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Study design
The study was a single-center, randomized, double-blind, controlled study, stratified by sex in four parallel groups with a 1:1:1:1 allocation ratio: the Test 1, Control 1, Test 3 and Control 3 groups, receiving one (Test 1 and Control 1) or three (Test 3 and Control 3) bottles per day of the Test or the Control product. The study period was split into three subperiods (Fig. 1): a 2-week washout period (day 14 to day 0), a 4-week period of Test or Control product consumption (day 0 to day 28) and a 4-week follow-up period (day 28 to day 56). Dietary restrictions were imposed throughout the entire study period (from day 14 to day 56), with prohibition of the consumption of other fermented dairy products, probiotics, vitamins and mineral supplements, to limit potential interference with the evaluation of the Test product effects. Each subject attended five visits to a clinical unit (Harrison Clinical Research, Munich, Germany): inclusion visit (V1-day 14), randomization visit (V2-day 0), two evaluation visits (V3-day 14, V4-day 28), and an end-of-study evaluation visit (V5-day 56). Blood and stool samples were collected for assessments of eligibility and of the safety evaluation criteria at V1, 2, 3 and 4 (blood) and V2, 3, 4, and 5 (stool). Each visit had to take place within 2 days of the scheduled visit date (± 2 days) to ensure a consistent adequacy between the times of clinical and biological measures and the duration of each corresponding period of product intake or follow-up between subjects. This study was performed in accordance with the principles of the Declaration of Helsinki, the French Huriet law, and ICH-GCP recommendations, and was approved by the ethics committee of the Bavarian Medical Association, Munich, Germany. All volunteers provided written informed consent. This trial was registered on the ClinicalTrials.gov, with the registration number NCT01108419 (date of registration April 22, 2010). The study was funded by Danone Research (France).
Figure 1

Clinical study design.

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Subject selection
Subjects were screened between March and April 2010, and the study lasted from March 29th 2010 (first subject included) to June 25th 2010 (last subject completed). The following eligibility criteria were assessed at subject inclusion (V1). The inclusion criteria were: male or female volunteers providing written informed consent, aged from 18 to 55 years, with a body mass index (BMI) of 18.5 to 30.0 kg/m2, free-living and considered to be in good health on the basis of a clinical examination, with a normal defecation pattern and either menopausal or with an approved method of contraception if female. Non-inclusion criteria were: any allergy, hypersensitivity to any component of the study product, including lactose, systemic or topical treatment (at the time of inclusion or in the previous 4 weeks) likely to interfere with the evaluation of the study parameters (antibiotics, intestinal or respiratory antiseptics, antirheumatic agents, anti-inflammatory drugs [except for aspirin or equivalent at doses preventing from platelet aggregation or blood clotting] and steroids prescribed for chronic inflammatory diseases), any symptoms of respiratory or gastrointestinal common infectious diseases, a history of chronic metabolic or gastrointestinal disease, abdominal pain or any other severe progressive or chronic disease (cardiac, respiratory, etc.), immunodeficiency, eating disorders or a medicated diet, pregnancy or breast-feeding. The following eligibility criteria were also assessed at the randomization visit (V2): compliance with the dietary and medication restriction (as defined in the non-inclusion criteria) between V1 and V2, negative pregnancy test and parameters within the normal range in the blood samples collected at V1, and absence of common infectious disease symptoms.
Product intervention
The Test product was a fermented dairy drink containing Lactobacillus paracasei CNCM I-1518, Lactobacillus paracasei CNCM I-3689 and Lactobacillus rhamnosus CNCM I-3690 strains, with 107 to 109 colony-forming units (CFU)/g of product, and four yogurt strains (Lactobacillus bulgaricus CNCM I-2787, Streptococcus thermophilus CNCM I-2773, Streptococcus thermophilus CNCM I-2835, Streptococcus thermophilus CNCM I-2778). Counts were measured for each of the bacterial strains present in the Test product, at the start and end of the authorized storage period (shelf life). Means and ranges of strains counts from the batches of product used in the study are provided in Supplementary Table S1. The Control product was a non-fermented dairy drink, acidified with lactic acid and containing pectin as a stabilizer. Both the Test and Control products were sweetened and multi-fruit flavored. Both products were similar in terms of their appearance, packaging, nutritional content (isocaloric) and taste, to ensure the maintenance of double-blinding (both the participants and key study personnel, including the outcome assessors) until the database was locked and the request by the statistician for unblinding (the only staff not blinded being those involved in the preparation of the study products). Products were manufactured in a pilot plant approved by the national health authorities for the production of dairy products for human consumption. They were supplied by Danone Research, France and stored at + 4 ± 2 °C, with a shelf life of 37 days. Analyses were performed to guarantee the absence of microbiological contaminants in all products. Subjects were randomly assigned to the Test or Control group according to a randomization list established before the start of the study by an external statistician. The randomization list contained balanced blocks, stratified by sex, with the allocation of an incremental number linked to product number given by an IWRS system, and was kept confidential at the sponsor’s premises in order to ensure allocation concealment. The subjects were then asked to ingest either one (100 g) or three (3 × 100 g) bottles of the Test or Control product daily, in accordance with their randomization group, for the entire 4-week product-consumption period (28 days). Subjects with three doses per day were recommended to consume no more than two doses at the same time. Compliance was evaluated by the investigator on the basis of the daily reporting of product consumption by each participant in a personal diary and a count of unused bottles.
Outcomes
The primary aim of the study was to compare product safety between the Test 1 and Control 1 groups over the 4-week period of product consumption. The safety evaluation was based on the following parameters: adverse events, physical examination, hematology, metabolism profile, markers of hepatic, kidney and thyroid function, inflammatory markers, bowel habits and frequency of digestive symptoms. Additional information about safety parameters is provided in Supporting Information.
As secondary criteria, safety parameters were also analyzed for the Test 3 and Control 3 groups, over the period of product consumption (V2 to V4), and for both 1 and 3 product doses during other periods: the follow-up period (V4–V5) and the whole experimental period (V2–V5). Stool samples were also subjected to testing to detect and quantify the strains present in the Test product and to analyze the microbiota, for both doses and different study periods (see details and methods below).
Procedure
At each visit, from V1 to V5, subjects underwent a physical examination and vital signs were recorded. Subjects completed a personal diary throughout the 10-week study period, which was collected and examined at each visit by the investigator. This diary included daily reports of study product consumption, the intake of unauthorized products, concomitant medication, symptoms, frequency and consistency of stool and a weekly scoring from the Frequency of Digestive Symptoms questionnaire. The physical activity and smoking habits of the subjects were recorded at each visit. Blood samples were collected for analyses after overnight fasting every two weeks from V1 to V4. The measure of calprotectin concentration, the detection and quantification of strains from the Test product, and the evaluation of the microbiota profile were performed on stool samples collected at each visit from V2 to V5. The study was performed in accordance with the protocol and the statistical analysis plan with no major change during the course of the trial.
Safety monitoring committee
A safety and monitoring committee (SMC), composed of three independent experts in internal medicine, hepato-gastro-enterology and pharmacology, performed an unblinded review of the subject withdrawals, the protocol deviations, the statistical analyses of study parameters and the individual data in the event of abnormal values for safety results. The statistical results were presented after the database lock by the study scientist and statistician to the SMC during two meetings. The SMC then presented its conclusions concerning the safety of the daily ingestion of the Test product at the two doses evaluated.
Stool collection, DNA extraction
We collected fecal samples from 90 subjects at four time points (Test 1 (N = 22), Test 3 (N = 23), Control 1 (N = 21), Control 3 (N = 24)) in RNAlater solution (Ambion, Courtaboeuf, France). Fecal DNA was extracted by mechanical lysis (FastprepFP120; ThermoSavant, Illkirch, France) followed by phenol/chloroform-based extraction, as previously described39. The DNA preparation was subjected to quality control by spectrophotometry on a NanoDrop 2000c spectrophotometer (Thermo Fisher). The DNA was analyzed by quantitative polymerase chain reaction (qPCR), 16S rRNA gene sequencing and whole-genome sequencing.
Quantitative PCR
Three strains, Lactobacillus paracasei subsp. paracasei CNCM I-1518, Lactobacillus paracasei subsp. paracasei CNCM I-3689 and Lactobacillus rhamnosus CNCM I-3690, were quantified by qPCR, as previously described39, with specific primers (Supplementary Table S2). Values were reported as median and interquartile range.
16S RNA gene sequencing, processing and analysis
16S RNA gene sequencing was performed as previously described18. Amplification was performed with the V3-V4 primers for the 16S rRNA (forward: CCTACGGGNGGCWGCAG, reverse: GACTACHVGGGTATCTAATCC). The samples were loaded into flow cells in an Illumina MiSeq 300PE Sequencing Platform, in accordance with the manufacturer’s instructions. Analyses were performed with QIIME (v. 19). The sequences were filtered for quality and a mean of 99,437 ± 36,973 reads per sample were retained. Reads were clustered into operational taxonomic units (OTUs; 97% identity threshold) with VSEARCH, and representative sequences for each OTU were aligned and taxonomically assigned with the SILVA database (v. 119). Alpha-diversity was assessed at genus level. Beta diversity was assessed with Bray–Curtis dissimilarity, Jensen-Shannon divergence, and weighted and unweighted UniFrac on genera and OTUs.
Metagenomic shotgun sequencing and preprocessing
Following standard DNA quality control and quantification, sequencing libraries were prepared with the Nextera XT DNA sample preparation kit in accordance with the manufacturer’s instructions. An overview of the bioinformatic pipeline used in this study is provided in Supplementary Fig. S1. We generated a mean of 35 million (± 8 million) paired-end reads per sample. Read cleaning, filtering and mapping were performed with NGLess version 0.740. An augmented catalog was built from the Integrated Gene Catalog (IGC)41 enriched with genes from the sequencing and de novo assembly of these 107 metagenomes and the seven bacterial genomes present in the Test product (Supplementary Fig. S2). Mapping and count matrix generation were also performed with NGLess. The taxonomic profile was extracted from the count matrix with the Metagenomic Species Pan-Genomes database42. For functional characterization, the catalog was annotated with functional data from the Kyoto encyclopedia of genes and genomes (KEGG, https://www.genome.jp/kegg/)43.
Functional contribution
Metagenomic gene count matrices were aggregated at KEGG orthologous (KO) levels, for the whole gene set and for genes from L. rhamnosus and L. paracasei from the Test product only. We estimated the contribution of the Test product to each KO, by dividing each KO relative abundance level for the Test product by the corresponding value for the whole gene set. A pseudocount of one was added. Corresponding KO relative abundances for the 31 universally distributed marker genes from Ciccarelli et al.44 were also obtained, to estimate the minimal functional contribution of each Test product gene. All KOs for the Test product with a contribution strictly higher than the minimal contribution, constituting a significant functional contribution of the Test product to the gut metagenome, were extracted for downstream analysis. KEGG BRITE and module annotations were used to explore this functional contribution, focusing on enzymes and transporters. We then assessed the extent to which this significant functional contribution set was shared by the other metagenomic species pan-genomes (MSPs).
Statistical analysis
Clinical parameters
No data on adverse events were available to assess the sample size required. The decision to include 24 subjects per group was thus made on the basis of previously published safety studies45,46. For assessment of the safety of consuming the Test product, in comparison to the Control product, adverse events were recorded (MedDRA version 13) and used to evaluate the number of subjects with at least one adverse event, and the total number of adverse events overall, and by relationship to the study product, intensity, seriousness, action taken, and subject outcome. Additional physical examination data, blood parameters, calprotectin concentration in feces, and questionnaires about bowel movements, stool consistency and the frequency of digestive symptoms were collected throughout the period of product consumption and were analyzed as raw data or in terms of clinical significance relative to the baseline value. No formal statistical tests has been performed to assess the safety and study conclusions were based on nominal statistics as described hereafter, on individual data and on overall agreement of the SMC. For quantitative variables, Cohen’s d was calculated for the change from baseline after 4-week product consumption in Test and Control groups as follows: Cohen’s d = (Average raw change from baseline in Test group − Average raw change from baseline in Control group)/Pooled standard deviation at baseline. Cohen’s d values around 0.50 are considered to be of medium magnitude, and those around or above 0.80 are considered to be large47,48. In this study, an absolute Cohen’s d value above 0.5 was considered to be large enough to detect a potential difference between the Test and Control groups. For qualitative binary parameters, the relative risk (RR) and its 95% confidence interval (CI) were calculated by the normal approximation method. Safety analyses were performed on all randomized subjects who had consumed the Test or Control product at least once, i.e. the full analysis set (FAS) population. Statistical analyses were performed with the Statistical Analysis Systems statistical software package version 9.1.3 (Windows XP Professional; SAS Institute, Cary, NC, USA).
Gut microbiota
We used non-parametric tests to analyze qPCR data, alpha and beta-diversity, gene and species richness within individuals, between groups, at baseline and over time. Differential analyses were performed with DESeq2 (version 1.14.1)49 and ZIBR50. For all tests, the alpha risk was set at 0.05 after FDR adjustment by the Benjamini–Hochberg procedure. Network analysis was performed with the SPIEC-EASI R package (version 1.0.751). All statistical analyses were performed, and graphs were plotted with R software (version 3.6.0). Details of the analyses and parameters are provided in Supporting Information. More

Coupling of SM and VPD confounds ecosystem dryness stress
The difficulty to disentangle the respective effects of SM and VPD stems from the fact that SM and VPD are strongly coupled through land–atmosphere interactions7,20. In addition, field experiments that manipulate atmospheric humidity and temperature at the ecosystem scale are lacking21. Given the strong SM-VPD coupling (Fig. 1c), e.g., on the yearly scale, both lower SM and higher VPD are associated with lower ecosystem gross primary production (GPP), indicated by SIF (Fig. 1a, b). This underlies the use of either SM or VPD alone as proxy for dryness stress on ecosystem production in many current models. Note a global spatially contiguous SIF data set was mainly used in this study, which was generated by using the machine-learning algorithm to train SIF observations from Orbiting Carbon Observatory-2 (OCO-2)22. We display the yearly scale because it is typically used to represent the condition of strong SM-VPD coupling globally11, and the study time period mainly spans from 2001 to 2016. However, as SM and VPD are strongly coupled, it is possible that the correlation between SM and SIF is a byproduct of the correlation between VPD and SIF, or vice versa. As a consequence of SM-VPD coupling, the correlations of yearly SM and VPD with SIF is very similar globally (Fig. 1d). Consequently, the correlation between SM and VPD constitutes a confounding factor that is often overlooked when assessing the role of SM and VPD in determining the impact of dryness stress on ecosystem production. There are still low correlations between SIF and SM or VPD in the northern high latitudes or tropical regions, which suggests possible temperature or radiation effects and requires further investigation.
Fig. 1: Strong coupling of soil moisture and vapor pressure deficit confounds ecosystem dryness stress.

a–c Spatial distribution of Pearson’s correlation coefficient between solar-induced chlorophyll fluorescence (SIF) and soil moisture (SM) (r(SIF, SM)), SIF and vapor pressure deficit (VPD) (r(SIF, VPD)), and SM and VPD (r(SM, VPD)), at the yearly scale. Regions with sparse vegetation and regions without valid data are masked in gray. d Relationship between yearly r(SIF, VPD) and yearly r(SIF,SM) across land vegetated areas. Color shows the relative density of data points, with higher density in black and lower density in yellow.

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Decoupling of SM and VPD globally
At yearly scale, there is a strong negative correlation between SM and VPD, indicating that low SM is always accompanied by high VPD (Fig. 1c), which is consistent with previous findings7,20. From yearly to monthly, weekly, and daily scale, the correlations between SM and VPD are generally decreasing (Fig. 2d), but remain large across extensive areas, such as central South America, Sub-Saharan Africa, India, and Southeast Asia (Fig. 2a and Supplementary Fig. 1). However, when binning the data into 10 bins according to percentiles of either SM or VPD per pixel, we find that the correlation coefficient between SM and VPD in each bin becomes approximately zero (Fig. 2b–d and Supplementary Figs. 2 and 3). This shows that SM and VPD are generally decoupled at daily scale in both SM and VPD bins.
Fig. 2: Decoupling of soil moisture and vapor pressure deficit.

a–c Spatial distribution of Pearson’s correlation coefficient between soil moisture (SM) and vapor pressure deficit (VPD) at daily scale, averaged over daily SM bins, and averaged over daily VPD. Regions with sparse vegetation and regions without valid data are masked in gray. d Violin plots of correlations between SM and VPD from yearly to daily bins across land vegetated areas. White dots indicate the median values, gray boxes cover the interquartile range, and thin gray lines reach the 5th and 95th percentiles.

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Disentangling the relative role of SM of VPD
We now disentangle the respective effects of SM and VPD in limiting ecosystem production by exploiting the fact that SM and VPD are decoupled in binned daily SM or VPD data (Fig. 2). SM and VPD are also largely decoupled in 4-day bins, which is the temporal resolution of the mainly used SIF data set (Supplementary Figs. 4 and 5). The analysis is guided by the assumption that if SM dominates dryness stress, low SM will limit ecosystem production regardless of VPD variations (Supplementary Fig. 6a, c). In the same way, if VPD dominates dryness stress, high VPD will limit ecosystem production regardless of SM variations (Supplementary Fig. 6b, d).
To illustrate this further, we select an example pixel located in Mali (West Africa). Without decoupling SM and VPD, it is difficult to conclude whether the decrease in SIF is caused by low SM, high VPD, or both in conjunction (Fig. 3a, b). However, when looking at the variation of SIF across VPD gradients in SM bins (without SM-VPD coupling), high VPD does not reduce SIF but even increase SIF a bit under moderate SM conditions (Fig. 3c). In contrast, low SM reduces SIF noticeably in VPD bins (Fig. 3d). This shows that high VPD does not limit SIF in the absence of the SM-VPD coupling at the example pixel, whereas low SM can still limit SIF. In other words, the apparent VPD limitation on SIF is largely the byproduct of SM-VPD coupling. The respective effects of SM and VPD on SIF is also illustrated in Fig. 3e. The changes in SIF from low VPD to high VPD without SM-VPD coupling (termed ΔSIF(VPD|SM)) can quantify the VPD stress on SIF. Likewise, changes in SIF from high SM to low SM without SM-VPD coupling (termed ΔSIF(SM|VPD)) quantify the SM stress on SIF. The effect of SM and VPD on SIF is estimated using two approaches: (i) SIF in the maximum VPD bin minus SIF in the minimum VPD bin or SIF in the minimum SM bin minus SIF in the maximum SM bin; (ii) using linear regression to derive changes in SIF caused by high VPD or low SM. The two approaches lead to similar results (Methods and Supplementary Fig. 16). As shown in Fig. 3f, the SM effect is strong at the example location (ΔSIF(SM|VPD) = −0.17 mW m−2 nm−2 sr−1), in contrast to the VPD effect (ΔSIF(VPD|SM) = −0.03 mW m−2 nm−2 sr−1). Thus, the comparison of (ΔSIF(SM|VPD) and ΔSIF(VPD|SM) enables the disentangling of their relative role in governing dryness stress.
Fig. 3: Disentangling soil moisture and vapor pressure deficit limitation effects.

a Daily solar-induced chlorophyll fluorescence (SIF) versus daily vapor pressure deficit (VPD). b Daily SIF versus daily soil moisture (SM). c Daily SIF versus daily VPD, binned by SM. d Daily SIF versus daily SM, binned by VPD. c, d circles denote the averaged SIF within each bin of VPD and SM. e Average SIF in each percentile bin of SM and VPD. The cyan arrows indicate the VPD limitations on SIF without SM-VPD coupling (ΔSIF(VPD|SM)), and the orange arrows indicate the SM limitations on SIF without SM-VPD coupling (ΔSIF(SM|VPD)). For better readability, only four arrows are shown. f Distribution of ΔSIF(VPD|SM) and ΔSIF(SM|VPD). Circles denote the ΔSIF(VPD|SM) and ΔSIF(SM|VPD) in each bin. Squares denote the corresponding mean. The example pixel is located in Mali, West Africa at 14.25°N, −4.75°E. See Methods for more details.

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Next, we examine the respective SM and VPD effects on SIF globally. To ensure comparability in space, the SIF time series at each pixel are normalized by the average SIF exceeding the 90th percentile. Temperature and radiation can also limit ecosystem production, therefore, we have filtered out days when other meteorological drivers were likely to be more important than SM or VPD in limiting ecosystem carbon and water fluxes throughout the analyses, following previous studies12,23. We find that ΔSIF(SM|VPD) is negative across most vegetated land areas, robustly indicating the limiting role of low SM to SIF (Fig. 4a, b) and consistent with plant physiological understanding and previous studies4,7. The units refer to the fractions relative to average SIF exceeding the 90th percentile in each grid cell. Large ΔSIF(SM|VPD) are identified in mid-latitudes, including southern North America, central Eurasia, southern Africa, and Australia. In contrast, ΔSIF(VPD|SM) is small and close to 0 across large areas, but it was larger than ΔSIF(SM|VPD) in tropical Africa surrounding the equator (Fig. 4c, d). Globally, a change from the wettest SM to the driest SM under constant VPD reduces SIF by up to 14.9% on average, whereas a change in VPD from lowest to highest quantiles under constant SM has little effect on SIF (−3.8%) on average. Locally, the areas where the strength of SM effects on SIF (|ΔSIF(SM|VPD)|) exceeds that of VPD effects (|ΔSIF(VPD|SM)|) are widespread, which is also visible along the latitudinal gradient (Fig. 4e, f). In total, |ΔSIF(SM|VPD)| is larger than |ΔSIF(VPD|SM)| across 71.3% of land vegetated areas with valid data, by contrast, VPD is more important than SM in 26.7% of corresponding areas. Furthermore, our findings suggest that many previous estimates of the role of VPD on ecosystem production are likely exaggerated16,24 as they did not account for the strong SM-VPD coupling as a confounding factor. In boreal and tropical regions, both SM and VPD have little effect on SIF, which is controlled by radiation and temperature7,25. The spatial patterns of ΔSIF(SM|VPD)—ΔSIF(VPD|SM) are robust to the choice of the particular forcing data set (Supplementary Figs. 7–11). However, when using the GOME-2 SIF and SCIAMACHY SIF with the local overpass time at 9:30 am and 10:00 am, the VPD effects are weaker than that in CSIF (reducing SIF by 0.1% and 0.02% on average globally), including most of Africa (excluding the Sahara) as well as large areas of central South America, southern Asia, and Australia (Supplementary Figs. 9–11). This raise a caveat that using SIF retrieved in the morning would underestimate the VPD effects. To further test the robustness of our result, we standardized the SIF by photosynthetically active radiation (PAR) to remove possible radiation effects26, limited the data to a narrow temperature range to remove possible temperature effects and aggregated data to a coarser time resolution or using 20 percentile bins, yielding similar results (Supplementary Figs. 12–15). Thus, we demonstrate that SM is the dominant factor in driving the response of ecosystem production to dryness at the ecosystem scale across most land vegetated areas, except for tropical and boreal areas.
Fig. 4: Effect of soil moisture and vapor pressure deficit on ecosystem production globally.

a, c, e Spatial distribution of the changes in solar-induced chlorophyll fluorescence (SIF) caused by low soil moisture (SM) (ΔSIF(SM|VPD)) and high vapor pressure deficit (VPD) (ΔSIF(VPD|SM)), and their differences in absolute values (i.e., |ΔSIF(SM|VPD)|−|ΔSIF(VPD|SM)|). b, d, f Zonal means of SM and VPD effects on SIF and their differences in absolute values. The units refer to the fractions relative to average SIF exceeding the 90th percentile in each grid cell. Black lines indicate the mean values, and gray shaded bands show the standard deviation. Regions with sparse vegetation and regions without valid data are masked in white.

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Different from a recent global assessment of SM stress on ecosystem production that estimates the relation between SM stress and background climate from a small sample of flux sites18, our results build on data with global coverage and hence provide spatially explicit information of SM stress. Further converting the SIF decrease to the actual carbon loss would largely help quantify changes in terrestrial carbon fluxes under drought. Furthermore, our conclusions contradict many laboratory experiments that show strong VPD effects on stomatal conductance at the leaf scale27,28. This again indicates that the stomatal sensitivity to VPD do not definitely determine the same VPD response of plant water and carbon fluxes at the ecosystem scale29,30, but some ecosystem scale measurements reveal that stomatal sensitivity to VPD can matter in some cases11,12. Key processes driving the weak plant photosynthesis response to VPD at the ecosystem scale need to be addressed in future work, such as the role of ecosystem water use efficiency, water storage and hydraulic strategies29.
Dependence of SM stress on climate and vegetation gradients
We find that SM limitation effects (ΔSIF(SM|VPD) are largest in semi-arid ecosystems (Fig. 5a), including shrubland, grassland, and savannah ecosystems. These are the ecosystems that are the main drivers of the interannual variability in global terrestrial CO2 flux31,32. In contrast, VPD effects are much weaker in these regions (Fig. 4c). This suggests that SM could be more important than VPD in driving interannual variability of global terrestrial carbon uptake. As SM stress is strongest in drylands, the projected expansion of drylands33 is likely to increase the influence of SM on the future global carbon cycle. In addition, we find that regions with lower tree fraction exhibit a larger response to SM stress globally (Fig. 5b). This is in line with recent findings34, and further verifies the robustness of our results. Our findings also highlights the differential dryness response of ecosystems along a tree cover gradient.
Fig. 5: Dependence of soil moisture dryness stress on climate and vegetation gradients.

Violin plots of soil moisture (SM) limitation effects (ΔSIF(SM|VPD)) across a aridity gradients and b tree cover gradients. c Violin plots of the sensitivity of solar-induced chlorophyll fluorescence (SIF) to SM (i.e., (frac{{delta SIF}}{{delta SM}}|_{VPD})) within different plant functional types: SHR(S), shrubland (south of 45° N); GRA, grassland; CRO, cropland; WSA(S), woody savanna (south of 45° N); SAV, savanna. White dots indicate the median values, gray boxes cover the interquartile range, and thin gray lines reach the 5th and 95th percentiles.

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The representation of dryness stress on plant photosynthetic CO2 assimilation can differ largely between TEMs and is considered one of the largest uncertainties in predicting future land carbon uptake and climate35,36,37. Their representations in TEMs often uses an empirical function that only varies by plant functional type (PFT)38, which have generally not been validated against observational empirical data. Therefore, we explored the observed standardized sensitivity of SIF to SM. We find that the sensitivity of ecosystem production to changes in SM can vary largely even in the same PFT with strong observed dryness effects (Fig. 5c). This is consistent with recent findings that the grassland’s sensitivity to dryness can vary greatly39. The differences of dryness response in the same PFT are, e.g., related to plant species, plant height and plant hydraulic processes, such as plasticity variations in xylem and mesophyll conductance, embolism resistance, or water storage40. At present, evaluating and incorporating more plant hydraulic processes into the next generation of terrestrial ecosystems is on the way41. Our results of dryness effects on ecosystem production thus enables an evaluation of further TEM evolution.
In summary, we provide global results of SM and VPD stress on SIF and demonstrate that SM, rather than VPD, is the dominant driver leading to drought limitation on vegetation productivity at the ecosystem level across most vegetated land areas. VPD stress on ecosystem production is almost lost across large areas without SM-VPD coupling. We thus make the case for revisiting the role of VPD in previous studies that neglected the strong SM-VPD coupling. Furthermore, models that do not correctly disentangle the respective VPD and SM limitations cannot adequately predict the dryness stress on ecosystems and associated rough risks to human well-being. The next challenge is to incorporate the observations to constrain the representation of dryness stress on plants in models, which would also reduce uncertainties in the projection of terrestrial CO2 fluxes and associated climate projections. More

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Study areas
Time series of population survey data were used from nonmigratory elk populations in three different locations along the West Coast of the USA (Fig. 4). Five of the populations were in the Prairie Creek drainage (Davison), the Lower Redwood Creek drainage (Levee Soc), the Stone Lagoon area, the Gold Bluffs region, and the Bald Hills region of Redwood National and State Parks (RNSP), Humboldt County, California (41.2132° N, 124.0046° W). These populations occupy an area of about 380 km2. The climate in this region was mild, with cool summers and rainy winters. Annual precipitation was usually between 120 and 180 cm and most of the precipitation fell between October and April. Snow was rare since average winter temperatures rarely dropped below freezing and ranged from 3 to 5 °C. Average summer temperatures ranged from 10 to 27 °C, depending on the distance inland. Elk in RNSP were not legally hunted, and displayed strong social bonding between females, juveniles, and sub-adult males7.
Figure 4

Map of study areas in Arid Lands Ecology (ALE) Reserve, southern part of Redwood National and State Parks, and Tomales Point Elk Reserve in Point Reyes National Seashore. This map was created in ArcMap (Version 10.6; https://desktop.arcgis.com/en/arcmap/).

Full size image

An elk population in the Point Reyes National Seashore inhabited part of the Point Reyes Peninsula in Marin County, California (38.0723° N, 122.8817° W). The elk were restricted to an area of 10.52 km2 on the northern tip of the peninsula by a 3-m-tall fence. The climate of this study area was Mediterranean, with an average annual precipitation of 87 cm27. Most of the precipitation fell from autumn to early spring. Temperatures averaged about 7 °C in winter and 13 °C in summer27,35.
Another elk population was in the Arid Lands Ecology (ALE) Reserve and occupied a 300 km2 area within the U.S. Department of Energy’s Hanford Site, Washington (46.68778° N, 119.6292° W). The climate in this area was semi-arid with dry, hot summers and wet, moderately-cold winters. Average summer temperatures were around 20 °C and average winter temperatures were around 5 °C with an average annual precipitation of 16 cm, half of which fell in the winter as rain36.
Population surveys
In RNSP, females, juveniles, and subadult males were often in the same group and tended to use open meadow habitat more frequently than adult males37,38. These behavioral patterns likely explain why females, juveniles, and subadult males were sighted more frequently than adult males7. Moreover, in size-dimorphic ungulates such as elk, recruitment was strongly correlated with female abundance and weakly correlated with male abundance7,13,39. In RNSP, the abundance of groups of females, juveniles, and subadult males drove the dynamics of the group and of adult males7. Therefore, for the RNSP populations, we used herd counts where a herd was comprised of females, juveniles, and subadult males. We also used herd counts for the Point Reyes and ALE Reserve populations to remain consistent.
Systematic herd surveys of elk were conducted during January from 1997 to 2019 in RNSP. Surveys in the Davison meadows, the Levee Soc area, the Stone Lagoon area, the Gold Bluffs region, and the Bald Hills region were conducted by driving specified routes 4 to 10 times on different days throughout the month of January. The time series for these five herds ranged from 19 to 23 years of data. The elk were counted and classified by age and sex as adult males, subadult males, females, and juveniles. Females could not be visually differentiated into adult and subadult age categories37. The highest count of females, juveniles, and subadult males from the surveys conducted each year was used as an index of abundance of each herd since the detection probabilities were high both on an absolute basis ( > 0.8) and relative to variation in detection probabilities (CVsighting = 0.05)7,40. For the Bald Hills herd, which is the only herd in RNSP where harvests occurred, we added hunter harvests to the highest count of each year to account for this source of mortality. These harvests occurred only when elk from the Bald Hills herd left RNSP.
Elk population surveys were conducted at the Point Reyes National Seashore from 1982 to 2008. Weekly surveys were conducted after the mating season. Surveys were conducted on foot or horseback of female elk that were ear-tagged or had a collar containing radio telemetry32,35. Individuals counted were classified as females, juveniles, subadult males, and adult males. Data were not available for the years 1984 to 1989 and 1993, so the time series included 20 years of data. We used the highest count of females, juveniles, and subadult males in each year in our analyses. This herd was also not hunted.
Elk population surveys in the ALE Reserve were conducted in winters after hunting and before parturition. From 1982 to 2000, biologists used aerial telemetry studies, in which they located all collared elk during each survey and classified them by sex and age. We used the total counts of females, juveniles and subadult males. For years in which multiple surveys were conducted, we used the highest count in each year as an index of abundance for that year25,41. We omitted population survey data collected in 1982 from our analysis because individuals were not classified by sex and age in this year. Consequently, the time series included 18 years of data. For all years of data used, we added hunter harvests to the highest count of each year to account for this source of mortality. The count in 2000 was much lower than in the previous year, likely due in part to a large wildfire which occurred in the summer of 2000, which probably had an immediate effect of reducing available elk forage in the reserve and caused elk to spend more time outside of the ALE Reserve42,43. In addition, the highest recorded number of elk (about 291) were harvested that year43.
Ricker growth models
We fit linearized Ricker growth models simultaneously to the seven time series to estimate population growth parameters as well as temporal variation in r and β. We estimated K as the x-intercept of the Ricker growth model (i.e., when r = 0). Notably, preliminary analyses showed that not accounting for observer error did not bias our results (see Supplementary Information).
We used a Bayesian Markov Chain Monte Carlo (MCMC) algorithm with 3 chains, 150,000 iterations, a burn-in period of 75,000, an adaptation period of 75,000, and no thinning. We used Bayesian inference and MCMC because these methods offer advantages when fitting hierarchical models to model variation in ecological data44,45. We conducted these analyses in the RJAGS program (JAGS Version 4.0.0; https://sourceforge.net/projects/mcmc-jags/files/JAGS/4.x/Windows/) in RStudio (R Version 3.5.0; https://cran.r-project.org/bin/windows/base/old/3.5.0/). We used uninformative priors for the y-intercept (i.e., rmax) and the slope (i.e., β) in order to allow solely the data to influence posterior estimates of these parameters. Informative priors were not necessary as long as parameter estimates from each chain converged. Convergence among chains was determined when the Gelman-Rubin diagnostic ((hat{R})) was less than 1.01, and through visual checks of trace and density plots46.
The estimate of rmax borrowed information among herds because this parameter should be similar among populations within a species22. Therefore, we modeled rmax for each herd (j) as a random effect following a normal distribution with (mu_{{r_{max} }} sim Normalleft( {0, 0.001} right)) and (sigma_{{r_{max} }} sim Uniformleft( {0, 100} right)). To model temporal variation in r for each herd, we included a zero-centered random effect which was also modeled following the normal distribution (gamma_{t,j} sim Normalleft( {0,sigma_{{gamma_{j} }} } right)), where (sigma_{{gamma_{j} }} sim Uniformleft( {0, 100} right)). The estimate of β did not borrow information among herds because this parameter can vary widely among herds18. The prior for β for each herd (j) followed the normal distribution (beta_{j} sim Normalleft( {0, 0.001} right)). To model temporal variation in β for each herd, we modified how we modeled β by using a normal distribution ({beta_{{delta }_{t,j}}} sim Normalleft( {mu_{{beta_{{delta }_{j} }}}} , {sigma_{{beta_{{delta }_{j}} }} } right)), where ({mu_{{beta_{{delta }_{j}} }}} sim Normalleft( {0, 0.001} right)) and ({sigma_{{beta_{{delta }_{j}} }}} sim Uniformleft( {0, 100} right)). Thus, there were four possible Ricker growth models for each herd; (1) no temporal variation in r and β,

$$ r_{t} = r_{max} + beta N_{t} + varepsilon , $$
(3)

(2) temporal variation in r,

$$ r_{t} = r_{max} + beta N_{t,} + gamma_{t} + varepsilon , $$
(4)

(3) temporal variation in β,

$$ r_{t} = r_{max} + {beta_{{delta }_{t}}} N_{t} + varepsilon , $$
(5)

and
(4) temporal variation in both rmax and β

$$ r_{t} = r_{max} + {beta_{{delta }_{t}}} N_{t} + gamma_{t} + varepsilon . $$
(6)

The residual variance was modeled as (varepsilon sim Uniformleft( {0,100} right)). We fit the model with no temporal variation (Eq. (3)) in either parameter to all seven time series simultaneously. All parameters except for rmax were estimated independently for each herd. For each time series of population survey data, we determined whether models with more parameters provided a better fit. We did so by fitting each possible growth model (Eqs. (4)–(6)) to each time series one at a time, while modeling all other time series with no temporal variation in rmax or β (Eq. (3)). The model with the lowest mean deviance from RJAGS by more than 2 was selected for that herd47.
Environmental and demographic stochasticity
We estimated fluctuation in abundance which can be attributed to demographic and environmental stochasticity for herds with different K for each herd. The stochasticity model was outlined by Ferguson and Ponciano9;

$$ Varleft( {N_{t – 1} } right) = Var_{dem} left( {N_{t – 1} } right) + Var_{r} left( {N_{t – 1} } right) + Var_{{upbeta }} left( {N_{t – 1} } right), $$
(7)

where (Varleft( {N_{t – 1} } right)) was total population stochasticity, (Var_{dem} left( {N_{t – 1,} } right)) was population abundance fluctuation due to demographic stochasticity, (Var_{r} left( {N_{t – 1} } right)) was population abundance fluctuation due to changes in r (i.e., density-independent environmental stochasticity), and (Var_{beta } left( {N_{t – 1} } right)) was population abundance fluctuation due to changes in β. The model assumes density-dependent survival following the Ricker model. Demographic stochasticity was calculated as follows;

$$ Var_{dem} left( {N_{t – 1} } right) = alpha N_{t – 1} e^{{ – beta_{Delta } left( {N_{t – 1} } right)}} left( {1 – e^{{ – beta_{Delta } left( {N_{t – 1} } right)}} } right) + sigma_{dem}^{2} N_{t – 1} e^{{ – 2beta_{Delta } left( {N_{t – 1} } right)}} $$
(8)

where (sigma_{dem}^{2}) was assumed to be equal to α9. Environmental stochasticity that is expressed as changes in r, otherwise known as density-independent or additive stochasticity, was calculated as follows;

$$ Var_{r} left( {N_{t – 1} } right) = sigma_{{beta_{Delta } }}^{2} alpha^{2} N_{t – 1}^{2} e^{{ – 2beta_{Delta } left( {N_{t – 1} } right)}} , $$
(9)

and environmental stochasticity that is expressed as changes in β, otherwise known as density-dependent or multiplicative stochasticity, was calculated as follows;

$$ Var_{{upbeta }} left( {N_{t – 1} } right) = sigma_{{beta_{Delta } }}^{2} alpha^{2} N_{t – 1}^{2} left( {N_{t – 1} } right)^{2} e^{{ – 2beta_{Delta } left( {N_{t – 1} } right)}} . $$
(10)

Population growth parameters from the selected Ricker growth model for each herd were used in these equations to estimate each of these sources of stochasticity for each herd across abundances ranging from five to above K. The relative total population stochasticity was expressed as the total population stochasticity at K for each herd divided by that herd’s K. More

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