Philippa Kaur

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Goose capture and trackingWe used rocket netting and leg snares to capture white-fronted geese in three regions in Texas (Rolling Plains, Lower Texas Coast, and South Texas Brushlands) and one region in Louisiana (Chenier Plain) from October to February 2016–2018 (Fig. 1). We determined age and sex of individuals by cloacal inversion, rectrices and other plumage characteristics27,28. We fit a solar powered GPS/ACC/Global System for Mobile communication (GSM) neckband tracking device (Cellular Tracking Technologies Versions BT3.0, BT3.5 and BT3.75; 44–54 g; Rio Grande, New Jersey, USA, and Ornitela OrniTrack-N38; 36 g; Vilnius, Lithuania), and an aluminum U.S. Geological Survey Bird Banding Laboratory metal leg band (Supplementary Fig. S1) on each bird. Geese were captured and tagged under USGS Bird Banding Permits #21314 and #23792, and Texas A&M University-Kingsville Institutional Animal Care and Use Committee #2015-09-01B. Captive geese were permitted under TAMUK IACUC #2018-01-11 and United States Fish and Wildlife Service Waterfowl Sale and Disposal permit #MB03808D-0. All applicable field methods were carried out in accordance with relevant guidelines and regulations. All animal handling protocols were approved by TAMUK IACUC committees and the USGS Bird Banding Laboratory. When multiple white-fronted geese were captured simultaneously, devices were only placed on adult females or adult males to eliminate the potential of placing devices on mated pairs, thus biasing independent data collection due to monogamous, long-term pair bonds in white-fronted geese. Location duty cycles were set to collect a GPS location every 30 min (i.e., 48/day) and location accuracy was 7.2 and 6.5 m for CTT and Ornitela devices, respectively. Data were uploaded once daily to respective online user interface websites when within areas of GSM coverage. When not in coverage areas, data were stored onboard the device until birds returned to coverage areas. All devices were equipped with a tri-axial ACC sensor which measured G-force (g; CTT devices) or millivolts (mV; Ornitela devices) at a fixed sampling scheme; CTT BT3.5 and Ornitela devices collected ACC data for a duration of 3 s every 6 min at 10 Hz, while BT3.0 devices collected data for a duration of 10 s every 6 min at 10 Hz. Generation BT3.0 devices were subsampled to match the sampling scheme of 3 s bursts before analyses. Ornitela units measured in mV were converted to G-force. We applied manufacturer- and tag-specific ACC calibration to all units, respectively, by collecting ACC data on each possible rotation for all axes when the device was stationary and applying the calibration to the raw ACC values (see Ref.29 for full calibration procedure). All devices recorded temperature in °C at each GPS fix. We censored GPS and ACC data from the time of release until individuals appeared to resume normal movement activity (i.e., roosting and foraging), as geese typically flew to the nearest wetland immediately after release where they remained without leaving while acclimating to wearing devices, which ranged from 1 to 7 days30. We defined the start of the winter period following a southward migratory movement from staging areas in Canada, without additional migratory movements southward below 40° 0′ 00″ N, or from the time of device deployment (minus device acclimation period) until geese made large northward migratory movements, or 28 February if geese remained in wintering areas.Figure 1Primary wintering regions of the Midcontinent population of greater white-fronted goose (Anser albifrons frontalis) in North America (excluding regions in Mexico). Transmitters were deployed during winters 2016–2018 in the Chenier Plain (Louisiana), Lower Texas Coast, and Rolling/High Plains regions. Geese that made winter movements outside of these defined regions were classified as ‘Other’ regions. Map created using Esri ArcMap (version 10.3.1; www.esri.com).Full size imageLand cover covariatesWe used publicly available spatial landcover data sets (30-m resolution) in combination with remote sensing to create landscape layers using programs Esri ArcMap (version 10.3.1), Erdas Imagine, and Program R (version 3.5.231). We used 2017 and 2018 National Agricultural Statistics Service Cropland Data Layer (CDL) data sets for agricultural crop types and freshwater wetlands, and the 2010 Coastal Change Analysis Program layer for saltwater and coastal wetland classifications29,32. Additionally, we used multi-spectral Landsat 8 Operational Land Imager satellite imagery, with principal component analysis on eight Landsat bands and a normalized difference vegetation index band, and unsupervised classification33,34 to accurately identify and create a spatial layer for peanut fields. We developed this layer for two regions with annual peanut agriculture (i.e., the Rolling/High Plains and South Texas Brushlands) using ground-truthed peanut fields, because the CDL layer did not identify this crop accurately based on our field observations during captures. We achieved  > 90% accuracy of peanut identification for each image independently based on annual ground-truthed observations of peanut fields. Finally, we grouped like-habitat categories to reduce the total number of categories to eight: corn, grass/winter wheat, herbaceous wetlands, other grains (i.e., soybeans, sorghum, and peanuts), rice, woody wetlands, open water/unconsolidated shore and other (Supplementary Table S1). White-fronted geese used several ecologically distinct regions in both winters of our study (Fig. 1), where the landscape composition of specific landcover types varied. To account for regional variability, we added region ID as a categorical variable to all GPS locations. Regions included the MAV, Chenier Plain, Texas Mid-coast, Lower Texas Coast, South Texas Brushlands, Texas Rolling/High Plains, and Other (i.e., locations outside of these identified wintering regions; Fig. 1). We used regional shapefiles of Gulf Coast Joint Venture Initiative Areas (Laguna Madre [Lower Texas Coast], Texas Mid-coast, and Chenier Plain35), and Level III Ecoregions (Mississippi Alluvial Valley, Texas Rolling/High Plains, and South Texas Brushlands36) as boundaries to classify data into regions. Due to insufficient and incompatible spatial layers for Mexico, we limited analyses to locations within the US.Location and acceleration data collectionRemotely determining behaviors of individuals using ACC data is most accurately addressed by developing a training dataset of known behaviors linked with ACC measurements of those behaviors18,37. To develop a training dataset, we collected video footage of two domestic white-fronted geese in Texas, US, and 18 tagged wild Greenland white-fronted geese (A. a. flavirostris) fitted with the same device types and the same data collection scheme, in Wexford, Ireland and Hvanneyri, Iceland during winters 2017–2018. We supplemented wild recordings with behavioral recordings of captive white-fronted geese as a proxy for wild individuals due to difficulty filming wild geese in inclement weather and obstructed video footage, which is common in ACC literature19,20,38,39. To replicate devices placed on wild white-fronted geese and account for potential variation in ACC measurements between device brands, among device versions and individual geese, we deployed three versions of devices used in this study on captive white-fronted geese during filming sessions38,40. We attached tracking devices to captive geese one week prior to video collection to allow geese to adjust to wearing devices. We collected ACC measurements for 3 s bursts, at 1 min intervals, at 10 Hz. We constructed a 149 m2 enclosure in an agricultural field to imitate an environment that wild geese may encounter. We created two enclosure settings allowing captive geese to forage on sprouted winter wheat (~ 2–15 cm) or on a randomly dispersed mixture of grain seeds (corn, wheat, sorghum) to account for both ‘grazing’ of vascular vegetation and ‘gleaning’ of agricultural grains to imitate foraging in wild geese. We used Sony Handycam DCR-SR45 video cameras, matched internal camera clocks with a running Universal Coordinated Time clock, and verbally re-calibrated the current time every 2 min during video footage collection. We filmed 119.5 h of video footage, and matched behavior with recorded ACC measurements by pairing video and device timestamps for each device using JWatcher41 and Program R.We characterized goose behaviors into four categories: ‘stationary’, ‘walk’, and ‘foraging’ from ground-truthed video footage, and ‘flight’ from visual inspection of the ACC data and consecutive GPS tracks during migration where device-measured speed remained  > 4.63 km/h (based on a natural break in the speed density distribution of all GPS locations). Each ACC burst was classified as only one behavior (i.e., a goose that was walking as it foraged was classified as ‘foraging’). We combined wild goose behaviors and captive goose behaviors after identifying minimal differences in ACC burst summary statistics29 for ‘stationary’ and ‘walk’ behaviors. We used ‘graze’ behaviors only from wild geese because of low sample size for captive geese and slight differences in ACC summary statistics between captive and wild geese for this behavior. ‘Glean’ foraging behavior was only classified from captive geese. We then combined ‘graze’ and ‘glean’ behaviors into an overall ‘foraging’ behavior to account for variation in foraging behavior of wild geese, and because machine learning models could not accurately distinguish between the two foraging modes40. We randomly subsampled all behaviors to 150 bursts if our dataset contained at least that many bursts to reduce the risk of artificially increasing prediction accuracy20. We determined there were insufficient differences in ACC signatures between CTT BT3.0 and BT3.5 versions by visual comparison of signatures and summary statistics, and merged all bursts into an overall CTT-specific training data set, and retained CTT- and Ornitela-specific training data sets to account for brand-specific ACC measurement schemes. The final training data sets consisted of 150 stationary, 150 walking, 118 foraging, and 150 flying bursts (CTT), and 150 stationary, 75 walking, 120 foraging, and 150 flying bursts (Ornitela).We used the training data sets to predict behaviors of tagged, wild white-fronted geese during winter with temporally aligned GPS and ACC data. We used a suite of supervised machine-learning algorithms and selected the algorithm with greatest prediction accuracy based on an 80% training, 20% testing sample approach. We tested random forest, support vector machines, K-nearest neighbors, classification and regression trees, and linear discriminant analysis, all with cross validation in Program R18,29,42. We evaluated models using three metrics defined in Ref.42: (1) overall classification accuracy as the percent of classifications in the test data set that were predicted correctly, (2) precision of assignment, the probability that an assigned behavior in the test data set was correct, and (3) model recall, the probability that a sample with a specific behavior in the test data set was correctly classified as that behavior by the model. Random forests provided the highest overall classification accuracy (95.6% for CTT and 96.0% for Ornitela), as well as high precision and recall for each behavior (CTT range 93.1–99.3, Ornitela range 88.9–100.0%), and therefore we labeled behaviors from wild goose ACC data using the random forests.Habitat transition modelOur habitat-transition model required temporally matched GPS and ACC datasets. Therefore, we subset all GPS locations to match the time-series of ACC data per individual because devices typically acquired GPS data longer than ACC data before device failure or individual mortality. For each GPS location, we extracted the landcover type and wintering region from spatial layers and retained temperature recorded from the device. To link classified ACC behaviors to GPS locations, we matched ACC timestamps between two GPS locations with the previous GPS timestamp. That is, all ACC bursts between two GPS locations were assigned backward to the previous GPS location. In this way, an individual’s first location is collected in GPS landcover type A, ACC data are collected in 5 bursts, their behaviors are classified and assigned to the first GPS location A and associated landcover type, followed by collection of GPS location B, in which the subsequent 5 ACC bursts are associated to GPS location/landcover type B. In the case of missing GPS locations, we matched ACC bursts to the previous GPS location only if the ACC timestamps were within 60 min of the GPS timestamp, and ACC bursts occurring greater than 60 min after GPS acquisition were removed until the next GPS fix. To account for temporal variation in habitat-behavior relationships, we calculated two continuous covariates representing time-of-day based on the local time associated with the timestamp of each GPS location for each individual. The variable cos(Diel) represented diurnal (negative values) and nocturnal (positive values) periods, and sin(Time) represented midnight until 11:59 a.m. (positive values) and noon until the following 11:59 p.m. (negative values), where high and low values ranged continuously between 1 and − 143. Our temporally matched time series of GPS and ACC data yielded 53,502 GPS locations linked with 300,348 ACC bursts across both winters.We used a Bayesian Markov model with Pólya-Gamma sampling following43), [cf. Refs.44,45] to determine how transitions between landcover types were influenced by behavior, temperature, time-of-day, and wintering region. The proportion of time spent foraging, walking, and stationary between each successive GPS fix was included as a covariate; flight was not included to reduce multicollinearity due to behavior proportions summing to one. Markov models account for non-independence among observations by assuming that the current state (i.e., landcover type) is dependent upon the previous state, and allow the determination of covariate influences on the probability of transitioning among states through a logistic link function. The transition probability from habitat i to habitat j at time t for individual n is modeled with multinomial logistic regression:$$begin{aligned} & logitleft( {p_{nijt} } right) = logleft( {frac{{p_{nijt} }}{{p_{niJt} }}} right) = mathop sum limits_{{r in {mathcal{R}}_{j} }} beta_{0jr} Ileft( {Region_{nt} = r} right) + beta_{1j} {text{cos}}left( {Diel_{nt} } right) \ & quad + beta_{2j} {text{sin}}left( {Time_{nt} } right) + beta_{3ij} Forage_{nt} + beta_{4ij} Walk_{nt} + beta_{5ij} Stationary_{nt} + beta_{6ij} Temperature_{nt} , \ end{aligned}$$where ({mathcal{R}}_{j}) is the set of wintering regions (r) where habitat (j) occurs, (Regio{n}_{rnt}) indicated wintering region (r), and (mathrm{cos}left({Diel}_{nt}right)) and (mathrm{sin}({Time}_{nt})) were temporal covariates (described above) for habitat j. Quantities ({Forage}_{nt}, {Walk}_{nt},mathrm{ and }{Stationary}_{nt}) were the scaled (mean = 0, standard deviation = 1) proportion of time spent in each behavior between transitions from habitat i to habitat j, and ({Temperature}_{nt}) was scaled ambient temperature (°C) for transitions from habitat i to habitat j. All coefficients for transitions to the baseline habitat (J) were set to 0 (i.e., ({beta }_{0Jr}) for all (r), ({beta }_{1J}), ({beta }_{2J}), ({beta }_{3iJ}), ({beta }_{4iJ}), ({beta }_{5iJ}),({beta }_{6iJ}), for all (i)). We set the baseline habitat (J) as open water/unconsolidated shore because this habitat is used primarily for both nocturnal roosting and diurnal loafing, included all behaviors, and transitions to all other landcover types were frequent in each region.The prior for the set of winter region intercepts for each habitat was:$${beta }_{0jr}sim N({beta }_{0j},{sigma }_{0jr}^{2}),$$for (rin {mathcal{R}}_{j}), ({beta }_{0j}) was the mean intercept, and ({sigma }_{0jr}^{2}) was set to 100. For ({beta }_{0j}), a vague prior mean 0 and σ2 = 100 was used with an assumed normal distribution.The Markov model was executed within a Bayesian framework to robustly quantify uncertainty. The Markov model assumed that data were collected at regular time intervals for both GPS (30 min) and ACC (6 min), however imperfect collection by devices created irregular data sets. Therefore, we subsampled GPS locations and constrained time series data to sequences where GPS locations missing  > 120 min intervals (i.e., 4 locations) were separated into sequences of regular time series data for each individual46. We extended43 by including a mix of both transition-specific effects (i.e., behaviors, temperature) and habitat-specific effects (i.e., wintering region, cos(Diel), and sin(Time)), where transition-specific effects were allowed to vary for a current habitat state, while habitat-specific effects were not. We included a mix of coefficients because initial model runs indicated that some effects were similar regardless of the current habitat (i.e., were habitat- and not transition-specific decisions). We also incorporated a model feature to exclude estimation of transitions that did not occur either within the dataset as a whole or within each specific wintering region because landcover types varied among them by setting those specific transition probabilities to zero. We centered and standardized all behavior and temperature covariates, sampled 50,000 iterations from the model posterior using one chain, and discarded the first 10,000 iterations as burn-in. We assessed model convergence by evaluating trace plots and setting random initial values, examined autocorrelation plots, and Geweke diagnostics using the R package ‘coda’47,48,49. More

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Authors and AffiliationsJacob Blaustein Center for Scientific Cooperation, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, IsraelGopal MuraliMitrani Department of Desert Ecology, The Swiss Institute for Dryland Environments and Energy Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, IsraelGopal Murali & Uri RollDepartment F.-A. Forel for Aquatic and Environmental Sciences, Faculty of Science, University of Geneva, Geneva, SwitzerlandTakuya IwamuraDepartment of Forest Ecosystems and Society, College of Forestry, Oregon State University, Corvallis, OR, USATakuya IwamuraSchool of Zoology, Tel Aviv University, Tel Aviv, IsraelShai MeiriThe Steinhardt Museum of Natural History, Tel Aviv University, Tel Aviv, IsraelShai MeiriAuthorsGopal MuraliTakuya IwamuraShai MeiriUri RollCorresponding authorCorrespondence to
Gopal Murali. More

Oil palm plantations can supplant once biodiverse tropical forests. As planted areas expand, it is vital to plan landscapes to better balance biodiversity and oil palm production. Strategic ‘set-asides’ offer a key approach.In recent decades, oil palm has expanded spectacularly in some of the most biodiverse areas of the tropics, especially in Indonesia and Malaysia. This expansion has caused extensive deforestation (including loss of more than 2.1 million ha of primary forests in Borneo2, as well as other forests and agroforests), and management of plantations often relies heavily on clearing, herbicides and pesticides. This has generated many direct and indirect impacts on wildlife, ecosystems, climate and human communities3. Further expansion is ongoing, and global demand continues to rise4. More

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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