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The heterogeneity of a dense sand specimen in triaxial compression has been revealed in many different studies using tools such as x-ray computed tomography. It has been shown that a significant variation of the soil variables already exists at the initial state and that, if shear banding occurs, all variables localise inside the specimen. To resolve the discrepancy between such observations and the assumption of a homogeneous specimen, which is commonly made in the interpretation of triaxial tests, one could either extract the local soil behaviour rather than the global one or use the initial distribution of the variables as the initial state of a boundary value problem. For both purposes, the size of a representative elementary volume (REV) is determined regarding the void ratio, two contact fabric descriptors, the volumetric and deviatoric strain. The size of the REV is either determined for individual loading states or by considering the evolution of deforming elements throughout the triaxial test. At the final loading state, a REV size of 3.6 is identified, which is also the size where the statistical distribution of the variables becomes independent of the element size. The same size is determined for the deforming elements and is therefore used to extract the soil behaviour from the evolving shear band. The local soil behaviour is found to be much simpler than the global one, which suggests that the complexity of the global behaviour mainly results from homogenising the highly different zones inside the specimen. Extraction of the soil behaviour inside the evolving shear band with the help of deforming representativeelementary volumes. The volumetric behaviour is represented by the evolution of the void ratio and the evolution ofthe contact fabric anisotropy is closely connected to the stress-strain behaviour. The soil behaviour on the REVscale might form the basis for an alternative approach for the development and calibration of constitutive modelsconsidering the heterogeneity of a soil specimen. [ABSTRACT FROM AUTHOR]

An accurate characterization of the nonlinear behavior of stock markets is of prime importance for the proper design of investment portfolios and the pricing of financial instruments. Surrogate data analysis based on phase randomization and singular value decomposition (SVD) was used to test for multiresolution nonlinear dynamics in the US stock market. The study pointed to the presence of nonlinear dynamics acting at different time scales. Nonlinearity is stronger for larger time horizons and is directly linked to the diversity of patterns, quantified in terms of the SVD entropy, displayed by returns. [ABSTRACT FROM AUTHOR]

Studying the patterns and properties of biological diversity at multiple geographic scales is essential to answering biogeographical and macroecological questions. Here, we tested the hypothesis that diversity estimates derived from stacked species distribution models (stacked SDMs) would be robust and positively correlated when compared to estimates from well-surveyed areas with species checklists, but potentially more ambiguous when compared to estimates based on species' occurrences. We used these three diversity sources to evaluate alpha and beta diversity, per-site range size, total nestedness and completeness at five geographic scales (1/2°, 1/4°, 1/8°, 1/16°, and 1/32°). Estimates from the species' occurrences dataset and stacked SDMs showed poor positive correlation with alpha diversity in well-surveyed areas (except for stacked SDMs at coarse scales). However, beta diversity in well-surveyed areas exhibited a strong correlation with both the species' occurrence dataset and stacked SDMs at finer scales. The nestedness pattern from stacked SDMs remained relatively constant across all geographic scales; in contrast, nestedness in occurrence datasets was influenced by finer scales, thereby affecting community traits such as incidence and composition of species. Our study demonstrates that stacked SDMs was reliable for inferring effective diversities across multiple geographic scales, whereas occurrence datasets are not and may fail to accurately infer diversity patterns. Even well-surveyed areas with species checklists showed low completeness, sharing similarities with occurrence datasets at 1/4° and 1/16°. We recommend conducting complementary analysis of completeness properties of sample coverage to ensure the reliability of diversity assessments. [ABSTRACT FROM AUTHOR]

The urban texture is the physical manifestation of the urban form's evolution. In the rapid process of urbanization, protecting and reshaping the urban texture has become an essential means to sustain the overall form and vitality of cities. Previous studies in this field have primarily relied on image analysis or typological methods, lacking a quantitative approach to identify and analyze the urban texture on a large scale. Moreover, the hierarchical structure and networked organization of the urban texture are gradually being elucidated and emphasized. This study takes a complex network perspective and applies percolation theory to identify and analyze the urban texture. The hierarchical evolutionary characteristics of the urban fabric and the underlying mechanisms driving the scale-dependent differences are analyzed, and the toughness of the urban texture is evaluated based on hierarchical connections. The research findings reveal the key scale in the cross-scale evolution of urban textures, with variations in scale dependence and hierarchical evolution characteristics among different types of urban texture. The traditional urban texture displays sensitivity to scale changes, maintaining its integrity and internal connectivity at small scales. On the other hand, the texture characteristics of modern and contemporary urban areas are only discernible at larger scales. The emergence of large-scale texture clusters at specific scale levels can be explained using multiple index systems. This study has reference significance for the preservation and renewal of the urban fabric in urban renewal processes. [ABSTRACT FROM AUTHOR]

Considering a whole summer season in central Europe, we find that the operational, convection‐permitting ICON‐D2 ensemble prediction system is spatially underdispersive in convective precipitation forecasts. The spatial spread of hourly precipitation is insufficient to capture the inherent error adequately across all scales (up to 300 km) and forecast times (up to 24 h). This lack of spread becomes more pronounced in the weak convective forcing regime. Using physically based stochastic perturbations in the planetary boundary layer is beneficial and leads to a reduction in spatial error at scales larger than 20 km and increases the spread at scales less than 50 km during weak forcing of convection, whereas the effect is almost neutral during strong forcing. Complementing the stochastic perturbations by perturbed parameters in the microphysics scheme shows an additive effect on spatial error and spread for a characteristic case study. Assessing the practical predictability of convective precipitation in a flow‐dependent manner is crucial, and our approach of combining multiple sources of uncertainty proves beneficial in mitigating the spatial underdispersion across scales, particularly during weak convective forcing. [ABSTRACT FROM AUTHOR]

Latitudinal biodiversity gradients vary across taxonomic groups and spatial scales, and various environmental factors have been associated with those patterns. However, it remains unknown whether taxonomic groups with strong ecological associations have similar or different latitudinal patterns. Macroalgae are foundation assemblages on rocky intertidal shores and are often inhabited by invertebrates, predominantly polychaetes. This study analysed latitudinal patterns of macroalgae and their associated polychaetes at different spatial scales and determined how environmental factors influenced those patterns. Macroalgae and polychaetes were collected from transects within 38 rocky intertidal shores of Western Australia at 14 latitudes between 18° S and 34° S. Latitudinal gradients in species richness, diversity (Simpson's diversity index) and abundance were evaluated at transect, site and latitudinal scales. Relationships between environmental factors and rocky intertidal assemblages were analysed using piecewise structural equation modelling based on direct, indirect and complex models. Macroalgae showed increases in species richness, diversity and abundance at transect and site scales towards high latitudes, but species richness and diversity patterns were unclear at the latitudinal scale where transect and site data were pooled. In contrast, polychaete diversity decreased towards high latitudes, although this pattern was unclear at the transect scale. Polychaete richness and abundance tended to follow parabolic patterns that peaked at 27° S. Relationships between environmental factors and rocky intertidal assemblages were best described by a complex model, with significant relationships more often at transect and site scales. Sea surface temperatures showed the strongest relationship with macroalgal and polychaete distributions. [ABSTRACT FROM AUTHOR]

The land use and ecological environment of the Bailong River Basin (BRB) have undergone significant changes in the context of developing urban–rural integration and ecological conservation in western China. As a key ecologically fragile area in the west region, a landscape ecological risk (LER) assessment can reflect the extent to which human activities and environmental changes threaten the ecosystems in the BRB. This study aims to explore the empowerment of indicator weights in an LER assessment. Landscape index weights and LER were analyzed based on land use data for three periods using objective and combined empowerment methods. It was found that the weighting results had apparent scale dependence, and the entropy weight method had the best results in indicator empowerment. From 2000–2020, the LER presented reduced risk, increased heterogeneity, and reduced aggregation. The shift from a medium-risk area to a lower-risk area was the primary transfer type of LER in the study area, and the LER showed a decreasing development trend. So far, research on weight empowerment in LER evaluations has been urgent. This study improved the landscape ecological risk assessment system by selecting an empowerment method that optimally takes into account scale dependence while providing valuable insights into the sustainability of the landscape in this watershed. [ABSTRACT FROM AUTHOR]

In this article, we summarize the main takeaways from a symposium and hybrid virtual and in-person participatory discussion focused on the challenges of scale in understanding the ecology and management of phyllosphere microbial communities. We provide an overview of the confounding effects of spatial scale on inference in microbial ecology, the spatial organization of microbial interactions in the phyllosphere, advances and remaining gaps in measuring phyllosphere colonization across scales, and the epidemiology in the phyllosphere. We hope to motivate further discussion and the development and adoption of creative approaches to solving the challenges of scale to enhance fundamental understanding and practical management of the phyllosphere microbiomes.

Expert range maps (ExpRMs) are frequently used to inform species distributions, but often incomplete or missing for many species, particularly among plants and invertebrates. Many species without ExpRMs also have too few occurrence records for reliable application of species distribution models (SDMs). Here we evaluate the performance of commonly used range surrogates and recommend tools that can help fill this significant knowledge gap across a wide range of understudied taxa. Specifically, we explore an alternative range surrogate (ecoregional range maps; EcoRMs), assess its performance versus traditional approaches for 624 North American butterfly species, and outline its use alone and as part of SDMs. As an alternative range estimate, we use terrestrial ecoregions that represent a regionalization of biogeographical zones and we suggest geographical filters and simplifications that improve their performance. We show that consistently across different spatial scales and both in comparison with ExpRMs and SDMs, EcoRMs have an exceptionally high sensitivity and generally a high mean performance. Particularly for species with fewer than 100 occurrence records, EcoRMs outperform other range surrogates. The congruence of species richness patterns was also similar for all approaches. The use of EcoRMs as substitute for data‐poor species without ExpRMs will strongly boost taxonomic coverage of range maps. Additionally, integrating EcoRMs as domains/masks/offsets into SDMs promises significant improvements to model accuracy. For butterflies alone, EcoRMs would thereby provide new range information for 17% and improve basic range information for 43% of all approximately nineteen thousand species. Other technical advantages of generating EcoRMs may also help to overcome issues of the availability, updateability, reproducibility, and circularity of ExpRMs, SDMs and minimum convex hulls (MCVs). In summary, ecoregion‐based range maps offer a versatile tool for ecology and conservation of terrestrial taxa and the application of the EcoRM approach may prove similarly useful for freshwater and marine ecoregions. [ABSTRACT FROM AUTHOR]

Context: Industrial development in Canada's boreal forest creates cumulative environmental effects on biodiversity. Some effects may be scale-dependent, creating uncertainty in understanding and hindering effective management. Objectives: We estimated cumulative effects of energy sector development on distributions of sixteen migratory songbird species at multiple spatial scales within the boreal region of Alberta, Canada, and evaluated evidence for scale domains in species responses. Methods: We used a hierarchical, multi-scale sampling and modelling framework to compare effects of oil and gas footprint on songbirds at five spatial scales. We used Bayesian Lasso to facilitate direct comparison of parameter estimates across scales, and tested for differences in grouped parameter estimates among species. Results: We found consistent scale-dependent patterns across species, showing variable responses to development occurring at the smallest scale, little effect at intermediate scales, and stronger, mainly positive effects at the largest scales. Differences in grouped parameter estimates across scales showed strong evidence for scale domains in the response of songbirds to energy sector development. Conclusions: We concluded that variable effects at the smallest scale represented individual habitat selection, while larger scale positive effects reflected expanding distributions of open habitat- and disturbance-associated species in areas of high oil and gas footprint. Our results show that single-scale analyses do not reflect population processes occurring at other scales. Future research on linking patterns at different scales is required to fully understand cumulative effects of land use change on wildlife populations. [ABSTRACT FROM AUTHOR]

The idea of quantum mechanical vacuum energy contributing to the cosmological vacuum energy density is not new. However, despite the persisting cosmological constant problem, few investigations have focused on this subject. We explore the possibility that the quantum vacuum energy density contributes to the (local) gravitational energy density in the framework of a scale-dependent cosmological constant Λ and Newton's constant G. This hypothesis has several important consequences, ranging from quantum scale-dependence to the hypothetical prospect of novel experimental insight concerning the quantum origin of cosmological energy density. [ABSTRACT FROM AUTHOR]

Context: The role of landscape diversity and structure is crucial for maintaining biodiversity. Both landscape diversity and structure have often been analysed on one thematic layer, focusing on Shannon diversity. The application of compositional diversity, however, has received little attention yet. Objectives: Our main goal was to introduce a novel framework to assess both landscape compositional diversity and structure in one coherent framework. Moreover, we intended to demonstrate the significance of the use of a neutral model for landscape assessments. Methods: Both entire Hungary and nine of its regions were used as study areas. Juhász-Nagy's information theory-based functions, i.e. "compositional diversity" and "associatum", were introduced and applied in landscape context. Potential and actual landscape characteristics were compared by analysing a probabilistic representation of potential natural vegetation (multiple PNV, MPNV) and actual vegetation (AV), treating MPNV as a neutral model. Results: A significant difference was found between the MPNV- and AV-based, maximal compositional diversity estimates. MPNV-based maximal compositional diversity was higher and the maximum appeared at a finer spatial scale. The differences were more prominent in human-modified regions. Associatum implied the spatial aggregation of both MPNV and AV. Fragmentation of AV was indicated by larger units carrying maximal compositional diversity and maximal associatum values. Conclusions: Applying the multiscale Juhász-Nagy's functions to landscape composition allowed more precise characterization of the landscape state than traditional Shannon diversity. Our results underline, that increasingly transformed landscapes host decreasing complexity of vegetation type combinations and increasing grain that carries the richest information on landscape vegetation patterns. [ABSTRACT FROM AUTHOR]

The urban texture is the physical manifestation of the urban form’s evolution. In the rapid process of urbanization, protecting and reshaping the urban texture has become an essential means to sustain the overall form and vitality of cities. Previous studies in this field have primarily relied on image analysis or typological methods, lacking a quantitative approach to identify and analyze the urban texture on a large scale. Moreover, the hierarchical structure and networked organization of the urban texture are gradually being elucidated and emphasized. This study takes a complex network perspective and applies percolation theory to identify and analyze the urban texture. The hierarchical evolutionary characteristics of the urban fabric and the underlying mechanisms driving the scale-dependent differences are analyzed, and the toughness of the urban texture is evaluated based on hierarchical connections. The research findings reveal the key scale in the cross-scale evolution of urban textures, with variations in scale dependence and hierarchical evolution characteristics among different types of urban texture. The traditional urban texture displays sensitivity to scale changes, maintaining its integrity and internal connectivity at small scales. On the other hand, the texture characteristics of modern and contemporary urban areas are only discernible at larger scales. The emergence of large-scale texture clusters at specific scale levels can be explained using multiple index systems. This study has reference significance for the preservation and renewal of the urban fabric in urban renewal processes.

Beta‐diversity, or the spatio‐temporal variation in community composition, can be partitioned into turnover and nestedness components in a multidimensional framework. Forest structure, including comprehensive characteristics of vertical and horizontal complexity, strongly affects species composition and its spatial variation. However, the effects of forest structure on beta‐diversity patterns in multidimensional and multiple‐scale contexts are poorly understood. Here, we assessed beta‐diversity at local (a 20‐ha forest dynamics plot) and regional (a plot network composed of 19 1‐ha plots) scales in a Chinese subtropical evergreen broad‐leaved forest. We then evaluated the relative importance of forest structure, topography, and spatial structure on beta‐diversity and its turnover and nestedness components in taxonomic, functional, and phylogenetic dimensions at local and regional scales. We derived forest structural parameters from both unmanned aerial vehicle light detection and ranging (UAV LiDAR) data and plot inventory data. Turnover component dominated total beta‐diversity for all dimensions at the two scales. With the exception of some components (taxonomic and functional turnover at the local scale; functional nestedness at the regional scale), environmental factors (i.e., topography and forest structure) contributed more than pure spatial variation. Explanations of forest structure for beta‐diversity and its component patterns at the local scale were higher than those at the regional scale. The joint effects of spatial structure and forest structure influenced component patterns in all dimensions (except for functional turnover) to some extent at the local scale, while pure forest structure influenced taxonomic and phylogenetic nestedness patterns to some extent at the regional scale. Our results highlight the importance and scale dependence of forest structure in shaping multidimensional beta‐diversity and its component patterns. Clearly, further studies need to link forest structure directly to ecological processes (e.g., asymmetric light competition and disturbance dynamics) and explore its roles in biodiversity maintenance. [ABSTRACT FROM AUTHOR]

A better understanding of the relationships between non-point source (NPS) pollution–related processes and their drivers will help to develop scientific watershed management measures. Although various studies have explored the drivers' impact on NPS pollution–related processes, quantitative knowledge of the properties within these relationships is still needed. This study uses the Integrated Valuation of Ecosystem Services and Trade-offs (InVEST) model to produce three related processes of NPS pollution, quick flow (QF), nitrogen export (NE), and sediment export (SE), in the upstream watershed of Chaohu Lake, China. The spatial distributions of QF, NE, and SE and their responses to multiple natural-socioeconomic drivers at nine spatial scales (1 km2, 10 km2, 20 km2, 30 km2, 50 km2, 75 km2, 100 km2, 200 km2, and town) were compared. The results showed that the spatial scale has little impact on the spatial distributions of NPS pollution–related processes. Across the nine scales, the socioeconomic drivers related to agricultural activities, area proportions of cultivated land (cultivated) and paddy field (paddy), have dominant impacts on NE, while the topographical drivers, the connectivity index (IC) and slope, have dominant impacts on both SE and QF. The magnitudes of single and paired natural-socioeconomic drivers' impacts on NPS pollution–related processes increase logarithmically or linearly with increasing spatial scale, but they tend to reach a stable threshold at a certain coarse scale. Our results emphasized the necessity and importance of embracing spatial scale effects in watershed water environmental management. [ABSTRACT FROM AUTHOR]

Aim: Understanding connections between environment and biodiversity is crucial for conservation, identifying causes of ecosystem stress, and predicting population responses to changing environments. Explaining biodiversity requires an understanding of how species richness and environment covary across scales. Here, we identify scales and locations at which biodiversity is generated and correlates with environment. Location: Full latitudinal range per continent. Time Period: Present day. Major Taxa Studied: Terrestrial vertebrates: all mammals, carnivorans, bats, songbirds, hummingbirds, amphibians. Methods: We describe the use of wavelet power spectra, cross‐power and coherence for identifying scale‐dependent trends across Earth's surface. Spectra reveal scale‐ and location‐dependent coherence between species richness and topography (E), mean annual precipitation (Pn), temperature (Tm) and annual temperature range (ΔT). Results: >97% of species richness of taxa studied is generated at large scales, that is, wavelengths ≳103 km, with 30%–69% generated at scales ≳104 km. At these scales, richness tends to be highly coherent and anti‐correlated with E and ΔT, and positively correlated with Pn and Tm. Coherence between carnivoran richness and ΔT is low across scales, implying insensitivity to seasonal temperature variations. Conversely, amphibian richness is strongly anti‐correlated with ΔT at large scales. At scales ≲103 km, examined taxa, except carnivorans, show highest richness within the tropics. Terrestrial plateaux exhibit high coherence between carnivorans and E at scales ∼103 km, consistent with contribution of large‐scale tectonic processes to biodiversity. Results are similar across different continents and for global latitudinal averages. Spectral admittance permits derivation of rules‐of‐thumb relating long‐wavelength environmental and species richness trends. Main Conclusions: Sensitivities of mammal, bird and amphibian populations to environment are highly scale dependent. At large scales, carnivoran richness is largely independent of temperature and precipitation, whereas amphibian richness correlates strongly with precipitation and temperature, and anti‐correlates with temperature range. These results pave the way for spectral‐based calibration of models that predict biodiversity response to climate change scenarios. [ABSTRACT FROM AUTHOR]

Scale dependence of dispersion coefficient (D) in the advection-dispersion equation (ADE) for solute transport in porous media was investigated by a series of experiments using image analysis. A hexahedral plexiglass box sized 200×8×1.5 cm (L×W×H) was set and packed with glass beads as porous media. The solute transport under different conditions was simulated by changing the particle size of glass beads, flow rate, and detection scale using Bright Blue as tracer. The image analysis method was used to dynamically monitor and identify the spatiotemporal variation of solute concentration distribution. The results showed that image analysis can effectively monitor and identify the solute concentration in porous media, as indicated by an R2 value of 0.9890. There is an obvious linear relationship between hydraulic gradient (J) and velocity (v) in porous media under different experimental conditions. The ADE model is suitable for solute breakthrough curve (BTC) with good fitting accuracy, and can effectively reflect the concentration variation during solute transport. The key parameters controlling the solute transport were analyzed. D has abnormal diffusion (i.e., non-Fickian phenomenon) and scale dependence, and BTCs had a long tail, which becomes more obvious with the increase of flow rate, medium particle size, and transport scale. [ABSTRACT FROM AUTHOR]

Aim: Patterns of evolutionary relatedness among co‐occurring species are driven by scale‐dependent contemporary and historical processes. Yet, we still lack a detailed understanding of how these drivers impact the phylogenetic structure of biological communities. Here, we focused on bats (one of the most species‐rich and vagile groups of mammals) and tested the predictions of three general biogeographical hypotheses that are particularly relevant to understanding how palaeoclimatic stability, local diversification rates and geographical scales shaped their present‐day phylogenetic community structure. Location: World‐wide, across restrictive geographical extents: global, east–west hemispheres, biogeographical realms, tectonic plates, biomes and ecoregions. Time period: Last Glacial Maximum (~22,000 years ago) to the present. Major taxa studied: Bats (Chiroptera). Methods: We estimated bat phylogenetic community structure across restrictive geographical extents and modelled it as a function of palaeoclimatic stability and in situ net diversification rates. Results: Limiting geographical extents from larger to smaller scales greatly changed the phylogenetic structure of bat communities. The magnitude of these effects is less noticeable in the western hemisphere, where frequent among‐realm biota interchange could have been maintained through the adaptive traits of bats. Bat communities with high phylogenetic relatedness are generally more common in regions that have changed less in climate since the Last Glacial Maximum, supporting the expectation that stable climates allow for increased phylogenetic clustering. Finally, increased in situ net diversification rates are associated with greater phylogenetic clustering in bat communities. Main conclusions: We show that the world‐wide phylogenetic structure of bat assemblages varies as a function of geographical extents, dispersal barriers, palaeoclimatic stability and in situ diversification. The integrative framework used in our study, which can be applied to other taxonomic groups, has not only proved useful to explain the evolutionary dynamics of community assembly, but could also help to tackle questions related to scale dependence in community ecology and biogeography. [ABSTRACT FROM AUTHOR]

Investigating hydraulic and petrophysical properties of porous media has been an active area of research. Despite numerous progress in modeling flow and transport over the past decades, we are still far from accurately estimating the scale dependence of soil and rock properties. In this study, we propose applying renormalization group theory (RGT) at the pore scale. Using the RGT, we determine the scale dependence of effective pore‐throat radius (rteff) and develop two theoretical models to estimate permeability (k) in pore networks of various sizes. The first theoretical model estimates k(L) from the rteff(L) and simulated formation factor F(L), while the second model uses information at the smallest scale (L = Lmin) in addition to rteff(L) and F(L). By comparing with 25 pore‐network simulations, we show that the RGT estimates the scale‐dependent k reasonably well. The first model estimates k(L) with average relative errors ranged between −53.1% and −3.0%, while the second model between −1.0% and 14.33%. We also conduct fluid flow simulations in 40 other pore networks above the representative elementary volume and compare the results of the RGT with those of the effective‐medium approximation (EMA). Results showed that both RGT and EMA accurately estimate k from pore‐throat radius distribution and formation factor with root mean square log‐transformed error = 0.119 and 0.096, respectively. Key Points: Scale dependence of permeability at the pore scale is investigated using pore‐network simulationsRenormalization group theory estimates scale‐dependent permeability with good accuracyEffective‐medium and renormalization group theories similarly estimate permeability in the studied networks [ABSTRACT FROM AUTHOR]

IssueGeodiversity (i.e., the variation in Earth's abiotic processes and features) has strong effects on biodiversity patterns. However, major gaps remain in our understanding of how relationships between biodiversity and geodiversity vary over space and time. Biodiversity data are globally sparse and concentrated in particular regions. In contrast, many forms of geodiversity can be measured continuously across the globe with satellite remote sensing. Satellite remote sensing directly measures environmental variables with grain sizes as small as tens of metres and can therefore elucidate biodiversity-geodiversity relationships across scales.EvidenceWe show how one important geodiversity variable, elevation, relates to alpha, beta and gamma taxonomic diversity of trees across spatial scales. We use elevation from NASA's Shuttle Radar Topography Mission (SRTM) and c. 16,000 Forest Inventory and Analysis plots to quantify spatial scaling relationships between biodiversity and geodiversity with generalized linear models (for alpha and gamma diversity) and beta regression (for beta diversity) across five spatial grains ranging from 5 to 100 km. We illustrate different relationships depending on the form of diversity; beta and gamma diversity show the strongest relationship with variation in elevation.ConclusionWith the onset of climate change, it is more important than ever to examine geodiversity for its potential to foster biodiversity. Widely available satellite remotely sensed geodiversity data offer an important and expanding suite of measurements for understanding and predicting changes in different forms of biodiversity across scales. Interdisciplinary research teams spanning biodiversity, geoscience and remote sensing are well poised to advance understanding of biodiversity-geodiversity relationships across scales and guide the conservation of nature.

Exploring the complex effects of landscape patterns on ecosystem services (ESs) has become increasingly important in offering scientific support for effective spatial planning and ecosystem management. However, there is a particular lack of research on the nonlinear effects of landscape patterns on ESs and scale dependence. Taking Huainan City (in China) as a case study, this study adopted the InVEST model to estimate four key ESs including carbon storage (CS), habitat quality (HQ), nitrogen export (NE), and water yield (WY). Then, we calculated the selected landscape metrics at multiple spatial scales. Furthermore, the gradient boosting decision tree (GBDT) model was developed to investigate the relative importance of landscape metrics in explaining ESs and their nonlinear interrelation. The results indicated that most of the selected landscape metrics were significantly correlated with ESs. The GBDT model, which can explore nonlinear relationships, performed better than the linear regression model in explaining the variations in ESs. The landscape-level metrics of the Shannon's diversity index (SHDI) and the contagion index (CONTAG) and the class-level metrics of the aggregation index (AI) and edge density (ED) were the most important variables that influenced ESs. The landscape metrics affected ESs within a certain range, and the nonlinear effects varied with scale. [ABSTRACT FROM AUTHOR]

Human impacts have led to dramatic biodiversity change which can be highly scale‐dependent across space and time. A primary means to manage these changes is via passive (here, the removal of disturbance) or active (management interventions) ecological restoration. The recovery of biodiversity, following the removal of disturbance, is often incomplete relative to some kind of reference target. The magnitude of recovery of ecological systems following disturbance depends on the landscape matrix and many contingent factors. Inferences about recovery after disturbance and biodiversity change depend on the temporal and spatial scales at which biodiversity is measured.We measured the recovery of biodiversity and species composition over 33 years in 17 temperate grasslands abandoned after agriculture at different points in time, collectively forming a chronosequence since abandonment from 1 to 80 years. We compare these abandoned sites with known agricultural land‐use histories to never‐disturbed sites as relative benchmarks. We specifically measured aspects of diversity at the local plot‐scale (α‐scale, 0.5 m2) and site‐scale (γ‐scale, 10 m2), as well as the within‐site heterogeneity (β‐diversity) and among‐site variation in species composition (turnover and nestedness).At our α‐scale, sites recovering after agricultural abandonment only had 70% of the plant species richness (and ~30% of the evenness), compared to never‐ploughed sites. Within‐site β‐diversity recovered following agricultural abandonment to around 90% after 80 years. This effect, however, was not enough to lead to recovery at our γ‐scale. Richness in recovering sites was ~65% of that in remnant never‐ploughed sites. The presence of species characteristic of the never‐disturbed sites increased in the recovering sites through time. Forb and legume cover declines in years since abandonment, relative to graminoid cover across sites.Synthesis. We found that, during the 80 years after agricultural abandonment, old fields did not recover to the level of biodiversity in remnant never‐ploughed sites at any scale. β‐diversity recovered more than α‐scale or γ‐scale. Plant species composition recovered, but not completely, over time, and some species groups increased their cover more than others. Patterns of ecological recovery in degraded ecosystems across space and long time‐scales can inform targeted active restoration interventions and perhaps, lead to better outcomes. [ABSTRACT FROM AUTHOR]

The construction of banks and surface soil cutting involved in newly reclaiming orchards may cause spatial variability in soil properties, which could cause poor fruit tree productivity. This study examined spatial relationships between variations in peach tree properties and soil properties around each tree and assessed the possibility of site-specific field management for individual trees in a newly reclaimed orchard. Three and four years after reclamation in 2016, the 0.1-ha field located in Kyoto, Japan was divided into 32 grid cells at 5-m intervals for all individual peach trees and 128 grid cells at 2.5-m intervals for measuring soil properties around each tree (field scale). The 128 grid cells were each further divided into five positions at 0.71-m intervals for assessing selected soil properties (grid-cell scale). The soil data were geostatistically analyzed by calculating the nugget/sill ratios and anisotropy ratios (degree of variation in relation to direction) and drawing kriged maps. Coefficients of variation of soil properties at the grid-cell scale were much higher than those at the field scale. Pearson's correlation analysis at the field scale indicated that the tree productivity was most strongly correlated with relative altitude, followed by the degree of soil reduction, time-domain reflectometry electrical conductivity (TDR-EC), subsoil pH (H2O), and TDR-volumetric water content. Tree productivity tended to be lower at lower elevations, where the degree of soil reduction, TDR-EC, subsoil pH (H2O), and soil water content tended to be high. Poor productivity appeared to be related to wet injury. Semivariograms of the soil properties related to soil water showed strong spatial dependence and had nugget/sill ratios of ≤24.0%. Kriged maps and anisotropy ratios further indicated that most tree property values decreased from southeast to northwest and showed variations similar to those of the soil properties related to soil water. Fine-scale mapping of soil properties in the orchard could reveal spatial soil-property variations around individual peach trees, and the result would imply the importance of soil management practices on a per-tree basis. Our findings could help to improve tree productivity in the northwestern area by increasing soil drainage for individual trees. [ABSTRACT FROM AUTHOR]

Summary: Feedbacks between plants and soil microbes form a keystone to terrestrial community and ecosystem dynamics. Recent advances in dissecting the spatial and temporal dynamics of plant–soil feedbacks (PSFs) have challenged longstanding assumptions of spatially well‐mixed microbial communities and exceedingly fast microbial assembly dynamics relative to plant lifespans. Instead, PSFs emerge from interactions that are inherently mismatched in spatial and temporal scales, and explicitly considering these spatial and temporal dynamics is crucial to understanding the contribution of PSFs to foundational ecological patterns. I propose a synthetic spatiotemporal framework for future research that pairs experimental and modeling approaches grounded in mechanism to improve predictability and generalizability of PSFs. [ABSTRACT FROM AUTHOR]

Context: Land-cover class definitions are scale-dependent. Up-scaling categorical data must account for that dependence, but most decision rules aggregating categorical data do not produce scale-specific class definitions. However, non-hierarchical, empirically derived classification systems common in phytosociology define scale-specific classes using species co-occurrence patterns. Objectives: Evaluate tradeoffs in class precision and representativeness when up-scaling categorical data across natural landscapes using the multi-dimensional grid-point (MDGP)-scaling algorithm, which generates scale-specific class definitions; and compare spectral detection accuracy of MDGP-scaled classes to 'majority-rule' aggregated classes. Methods: Vegetation maps created from 2-m resolution WorldView-2 data for two Everglades wetland areas were scaled to the 30-m Landsat grid with the MDGP-scaling algorithm. A full-factorial analysis evaluated the effects of scaled class-label precision and class representativeness on compositional information loss and detection accuracy of scaled classes from multispectral Landsat data. Results: MDGP‐scaling retained between 3.8 and 27.9% more compositional information than the majority rule as class-label precision increased. Increasing class-label precision and information retention also increased spectral class detection accuracy from Landsat data between 1 and 8.6%. Rare class removal and increase in class-label similarity were controlled by the class representativeness threshold, leading to higher detection accuracy than the majority rule as class representativeness increased. Conclusions: When up-scaling categorical data across natural landscapes, negotiating trade-offs in thematic precision, landscape-scale class representativeness and increased information retention in the scaled map results in greater class-detection accuracy from lower-resolution, multispectral, remotely sensed data. MDGP-scaling provides a framework to weigh tradeoffs and to make informed decisions on parameter selection. [ABSTRACT FROM AUTHOR]

Changes in grassland soil organic carbon stock (SOCS) may significantly affect the regional climate and carbon cycle of terrestrial ecosystems. However, how the impact of climate factors on SOCS and the dominant climate factors are regulated by the area scale of grasslands remains unclear. To understand the scale effects of climate on SOCS and how to accurately estimate SOCS at different scales, three area scales were defined by extending grassland types on the basis of meadow, typical and desert grasslands (Scale I (average area 37.22 × 104 km2) included each of these three types of grasslands, Scale II (average area 74.45 × 104 km2) was achieved by a pairwise combination of these three types of grasslands. Scale III (area 111.67 × 104 km2) was an aggregate of these three types of grasslands), the relationship between climate factors (i.e., mean annual precipitation, mean annual temperature, annual maximum temperature, annual minimum temperature, mean annual ground temperature, mean annual humidity, annual sunshine duration, annual maximum depth of accumulated snow, and the number of snow-covered days) and SOCS at the three scales were explored in the grasslands of northern China. Our results indicated that the total SOCS in grasslands at the three scales was ordered as desert grassland

The inner-alpine dry valleys of the Swiss Alps are characterized by subcontinental climate, leading to many peculiarities in dry grassland species composition. Despite their well-known uniqueness, comprehensive studies on biodiversity patterns of the dry grasslands in these valleys were still missing. To close this gap, we sampled 161 10-m2 vegetation plots in the Rhône, Rhine and Inn valleys, recording vascular plants, terricolous bryophyte and lichen species, as well as environmental data. Additionally, we tested the scale-dependence of environmental drivers using 34 nested-plot series with seven grain sizes (0.0001–100 m2). We analysed the effects of environmental drivers related to productivity/stress, disturbance and within-plot heterogeneity on species richness. Mean species richness ranged from 2.3 species in 0.0001 m2 to 58.8 species in 100 m2. For all taxa combined, the most relevant drivers at the grain size of 10 m2 were southing (negative), litter (negative), mean annual precipitation (unimodal), gravel cover (negative), inclination (unimodal) and mean annual precipitation (unimodal). For vascular plants the pattern was similar, while bryophyte and lichen richness differed by the opposite relationship to mean annual precipitation as well as negative influences of mean herb layer height, grazing and mowing. The explained variance of the multiple regression model increased with grain size, with very low values for the smallest two grain sizes. While southing and litter had high importance for the fiver larger grain sizes, pH and gravel cover were particularly important at the intermediate grain sizes, and inclination and mean annual precipitation for the two largest grain sizes. The findings emphasize the importance of taxonomic group and grain size for patterns and drivers of species richness in vegetation, consistent with ecological theory. Differences in the diversity–environment relationships among the three taxonomic groups can partly be explained by asymmetric competition that leads to low bryophyte and lichen diversity where vascular plants do well and vice versa. The relatively low alpha diversity of vascular plants in dry grasslands in Swiss inner-alpine valleys compared to similar communities in other parts of the Palaearctic remains puzzling, especially because Swiss stands are often large and well-preserved. [ABSTRACT FROM AUTHOR]

Estimating forest above‐ground biomass (AGB) productivity constitutes one of the most fundamental topics in forest ecological research. Based on a 30‐ha permanent field plot in Northeastern China, we modeled AGB productivity as output, and topography, species diversity, stand structure, and a stand density variable as input across a series of area scales using the Random Forest (RF) algorithm. As the grain size increased from 10 to 200 m, we found that the relative importance of explanatory variables that drove the variation of biomass productivity varied a lot, and the model accuracy was gradually improved. The minimum sampling area for biomass productivity modeling in this region was 140 × 140 m. Our study shows that the relationship of topography, species diversity, stand structure, and stand density variables with biomass productivity modeled using the RF algorithm changes when moving from scales typical of forest surveys (10 m) to larger scales (200 m) within a controlled methodology. These results should be of considerable interest to scientists concerned with forest assessment. [ABSTRACT FROM AUTHOR]

Summary: First principles predict that diversity at one trophic level often begets diversity at other levels, suggesting plant and mycorrhizal fungal diversity should be coupled. Local‐scale studies have shown positive coupling between the two, but the association is less consistent when extended to larger spatial and temporal scales. These inconsistencies are likely due to divergent relationships of different mycorrhizal fungal guilds to plant diversity, scale dependency, and a lack of coordinated sampling efforts. Given that mycorrhizal fungi play a central role in plant productivity and nutrient cycling, as well as ecosystem responses to global change, an improved understanding of the coupling between plant and mycorrhizal fungal diversity across scales will reduce uncertainties in predicting the ecosystem consequences of species gains and losses. [ABSTRACT FROM AUTHOR]

The objective of the current study is to utilize an innovative method called "change probabilities" for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional profiles taken in different directions is quantified. The central quantifiers, change probabilities, are based on counting monotonic changes in discretizations of a profile. These probabilities, which usually vary with the scale, can be reinterpreted as scale-dependent Hurst exponents. For a large class of Gaussian stochastic processes, change probabilities are shown to be directly related to the classical Hurst exponent, which generalizes a relationship known for fractional Brownian motion. While related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing the flexibility of modeling and investigating surface profiles. In particular, it allows a quick and efficient visualization and detection of roughness anisotropy and scale dependence of roughness. [ABSTRACT FROM AUTHOR]

Predicting the ecological effects of environmental perturbations remains challenging due to complex interactions between species and the environment, which constantly adapt the ecological memory and, thus, the future response of ecosystems. General theoretical frameworks like the Complex Adaptive Systems (CAS) theory might provide a solution. Here I discuss the applicability of the CAS theory for ecosystems by examining its three major principles (interaction, adaptation and scale dependence) for spring fens. For these ecosystems, adaptation of plant communities to historical environmental stressors (acidification) affecting the resilience to subsequent perturbations (climatic extremes) is empirically shown. Alternative stable states in community composition initiated by acidification turned out to be stabilized by abiotic-biotic feedbacks. Furthermore, ecological response of species to temperature showed high cross-scale similarity. I argue that the exceptional environmental character of spring fens qualifies these ecosystems as ideal model systems to test and further develop CAS theory for ecology and biogeography.

Examining community responses to habitat configuration across scales informs basic and applied models of ecosystem function. Responses to patch‐scale edge effects (i.e., ecological differences between patch edges and interiors) are hypothesized to underpin the effects of landscape‐scale fragmentation (i.e., mosaics of multipatch habitat and matrix). Conceptually, this appears justifiable because fragmented habitats typically have a greater proportion of edge than continuous habitats. To critically inspect whether patch‐scale edge effects translate consistently (i.e., scale up) into patterns observed in fragmented landscapes, we conducted a meta‐analysis on community relationships in seagrass ecosystems to synthesize evidence of edge and fragmentation effects on shoot density, faunal densities, and predation rates. We determined effect sizes by calculating log response ratios for responses within patch edges versus interiors to quantify edge effects, and fragmented versus continuous landscapes to quantify fragmentation effects. We found that both edge and fragmentation effects reduced seagrass shoot densities, although the effect of edge was statistically stronger. By contrast, fauna often exhibited higher densities in patch edges, while fragmentation responses varied directionally across taxa. Fish densities trended higher in patch edges and fragmented landscapes. Benthic fishes responded more positively than benthopelagic fishes to edge effects, although neither guild strongly responded to fragmentation. Invertebrate densities increased in patch edges and trended lower in fragmented landscapes; however, these were small effect sizes due to the offsetting responses of two dominant epifaunal guilds: decapods and smaller crustaceans. Edge and fragmentation affected predation similarly, with prey survival trending lower in patch edges and fragmented landscapes. Overall, several similarities suggested that edge effects conform with patterns of community dynamics in fragmented seagrass. However, across all metrics except fish densities, variability in fragmentation effects was twice that of edge effects. Variance patterns combined with generally stronger responses to edge than fragmentation, warrant caution in unilaterally "scaling‐up" edge effects to describe fragmentation effects. Alternatively, fragmentation includes additional factors (e.g., matrix effects, patch number, mean patch size, isolation) that may enhance or offset edge effects. Fragmentation and increased edge are syndromes of habitat degradation, therefore this analysis informs mechanistic models of community change in altered terrestrial and marine systems. [ABSTRACT FROM AUTHOR]

Comparison of the spatial distribution and assembly processes between bulk and rhizosphere bacterial communities at multiple spatial scales is vital for understanding the generation and maintenance of microbial diversity under the influence of plants. However, biogeographical patterns and the underlying mechanisms of microbial communities in bulk and rhizosphere sediments of aquatic ecosystems remain unclear. Here, we collected 140 bulk and rhizosphere sediment samples of Phragmites australis from 14 lakeshore zones across a 510‐km transect in the Middle–Lower Yangtze plain. We performed high‐throughput sequencing to investigate the bacterial diversity, composition, spatial distribution and assembly processes of these samples. Bacterial communities in the rhizosphere sediment exhibited higher alpha diversity but lower beta diversity than those in the bulk sediment. Both bulk and rhizosphere sediment bacterial communities had significant distance–decay relationships, but spatial turnover of the rhizosphere sediment bacterial community was strikingly lower than that of bulk sediment. Despite variable selection dominating the assembly processes of bacterial communities in bulk sediment, the rhizosphere of P. australis enhanced the role of dispersal limitation in governing bacterial communities. The relative importance of different ecological processes in determining bacterial assembly presented distinct patterns of increasing or decreasing linearly with an increase of scale. This investigation highlights the convergent selection of the aquatic plant rhizosphere for surrounding bacterial communities and emphasizes the importance of different ecological processes on bacterial community assembly in sediment environments over different scales. Furthermore, we provide a preliminary framework for exploring the scale dependence of microbial community assembly in aquatic ecosystems. [ABSTRACT FROM AUTHOR]

Abstract The relationship between biodiversity and productivity has stimulated an increasing body of research over the past decades, and this topic still occupies a central place in ecology. While most studies have focused on biomass production in quadrats or plots, few have investigated the scale‐dependent relationship from an individual plant perspective. We present an analysis of the effects of biodiversity (species diversity and functional diversity) on individual tree growth with a data set of 16,060 growth records from a 30‐ha temperate forest plot using spatially explicit individual tree‐based methods. A significant relationship between species diversity and tree growth was found at the individual tree level in our study. The magnitude and direction of biodiversity effects varies with the spatial scale. We found positive effects of species diversity on tree growth at scales exceeding 9 m. Individual tree growth rates increased when there was a greater diversity of species in the neighborhood of the focal tree, which provides evidence of a niche complementarity effect. At small scales (3–5 m), species diversity had negative effects on tree growth, suggesting that competition is more prevalent than complementarity or facilitation in these close neighborhoods. The results also revealed many confounding factors which influence tree growth, such as elevation and available sun light. We conclude that the use of individual tree‐based methods may lead to a better understanding of the biodiversity‐productivity relationship in forest communities.

Multiscale processes through dynamic boundaries drive the local contributions (LCBD; uniqueness in species composition and abundance) and species contributions (SCBD; individual species abundance variation) to fish beta diversity in coastal seascapes. We partitioned LCBD into LCBDRepl (replacement) and LCBDAbDiff (abundance difference), and used model-based approaches to investigate whether seascape size influences environmental and spatial drivers of LCBD, and effects of species (distribution, prevalence, and coastal dependence) on SCBD. Three large bays (bay level) and three zones per bay (zone level), southeastern Brazil, were seascape models during 1 year. At the bay level, more locations had higher LCBD, related to species composition, lower water transparency, and much less to flood/high tides and higher number of estuaries. LCBDRepl was also prevalent and stronger positive effects of transparency and mangrove cover reinforced the importance of environmental filtering and alternative habitats driving local contributions to replacement processes in larger seascapes. Species richness influenced positively LCBD primarily at the zone level, and negative effects of vegetal cover and primarily human settlements suggested species loss under lower heterogeneity. Also, more similar LCBDRepl and LCBDAbDiff evidenced the increasing local contributions to abundance differences in smaller species pools. At both levels, larger- and finer-scale spatial effects evidenced possible influences of dispersal and biotic interactions, respectively, on LCBDRepl and LCBDAbDiff. SCBD was positively related to species prevalence at locations and distribution at both levels. Therefore, multiscale mechanisms dependent and irrespective of seascape size support the critical importance of habitat availability, complexity, and variety to beta diversity of coastal fishes. [ABSTRACT FROM AUTHOR]

Questions: Ungulate herbivory and its impact on one plant species may be driven by other plants in the neighbourhood. Although such neighbourhood effects have long been recognized, there is limited understanding of how spatial variation in these effects relates to local plant density and distances between plants. Our goal was to examine if the density of or distance to conspecific and heterospecific neighbouring woody individuals produces neighbourhood effects on bark stripping by deer, and how these effects differ in spatial scale and type (reduce/increase herbivory). Location: Lowland old-growth forest, Czech Republic. Methods: Woody individuals were assessed for evidence of bark stripping and the level of damage done by deer in a square 4-ha plot, mapping all woody stems ≥1 cm diameter at breast height. The spatial distribution of stripping was used to examine neighbourhood effects using spatial point pattern methods. Results: The density and distance to neighbours and species identity of focal and neighbouring individuals contributed to a large spatial variation in neighbourhood effects (up to distances of 2-30 m from neighbours). Neighbourhood effects arose mainly from the interactions between neighbouring shrub species and all tree species, and interactions between individual species pairs. Neighbourhood effects more often increased than reduced the stripping of focal individuals. The stripping of Ulmus laevis, Acer campestre and Crataegus laevigata increased near conspecifics, while the stripping of all tree species was more likely near Ulmus laevis, Fraxinus angustifolia and shrubs. Heterospecific tree species were less susceptible to stripping near Tilia cordata and especially Carpinus betulus. Conclusion: Our study provides new insight into neighbourhood effects by showing how and at which spatial scales woody plant interactions modify deer herbivory. We advocate considering the life stage and relevant plant traits with multivariate spatial methods in order to elucidate the role of neighbourhood effects in complex plant communities. [ABSTRACT FROM AUTHOR]

Heavy mesons and doubly heavy baryons with the dynamic properties governed by the light quark motion relative to the fixed center of forces are studied within the Heavy Quark Effective Theory. The distribution amplitudes of the hadrons in question are compared, model functions of these amplitudes for the doubly heavy baryons are introduced, and their scale dependence is investigated. [ABSTRACT FROM AUTHOR]

Livestock grazing is a major driver shaping grassland biodiversity, functioning and stability. Whether grazing impacts on grassland ecosystems are scale‐dependent remains unclear. Here, we conducted a sheep‐grazing experiment in a temperate grassland to test grazing effects on the temporal stability of productivity across scales. We found that grazing increased species stability but substantially decreased local community stability due to reduced asynchronous dynamics among species within communities. The negative effect of grazing on local community stability propagated to reduce stability at larger spatial scales. By decreasing biodiversity both within and across communities, grazing reduced biological insurance effects and hence the upscaling of stability from species to communities and further to larger spatial scales. Our study provides the first evidence for the scale dependence of grazing effects on grassland stability through biodiversity. We suggest that ecosystem management should strive to maintain biodiversity across scales to achieve sustainability of grassland ecosystem functions and services. [ABSTRACT FROM AUTHOR]

Aims: Understanding fine-grain diversity patterns across large spatial extents is fundamental for macroecological research and biodiversity conservation. Using the GrassPlot database, we provide benchmarks of fine-grain richness values of Palaearctic open habitats for vascular plants, bryophytes, lichens and complete vegetation (i.e., the sum of the former three groups). Location: Palaearctic biogeographic realm. Methods: We used 126,524 plots of eight standard grain sizes from the GrassPlot database: 0.0001, 0.001, 0.01, 0.1, 1, 10, 100 and 1,000 m2 and calculated the mean richness and standard deviations, as well as maximum, minimum, median, and first and third quartiles for each combination of grain size, taxonomic group, biome, region, vegetation type and phytosociological class. Results: Patterns of plant diversity in vegetation types and biomes differ across grain sizes and taxonomic groups. Overall, secondary (mostly semi-natural) grasslands and natural grasslands are the richest vegetation type. The open-access file ”GrassPlot Diversity Benchmarks” and the web tool “GrassPlot Diversity Explorer” are now available online (https://edgg.org/datab ases/Grass landD ivers ityEx plorer) and provide more insights into species richness patterns in the Palaearctic open habitats. Conclusions: The GrassPlot Diversity Benchmarks provide high-quality data on species richness in open habitat types across the Palaearctic. These benchmark data can be used in vegetation ecology, macroecology, biodiversity conservation and data quality checking. While the amount of data in the underlying GrassPlot database and their spatial coverage are smaller than in other extensive vegetation-plot databases, species recordings in GrassPlot are on average more complete, making it a valuable complementary data source in macroecology. [ABSTRACT FROM AUTHOR]

Understanding the multiple biotic and abiotic controls of aboveground biomass (AGB) is important for projecting the consequences of global change and to effectively manage carbon storage. Although large-scale studies have identified the major environmental and biological controls of AGB, drivers of local-scale variation are less well known. Additionally, involvement of multiple causal paths and scale dependence in effect sizes potentially confounds comparisons among studies differing in methodology and sampling grain. We tested for scale dependence in evidence supporting selection, complementarity and environmental factors as the main determinants of AGB variation over a 50 ha study extent in subtropical China, modelling this at four sampling grains (0.01, 0.04, 0.25 and 1 ha). At each grain, we used piecewise structural equation models to quantify the direct and indirect effects of environmental (topographic and edaphic properties) and forest attributes (structure, diversity and functional traits) on AGB, while controlling for spatial autocorrelation. Direct scale-invariant effects on AGB were evident for structure and community-mean traits, supporting dominance of selection effects. However, diversity had strong indirect effects on AGB via forest structure, particularly at larger sampling grains (≥ 0.25 ha), while direct effects only emerged at the smallest grain size (0.01 ha). The direct and indirect effects of edaphic and topographic factors were also important for explaining both forest attributes and AGB across all scales. Although selection effects appeared to be more influential on ecosystem function, ignoring indirect causal pathways for diversity via structural attributes risks overlooking the importance of complementarity on ecosystem functioning, particularly as sampling grain increases. [ABSTRACT FROM AUTHOR]

Questions: Which environmental factors influence fine‐grain beta diversity of vegetation and do they vary among taxonomic groups? Location: Palaearctic biogeographic realm. Methods: We extracted 4,654 nested‐plot series with at least four different grain sizes between 0.0001 m² and 1,024 m² from the GrassPlot database, covering a wide range of different grassland and other open habitat types. We derived extensive environmental and structural information for these series. For each series and four taxonomic groups (vascular plants, bryophytes, lichens, all), we calculated the slope parameter (z‐value) of the power law species–area relationship (SAR), as a beta diversity measure. We tested whether z‐values differed among taxonomic groups and with respect to biogeographic gradients (latitude, elevation, macroclimate), ecological (site) characteristics (several stress–productivity, disturbance and heterogeneity measures, including land use) and alpha diversity (c‐value of the power law SAR). Results: Mean z‐values were highest for lichens, intermediate for vascular plants and lowest for bryophytes. Bivariate regressions of z‐values against environmental variables had rather low predictive power (mean R² = 0.07 for vascular plants, less for other taxa). For vascular plants, the strongest predictors of z‐values were herb layer cover (negative), elevation (positive), rock and stone cover (positive) and the c‐value (U‐shaped). All tested metrics related to land use (fertilization, livestock grazing, mowing, burning, decrease in naturalness) led to a decrease in z‐values. Other predictors had little or no impact on z‐values. The patterns for bryophytes, lichens and all taxa combined were similar but weaker than those for vascular plants. Conclusions: We conclude that productivity has negative and heterogeneity positive effects on z‐values, while the effect of disturbance varies depending on type and intensity. These patterns and the differences among taxonomic groups can be explained via the effects of these drivers on the mean occupancy of species, which is mathematically linked to beta diversity.We analysed fine‐grain beta diversity of grasslands and other open habitats in the Palaearctic using 4,654 nested‐plot series and the z‐values of power‐law species–area relationships. Mean z‐values were highest for lichens, intermediate for vascular plants and lowest for bryophytes. The strongest environmental predictors of z‐values were herb layer cover (negative), elevation (positive), rock and stone cover (positive) and the c‐value (U‐shaped). In a conceptual figure, we summarize the resulting hypotheses how different predictors could influence z‐values via mean occupancy. [ABSTRACT FROM AUTHOR]

Questions: Species–area relationships (SARs) are fundamental for understanding biodiversity patterns and are generally well described by a power law with a constant exponent z. However, z‐values sometimes vary across spatial scales. We asked whether there is a general scale dependence of z‐values at fine spatial grains and which potential drivers influence it. Location: Palaearctic biogeographic realm. Methods: We used 6,696 nested‐plot series of vascular plants, bryophytes and lichens from the GrassPlot database with two or more grain sizes, ranging from 0.0001 m² to 1,024 m² and covering diverse open habitats. The plots were recorded with two widespread sampling approaches (rooted presence = species “rooting” inside the plot; shoot presence = species with aerial parts inside). Using Generalized Additive Models, we tested for scale dependence of z‐values by evaluating if the z‐values differ with gran size and tested for differences between the sampling approaches. The response shapes of z‐values to grain were classified by fitting Generalized Linear Models with logit link to each series. We tested whether the grain size where the maximum z‐value occurred is driven by taxonomic group, biogeographic or ecological variables. Results: For rooted presence, we found a strong monotonous increase of z‐values with grain sizes for all grain sizes below 1 m². For shoot presence, the scale dependence was much weaker, with hump‐shaped curves prevailing. Among the environmental variables studied, latitude, vegetation type, naturalness and land use had strong effects, with z‐values of secondary peaking at smaller grain sizes. Conclusions: The overall weak scale dependence of z‐values underlines that the power function generally is appropriate to describe SARs within the studied grain sizes in continuous open vegetation, if recorded with the shoot presence method. When clear peaks of z‐values occur, this can be seen as an expression of granularity of species composition, partly driven by abiotic environment.Fine‐grain species‐area relationships can be well described with the power function, but at closer look the exponent z (a measure of multiplicative beta diversity) might vary across scales. Using nearly 7,000 nested‐plot series from Palaearctic open habitats, we found that for rooted presence sampling z strongly increases from 1 m² towards smallest grains, whereas for shoot presence sampling there is typically a weak peak somewhere below 1 m². Peak position was mainly influenced by taxonomic group, latitude and naturalness. [ABSTRACT FROM AUTHOR]

The detection of Primordial Gravitational Waves (PGWs) is one of the most important goals of modern cosmology since PGWs can both provide substantial evidence for primordial inflation and shed light on its physical nature. Small scale experiments on gravitational waves such as LIGO/VIRGO and, in future, LISA and Einstein Telescope (ET), being sensitive to the stochastic background of gravitational waves, can be used together with the CMB data to constrain the inflationary parameters. In performing these analyses the primordial tensor spectrum is usually parametrized with a power law that includes only the amplitude and a scale independent tilt. In this paper, we investigate the robustness of assuming the tensor tilt as scale independent. We show that due to the huge difference in the scales probed by CMB and GWs data, even a small scale dependence can remarkably affect the shape of the primordial spectrum possibly breaking the power-law assumption. When the non-linear corrections are considered the final constraints can be significantly changed. We also study the scale dependence in two different physical models of inflation providing an example of negligible scale dependence and an example of non-negligible scale dependence.

The input of mechanical power to the ocean due to the surface wind stress, in regions which correspond to different regimes of ocean dynamics, is considered using data from satellites observations. Its dependence on the coarse-graining range of the atmospheric and oceanic velocity in space from 0.5 to 10∘ and time from 6 h to 40 days is determined. In the area of the Gulf Stream and the Kuroshio extensions, the dependence of the power input on space-time coarse-graining varies over tenfold for the coarse-graining considered. It decreases over twofold for the Gulf Stream extension and threefold for the Kuroshio extension, when the coarse-graining length scale passes from a few degrees to 0.5∘ at a temporal coarse-graining scale of a few days. It increases over threefold in the Gulf Stream and the Kuroshio extensions when the coarse-graining passes from several days to 6 h at a spatial coarse-graining of a few degrees. The power input is found to increase monotonically with shorter coarse-graining in time. Its variation with coarse-graining in space has no definite sign. Results show that including the dynamics at scales below a few degrees reduces considerably the power input by air-sea interaction in regions of strongly nonlinear ocean currents. When the ocean velocities are not considered in the shear calculation, the power input is considerably (up to threefold) increased. The dependence of the power input on coarse-graining in space and time is close to being multiplicatively separable in all regions and for most of the coarse-graining domain considered. [ABSTRACT FROM AUTHOR]

Questions: Which are the main environmental drivers of plot scale alpha‐diversity and beta‐diversity in arid steppes? Do they vary between functional groups and across grain sizes? Location: Central Alborz Mts., N Iran. Methods: We sampled vascular plants in 23 nested‐plot series with nine grain sizes from 0.0001 m2 to 1,000 m2 and 334 25‐m2 vegetation plots in different vegetation types of natural dry steppe grasslands. To assess beta‐diversity, we calculated overall and local z‐values of species–area relationships modelled with the power function. As potential drivers of species richness and z‐values, we used topographic, edaphic and climatic variables as well as management types. Generalised linear models (GLMs), and generalised linear mixed‐effect models (GLMMs) if spatial autocorrelation occurred, were used in a multi‐model inference framework to build statistical models. Results: Mean annual temperature was the most important predictor for total species richness and richness of functional groups across grain sizes, with a unimodal relationship for grains of 25–100 m2, but mostly increasing for finer grain sizes. Precipitation of the driest month and cover of gravel were influential drivers at the smallest grains. The explanatory power of regression models increased towards larger grain sizes. The overall z‐values showed a high positive relationship with precipitation of the driest month, mean annual temperature and mean soil depth. Conclusions: Related to our more than 3,000‐m elevational gradient, mean annual temperature (highly negatively correlated with elevation) was the most influential and consistent driver across functional groups and grain sizes with mostly unimodal relationships for alpha‐diversity and a positive effect on beta‐diversity. Findings for other drivers were less consistent, and overall the explained variance of our models was relatively low, calling for additional studies to determine whether in the arid grasslands of Iran stochasticity is just higher or there are additional important variables.In a 3,000‐m elevational gradient of Iranian mountains, species richness of vascular plants was recorded across nine spatial grain sizes and for functional groups. Mean annual temperature (highly negatively correlated with elevation) was the most influential and consistent driver across functional groups and grain sizes with mostly unimodal relationships for alpha‐diversity and a positive effect on beta‐diversity. [ABSTRACT FROM AUTHOR]

Aim: Despite global biodiversity losses, trends at local and regional scales are context dependent. Recent studies have been criticized for lacking baselines preceding human impacts, and few such studies have addressed the landscape scale. Our aim was to quantify temporal trends in landscape‐scale tree diversity during an unambiguous period of massively increased anthropogenic disturbance and to test the hypothesis that land use can increase landscape‐scale diversity via increased environmental heterogeneity. Location: Eastern USA. Time period: 1620–2008. Major taxa studied: Trees. Methods: We combined data from archival land surveys and modern‐day forest inventories in the north‐eastern USA to quantify tree genus diversity at the scale of towns ("landscapes"). We modelled change in diversity over time as a function of the proportion of the landscape historically converted to agriculture, historical temperature increases and nitrogen deposition, and other abiotic and spatial variables. We also tested for scale‐dependent changes in beta diversity. Results: Overall, tree genus diversity (Shannon and Simpson indices) changed minimally over time on average, but the magnitude of change increased with the maximum historical percentage of the town in agriculture. Other predictor variables had minimal influence. Beta diversity increased over time for nearby pairs of towns and decreased over time for more distant towns. Main conclusions: Forests have regrown on much former agricultural land, and our results support the hypothesis that increased landscape‐scale environmental heterogeneity, attributable to land use, increased tree diversity. Where agricultural land use was uncommon, declines in diversity might be attributable to effects of logging and fire suppression. Even the strongest driver of biodiversity loss at local and global scales (human land use) can lead to increases in biodiversity at the landscape scale, in addition to scale dependence of biotic differentiation versus homogenization. [ABSTRACT FROM AUTHOR]

Abstract Assumed‐PDF (probability density function) higher‐order turbulence closures (APHOCs) are now widely used for parameterizing boundary layer turbulence and shallow convection in Earth system models (ESMs). A better understanding of the resolution‐dependent behavior of APHOCs is essential for improving the performance of next‐generation ESMs with intended horizontal resolutions finer than 10 km. In this study, we evaluate the PDF family of Analytic double‐Gaussian 1 implemented in Cloud Layers Unified By Binormals (CLUBB) over a range of spatial scales (Dx) from 2 to 100 km. A 120‐km‐wide large eddy simulation (LES) for a continental convection case during 2016 Holistic Interactions of Shallow Clouds, Aerosols, and Land‐Ecosystems (HI‐SCALE) field campaign serves as benchmark to evaluate the PDF closure using an off‐line approach. We find during the shallow convection period, the CLUBB PDF closure tends to produce positive biases of cloud properties and liquid water flux near cloud base for all scales of analysis. It produces negative biases for these variables near cloud top that are more severe for Dx larger than 25 km. Results show that replacing the CLUBB‐parameterized moisture and temperature skewnesses with LES‐derived ones can fix most of the biases if clipping of input moments is allowed to prevent the occurrence of unrealizable solutions. Overall, the performance of the PDF closure is better for smaller Dx = 2–5 km than for larger Dx = 50–100 km; for a given grid spacing, it is better when the convective clouds become deeper in the late afternoon. Likely causes for the resolution dependence and implications for improving the PDF closure are discussed.