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Functional diversity (FD) has the potential to address many ecological questions, from impacts of global change on biodiversity to ecological restoration. There are several methods estimating the different components of FD. However, most of these methods can only be computed at limited spatial scales and cannot account for intraspecific trait variability (ITV), despite its significant contribution to FD. Trait probability density (TPD) functions (which explicitly account for ITV) reflect the probabilistic nature of niches. By doing so, the TPD approach reconciles existing methods for estimating FD within a unifying framework, allowing FD to be partitioned seamlessly across multiple scales (from individuals to species, and from local to global scales), and accounting for ITV. We present methods to estimate TPD functions at different spatial scales and probabilistic implementations of several FD concepts, including the primary components of FD (functional richness, evenness, and divergence), functional redundancy, functional rarity, and solutions to decompose beta FD into nested and unique components. The TPD framework has the potential to unify and expand analyses of functional ecology across scales, capturing the probabilistic and multidimensional nature of FD. The R package TPD (https://CRAN.R-project.org/package=TPD) will allow users to achieve more comparative results across regions and case studies. ; CPC was supported by the Estonian Research Council (project PSG293), and by the European Union through the European Regional Development Fund (Centre of Excellence EcolChange)

Questions. Compensatory dynamics are described as one of the main mechanisms that increase community stability, e.g., where decreases of some species on a year‐to‐year basis are offset by an increase in others. Deviations from perfect synchrony between species (asynchrony) have therefore been advocated as an important mechanism underlying biodiversity effects on stability. However, it is unclear to what extent existing measures of synchrony actually capture the signal of year‐to‐year species fluctuations in the presence of long‐term directional trends in both species abundance and composition (species directional trends hereafter). Such directional trends may lead to a misinterpretation of indices commonly used to reflect year‐to‐year synchrony. Methods. An approach based on three‐term local quadrat variance (T3) which assesses population variability in a three‐year moving window, was used to overcome species directional trend effects. This "detrending" approach was applied to common indices of synchrony across a worldwide collection of 77 temporal plant community datasets comprising almost 7,800 individual plots sampled for at least six years. Plots included were either maintained under constant "control" conditions over time or were subjected to different management or disturbance treatments. Results. Accounting for directional trends increased the detection of year‐to‐year synchronous patterns in all synchrony indices considered. Specifically, synchrony values increased significantly in ~40% of the datasets with the T3 detrending approach while in ~10% synchrony decreased. For the 38 studies with both control and manipulated conditions, the increase in synchrony values was stronger for longer time series, particularly following experimental manipulation. Conclusions. Species' long‐term directional trends can affect synchrony and stability measures potentially masking the ecological mechanism causing year‐to‐year fluctuations. As such, previous studies on community stability might have overemphasised the role of compensatory dynamics in real‐world ecosystems, and particularly in manipulative conditions, when not considering the possible overriding effects of long‐term directional trends. ; We thank multiple entities for the financial support necessary to obtain the different databases: the U.S. National Science Foundation under grant numbers DEB‐8114302, DEB‐8811884, DEB‐9411972, DEB‐0080382, DEB‐0620652, DEB‐1234162, DEB‐9707477, DEB‐0316402, DEB‐08‐16453, and DEB‐12‐56034, DEB‐0618210, the Nutrient Network (http://www.nutnet.org) experiment from the National Science Foundation Research Coordination Network (NSF‐DEB‐1042132), the New Zealand National Vegetation Survey Databank, the Spanish MINECO (Project CGL2014‐53789‐R), the Madrid Regional Government (Projects REMEDINAL‐3 and REMEDINAL‐TE), the European Research Council Synergy grant 610028 (IMBALANCE‐P), the Institute on the Environment (DG‐0001‐13), the SOERE‐ACBB financed through French National Agency for Research (ANAEE‐F, ANR‐11‐INBS‐0001), the Estonian Research Council (IUT 20‐28, IUT 20‐29), Czech Science Foundation (GAČR 17‐05506S and 19‐28491X), the European Regional Development Fund (Centre of Excellence EcolChange), the German Federal Environmental Foundation (DBU) for a grant to the NABU Hamburg (management experiment Calamagrostis epigejos), and the German Federal Ministry of Education and Research within the framework of the project BIOTA Southern Africa (promotion numbers 01LC0024, 01LC0024A and 01LC0624A2), Task 159 of SASSCAL (promotion number 01LG1201) and the Scottish Government's Rural and Environmental Science and Analytical Services division. Acknowledgement Data owned by NERC© Database Right/Copyright NERC. Further support was provided by the Jornada Basin Long‐Term Ecological Research (LTER) project, Cedar Creek Ecosystem Science Reserve and the University of Minnesota. We also thank the Lawes Agricultural Trust and Rothamsted Research for data from the e‐RA database. The Rothamsted Long‐term Experiments National Capability (LTE‐NCG) is supported by the UK Biotechnology and Biological Sciences Research Council (Grant BBS/E/C/000J0300) and the Lawes Agricultural Trust. ; Peer reviewed

Analysing temporal patterns in plant communities is extremely important to quantify the extent and the consequences of ecological changes, especially considering the current biodiversity crisis. Long-term data collected through the regular sampling of permanent plots represent the most accurate resource to study ecological succession, analyse the stability of a community over time and understand the mechanisms driving vegetation change. We hereby present the LOng-Term Vegetation Sampling (LOTVS) initiative, a global collection of vegetation time-series derived from the regular monitoring of plant species in permanent plots. With 79 data sets from five continents and 7,789 vegetation time-series monitored for at least 6 years and mostly on an annual basis, LOTVS possibly represents the largest collection of temporally fine-grained vegetation time-series derived from permanent plots and made accessible to the research community. As such, it has an outstanding potential to support innovative research in the fields of vegetation science, plant ecology and temporal ecology. ; The authors acknowledge institutional support as follows. Nicola J. Day: Te Apārangi Royal Society of New Zealand (Rutherford Postdoctoral Fellowship). Jiří Danihelka: Czech Science Foundation (project no. 19-28491X) and Czech Academy of Sciences (project no. RVO 67985939). Francesco de Bello: Spanish Plan Nacional de I+D+i (project PGC2018-099027-B-I00). Eric Garnier: La Fage INRA experimental station. Tomáš Herben: GAČR grant 20-02901S. Anke Jentsch: German Federal Ministry of Education and Research (grant 031B0516C - SUSALPS) and Oberfrankenstiftung (grant OFS FP00237). Norbert Juergens: German Federal Ministry of Education and Research (grant 01LG1201N - SASSCAL ABC). Frédérique Louault and Katja Klumpp: AnaEE-France (ANR-11-INBS-0001). Robin J. Pakeman: Strategic Research Programme of the Scottish Government's Rural and Environment Science and Analytical Services Division. Meelis Pärtel: Estonian Research Council (PRG609) and European Regional Development Fund (Centre of Excellence EcolChange). Josep Peñuelas: Spanish Government (grant PID2019-110521GB-I00), Fundación Ramon Areces (grant ELEMENTAL-CLIMATE), Catalan Government (grant SGR 2017-1005), and European Research Council (Synergy grant ERC-SyG-2013-610028, IMBALANCE-P). Ute Schmiedel: German Federal Ministry of Education and Research (Promotion numbers 01LC0024, 01LC0024A, 01LC0624A2, 01LG1201A, 01LG1201N). Hana Skálová: GAČR grant 20-02901S. Karsten Wesche: International Institute Zittau, Technische Universität Dresden. Susan K. Wiser: New Zealand Ministry for Business, Innovation and Employment's Strategic Science Investment Fund. Ben A. Woodcock: NERC and BBSRC (NE/N018125/1 LTS-M ASSIST - Achieving Sustainable Agricultural Systems). Enrique Valencia: Program for attracting and retaining talent of Comunidad de Madrid (no. 2017-T2/AMB-5406) and Community of Madrid and Rey Juan Carlos University (Young Researchers R&D Project. Ref. M2165 – INTRANESTI). Truman P. Young: National Science Foundation (LTREB DEB 19-31224). ; Peer reviewed

© 2021 The Authors. ; 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 m 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/databases/GrasslandDiversityExplorer) 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. ; GrassPlot development has been supported by the Bavarian Research Alliance (BayIntAn_UBT_2017_58), the Eurasian Dry Grassland Group (EDGG) and the International Association for Vegetation Science (IAVS); IB, CorM, JAC, IGM, DGM, MHe, DL and MTo were supported by the Basque Government (IT936‐16); CorM, IAx, MCh, JDa, PD, MHá, ZL, ZPr, EŠ and LT were supported by the Czech Science Foundation (19‐28491X); TR was supported by the Estonian Research Council (PUT1173); RJP was funded by the Strategic Research Programme of the Scottish Government's Rural and Environmental Science and Analytical Services Division"; SBa was supported by the GINOP‐2.3.2‐15‐2016‐00019 project; GFi was partially supported by the MIUR initiative "Department of excellence" (Law 232/2016)"; BJA was funded by the Spanish Research Agency (grant AEI/ 10.13039/501100011033); AK, VB, IM, DS, IV and DV were supported by the National Research Foundation of Ukraine (2020.01/0140); MP and AH were supported by the Estonian Research Council (PRG874, PRG609), and the European Regional Development Fund (Centre of Excellence EcolChange); Data collection of HCP was funded by FORMAS (Swedish Research Council for Environment, Agricultural Science and Spatial Planning) and The Swedish Institute; JR was supported by the Czech Science Foundation (grant No. 20‐09895S) and the long‐term developmental project of the Czech Academy of Sciences (RVO 67985939); ATRA was funded by the Grant of Excellence Departments, MIUR‐Italy (ARTICOLO 1, COMMI 314 – 337 LEGGE 232/2016); JMA was supported by Carl Tryggers stiftelse för vetenskaplig forskning and Qatar Petroleum; AAli was supported by the Jiangsu Science and Technology Special Project (Grant No. BX2019084), and Metasequoia Faculty Research Startup Funding at Nanjing Forestry University (Grant No. 163010230), and he is currently supported by Hebei University through Faculty Research Startup Funding Program; ZB was supported by the NKFI K 124796 grant; The GLORIA‐ Aragón project of JLBA was funded by the Dirección General de Cambio Climático del Gobierno de Aragón (Spain); MCs and LDem were supported by DG Environment through the European Forum on Nature Conservation and Pastoralism and Barbara Knowles Fund, in collaboration with Pogány‐havas Association, Romania; JDa was partially supported by long‐term research development project no. RVO 67985939 of the Czech Academy of Sciences; BD and OV were supported by the NKFI KH 126476, NKFI KH 130338, NKFI FK 124404 and NKFI FK 135329 grants; BD, OV and AKe were supported by the Bolyai János Scholarship of the Hungarian Academy of Sciences; BE was funded by the Environmental Department of the Tyrolean Federal State Government, the MAB Programme of the Austrian Academy of Science, the Mountain Agriculture Research Unit and the Alpine Research Centre Obergurgl of Innsbruck University. The GLORIA projects of BE were funded by the EU project no. EVK2‐CT‐2000‐00056, the Earth System Sciences Program of the Austrian Academy of Sciences (project MEDIALPS), the Amt für Naturparke, Autonome Provinz Bozen‐Südtirol, the Südtiroler Wissenschaftsfonds and the Tiroler Wissenschaftsfonds; RGG was supported by the Spanish Ministry of Research to sample GLORIA sites in central Spain (CGL 2008‐00901/BOS) and present works by the Autonomous Region of Madrid (REMEDINAL TE‐CM, S2018/EMT‐4338); MJ was supporteLatviaed by Latvia Grant No. 194051; NP and SŠ were partly supported by the Slovenian Research Agency, core fundings P1‐0403 and J7‐1822.