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The process of standardizing taxon names, taxonomic name harmonization, is necessary to properly merge data indexed by taxon names. The large variety of taxonomic databases and related tools are often not well described. It is often unclear which databases are actively maintained or what is the original source of taxonomic information. In addition, software to access these databases is developed following non‐compatible standards, which creates additional challenges for users. As a result, taxonomic harmonization has become a major obstacle in ecological studies that seek to combine multiple datasets. Here, we review and categorize a set of major taxonomic databases publicly available as well as a large collection of R packages to access them and to harmonize lists of taxon names. We categorized available taxonomic databases according to their taxonomic breadth (e.g. taxon specific vs. multi‐taxa) and spatial scope (e.g. regional vs. global), highlighting strengths and caveats of each type of database. We divided R packages according to their function, (e.g. syntax standardization tools, access to online databases, etc.) and highlighted overlaps among them. We present our findings (e.g. network of linkages, data and tool characteristics) in a ready‐to‐use Shiny web application (available at: https://mgrenie.shinyapps.io/taxharmonizexplorer/). We also provide general guidelines and best practice principles for taxonomic name harmonization. As an illustrative example, we harmonized taxon names of one of the largest databases of community time series currently available. We showed how different workflows can be used for different goals, highlighting their strengths and weaknesses and providing practical solutions to avoid common pitfalls. To our knowledge, our opinionated review represents the most exhaustive evaluation of links among and of taxonomic databases and related R tools. Finally, based on our new insights in the field, we make recommendations for users, database managers and package developers alike.

Functional diversity is widely used and widespread. However, the main packages used to compute functional diversity indices are not flexible and not adapted to the volume of data used in modern ecological analyses. We here present fundiversity, an R package that eases the computation of classical functional diversity indices. It leverages parallelization and memoization (caching results in memory) to maximize efficiency with data with thousands of columns and rows. We also did a performance comparison with packages that provide analog functions. In addition to being more flexible, fundiversity was always an order of magnitude quicker than alternatives. fundiversity aims to be a lightweight, efficient tool to compute functional diversity indices, which can be used in a variety of contexts. Because it has been designed following clear principles, it is easy to extend. We hope the wider community will adopt it and we welcome all contributions.

Identifying species that are both geographically restricted and functionally distinct, i.e. supporting rare traits and functions, is of prime importance given their risk of extinction and their potential contribution to ecosystem functioning. We use global species distributions and functional traits for birds and mammals to identify the ecologically rare species, understand their characteristics, and identify hotspots. We find that ecologically rare species are disproportionately represented in IUCN threatened categories, insufficiently covered by protected areas, and for some of them sensitive to current and future threats. While they are more abundant overall in countries with a low human development index, some countries with high human development index are also hotspots of ecological rarity, suggesting transboundary responsibility for their conservation. Altogether, these results state that more conservation emphasis should be given to ecological rarity given future environmental conditions and the need to sustain multiple ecosystem processes in the long-term. There are many available ways to rank species for conservation prioritization. Here the authors identify species of mammals and birds that are both spatially restricted and functionally distinct, finding that such species are currently insufficiently protected and disproportionately sensitive to current and future threats.

Assuming Generalized Riemann’s Hypothesis, Bach proved that the class group CℓK\\mathcal C\\!\\ell _{\\mathbf {K}} of a number field K\\mathbf {K} may be generated using prime ideals whose norm is bounded by 12log2⁡ΔK12\\log ^2\\Delta _{\\mathbf {K}}, and by (4+o(1))log2⁡ΔK(4+o(1))\\log ^2\\Delta _{\\mathbf {K}} asymptotically, where ΔK\\Delta _{\\mathbf {K}} is the absolute value of the discriminant of K\\mathbf {K}. Under the same assumption, Belabas, Diaz y Diaz and Friedman showed a way to determine a set of prime ideals that generates CℓK\\mathcal C\\!\\ell _{\\mathbf {K}} and which performs better than Bach’s bound in computations, but which is asymptotically worse. In this paper we show that CℓK\\mathcal C\\!\\ell _{\\mathbf {K}} is generated by prime ideals whose norm is bounded by the minimum of 4.01log2⁡ΔK4.01\\log ^2\\Delta _{\\mathbf {K}}, 4(1+(2πeγ)−NK)2log2⁡ΔK4\\big (1+\\big (2\\pi e^{\\gamma })^{-N_{\\mathbf {K}}}\\big )^2\\log ^2\\Delta _{\\mathbf {K}} and 4(log⁡ΔK+log⁡log⁡ΔK−(γ+log⁡2π)NK+1+(NK+1)log⁡(7log⁡ΔK)log⁡ΔK)24\\big (\\log \\Delta _{\\mathbf {K}} +\\log \\log \\Delta _{\\mathbf {K}}-(\\gamma +\\log 2\\pi )N_{\\mathbf {K}}+1+(N_{\\mathbf {K}}+1)\\frac {\\log (7\\log \\Delta _{\\mathbf {K}})} {\\log \\Delta _{\\mathbf {K}}}\\big )^2. Moreover, we prove explicit upper bounds for the size of the set determined by Belabas, Diaz y Diaz and Friedman’s algorithms, confirming that it has size ≍(log⁡ΔKlog⁡log⁡ΔK)2\\asymp (\\log \\Delta _{\\mathbf {K}}\\log \\log \\Delta _{\\mathbf {K}})^2. In addition, we propose a different algorithm which produces a set of generators which satisfies the above mentioned bounds and in explicit computations turns out to be smaller than log2⁡ΔK\\log ^2\\Delta _{\\mathbf {K}} except for 77 out of the 3129231292 fields we tested.

Let ψK\\psi _{\\mathbb {K}} be the Chebyshev function of a number field K\\mathbb {K}. Under the Generalized Riemann Hypothesis we prove an explicit upper bound for |ψK(x)−x||\\psi _{\\mathbb {K}}(x)-x| in terms of the degree and the discriminant of K\\mathbb {K}. The new bound improves significantly on previous known results.

Let ψK\\psi _{\\mathbb {K}} be the Chebyshev function of a number field K\\mathbb {K}. Let ψK(1)(x):=∫0xψK(t)dt\\psi ^{(1)}_{\\mathbb {K}}(x):=\\int _{0}^{x}\\psi _{\\mathbb {K}}(t)\\,\\mathrm {d} t and ψK(2)(x):=2∫0xψK(1)(t)dt\\psi ^{(2)}_{\\mathbb {K}}(x):=2\\int _{0}^{x}\\psi ^{(1)}_{\\mathbb {K}}(t)\\,\\mathrm {d} t. We prove under GRH (Generalized Riemann Hypothesis) explicit inequalities for the differences |ψK(1)(x)−x22||\\psi ^{(1)}_{\\mathbb {K}}(x) - \\tfrac {x^2}{2}| and |ψK(2)(x)−x33||\\psi ^{(2)}_{\\mathbb {K}}(x) - \\tfrac {x^3}{3}|. We deduce an efficient algorithm for the computation of the residue of the Dedekind zeta function and a bound on small-norm prime ideals.

Pollination niches are important components of ecological niches and have played a major role in the diversification of Angiosperms. In this study, we focused on Euro‐Mediterranean orchids, which use diverse pollination strategies and interact with various functional groups of insects. In these orchids, we investigated the determinants of pollination niche breadth and overlap by analysing the orchid–pollinator network and the factors that may have shaped it. We constructed a database reporting 1,278 interactions between 243 orchid and 773 pollinator species based on a thorough literature review. We then focused on 153 orchid species for which phylogenetic data were available. We used Bayesian phylogenetic mixed models to study the relationship between specialisation (as estimated by the degree and degree in the projected network), pollination strategy and breadths of orchids’ spatial and temporal distributions, while correcting for the effect of phylogenetic relationships among orchid species and sampling effort. We then used a singular value decomposition of the orchid–pollinator matrix combined to a redundancy and variation partitioning analyses to investigate the determinants of similarity in pollination niches between orchids. Specialisation was higher in deceptive than in nectar‐producing orchids and decreased with the breadth of orchids’ spatial distribution. When interactions were considered at the insect family level, similarity in pollination niches between orchids was solely explained by their pollination strategy and phylogeny. By contrast, when they were considered at the insect species level, this similarity was primarily explained by their geographical range and flowering time, although other factors had significant effects as well, with orchids using the same pollination strategy, being closely related and growing in the same habitats sharing more insect species than expected. Synthesis. Specialisation in orchid–pollinator interactions depends on orchids’ pollination strategy and geographical range. The pool of insect families with which orchids interact depends on their pollination strategy and phylogeny, with consistent associations between some functional or phylogenetic groups of orchids and some families of pollinators. By contrast, the pool of insect species with which orchids interact depends on their spatio‐temporal distribution, suggesting that at a finer scale, orchid–pollinator interactions are more opportunistic than previously thought.

Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in [T−a,T+a][T-a,T+a]. We also prove a bound for the multiplicity of the zeros.

Aim: Diet is key to understanding resource use by species, their relationships with their environment and biotic interactions. We aimed to identify the major strategies that shape the diet space of birds and to investigate their spatial distributions in association with biogeographical, bioclimatic and anthropogenic drivers. Location: Global. Time period: Current. Major taxa studied: Birds. Methods: We analysed score‐based assessments of eight diet categories for 8,937 out of 10,964 extant bird species. We constructed a multivariate diet space by ordinating these data in a principal coordinates analysis and assessed its dimensionality as a balance between the representation of original diet scores and parsimony. We averaged the positions of species along each dimension for 12,705 species assemblages and used quantile regressions to infer the relative contributions of species richness, climate, primary productivity, topography and human footprint to the spatial distribution of the diet space at a global scale. Results: The diet space of birds was structured by four dimensions ordinating species along continua ranging from insectivory to plant‐based strategies, granivory to frugivory, common to rare diets, and nectarivory to carnivory and piscivory. Although orthogonal at the species level, these dimensions were correlated among species assemblages, with regional variation consistent with past climatic and tectonic events. Human footprint packed bird assemblages in the diet space, whereas warm climate, high productivity and high topographic variability were associated with high variability in the prevalence of dietary strategies among assemblages. Main conclusions: The tremendous variability in bird diets can be explained by a few basic ecological continua sustained by morphological and ecophysiological differences among species. Strong biogeographical legacies on top of bioclimatic drivers distribute this diet space in species assemblages through environmental filtering and niche packing. However, these patterns are altered at macroecological scales by human‐mediated functional homogenization, which might, in turn, affect the global distribution of bird functions and services.

1. Understanding the causes of biodiversity change is essential for addressing environmental challenges. While causal attribution has advanced in other fields, ecologists remain cautious about causal claims or misinterpret predictive models as causal. With growing spatio-temporal data, computational power and crossdisciplinary collaboration, discussions on improving attribution methods in ecology are gaining momentum. However, practical guidance remains limited for non-experts. Here, we identify the challenges and decisions involved in detecting and attributing biodiversity change and provide an overview of suitable methods based on available data and specific research questions.2. The first challenge we address pertains to biodiversity and driver data. Unlike controlled experimental data in other disciplines, ecological data often stem from monitoring programs or field samplings with varying degrees of rigour, which complicates the analysis due to sampling biases, interacting drivers, measurement error or spatio-temporal variations. We specifically outline how data structure (e.g. structured vs. opportunistic data) and data coverage along the spatial and temporal scale impact detection and attribution.3. The second challenge involves the ability to detect directional change in the system of interest, which is associated with numerous hurdles. We provide an