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    Restoration of insect communities after land use change is shaped by plant diversity: a case study on carabid beetles (Carabidae)

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    Co-cultivation of Mortierellaceae with Pseudomonas helmanticensis affects both their growth and volatilome

    The growth behaviour of Linnemannia is strain-specificMost strains showed comparable morphological characteristics on both media as well as in pure and co-culture. However, Linnemannia solitaria and Entomortierella galaxiae produced more aerial mycelium on PDA compared to LcA. There was more/less aerial mycelium in co-cultures with P. helmanticensis compared to pure cultures depending on the strain (Fig. 1, SI Fig. S3).The comparison of Linnemannia and E. galaxiae daily radial growth rates did not support a difference between these genera (p ≥ 0.3). The overall linear model indicated that the fungal daily growth rates mainly differed among species (Table 1). In addition, the effect of strains highlighted the heterogeneity among strains within species (Fig. 2, SI Figs. S4, S5). Although there was no relevant main effect of medium on the daily radial growth rate of the fungi, the medium did affect the fungi in a strain-specific manner (Table 1, Fig. 2, SI Figs. S4, S5). On nutrient poor LcA, the fungal daily radial growth rates were reduced for all species, except for L. solitaria, which grew better on LcA (SI Figs. S3, S4).Table 1 The effect of experimental factors on the fungal daily radial growth rate.Full size tableFigure 2Daily radial growth rate of pure Linnemannia and Entomortierella cultures as well as co-cultures with P. helmanticensis on nutrient rich PDA medium. (a) L. exigua, (b) L. gamsii, (c) L. hyalina, (d) L. sclerotiella, (e) L. solitaria, (f) E. galaxiae.Full size imageThe main effect of co-plating P. helmanticensis on radial growth rate was small, yet significant (0.7%, p  More

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    Integrative taxonomy reveals new, widely distributed tardigrade species of the genus Paramacrobiotus (Eutardigrada: Macrobiotidae)

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    Globally invariant metabolism but density-diversity mismatch in springtails

    Data reportingThe data underpinning this study is a compilation of existing datasets and therefore, no statistical methods were used to predetermine sample size, the experiments were not randomized and the investigators were not blinded to allocation during experiments and outcome assessment. The measurements were taken from distinct samples, repeated measurements from the same sites were averaged in the main analysis.Inclusion & ethicsData were primarily collected from individual archives of contributing co-authors. The data collection initiative was openly announced via the mailing list of the 10th International Seminar on Apterygota and via social media (Twitter, Researchgate). In addition, colleagues from less explored regions (Africa, South America) were contacted via personal networks of the initial authors group and literature search. All direct data providers who collected and standardised the data were invited as co-authors with defined minimum role (data provision and cleaning, manuscript editing and approval). For unpublished data, people who were directly involved in sorting and identification of springtails, including all local researchers, were invited as co-authors. Principal investigators were normally not included as co-authors, unless they contributed to conceptualisation and writing of the manuscript. All co-authors were informed and invited to contribute throughout the research process—from the study design and analysis to writing and editing. The study provided an inclusive platform for researchers around the globe to network, share and test their research ideas.Data acquisitionBoth published and unpublished data were collected, using raw data whenever possible entered into a common template. In addition, data available from Edaphobase47 was included. The following minimum set of variables was collected: collectors, collection method (including sampling area and depth), extraction method, identification precision and resources, collection date, latitude and longitude, vegetation type (generalized as grassland, scrub, woodland, agriculture and other for the analysis), and abundances of springtail taxa found in each soil sample (or sampling site). Underrepresented geographical areas (Africa, South America, Australia and Southeast Asia) were specifically targeted by a literature search in the Web of Science database using the keywords ‘springtail’ or ‘Collembola’, ‘density’ or ‘abundance’ or ‘diversity’, and the region of interest; data were acquired from all found papers if the minimum information listed above was provided. All collected datasets were cleaned using OpenRefine v3.3 (https://openrefine.org) to remove inconsistencies and typos. Geographical coordinates were checked by comparing the dataset descriptions with the geographical coordinates. In total, 363 datasets comprising 2783 sites were collected and collated into a single dataset (Supplementary Fig. 1).Calculation of community parametersCommunity parameters were calculated at the site level. Here, we defined a site as a locality that hosts a defined springtail community, is covered by a certain vegetation type, with a certain management, and is usually represented by a sampling area of up to a hundred metres in diameter, making species co-occurrence and interactions plausible. To calculate density, numerical abundance in all samples was averaged and recalculated per square metre using the sampling area. Springtail communities were assessed predominantly during active vegetation periods (i.e., spring, summer and autumn in temperate and boreal biomes, and summer in polar biomes). Our estimations of community parameters therefore refer to the most favourable conditions (peak yearly densities). This seasonal sampling bias is likely to have little effect on our conclusions, since most springtails survive during cold periods38,48. Finally, we used mean annual soil temperatures49 to estimate the seasonal mean community metabolism (described below) and tested for the seasonal bias in additional analysis (see Linear mixed-effects models).All data analyses were conducted in R v. 4.0.250 with RStudio interface v. 1.4.1103 (RStudio, PBC). Data was transformed and visualised with tidyverse packages51,52, unless otherwise mentioned. Background for the global maps was acquired via the maps package53,54. To calculate local species richness, we used data identified to species or morphospecies level (validated by the expert team). Since the sampling effort varied among studies, we extrapolated species richness using rarefaction curves based on individual samples with the Chao estimator51,52 in the vegan package53. For some sites, sample-level data were not available in the original publications, but site-level averages were provided, and an extensive sampling effort was made. In such cases, we predicted extrapolated species richness based on the completeness (ratio of observed to extrapolated richness) recorded at sites where sample-level data were available (only sites with 5 or more samples were used for the prediction). We built a binomial model to predict completeness in sites where no sample-level data were available using latitude and the number of samples taken at a site as predictors: glm(Completeness~N_samples*Latitude). We found a positive effect of the number of samples (Chisq = 1.97, p = 0.0492) and latitude (Chisq = 2.07, p = 0.0391) on the completeness (Supplementary Figs. 17–19). We further used this model to predict extrapolated species richness on the sites with pooled data (435 sites in Europe, 15 in Australia, 6 in South America, 4 in Asia, and 3 in Africa).To calculate biomass, we first cross-checked all taxonomic names with the collembola.org checklist55 using fuzzy matching algorithms (fuzzyjoin R package56) to align taxonomic names and correct typos. Then we merged taxonomic names with a dataset on body lengths compiled from the BETSI database57, a personal database of Matty P. Berg, and additional expert contributions. We used average body lengths for the genus level (body size data on 432 genera) since data at the species level were not available for many morphospecies (especially in tropical regions), and species within most springtail genera had similar body size ranges. Data with no genus-level identifications were excluded from the analysis. Dry and fresh body masses were calculated from body length using a set of group-specific length-mass regressions (Supplementary Table 1)58,59 and the results of different regressions applied to the same morphogroup were averaged. Dry mass was recalculated to fresh mass using corresponding group-specific coefficients58. We used fresh mass to calculate individual metabolic rates60 and account for the mean annual topsoil (0–5 cm) temperature at a given site61. Group-specific metabolic coefficients for insects (including springtails) were used for the calculation: normalization factor (i0) ln(21.972) [J h−1], allometric exponent (a) 0.759, and activation energy (E) 0.657 [eV]60. Community-weighted (specimen-based) mean individual dry masses and metabolic rates were calculated for each sample and then averaged by site after excluding 10% of maximum and 10% of minimum values to reduce impact of outliers. To calculate site-level biomass and community metabolism, we summed masses or metabolic rates of individuals, averaged them across samples, and recalculated them per unit area (m2).Parameter uncertaintiesOur biomass and community metabolism approximations contain several assumptions. To account for the uncertainty in the length-mass and mass-metabolism regression coefficients, in addition to the average coefficients, we also used maximum (average + standard error) and minimum coefficients (average—standard error; Supplementary Table 1) in all equations to calculate maximum and minimum estimations of biomass and community metabolism reported in the main text. Further, we ignored latitudinal variation in body sizes within taxonomic groups62. Nevertheless, latitudinal differences in springtail density (30-fold), environmental temperature (from −16.0 to +27.6 °C in the air and from −10.2 to +30.4 °C in the soil), and genus-level community compositions (there are only few common genera among polar regions and the tropics)55 are higher than the uncertainties introduced by indirect parameter estimations, which allowed us to detect global trends. Although most springtails are concentrated in the litter and uppermost soil layers20, their vertical distribution depends on the particular ecosystem63. Since sampling methods are usually ecosystem-specific (i.e. sampling is done deeper in soils with developed organic layers), we treated the methods used by the original data collectors as representative of a given ecosystem. Under this assumption, we might have underestimated the number of springtails in soils with deep organic horizons, so our global estimates are conservative and we would expect true global density and biomass to be slightly higher. To minimize these effects, we excluded sites where the estimations were likely to be unreliable (see data selection below).Data selectionOnly data collection methods allowing for area-based recalculation (e.g. Tullgren or Berlese funnels) were used for analysis. Data from artificial habitats, coastal ecosystems, caves, canopies, snow surfaces, and strong experimental manipulations beyond the bounds of naturally occurring conditions were excluded (Supplementary Fig. 1). To ensure data quality, we performed a two-step quality check: technical selection and expert evaluation. Collected data varied according to collection protocols, such as sampling depth and the microhabitats (layers) considered. To technically exclude unreliable density estimations, we explored data with a number of diagnostic graphs (Supplementary Table 2; Supplementary Figs. 12–20) and filtered it, excluding the following: (1) All woodlands where only soil or only litter was considered; (2) All scrub ecosystems where only ground cover (litter or mosses) was considered; (3) Agricultural sites in temperate zones where only soil with sampling depth 90% of cases were masked on the main maps; for the map with density-species richness visualisation, two corresponding masks were applied (Fig. 2).To estimate spatial variability of our predictions while accounting for the spatial sampling bias in our data (Fig. 1a) we performed a spatially stratified bootstrapping procedure. We used the relative area of each IPBES79 region (i.e., Europe and Central Asia, Asia and the Pacific, Africa, and the Americas) to resample the original dataset, creating 100 bootstrap resamples. Each of these resamples was used to create a global map, which was then reduced to create mean, standard deviation, 95% confidence interval, and coefficient of variation maps (Supplementary Figs. 4–7).Global biomass, abundance, and community metabolism of springtails were estimated by summing predicted values for each 30 arcsec pixel10. Global community metabolism was recalculated from joule to mass carbon by assuming 1 kg fresh mass = 7 × 106 J80, an average water proportion in springtails of 70%58, and an average carbon concentration of 45% (calculated from 225 measurements across temperate forest ecosystems)81. We repeated the procedure of global extrapolation and prediction for biomass and community metabolism using minimum and maximum estimates of these parameters from regression coefficient uncertainties (see Parameter uncertainties).Path analysisTo reveal the predictors of springtail communities at the global scale, we performed a path analysis. After filtering the selected environmental variables (see above) according to their global availability and collinearity, 13 variables were used (Supplementary Fig. 9b): mean annual air temperature, mean annual precipitation (CHELSA database67), aridity (CGIAR database68), soil pH, sand and clay contents combined (sand and clay contents were co-linear in our dataset), soil organic carbon content (SoilGrids database73), NDVI (MODIS database72), human population density (GPWv4 database74), latitude, elevation69, and vegetation cover reported by the data providers following the habitat classification of European Environment Agency (woodland, scrub, agriculture, and grasslands; the latter were coded as the combination of woodland, scrub, and agriculture absent). Before running the analysis, we performed the Rosner’s generalized extreme Studentized deviate test in the EnvStats package82 to exclude extreme outliers and we z-standardized all variables (Supplementary R Code).Separate structural equation models were run to predict density, dry biomass, community metabolism, and local species richness in the lavaan package83. To account for the spatial clustering of our data in Europe, instead of running a model for the entire dataset, we divided the data by the IPBES79 geographical regions and selected a random subset of sites for Eurasia, such that only twice the number of sites were included in the model as the second-most represented region. We ran the path analysis 99 times for each community parameter with different Eurasian subsets (density had n = 723 per iteration, local species richness had n = 352, dry biomass had n = 568, and community metabolism had n = 533). We decided to keep the share of the Eurasian dataset larger than other regions to increase the number of sites per iteration and validity of the models. The Eurasian dataset also had the best data quality among all regions and a substantial reduction in datasets from Eurasia would result in a low weight for high-quality data. We additionally ran a set of models in which the Eurasian dataset was represented by the same number of sites as the second-most represented region, which yielded similar effect directions for all factors, but slightly higher variations and fewer consistently significant effects. In the paper, only the first version of analysis is presented. To illustrate the results, we averaged effect sizes for the paths across all iterations and presented the distribution of these effect sizes using mirrored Kernel density estimation (violin) plots. We marked and discussed effects that were significant at p  More

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    Shifts in vegetation activity of terrestrial ecosystems attributable to climate trends

    Plant growth model without environmental forcingThe model without environmental forcing closely follows the original description of the Thornley transport resistance (TTR) model29. A summary of the model parameters is provided in Supplementary Table 2. The shoot and root mass pools (MS and MR, in kg structural dry matter) change as a function of growth and loss (equations (1) and (2)). The litter (kL) and maintenance respiration (r) loss rates (in kg kg−1 d−1) are treated as constants. In the original model description29 r = 0. The parameter KM (units kg) describes how loss varies with mass (MS or MR). Growth (Gs and Gr, in kg d−1) varies as a function of the carbon and nitrogen concentrations (equations (3) and (4)). CS, CR, NS and NR are the amounts (kg) of carbon and nitrogen in the roots and shoots. These assumptions yield the following equations for shoot and root dry matter,$${mathrm{MS}}[t+1]={mathrm{MS}}[t]+{G}_{{mathrm{S}}}[t]-frac{({k}_{{mathrm{L}}}+r){mathrm{MS}}[t]}{1+frac{{K}_{{{M}}}}{{mathrm{MS}}[t]}},$$
    (1)
    $${mathrm{MR}}[t+1]={mathrm{MR}}[t]+{G}_{{mathrm{R}}}[t]-frac{({k}_{{mathrm{L}}}+r){mathrm{MR}}[t]}{1+frac{{K}_{{{M}}}}{{mathrm{MR}}[t]}},$$
    (2)
    where GS and GR are$${G}_{{mathrm{S}}}=gfrac{{mathrm{CS}}times {mathrm{NS}}}{{mathrm{MS}}},$$
    (3)
    $${G}_{{mathrm{R}}}=gfrac{{mathrm{CR}}times {mathrm{NR}}}{{mathrm{MR}}},$$
    (4)
    and g is the growth coefficient (in kg kg−1 d−1).Carbon uptake UC is determined by the net photosynthetic rate (a, in kg kg−1 d−1) and the shoot mass (equation (5)). Similarly, nitrogen uptake (UN) is determined by the nitrogen uptake rate (b, in kg kg−1 d−1) and the root mass. The parameter KA (units kg) forces both photosynthesis and nitrogen uptake to be asymptotic with mass. The second terms in the denominators of equations (5) and (6) model product inhibitions of carbon and nitrogen uptake, respectively; that is, the parameters JC and JN (in kg kg−1) mimic the inhibition of source activity when substrate concentrations are high,$${U}_{{mathrm{C}}}=frac{a{mathrm{MS}}}{left(1+frac{{mathrm{MS}}}{{K}_{{mathrm{A}}}}right)left(1+frac{{mathrm{CS}}}{{mathrm{MS}}times {J}_{{mathrm{C}}}}right)},$$
    (5)
    $${U}_{{mathrm{N}}}=frac{b{mathrm{MR}}}{left(1+frac{{mathrm{MR}}}{{K}_{{mathrm{A}}}}right)left(1+frac{{mathrm{NR}}}{{mathrm{MR}}times {J}_{{mathrm{N}}}}right)}.$$
    (6)
    The substrate transport fluxes of C and N (τC and τN, in kg d−1) between roots and shoots are determined by the concentration gradients between root and shoot and by the resistances. In the original model description29, these resistances are defined flexibly, but we simplify and assume that they scale linearly with plant mass,$${tau }_{{mathrm{C}}}=frac{{mathrm{MS}}times {mathrm{MR}}}{{mathrm{MS}}+{mathrm{MR}}}left(frac{{mathrm{CS}}}{{mathrm{MS}}}-frac{{mathrm{CR}}}{{mathrm{MR}}}right)$$
    (7)
    $${tau }_{{mathrm{N}}}=frac{{mathrm{MS}}times {mathrm{MR}}}{{mathrm{MS}}+{mathrm{MR}}}left(frac{{mathrm{NR}}}{{mathrm{MR}}}-frac{{mathrm{NS}}}{{mathrm{MS}}}right)$$
    (8)
    The changes in mass of carbon and nitrogen in the roots and shoots are then$${mathrm{CS}}[t+1]={mathrm{CS}}[t]+{U}_{{mathrm{C}}}[t]-{f}_{{mathrm{C}}}{G}_{{mathrm{s}}}[t]-{tau }_{{mathrm{C}}}[t]$$
    (9)
    $${mathrm{CR}}[t+1]={mathrm{CR}}[t]+{tau }_{{mathrm{C}}}[t]-{f}_{{mathrm{C}}}{G}_{{mathrm{r}}}[t]$$
    (10)
    $${mathrm{NS}}[t+1]={mathrm{NS}}[t]+{tau }_{{mathrm{N}}}[t]-{f}_{{mathrm{N}}}{G}_{{mathrm{s}}}[t]$$
    (11)
    $${mathrm{NR}}[t+1]={mathrm{NR}}[t]+{U}_{{mathrm{N}}}[t]-{f}_{{mathrm{N}}}{G}_{{mathrm{r}}}[t]-{tau }_{{mathrm{N}}}[t]$$
    (12)
    where fC and fN (in kg kg−1) are the fractions of structural carbon and nitrogen in dry matter.Adding environmental forcing to the plant growth modelIn this section, we describe how the net photosynthetic rate (a), the nitrogen uptake rate (b), the growth rate (g) and the respiration rate (r) are influenced by environmental-forcing factors. These environmental-forcing effects are described in equations (13)–(17) and summarized graphically in Extended Data Fig. 1. All other model parameters are treated as constants. Previous work that implemented the TTR model as a species distribution model30 is used as a starting point for adding environmental forcing. As in this previous work30, we assume that parameters a, b and g are co-limited by environmental factors in a manner analogous to Liebig’s law of the minimum, which is a crude but pragmatic abstraction. The implementation here differs in some details.Unlike previous work30, we use the Farquhar model of photosynthesis47,48 to represent how solar radiation, atmospheric CO2 concentration and air temperature co-limit photosynthesis35. We assume that the Farquhar model parameters are universal and that all vegetation in our study uses the C3 photosynthetic pathway. The Farquhar model photosynthetic rates are rescaled to [0,amax] to yield afqr. The effects of soil moisture (Msoil) on photosynthesis are represented as an increasing step function ({{{{S}}}}(M_{mathrm{soil}},{beta }_{1},{beta }_{2})=max left{min left(frac{M_{mathrm{soil}}-{beta }_{1}}{{beta }_{2}-{beta }_{1}},1right),0right}). This allows us to redefine a as,$$a={a}_{{mathrm{fqr}}} {{{{S}}}}(M_{mathrm{soil}},{beta }_{1},{beta }_{2})$$
    (13)
    The processes influencing nitrogen availability are complex, and global data products on plant available nitrogen are uncertain. We therefore assume that nitrogen uptake will vary with soil temperature and soil moisture. That is, the nitrogen uptake rate b is assumed to have a maximum rate (bmax) that is co-limited by soil temperature Tsoil and soil moisture Msoil,$$b={b}_{{mathrm{max}}} {{{{S}}}}({T}_{soil},{beta }_{3},{beta }_{4}) {{{{Z}}}}(M_{mathrm{soil}},{beta }_{5},{beta }_{6},{beta }_{7},{beta }_{8}).$$
    (14)
    In equation (14), we have assumed that the nitrogen uptake rate is a simple increasing and saturating function of temperature. We have also assumed that the nitrogen uptake rate is a trapezoidal function of soil moisture with low uptake rates in dry soils, higher uptake rates at intermediate moisture levels and lower rates once soils are so moist as to be waterlogged. The trapezoidal function is ({{{{Z}}}}(M_{mathrm{soil}},{beta }_{5},{beta }_{6},{beta }_{7},{beta }_{8})=max left{min left(frac{M_{mathrm{soil}}-{{{{{beta }}}}}_{5}}{{{{{{beta }}}}}_{6}-{{{{{beta }}}}}_{5}},1,frac{{{{{{beta }}}}}_{8}-M_{mathrm{soil}}}{{beta }_{8}-{beta }_{7}}right),0right}).The previous sections describe how the assimilation of carbon and nitrogen by a plant are influenced by environmental factors. The TTR model describes how these assimilate concentrations influence growth (equations (3) and (4)). In our implementation, we additionally allow the growth rate to be co-limited by temperature (soil temperature, Tsoil) and soil moisture (Msoil),$$g={g}_{{mathrm{max}}} {{{{Z}}}}({T}_{{mathrm{soil}}},{beta }_{9},{beta }_{10},{beta }_{11},{beta }_{12}) {{{{S}}}}(M_{mathrm{soil}},{beta }_{13},{beta }_{14}).$$
    (15)
    We use Tsoil since we assume that growth is more closely linked to soil temperature, which varies slower than air temperature. The respiration rate (r, equations (1) and (2)) increases as a function of air temperature (Tair) to a maximum rmax,$$r={r}_{{mathrm{max}}}{{{{S}}}}({T}_{{mathrm{air}}},{beta }_{15},{beta }_{16}).$$
    (16)
    The parameter r is best interpreted as a maintenance respiration. Growth respiration is not explicitly considered; it is implicitly incorporated in the growth rate parameter (g, equation (15)), and any temperature dependence in growth respiration is therefore assumed to be accommodated by equation (15).Fire can reduce the structural shoot mass MS as follows,$${mathrm{MS}}[t+1]={mathrm{MS}}[t](1-{{{{S}}}}(F,{beta }_{17},{beta }_{18})).$$
    (17)
    where F is an indicator of fire severity at a point in time (for example, burnt area) and the function S(F, β17, β18) allows MS to decrease when the fire severity indicator F is high. If F = 0, this process plays no role. This fire impact equation was used in preliminary analyses, but the data on fire activity did not provide sufficient information to estimate β17 and β18; we therefore excluded this process from the final analyses.We further estimate two additional β parameters (βa and βb) so that each site can have unique maximum carbon and nitrogen uptake rates. Specifically, we redefine a as ({a}^{{prime} }={beta }_{a} a) and b as ({b}^{{prime} }={beta }_{b} b).Data sources and preparationTo describe vegetation activity, we use the GIMMS 3g v.1 NDVI data26,27 and the MODIS EVI28 data. The GIMMS data product has been derived from the AVHRR satellite programme and controls for atmospheric contamination, calibration loss, orbital drift and volcanic eruptions26,27. The data provide 24 NDVI raster grids for each year, starting in July 1981 and ending in December 2015. The spatial resolution is 1/12° (~9 × 9 km). The EVI data used are from the MODIS programme’s Terra satellite; it is a 1 km data product provided at a 16-day interval. We use data from the start of the record (February 2000) to December 2019. The MODIS data product (MOD13A2) uses a temporal compositing algorithm to produce an estimate every 16 days that filters out atmospheric contamination. The EVI is designed to reduce the effects of atmospheric, bare-ground and surface water on the vegetation index28.For environmental forcing, we use the ERA5-Land data31,32 (European Centre for Medium-Range Weather Forecasts Reanalysis v. 5; hereafter, ERA5). The ERA5 products are global reanalysis products based on hourly estimates of atmospheric variables and extend from present back to 1979. The data products are supplied at a variety of spatial and temporal resolutions. We used the monthly averages from 1981 to 2019 at a 0.1° spatial resolution (~11 km). The ERA5 data provide air temperature (2 m surface air temperature), soil temperature (0–7 cm soil depth), surface solar radiation and volumetric soil water (0–7 cm soil depth). Fire data were taken from the European Space Agency Fire Disturbance Climate Change Initiative’s AVHRR Long-Term Data Record Grid v.1.0 product49. This product provides gridded (0.25° resolution) data of monthly global (from 1982 to 2017) burned area derived from the AVHRR satellite programme. As mentioned, the fire data did not enrich our analysis, and the analyses we present here therefore exclude further consideration of the fire data.All data were resampled to the GIMMS grid. The mean pixel EVI was then calculated for each GIMMS cell for each time point in the MODIS EVI data. We used linear interpolation on the NDVI, EVI and ERA5 environmental-forcing data to estimate each variable on a weekly time step. This served to set the time step of the TTR difference equations to one week and to synchronize the different time series.Site selectionThe GIMMS grid cells define the spatial resolution of our sample points. GIMMS grid cells are large (1/12°, ~9 km), meaning that most grid cells contain multiple land-cover types. We focused on wilderness landscapes, and our aim was to find multiple grid cells for the major ecosystems of the world. We used the following classification of ecosystem types to guide the stratification of our grid-cell selection: tropical evergreen forest (RF), boreal forest (BF), temperate evergreen and temperate deciduous forest (TF), savannah (SA), shrubland (SH), grassland (GR), tundra (TU) and Mediterranean-type ecosystems (MT).We used the following criteria to select grid cells. (1) Selected grid cells should contain relatively homogeneous vegetation. Small-scale heterogeneity was allowed (for example, catenas, drainage lines, peatlands) as long as many of these elements are repeated in the scene (for example, rolling hills were accepted, but elevation gradients were rejected). (2) Sites should have no signs of transformative human activity (for example, tree harvesting, crop cultivation, paved surfaces). We used the Time Tool in Google Earth Pro, which provides annual satellite imagery of the Earth from 1984 onwards, to ensure that no such activity occurred during the observation period (note that the GIMMS record starts in July 1981; however, it is likely that evidence of transformative activity between July 1981 and 1984 would be visible in 1984). Grid cells with extensive livestock holding on non-improved pasture were included. In some cases, a small agricultural field or pasture was present, and such grid cells were used as long as the field or pasture was small and remained constant in size. (3) Grid cells should not include large water bodies, but small drainage lines or ponds were accepted as long as they did not violate the first criterion. (4) Grid cells should be independent (neighbouring grid cells were not selected) and cover the major ecosystems of the world. Using these criteria, we were able to include 100 sites in the study (Extended Data Figs. 2 and 3 and Supplementary Table 4).State-space modelWe used a Bayesian state-space approach. Conceptually, the analysis takes the form,$$M[t]=f(M[t-1],{boldsymbol{beta}},{boldsymbol{theta}}_{t-1},{epsilon }_{t-1})$$
    (18)
    $${mathrm{VI}}[t]=m M[t]+eta .$$
    (19)
    Here M[t] is the plant growth model’s prediction of biomass (M = MS + MR) at time t, and ϵt−1 is the process error associated with the state variables. In the model, each underlying state variable (MS, MR, CS, CR, NS and NR) has an associated process error term. The function f(M[t − 1], β, θt−1, ϵt−1) summarizes that the development of M is influenced by the state variables MS, MR, CS, CR, NS and NR, the environmental-forcing data θt−1 and the β parameters. The observation equation (equation (19)) uses the parameter m to link the VI (vegetation index, either NDVI or EVI) observations to the modelled state M. The parameter η is the observation error. Equation (19) assumes that there is a linear relationship between modelled biomass (M) and VI, which is a simplification of reality50,51,52. The observation error η is structured by our simplification of the data products quality scores (coded Q = 0, 1, 2, with 0 being good and 2 being poor; Supplementary Table 3) to allow the error to increase with each level of the quality score. Specifically, we define η = e0 + e1 × Q.The model was formulated using the R package LaplacesDemon53. All β parameters are given vague uniform priors. The parameter m is given a vague normal prior (truncated to be >0). The process error terms are modelled using normal distributions, and the variances of the error terms are given vague half-Cauchy priors. The ex parameters are given vague normal priors. The model also requires the parameterization of M[0], the initial vegetation biomass; M[0] is given a vague uniform prior. We used the twalk Markov chain Monte Carlo (MCMC) algorithm as implemented in LaplacesDemon53 and its default control parameters to estimate the posterior distributions of the model parameters. We further fitted the model using DEoptim54,55, which is a robust genetic algorithm that is known to perform stably on high-dimensional and multi-modal problems56, to verify that the MCMC algorithm had not missed important regions of the parameter space. The models estimated with MCMC had significantly lower log root-mean-square error than models estimated with DEoptim (paired t-test NDVI analysis: t = –2.9806, degrees of freedom (d.f.) = 99, P = 0.00362; EVI analysis: t = –4.6229, d.f. = 99, P = 1.144 × 10–5), suggesting that the MCMC algorithm performed well compared with the genetic algorithm.Anomaly extraction and trend estimationWe use the ‘seasonal and trend decomposition using Loess’ (STL57) as implemented in the R58 base function stl. STL extracts the seasonal component s of a time series using Loess smoothing. What remains after seasonal extraction (the anomaly or remainder, r) is the sum of any long-term trend and stochastic variation. We estimate the trend in two ways. First, we estimate the trend by fitting a quadratic polynomial (r = a + bx + cx2) to the remainder (r is the remainder, x is time and a, b and c are regression coefficients). The use of polynomials allows the data to specify whether a trend exists, whether the trend is linear, cup or hat shaped and whether the overall trend is increasing or decreasing. As a second method, we estimate the trend by fitting a bent-cable regression to the remainder. Bent-cable regression is a type of piecewise linear regression for estimating the point of transition between two linear phases in a time series59,60. The model takes the form r = b0 + b1x + b2 q(x, τ, γ)60. Here r is the remainder, x is time, b0 is the initial intercept, b1 is the slope in phase 1, the slope in phase 2 is b2 − b1 and q is a function that defines the change point: (q(x,tau ,gamma )=frac{{(x-tau +gamma )}^{2}}{4gamma }I(tau -gamma < tau +gamma )+(x-tau )I(x > tau +gamma )); τ represents the location of the change point and γ the span of the bent cable that joins the two linear phases; I(A) is an indicator function that returns 1 if A is true and 0 if A is false. The bent-cable model allows the data to specify whether a trend exists and whether there has been a switch in the trend, thereby allowing the identification of whether the trend is linear, cup or hat shaped and whether the overall trend is increasing or decreasing. Both the polynomial and bent-cable models were estimated using LaplacesDemon’s53 Adaptive Metropolis MCMC algorithm and vague priors, although for the bent-cable model we constrained τ to be in the middle 70% of the time series and γ to be at most two years.The STL extraction of the seasonal components in the air temperature, soil temperature, soil moisture and solar radiation data (there is no stochasticity or seasonal trend in the CO2 data we used) allows us to simulate detrended time series d of these forcing variables as (d=bar{y}+s+{{{{N}}}}(mu ,sigma )) where N(μ, σ) is a normally distributed random variable with mean and standard deviation estimated from the remainder r (we verified that r was well described by the normal distribution), (bar{y}) is the mean of the data over the time series and s is the seasonal component extracted by STL. For CO2, the detrended time series is simply the average CO2 over the time series. More