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The oceans absorb about a quarter of the annually produced anthropogenic atmospheric carbon dioxide (CO2), resulting in a decrease in surface water pH, a process termed ocean acidification (OA). Surprisingly little is known about how OA affects the physiology of heterotrophic bacteria or the coupling of heterotrophic bacteria to phytoplankton when nutrients are limited. Previous experiments were, for the most part, undertaken during productive phases or following nutrient additions designed to stimulate algal blooms. Therefore, we performed an in situ large-volume mesocosm (similar to 55 m(3)) experiment in the Baltic Sea by simulating different fugacities of CO2 (fCO(2)) extending from present to future conditions. The study was conducted in July-August after the nominal spring bloom, in order to maintain low-nutrient conditions throughout the experiment. This resulted in phytoplankton communities dominated by small-sized functional groups (picophytoplankton). There was no consistent fCO(2)-induced effect on bacterial protein production (BPP), cell-specific BPP (csBPP) or biovolumes (BVs) of either free-living (FL) or particle-associated (PA) heterotrophic bacteria, when considered as individual components (univariate analyses). Permutational Multivariate Analysis of Variance (PERMANOVA) revealed a significant effect of the fCO(2) treatment on entire assemblages of dissolved and particulate nutrients, metabolic parameters and the bacteria-phytoplankton community. However, distance-based linear modelling only identified fCO(2) as a factor explaining the variability observed amongst the microbial community composition, but not for explaining variability within the metabolic parameters. This suggests that fCO(2) impacts on microbial metabolic parameters occurred indirectly through varying physicochemical parameters and microbial species composition. Cluster analyses examining the co-occurrence of different functional groups of bacteria and phytoplankton further revealed a separation of the four fCO(2)-treated mesocosms from both control mesocosms, indicating that complex trophic interactions might be altered in a future acidified ocean. Possible consequences for nutrient cycling and carbon export are still largely unknown, in particular in a nutrient-limited ocean.
Carbon (C) sequestration in soils plays a key role in the global C cycle. It is therefore crucial to adequately monitor dynamics in soil organic carbon (Delta SOC) stocks when aiming to reveal underlying processes and potential drivers. However, small-scale spatial (10-30 m) and temporal changes in SOC stocks, particularly pronounced in arable lands, are hard to assess. The main reasons for this are limitations of the well-established methods. On the one hand, repeated soil inventories, often used in long-term field trials, reveal spatial patterns and trends in Delta SOC but require a longer observation period and a sufficient number of repetitions. On the other hand, eddy covariance measurements of C fluxes towards a complete C budget of the soil-plant-atmosphere system may help to obtain temporal Delta SOC patterns but lack small-scale spatial resolution.
To overcome these limitations, this study presents a reliable method to detect both short-term temporal dynamics as well as small-scale spatial differences of Delta SOC using measurements of the net ecosystem carbon balance (NECB) as a proxy. To estimate the NECB, a combination of automatic chamber (AC) measurements of CO2 exchange and empirically modeled aboveground biomass development (NPPshoot / were used. To verify our method, results were compared with Delta SOC observed by soil resampling.
Soil resampling and AC measurements were performed from 2010 to 2014 at a colluvial depression located in the hummocky ground moraine landscape of northeastern Germany. The measurement site is characterized by a variable groundwater level (GWL) and pronounced small-scale spatial heterogeneity regarding SOC and nitrogen (Nt) stocks. Tendencies and magnitude of Delta SOC values derived by AC measurements and repeated soil inventories corresponded well. The period of maximum plant growth was identified as being most important for the development of spatial differences in annual Delta SOC. Hence, we were able to confirm that AC-based C budgets are able to reveal small-scale spatial differences and short-term temporal dynamics of Delta SOC.
The study deals with the identification and characterization of rapid subsurface flow structures through pedo- and geo-physical measurements and irrigation experiments at the point, plot and hillslope scale. Our investigation of flow-relevant structures and hydrological responses refers to the general interplay of form and function, respectively. To obtain a holistic picture of the subsurface, a large set of different laboratory, exploratory and experimental methods was used at the different scales. For exploration these methods included drilled soil core profiles, in situ measurements of infiltration capacity and saturated hydraulic conductivity, and laboratory analyses of soil water retention and saturated hydraulic conductivity. The irrigation experiments at the plot scale were monitored through a combination of dye tracer, salt tracer, soil moisture dynamics, and 3-D time-lapse ground penetrating radar (GPR) methods. At the hillslope scale the subsurface was explored by a 3-D GPR survey. A natural storm event and an irrigation experiment were monitored by a dense network of soil moisture observations and a cascade of 2-D time-lapse GPR "trenches". We show that the shift between activated and non-activated state of the flow paths is needed to distinguish structures from overall heterogeneity. Pedo-physical analyses of point-scale samples are the basis for sub-scale structure inference. At the plot and hillslope scale 3-D and 2-D time-lapse GPR applications are successfully employed as non-invasive means to image subsurface response patterns and to identify flow-relevant paths. Tracer recovery and soil water responses from irrigation experiments deliver a consistent estimate of response velocities. The combined observation of form and function under active conditions provides the means to localize and characterize the structures (this study) and the hydrological processes (companion study Angermann et al., 2017, this issue).
Landscape evolution models (LEMs) allow the study of earth surface responses to changing climatic and tectonic forcings. While much effort has been devoted to the development of LEMs that simulate a wide range of processes, the numerical accuracy of these models has received less attention. Most LEMs use first-order accurate numerical methods that suffer from substantial numerical diffusion. Numerical diffusion particularly affects the solution of the advection equation and thus the simulation of retreating landforms such as cliffs and river knickpoints. This has potential consequences for the integrated response of the simulated landscape. Here we test a higher-order flux-limiting finite volume method that is total variation diminishing (TVD-FVM) to solve the partial differential equations of river incision and tectonic displacement. We show that using the TVD-FVM to simulate river incision significantly influences the evolution of simulated landscapes and the spatial and temporal variability of catchment-wide erosion rates. Furthermore, a two-dimensional TVD-FVM accurately simulates the evolution of landscapes affected by lateral tectonic displacement, a process whose simulation was hitherto largely limited to LEMs with flexible spatial discretization. We implement the scheme in TTLEM (TopoToolbox Landscape Evolution Model), a spatially explicit, raster-based LEM for the study of fluvially eroding landscapes in TopoToolbox 2.
In spite of the fundamental role of the landscape water balance for the Earth's water and energy cycles, monitoring the water balance and its components beyond the point scale is notoriously difficult due to the multitude of flow and storage processes and their spatial heterogeneity. Here, we present the first field deployment of an iGrav superconducting gravimeter (SG) in a minimized enclosure for long-term integrative monitoring of water storage changes. Results of the field SG on a grassland site under wet-temperate climate conditions were compared to data provided by a nearby SG located in the controlled environment of an observatory building. The field system proves to provide gravity time series that are similarly precise as those of the observatory SG. At the same time, the field SG is more sensitive to hydrological variations than the observatory SG. We demonstrate that the gravity variations observed by the field setup are almost independent of the depth below the terrain surface where water storage changes occur (contrary to SGs in buildings), and thus the field SG system directly observes the total water storage change, i.e., the water balance, in its surroundings in an integrative way. We provide a framework to single out the water balance components actual evapotranspiration and lateral subsurface discharge from the gravity time series on annual to daily timescales. With about 99 and 85% of the gravity signal due to local water storage changes originating within a radius of 4000 and 200m around the instrument, respectively, this setup paves the road towards gravimetry as a continuous hydrological field-monitoring technique at the landscape scale.
The isotopic composition of water in ice sheets is extensively used to infer past climate changes. In low-accumulation regions their interpretation is, however, challenged by poorly constrained effects that may influence the initial isotope signal during and after deposition of the snow. This is reflected in snow-pit isotope data from Kohnen Station, Antarctica, which exhibit a seasonal cycle but also strong interannual variations that contradict local temperature observations. These inconsistencies persist even after averaging many profiles and are thus not explained by local stratigraphic noise. Previous studies have suggested that post-depositional processes may significantly influence the isotopic composition of East Antarctic firn. Here, we investigate the importance of post-depositional processes within the open-porous firn (greater than or similar to 10 cm depth) at Kohnen Station by separating spatial from temporal variability. To this end, we analyse 22 isotope profiles obtained from two snow trenches and examine the temporal isotope modifications by comparing the new data with published trench data extracted 2 years earlier. The initial isotope profiles undergo changes over time due to downward advection, firn diffusion and densification in magnitudes consistent with independent estimates. Beyond that, we find further modifications of the original isotope record to be unlikely or small in magnitude (<< 1 parts per thousand RMSD). These results show that the discrepancy between local temperatures and isotopes most likely originates from spatially coherent processes prior to or during deposition, such as precipitation intermittency or systematic isotope modifications acting on drifting or loose surface snow.
The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.
Past climatic change can be reconstructed from sedimentary archives by a number of proxies. However, few methods exist to directly estimate hydrological changes and even fewer result in quantitative data, impeding our understanding of the timing, magnitude and mechanisms of hydrological changes.
Here we present a novel approach based on delta H-2 values of sedimentary lipid biomarkers in combination with plant physiological modeling to extract quantitative information on past changes in relative humidity. Our initial application to an annually laminated lacustrine sediment sequence from western Europe deposited during the Younger Dryas cold period revealed relative humidity changes of up to 15% over sub-centennial timescales, leading to major ecosystem changes, in agreement with palynological data from the region. We show that by combining organic geochemical methods and mechanistic plant physiological models on well characterized lacustrine archives it is possible to extract quantitative ecohydrological parameters from sedimentary lipid biomarker delta H-2 data.
Flood damage can be mitigated if the parties at risk are reached by flood warnings and if they know how to react appropriately. To gain more knowledge about warning reception and emergency response of private households and companies, surveys were undertaken after the August 2002 and the June 2013 floods in Germany. Despite pronounced regional differences, the results show a clear overall picture: in 2002, early warnings did not work well; e.g. many households (27 %) and companies (45 %) stated that they had not received any flood warnings. Additionally, the preparedness of private households and companies was low in 2002, mainly due to a lack of flood experience. After the 2002 flood, many initiatives were launched and investments undertaken to improve flood risk management, including early warnings and an emergency response in Germany. In 2013, only a small share of the affected households (5 %) and companies (3 %) were not reached by any warnings. Additionally, private households and companies were better prepared. For instance, the share of companies which have an emergency plan in place has increased from 10% in 2002 to 34% in 2013. However, there is still room for improvement, which needs to be triggered mainly by effective risk and emergency communication. The challenge is to continuously maintain and advance an integrated early warning and emergency response system even without the occurrence of extreme floods.
The phrase form and function was established in architecture and biology and refers to the idea that form and functionality are closely correlated, influence each other, and co-evolve. We suggest transferring this idea to hydrological systems to separate and analyze their two main characteristics: their form, which is equivalent to the spatial structure and static properties, and their function, equivalent to internal responses and hydrological behavior. While this approach is not particularly new to hydrological field research, we want to employ this concept to explicitly pursue the question of what information is most advantageous to understand a hydrological system. We applied this concept to subsurface flow within a hillslope, with a methodological focus on function: we conducted observations during a natural storm event and followed this with a hillslope-scale irrigation experiment. The results are used to infer hydrological processes of the monitored system. Based on these findings, the explanatory power and conclusiveness of the data are discussed. The measurements included basic hydrological monitoring methods, like piezometers, soil moisture, and discharge measurements. These were accompanied by isotope sampling and a novel application of 2-D time-lapse GPR (ground-penetrating radar). The main finding regarding the processes in the hillslope was that preferential flow paths were established quickly, despite unsaturated conditions. These flow paths also caused a detectable signal in the catchment response following a natural rainfall event, showing that these processes are relevant also at the catchment scale. Thus, we conclude that response observations (dynamics and patterns, i.e., indicators of function) were well suited to describing processes at the observational scale. Especially the use of 2-D time-lapse GPR measurements, providing detailed subsurface response patterns, as well as the combination of stream-centered and hillslope-centered approaches, allowed us to link processes and put them in a larger context. Transfer to other scales beyond observational scale and generalizations, however, rely on the knowledge of structures (form) and remain speculative. The complementary approach with a methodological focus on form (i.e., structure exploration) is presented and discussed in the companion paper by Jackisch et al. (2017).
In hydrological models, parameters are used to represent the time-invariant characteristics of catchments and to capture different aspects of hydrological response. Hence, model parameters need to be identified based on their role in controlling the hydrological behaviour. For the identification of meaningful parameter values, multiple and complementary performance criteria are used that compare modelled and measured discharge time series. The reliability of the identification of hydrologically meaningful model parameter values depends on how distinctly a model parameter can be assigned to one of the performance criteria.& para;& para;To investigate this, we introduce the new concept of connective strength between model parameters and performance criteria. The connective strength assesses the intensity in the interrelationship between model parameters and performance criteria in a bijective way. In our analysis of connective strength, model simulations are carried out based on a latin hypercube sampling. Ten performance criteria including Nash-Sutcliffe efficiency (NSE), Kling-Gupta efficiency (KGE) and its three components (alpha, beta and r) as well as RSR (the ratio of the root mean square error to the standard deviation) for different segments of the flow duration curve (FDC) are calculated.& para;& para;With a joint analysis of two regression tree (RT) approaches, we derive how a model parameter is connected to different performance criteria. At first, RTs are constructed using each performance criterion as the target variable to detect the most relevant model parameters for each performance criterion. Secondly, RTs are constructed using each parameter as the target variable to detect which performance criteria are impacted by changes in the values of one distinct model parameter. Based on this, appropriate performance criteria are identified for each model parameter.& para;& para;In this study, a high bijective connective strength between model parameters and performance criteria is found for low- and mid-flow conditions. Moreover, the RT analyses emphasise the benefit of an individual analysis of the three components of KGE and of the FDC segments. Furthermore, the RT analyses highlight under which conditions these performance criteria provide insights into precise parameter identification. Our results show that separate performance criteria are required to identify dominant parameters on low- and mid-flow conditions, whilst the number of required performance criteria for high flows increases with increasing process complexity in the catchment. Overall, the analysis of the connective strength between model parameters and performance criteria using RTs contribute to a more realistic handling of parameters and performance criteria in hydrological modelling.
Transition metals in inorganic systems and metalloproteins can occur in different oxidation states, which makes them ideal redox-active catalysts. To gain a mechanistic understanding of the catalytic reactions, knowledge of the oxidation state of the active metals, ideally in operando, is therefore critical. L-edge X-ray absorption spectroscopy (XAS) is a powerful technique that is frequently used to infer the oxidation state via a distinct blue shift of L-edge absorption energies with increasing oxidation state. A unified description accounting for quantum-chemical notions whereupon oxidation does not occur locally on the metal but on the whole molecule and the basic understanding that L-edge XAS probes the electronic structure locally at the metal has been missing to date. Here we quantify how charge and spin densities change at the metal and throughout the molecule for both redox and core-excitation processes. We explain the origin of the L-edge XAS shift between the high-spin complexes Mn-II(acac)(2) and Mn-III(acac)(3) as representative model systems and use ab initio theory to uncouple effects of oxidation-state changes from geometric effects. The shift reflects an increased electron affinity of Mn-III in the core-excited states compared to the ground state due to a contraction of the Mn 3d shell upon core-excitation with accompanied changes in the classical Coulomb interactions. This new picture quantifies how the metal-centered core hole probes changes in formal oxidation state and encloses and substantiates earlier explanations. The approach is broadly applicable to mechanistic studies of redox-catalytic reactions in molecular systems where charge and spin localization/delocalization determine reaction pathways.
The power spectral density (PSD) of any time-dependent stochastic processX (t) is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X-t over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT -> infinity. Alegitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.
Ice-rich yedoma-dominated landscapes store con-
siderable amounts of organic carbon (C) and nitrogen (N)
and are vulnerable to degradation under climate warming.
We investigate the C and N pools in two thermokarst-affected
yedoma landscapes – on Sobo-Sise Island and on Bykovsky
Peninsula in the north of eastern Siberia. Soil cores up to 3 m
depth were collected along geomorphic gradients and anal-
ysed for organic C and N contents. A high vertical sampling
density in the profiles allowed the calculation of C and N
stocks for short soil column intervals and enhanced under-
standing of within-core parameter variability. Profile-level C
and N stocks were scaled to the landscape level based on
landform classifications from 5 m resolution, multispectral
RapidEye satellite imagery. Mean landscape C and N storage
in the first metre of soil for Sobo-Sise Island is estimated to
be 20.2 kg C m −2 and 1.8 kg N m −2 and for Bykovsky Penin-
sula 25.9 kg C m −2 and 2.2 kg N m −2 . Radiocarbon dating
demonstrates the Holocene age of thermokarst basin de-
posits but also suggests the presence of thick Holocene-
age cover layers which can reach up to 2 m on top of in-
tact yedoma landforms. Reconstructed sedimentation rates
of 0.10–0.57 mm yr −1 suggest sustained mineral soil accu-
mulation across all investigated landforms. Both yedoma and
thermokarst landforms are characterized by limited accumu-
lation of organic soil layers (peat).
We further estimate that an active layer deepening of
about 100 cm will increase organic C availability in a sea-
sonally thawed state in the two study areas by ∼ 5.8 Tg
(13.2 kg C m −2 ). Our study demonstrates the importance of
increasing the number of C and N storage inventories in ice-
rich yedoma and thermokarst environments in order to ac-
count for high variability of permafrost and thermokarst en-
vironments in pan-permafrost soil C and N pool estimates.
Flash floods are caused by intense rainfall events and represent an insufficiently understood phenomenon in Germany. As a result of higher precipitation intensities, flash floods might occur more frequently in future. In combination with changing land use patterns and urbanisation, damage mitigation, insurance and risk management in flash-flood-prone regions are becoming increasingly important. However, a better understanding of damage caused by flash floods requires ex post collection of relevant but yet sparsely available information for research. At the end of May 2016, very high and concentrated rainfall intensities led to severe flash floods in several southern German municipalities. The small town of Braunsbach stood as a prime example of the devastating potential of such events. Eight to ten days after the flash flood event, damage assessment and data collection were conducted in Braunsbach by investigating all affected buildings and their surroundings. To record and store the data on site, the open-source software bundle KoBoCollect was used as an efficient and easy way to gather information. Since the damage driving factors of flash floods are expected to differ from those of riverine flooding, a post-hoc data analysis was performed, aiming to identify the influence of flood processes and building attributes on damage grades, which reflect the extent of structural damage. Data analyses include the application of random forest, a random general linear model and multinomial logistic regression as well as the construction of a local impact map to reveal influences on the damage grades. Further, a Spearman's Rho correlation matrix was calculated. The results reveal that the damage driving factors of flash floods differ from those of riverine floods to a certain extent. The exposition of a building in flow direction shows an especially strong correlation with the damage grade and has a high predictive power within the constructed damage models. Additionally, the results suggest that building materials as well as various building aspects, such as the existence of a shop window and the surroundings, might have an effect on the resulting damage. To verify and confirm the outcomes as well as to support future mitigation strategies, risk management and planning, more comprehensive and systematic data collection is necessary.
Here we report on a cyclic, physical ice-discharge instability in the Parallel Ice Sheet Model, simulating the flow of a three-dimensional, inherently buttressed ice-sheet-shelf system which periodically surges on a millennial timescale. The thermomechanically coupled model on 1 km horizontal resolution includes an enthalpy-based formulation of the thermodynamics, a nonlinear stress-balance-based sliding law and a very simple subglacial hydrology. The simulated unforced surging is characterized by rapid ice streaming through a bed trough, resulting in abrupt discharge of ice across the grounding line which is eventually calved into the ocean. We visualize the central feedbacks that dominate the subsequent phases of ice buildup, surge and stabilization which emerge from the interaction between ice dynamics, thermodynamics and the subglacial till layer. Results from the variation of surface mass balance and basal roughness suggest that ice sheets of medium thickness may be more susceptible to surging than relatively thin or thick ones for which the surge feedback loop is damped. We also investigate the influence of different basal sliding laws (ranging from purely plastic to nonlinear to linear) on possible surging. The presented mechanisms underlying our simulations of self-maintained, periodic ice growth and destabilization may play a role in large-scale ice-sheet surging, such as the surging of the Laurentide Ice Sheet, which is associated with Heinrich events, and ice-stream shutdown and reactivation, such as observed in the Siple Coast region of West Antarctica.
Hantavirus assembly and budding are governed by the surface glycoproteins Gn and Gc. In this study, we investigated the glycoproteins of Puumala, the most abundant Hantavirus species in Europe, using fluorescently labeled wild-type constructs and cytoplasmic tail (CT) mutants. We analyzed their intracellular distribution, co-localization and oligomerization, applying comprehensive live, single-cell fluorescence techniques, including confocal microscopy, imaging flow cytometry, anisotropy imaging and Number&Brightness analysis. We demonstrate that Gc is significantly enriched in the Golgi apparatus in absence of other viral components, while Gn is mainly restricted to the endoplasmic reticulum (ER). Importantly, upon co-expression both glycoproteins were found in the Golgi apparatus. Furthermore, we show that an intact CT of Gc is necessary for efficient Golgi localization, while the CT of Gn influences protein stability. Finally, we found that Gn assembles into higher-order homo-oligomers, mainly dimers and tetramers, in the ER while Gc was present as mixture of monomers and dimers within the Golgi apparatus. Our findings suggest that PUUV Gc is the driving factor of the targeting of Gc and Gn to the Golgi region, while Gn possesses a significantly stronger self-association potential.
Germination, a crucial phase in the life cycle of a plant, can be significantly influenced by competition and facilitation. The aim of this study was to test whether differences in cover of surrounding vegetation can lead to population differentiation in germination behaviour of an annual grassland species, and if so, whether such a differentiation can be found in the native as well as in the introduced range. We used maternal progeny of Erodium cicutarium previously propagated under uniform conditions that had been collected in multiple populations in the native and two introduced ranges, in populations representing extremes in terms of mean and variability of the cover of surrounding vegetation. In the first experiment, we tested the effect of germination temperature and mean cover at the source site on germination, and found interlinked effects of these factors. In seeds from one of the introduced ranges (California), we found indication for a 2-fold dormancy, hindering germination at high temperatures even if physical dormancy was broken and water was available. This behaviour was less strong in high cover populations, indicating cross-generational facilitating effects of dense vegetation. In the second experiment, we tested whether spatial variation in cover of surrounding vegetation has an effect on the proportion of dormant seeds. Contrary to our expectations, we found that across source regions, high variance in cover was associated with higher proportions of seeds germinating directly after storage. In all three regions, germination seemed to match the local environment in terms of climate and vegetation cover. We suggest that this is due to a combined effect of introduction of preadapted genotypes and local evolutionary processes.
Plant functional traits reflect individual and community ecological strategies. They allow the detection of directional changes in community dynamics and ecosystemic processes, being an additional tool to assess biodiversity than species richness. Analysis of functional patterns in plant communities provides mechanistic insight into biodiversity alterations due to anthropogenic activity. Although studies have considered of either anthropogenic management or nutrient availability on functional traits in temperate grasslands, studies combining effects of both drivers are scarce. Here, we assessed the impacts of management intensity (fertilization, mowing, grazing), nutrient stoichiometry (C, N, P, K), and vegetation composition on community-weighted means (CWMs) and functional diversity (Rao's Q) from seven plant traits in 150 grasslands in three regions in Germany, using data of 6 years. Land use and nutrient stoichiometry accounted for larger proportions of model variance of CWM and Rao's Q than species richness and productivity. Grazing affected all analyzed trait groups; fertilization and mowing only impacted generative traits. Grazing was clearly associated with nutrient retention strategies, that is, investing in durable structures and production of fewer, less variable seed. Phenological variability was increased. Fertilization and mowing decreased seed number/mass variability, indicating competition-related effects. Impacts of nutrient stoichiometry on trait syndromes varied. Nutrient limitation (large N:P, C:N ratios) promoted species with conservative strategies, that is, investment in durable plant structures rather than fast growth, fewer seed, and delayed flowering onset. In contrast to seed mass, leaf-economics variability was reduced under P shortage. Species diversity was positively associated with the variability of generative traits. Synthesis. Here, land use, nutrient availability, species richness, and plant functional strategies have been shown to interact complexly, driving community composition, and vegetation responses to management intensity. We suggest that deeper understanding of underlying mechanisms shaping community assembly and biodiversity will require analyzing all these parameters.
We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of
classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah–Singer formula for a pure Dirac operator in four dimensions and for a
twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell–Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.