the dispersal-limited group of oribatid mites, one of the most diverse and abundant soil animal groups. In a field survey in a German riparian forest, 73% of 40 collected slugs (Arion vulgaris) egested a total of 135 oribatid mites, belonging to 35 species. Notably, 70% of the egested mites were alive and survived the gut passage through slugs. Similar results were found for Roman snails (Helix pomatia), indicating the generality of our findings across different gastropod taxa. Complementary laboratory experiments confirmed our field observations, revealing that oribatid mites are, indeed, ingested and egested alive by slugs, and that they are able to independently escape the faeces and colonise new habitats. Our results strongly indicate that gastropods may help soil organisms to disperse within habitats, to overcome dispersal barriers, and to reach short-lived resource patches. Gastropods might even disperse whole multi-trophic micro-ecosystems, a discovery that could have profound implications for our understanding of dispersal mechanisms and the distribution of soil biodiversity.

Root chemistry and soil fauna, but not soil abiotic conditions explain the effects of plant diversity on root decomposition.

Plant diversity influences many ecosystem functions including root decomposition. However, due to the presence of multiple pathways via which plant diversity may affect root decomposition, our mechanistic understanding of their relationships is limited. In a grassland biodiversity experiment, we simultaneously assessed the effects of three pathways-root litter quality, soil biota, and soil abiotic conditions-on the relationships between plant diversity (in terms of species richness and the presence/absence of grasses and legumes) and root decomposition using structural equation modeling. Our final structural equation model explained 70% of the variation in root mass loss. However, different measures of plant diversity included in our model operated via different pathways to alter root mass loss. Plant species richness had a negative effect on root mass loss. This was partially due to increased Oribatida abundance, but was weakened by enhanced root potassium (K) concentration in more diverse mixtures. Equally, grass presence negatively affected root mass loss. This effect of grasses was mostly mediated via increased root lignin concentration and supported via increased Oribatida abundance and decreased root K concentration. In contrast, legume presence showed a net positive effect on root mass loss via decreased root lignin concentration and increased root magnesium concentration, both of which led to enhanced root mass loss. Overall, the different measures of plant diversity had contrasting effects on root decomposition. Furthermore, we found that root chemistry and soil biota but not root morphology or soil abiotic conditions mediated these effects of plant diversity on root decomposition.

Interannual variation in land-use intensity enhances grassland multidiversity.

Although temporal heterogeneity is a well-accepted driver of biodiversity, effects of interannual variation in land-use intensity (LUI) have not been addressed yet. Additionally, responses to land use can differ greatly among different organisms; therefore, overall effects of land-use on total local biodiversity are hardly known. To test for effects of LUI (quantified as the combined intensity of fertilization, grazing, and mowing) and interannual variation in LUI (SD in LUI across time), we introduce a unique measure of whole-ecosystem biodiversity, multidiversity. This synthesizes individual diversity measures across up to 49 taxonomic groups of plants, animals, fungi, and bacteria from 150 grasslands. Multidiversity declined with increasing LUI among grasslands, particularly for rarer species and aboveground organisms, whereas common species and belowground groups were less sensitive. However, a high level of interannual variation in LUI increased overall multidiversity at low LUI and was even more beneficial for rarer species because it slowed the rate at which the multidiversity of rare species declined with increasing LUI. In more intensively managed grasslands, the diversity of rarer species was, on average, 18% of the maximum diversity across all grasslands when LUI was static over time but increased to 31% of the maximum when LUI changed maximally over time. In addition to decreasing overall LUI, we suggest varying LUI across years as a complementary strategy to promote biodiversity conservation.

Plant functional diversity increases grassland productivity-related water vapor fluxes: an Ecotron and modeling approach.

The impact of species richness and functional diversity of plants on ecosystem water vapor fluxes has been little investigated. To address this knowledge gap, we combined a lysimeter setup in a controlled environment facility (Ecotron) with large ecosystem samples/monoliths originating from a long-term biodiversity experiment (The Jena Experiment) and a modeling approach. Our goals were (1) quantifying the impact of plant species richness (four vs. 16 species) on day- and nighttime ecosystem water vapor fluxes; (2) partitioning ecosystem evapotranspiration into evaporation and plant transpiration using the Shuttleworth and Wallace (SW) energy partitioning model; and (3) identifying the most parsimonious predictors of water vapor fluxes using plant functional-trait-based metrics such as functional diversity and community weighted means. Daytime measured and modeled evapotranspiration were significantly higher in the higher plant diversity treatment, suggesting increased water acquisition. The SW model suggests that, at low plant species richness, a higher proportion of the available energy was diverted to evaporation (a non-productive flux), while, at higher species richness, the proportion of ecosystem transpiration (a productivity-related water flux) increased. While it is well established that LAI controls ecosystem transpiration, here we also identified that the diversity of leaf nitrogen concentration among species in a community is a consistent predictor of ecosystem water vapor fluxes during daytime. The results provide evidence that, at the peak of the growing season, higher leaf area index (LAI) and lower percentage of bare ground at high plant diversity diverts more of the available water to transpiration, a flux closely coupled with photosynthesis and productivity. Higher rates of transpiration presumably contribute to the positive effect of diversity on productivity.

Bottom-up effects of plant diversity on multitrophic interactions in a biodiversity experiment.

Biodiversity is rapidly declining, and this may negatively affect ecosystem processes, including economically important ecosystem services. Previous studies have shown that biodiversity has positive effects on organisms and processes across trophic levels. However, only a few studies have so far incorporated an explicit food-web perspective. In an eight-year biodiversity experiment, we studied an unprecedented range of above- and below-ground organisms and multitrophic interactions. A multitrophic data set originating from a single long-term experiment allows mechanistic insights that would not be gained from meta-analysis of different experiments. Here we show that plant diversity effects dampen with increasing trophic level and degree of omnivory. This was true both for abundance and species richness of organisms. Furthermore, we present comprehensive above-ground/below-ground biodiversity food webs. Both above ground and below ground, herbivores responded more strongly to changes in plant diversity than did carnivores or omnivores. Density and richness of carnivorous taxa was independent of vegetation structure. Below-ground responses to plant diversity were consistently weaker than above-ground responses. Responses to increasing plant diversity were generally positive, but were negative for biological invasion, pathogen infestation and hyperparasitism. Our results suggest that plant diversity has strong bottom-up effects on multitrophic interaction networks, with particularly strong effects on lower trophic levels. Effects on higher trophic levels are indirectly mediated through bottom-up trophic cascades.

Plant diversity shapes microbe-rhizosphere effects on P mobilisation from organic matter in soil.

Plant species richness (PSR) increases nutrient uptake which depletes bioavailable nutrient pools in soil. No such relationship between plant uptake and availability in soil was found for phosphorus (P). We explored PSR effects on P mobilisation [phosphatase activity (PA)] in soil. PA increased with PSR. The positive PSR effect was not solely due to an increase in Corg concentrations because PSR remained significant if related to PA:Corg . An increase in PA per unit Corg increases the probability of the temporal and spatial match between substrate, enzyme and microorganism potentially serving as an adaption to competition. Carbon use efficiency of microorganisms (Cmic :Corg ) increased with increasing PSR while enzyme exudation efficiency (PA:Cmic ) remained constant. These findings suggest the need for efficient C rather than P cycling underlying the relationship between PSR and PA. Our results indicate that the coupling between C and P cycling in soil becomes tighter with increasing PSR.

Analysis of clinical trials with biologics using dose-time-response models.

Biologics such as monoclonal antibodies are increasingly and successfully used for the treatment of many chronic diseases. Unlike conventional small drug molecules, which are commonly given as tablets once daily, biologics are typically injected at much longer time intervals, that is, weeks or months. Hence, both the dose and the time interval have to be optimized during the drug development process for biologics. To identify an adequate regimen for the investigated biologic, the dose-time-response relationship must be well characterized, based on clinical trial data. The proposed approach uses semi-mechanistic nonlinear regression models to describe and predict the time-changing response for complex dosing regimens. Both likelihood-based and Bayesian methods for inference and prediction are discussed. The methodology is illustrated with data from a clinical study in an auto-immune disease.