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We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify injective objects, establish properties of injective and projective resolutions, construct a derived auto-duality, and so on. Our work is motivated by numerous connections of this theory to other areas, such as representation stability, commutative algebra, simplicial theory, and shuffle algebras.

Above-ground biomass (AGB) and the leaf area index (LAI) are important indicators for the assessment of crop growth, and are therefore important for agricultural management. Although improvements have been made in the monitoring of crop growth parameters using ground- and satellite-based sensors, the application of these technologies is limited by imaging difficulties, complex data processing, and low spatial resolution. Therefore, this study evaluated the use of hyperspectral indices, red-edge parameters, and their combination to estimate and map the distributions of AGB and LAI for various growth stages of winter wheat. A hyperspectral sensor mounted on an unmanned aerial vehicle was used to obtain vegetation indices and red-edge parameters, and stepwise regression (SWR) and partial least squares regression (PLSR) methods were used to accurately estimate the AGB and LAI based on these vegetation indices, red-edge parameters, and their combination. The results show that: (i) most of the studied vegetation indices and red-edge parameters are significantly highly correlated with AGB and LAI; (ii) overall, the correlations between vegetation indices and AGB and LAI, respectively, are stronger than those between red-edge parameters and AGB and LAI, respectively; (iii) Compared with the estimations using only vegetation indices or red-edge parameters, the estimation of AGB and LAI using a combination of vegetation indices and red-edge parameters is more accurate; and (iv) The estimations of AGB and LAI obtained using the PLSR method are superior to those obtained using the SWR method. Therefore, combining vegetation indices with red-edge parameters and using the PLSR method can improve the estimation of AGB and LAI.

Plants respond to resource stress by changing multiple aspects of their biomass allocation, morphology, physiology and architecture. To date, we lack an integrated view of the relative importance of these plastic responses in alleviating resource stress and of the consistency/variability of these responses among species. We subjected nine species (legumes, forbs and graminoids) to nitrogen and/or light shortages and measured 11 above-ground and below-ground trait adjustments critical in the alleviation of these stresses (plus several underlying traits). Nine traits out of 11 showed adjustments that improved plants’ potential capacity to acquire the limiting resource at a given time. Above ground, aspects of plasticity in allocation, morphology, physiology and architecture all appeared important in improving light capture, whereas below ground, plasticity in allocation and physiology were most critical to improving nitrogen acquisition. Six traits out of 11 showed substantial heterogeneity in species plasticity, with little structuration of these differences within trait covariation syndromes. Such comprehensive assessment of the complex nature of phenotypic responses of plants to multiple stress factors, and the comparison of plant responses across multiple species, makes a clear case for the high (but largely overlooked) diversity of potential plastic responses of plants, and for the need to explore the potential rules structuring them.

This work is devoted to the study of rates of convergence of the empirical measures \\mu_{n} = \\frac {1}{n} \\sum_{k=1}^n \\delta_{X_k}, n \\geq 1, over a sample (X_{k})_{k \\geq 1} of independent identically distributed real-valued random variables towards the common distribution \\mu in Kantorovich transport distances W_p. The focus is on finite range bounds on the expected Kantorovich distances \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) or \\big [ \\mathbb{E}(W_{p}^p(\\mu_{n},\\mu )) \\big ]^1/p in terms of moments and analytic conditions on the measure \\mu and its distribution function. The study describes a variety of rates, from the standard one \\frac {1}{\\sqrt n} to slower rates, and both lower and upper-bounds on \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.

Blood oxygen level dependent (BOLD) spontaneous signals from resting-state (RS) brains have typically been characterized by low-pass filtered timeseries at frequencies ≤0.1Hz, and studies of these low-frequency fluctuations have contributed exceptional understanding of the baseline functions of our brain. Very recently, emerging evidence has demonstrated that spontaneous activities may persist in higher frequency bands (even up to 0.8Hz), while presenting less variable network patterns across the scan duration. However, as an indirect measure of neuronal activity, BOLD signal results from an inherently slow hemodynamic process, which in fact might be too slow to accommodate the observed high-frequency functional connectivity (FC). To examine whether the observed high-frequency spontaneous FC originates from BOLD contrast, we collected RS data as a function of echo time (TE). Here we focus on two specific resting state networks — the default-mode network (DMN) and executive control network (ECN), and the major findings are fourfold: (1) we observed BOLD-like linear TE-dependence in the spontaneous activity at frequency bands up to 0.5Hz (the maximum frequency that can be resolved with TR=1s), supporting neural relevance of the RSFC at a higher frequency range; (2) conventional models of hemodynamic response functions must be modified to support resting state BOLD contrast, especially at higher frequencies; (3) there are increased fractions of non-BOLD-like contributions to the RSFC above the conventional 0.1Hz (non-BOLD/BOLD contrast at 0.4–0.5Hz is ~4 times that at <0.1Hz); and (4) the spatial patterns of RSFC are frequency-dependent. Possible mechanisms underlying the present findings and technical concerns regarding RSFC above 0.1Hz are discussed. •Resting-state functional connectivity (RSFC) persists above 0.1Hz.•We observe BOLD-like linear TE-dependence in spontaneous activity up to 0.5Hz.•Increased fractions of non-BOLD-like signal contributions to RSFC above 0.1Hz•HRF models at task conditions must be modified at rest.•Spatial patterns of RSFC are frequency-dependent.

1. Plant–soil feedback (PSF), plant trait and functional group concepts advanced our understanding of plant community dynamics, but how they are interlinked is poorly known. 2. To test how plant functional groups (FGs: graminoids, small herbs, tall herbs, legumes) and plant traits relate to PSF, we grew 48 grassland species in sterilized soil, sterilized soil with own species soil inoculum and sterilized soil with soil inoculum from all species, and quantified relative growth rate (RGR), specific leaf area (SLA), specific root length (SRL) and per cent arbuscular mycorrhizal fungi colonization (%AMF). 3. Plant growth response to the plant species' own soil biota relative to sterilized soil (PSFsterilized) reflects net effects of all (generalist + specialized) soil biota. Growth response to the plant species' own soil biota relative to soil biota of all plant species (PSFaway) reveals effects of more specialized soil organisms. 4. PSFsterilized showed that graminoids and small herbs have a negative and tall herbs a positive response to their own soil biota, whereas legumes responded neutrally. However, PSFaway showed that on average, all plant FGs benefitted from growing with other species' soil biota, suggesting that pathogens are more specialized than plant growth-promoting soil biota. Feedback to plant growth from all soil biota (PSFsterilized) was stronger than from more specialized soil biota (PSFaway) and could be predicted by SRL and especially by %AMF colonization. Species with high SRL and low %AMF colonization when grown in away soil experienced most negative soil feedback. 5. Synthesis. Plant species from all plant FGs grow better in soil from other species because of less net negative effects of soil biota (in graminoids), or because of more net positive soil biota effects (in tall herbs). Explorative plant species (high SRL, low %AMF colonization) suffer most from negative feedback of all soil biota, whereas more resource conservative species (low SRL, high %AMF colonization) benefit from soil feedback of all soil biota. These findings help to understand replacement of explorative species during succession. Moreover, we suggest a potentially larger role for species with positive feedback than for species with negative feedback to contribute to maintain plant community productivity of diverse communities over time.

Topography affects abiotic conditions which can influence the structure, function, and dynamics of ecological communities. An increasing number of studies have demonstrated biological consequences of fine-scale topographic heterogeneity but we have a limited understanding of how We merged high-resolution (1 sq. meter) data on topography and canopy height derived from airborne lidar with ground-based data from 15 forest plots in Puerto Rico distributed along a precipitation gradient spanning ca. 800 to 3,500 mm yr(exp -1). Ground-based data included species composition, estimated above-ground biomass (AGB), and two key functional traits (wood density and leaf mass per area, LMA) that reflect resource-use strategies and a trade-off between hydraulic safety and hydraulic efficiency. We used hierarchical Bayesian models to evaluate how the interaction between topography climate is related to metrics of forest structure (i.e., canopy height and AGB), as well as taxonomic and functional alpha- and beta-diversity. Fine-scale topography (characterized with the topographic wetness index, TWI) significantly affected forest structure and the strength (and in some cases direction) of these effects varied across the precipitation gradient. In all plots, canopy height increased with topographic wetness but the effect was much stronger in dry compared to wet forest plots. In dry forest plots, topographically wetter microsites also had higher levels of AGB but in wet forest plots, topographically drier microsites had higher AGB. Fine-scale topography influenced functional composition but had only weak or non-significant effects on taxonomic and functional alpha- and beta-diversity. For instance, community-weighted wood density followed a similar pattern to AGB across plots. We also found a marginally significant association between variation of wood density and topographic heterogeneity that depended on climate context. Synthesis: The effects of fine-scale topographic heterogeneity on tropical forest structure and composition depend on the climate context. Our study demonstrates how a stronger integration of topographic heterogeneity across precipitation gradients could improve estimates of forest structure and biomass, and may provide insight to the ways that topography might mediate species responses to drought and climate change.

QUESTIONS : Invasive species establish either by possessing traits, or trait trade‐offs similar to native species, suggesting pre‐adaptation to local conditions; or by having a different suite of traits and trait trade‐offs, which allow them to occupy unfilled niches. The trait differences between invasives and non‐invasives can inform on which traits confer invasibility. Here, we ask: (a) are invasive species functionally different or similar to native species? (b) which traits of invasives differ from traits of non‐invasive aliens and thus confer invasibility? and (c) do results from the sub‐Antarctic region, where this study was conducted, differ from findings from other regions? LOCATION : Sub‐Antarctic Marion Island. METHODS : We measured 13 traits of all terrestrial native, invasive and non‐invasive alien plant species. Using principal components analysis and phylogenetic generalized least‐squares models, we tested for differences in traits between invasive (widespread alien species) and native species. Bivariate trait relationships between invasive and native species were compared using standardized major axis regressions to test for differences in trait trade‐offs between the two groups. Second, using the same methods, we compared the traits of invasive species to non‐invasive aliens (alien species that have not spread). RESULTS : Between invasive and native species, most traits differed, suggesting that the success of invasive species is mediated by being functionally different to native species. Additionally, most bivariate trait relationships differed either in terms of their y‐intercept or their position on the axes, highlighting that plants are positioned differently along a spectrum of shared trait trade‐offs. Compared to non‐invasive aliens, invasive species had lower plant height, smaller leaf area, lower frost tolerance, and higher specific leaf area, suggesting that these traits are associated with invasiveness. The findings for the sub‐Antarctic corresponded to those of other regions, except lower plant height which provides a competitive advantage to invaders in the windy sub‐Antarctic context. CONCLUSION : Our findings support the expectation that trait complexes of invasive species are predominantly different to those of coexisting native species, and that high resource acquisition and low defence investment are characteristic of invasive plant species.

In this paper we introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various approaches to graph limits fit to this framework and that they naturally appear as “tractable cases” of a general theory. As an outcome of this, we provide extensions of known results. We believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, we consider limits of structures with bounded diameter connected components and we prove that in this case the convergence can be “almost” studied component-wise. We also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, we consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of

Above‐ground biomass (AGB) is an important metric used to quantify the mass of carbon stored in terrestrial ecosystems. For forests, this is routinely estimated at the plot scale (typically 1 ha) using inventory measurements and allometry. In recent years, terrestrial laser scanning (TLS) has appeared as a disruptive technology that can generate a more accurate assessment of tree and plot scale AGB; however, operationalising TLS methods has had to overcome a number of challenges. One such challenge is the segmentation of individual trees from plot level point clouds that are required to estimate woody volume, this is often done manually (e.g. with interactive point cloud editing software) and can be very time consuming. Here we present TLS2trees, an automated processing pipeline and set of Python command line tools that aims to redress this processing bottleneck. TLS2trees consists of existing and new methods and is specifically designed to be horizontally scalable. The processing pipeline is demonstrated on 7.5 ha of TLS data captured across 10 plots of seven forest types; from open savanna to dense tropical rainforest. A total of 10,557 trees are segmented with TLS2trees: these are compared to 1281 manually segmented trees. Results indicate that TLS2trees performs well, particularly for larger trees (i.e. the cohort of largest trees that comprise 50% of total plot volume), where plot‐wise tree volume bias is ±0.4 m3 and %RMSE is 60%. Segmentation performance decreases for smaller trees, for example where DBH ≤10 cm; a number of reasons are suggested including performance of semantic segmentation step. The volume and scale of TLS data captured in forest plots is increasing. It is suggested that to fully utilise this data for activities such as monitoring, reporting and verification or as reference data for satellite missions an automated processing pipeline, such as TLS2trees, is required. To facilitate improvements to TLS2trees, as well as modification for other laser scanning modes (e.g. mobile and UAV laser scanning), TLS2trees is a free and open‐source software.