Ecology

Study sites and experimental design
The study sites are part of the NutNet experiment (Supplementary Data 1; http://nutnet.org/)27. Plots at each site are 5 × 5 m separated by at least 1 m. All sites included in the analyses presented here included unmanipulated plots and fertilized plots with nitrogen (N), phosphorus (P), and potassium and micronutrients (K) added in combination (NPK+). N, P, and K were applied annually before the beginning of the growing season at rates of 10 gm−2 y−1. N was supplied as time-release urea ((NH2)2CO) or ammonium nitrate (NH4NO3). P was supplied as triple super phosphate (Ca(H2PO4)2), and K as potassium sulfate (K2SO4). In addition, a micronutrient mix (Fe, S, Mg, Mn, Cu, Zn, B, and Mo) was applied at 100 gm−2 y−1 to the K-addition plots, once at the start of the experiment, but not in subsequent years to avoid toxicity. Treatments were randomly assigned to the 25 m2 plots and were replicated in three blocks at most sites (some sites had fewer/more blocks or were fully randomized). Sampling was done in 1 m2 subplots and followed a standardized protocol at all sites27.
Site selection
Data were retrieved on 1 May 2020. To keep a constant number of communities per site and treatment, we used three blocks per site, excluding additional blocks from sites that had more than three (Supplementary Data 1). Sites spanned a broad envelope of seasonal variation in precipitation and temperature (Supplementary Fig. 1), and represent a wide range of grassland types, including alpine, desert and semiarid grasslands, prairies, old fields, pastures, savanna, tundra, and shrub-steppe (Supplementary Data 1).
Stability and asynchrony measurements are sensitive to taxonomic inconsistencies. We adjusted the taxonomy to ensure consistent naming over time within sites. This was usually done by aggregating taxa at the genus level when individuals were not identified to species in all years. Taxa are however referred to as “species”.
We selected sites that had a minimum of 4 years, and up to 9 years of posttreatment data. Treatment application started at most sites in 2008, but some sites started later resulting in a lower number of sites with increasing duration of the study, from 42 sites with 4 years of posttreatment duration to 15 sites with 9 years of duration (Supplementary Data 1). Longer time series currently exist, but for a limited number of sites within our selection criteria.
Primary productivity and cover
We used aboveground live biomass as a measure of primary productivity, which is an effective estimator of aboveground net primary production in herbaceous vegetation36. Primary productivity was estimated annually by clipping at ground level all aboveground live biomass from two 0.1 m2 (10 × 100 cm) quadrats per subplot. For shrubs and subshrubs, leaves and current year’s woody growth were collected. Biomass was dried to constant mass at 60 °C and weighed to the nearest 0.01 g. Areal percent cover of each species was measured concurrently with primary productivity in one 1 × 1 m subplot, in which no destructive sampling occurred. Cover was visually estimated annually to the nearest percent independently for each species, so that total summed cover can exceed 100% for multilayer canopies. Cover and primary productivity were estimated twice during the year at some sites with strongly seasonal communities. This allowed to assemble a complete list of species and to follow management procedures typical of those sites. For those sites, the maximum cover of each species and total biomass were used in the analyses.
Diversity, asynchrony, and stability across spatial scales
We quantified local scale and larger-scale diversity indices across the three replicated 1-m2 subplots for each site, treatment and duration period using cover data37,38. In our analysis, we treated each subplot as a “community” and the collective subplots as the “larger scale” sensu Whittaker28. Local scale diversity indices (species richness, species evenness, Shannon, and Simpson) were measured for each community, and averaged across the three communities for each treatment at each site resulting in one single value per treatment and site. Species richness is the average number of plant species. Shannon is the average of Shannon–Weaver indices39. Species evenness is the average of the ratio of the Shannon–Weaver index and the natural logarithm of average species richness (i.e., Pielou’s evenness40). Simpson is the average of inverse Simpson indices41. Due to strong correlation between species richness and other common local diversity indices (Shannon: r = 0.90 (95% confidence intervals (CIs) = 0.87–0.92), Simpson: r = 0.88 (0.86–0.91), Pielou’s evenness: r = 0.62 (0.55–0.68), with d.f. = 324 for each), we used species richness as a single, general proxy for those variables in our models. Results using these diversity indices did not differ quantitatively from those presented in the main text using species richness (Supplementary Fig. 5), suggesting that fertilization modulate diversity effects largely through species richness. Following theoretical models15,16, we quantified abundance-based gamma diversity as the inverse Simpson index over the three subplots for each treatment at each site and abundance-based beta diversity, as the multiplicative partitioning of abundance-based gamma diversity: abundance-based beta equals the abundance-based gamma over Simpson28,42, resulting in one single beta diversity value per treatment and site. We used abundance-based beta diversity index because it is directly linked to ecosystem stability in theoretical models15,16, and thus directly comparable to theories. We used the R functions “diversity”, “specnumber”, and “vegdist” from the vegan package43 to calculate Shannon–Weaver, Simpson, and species richness indices within and across replicated plots.
Stability at multiple scales was determined both without detrending and after detrending data. For each species within communities, we detrended by using species-level linear models of percent cover over years. We used the residuals from each regression as detrended standard deviations to calculate detrended stability17. Results using detrended stability did not differ quantitatively from those presented in the main text without detrending. Stability was defined by the temporal invariability of biomass (for alpha and gamma stability) or cover (for species stability and species asynchrony), calculated as the ratio of temporal mean to standard deviation14,17. Gamma stability represents the temporal invariability of the total biomass of three plots with the same treatment, alpha stability represents the temporal invariability of community biomass averaged across three plots per treatment and per site, and species stability represents the temporal invariability of species cover averaged across all species and the three plots per treatment14. The mathematical formula are:

$${mathrm{Species}},{mathrm{stability}} = frac{{sum _{i,k}m_{i,k}}}{{sum _{i,k}sqrt {w_{ii,kk}} }},$$
(1)

$${mathrm{Alpha}},{mathrm{stability}} = frac{{sum _kmu _k}}{{sum _ksqrt {v_{kk}} }},$$
(2)

$${mathrm{Gamma}},{mathrm{stability}} = frac{{sum _kmu _k}}{{sqrt {sum _{k,l}nu _{kl}} }},$$
(3)

where mi,k and wii,kk denote the temporal mean and variance of the cover of species i in subplot k; μk and vkk denote the temporal mean and variance of community biomass in subplot k, and vkl denotes the covariance in community biomass between subplot k and l. We then define species asynchrony as the variance-weighted correlation across species, and spatial asynchrony as the variance-weighted correlation across plots:

$${mathrm{Species}},{mathrm{asynchrony}} = frac{{sum _{i,k}sqrt {w_{ii,kk}} }}{{sum _ksqrt {sum _{ij,kl}w_{ij,kl}} }},$$
(4)

$${mathrm{Spatial}},{mathrm{asynchrony}} = frac{{sum _ksqrt {v_{kk}} }}{{sqrt {sum _{k,l}nu _{kl}} }},$$
(5)

where wij,kl denotes the covariance in species cover between species i in subplot k and species j in subplot l.
These two asynchrony indices quantify the incoherence in the temporal dynamics of species cover and community biomass, respectively, which serve as scaling factors to link stability metrics across scales14 (Fig. 1). To improve normality, stability, and asynchrony measures were logarithm transformed before analyses. We used the R function “var.partition” to calculate asynchrony and stability across spatial scales14.
Climate data
Precipitation and temperature seasonality were estimated for each site, using the long-term coefficient of variation of precipitation (MAP_VAR) and temperature (MAT_VAR), respectively, derived from the WorldClim Global Climate database (version 1.4; http://www.worldclim.org/)44.
Analyses
All analyses were conducted in R 4.0.2 (ref. 45) with N = 42 for each analysis unless specified. First, we used analysis of variance to determine the effect of fertilization, and period of experimental duration on biodiversity and stability at the two scales investigated. Models including an autocorrelation structure with a first-order autoregressive model (AR(1)), where observations are expected to be correlated from 1 year to the next, gave substantial improvement in model fit when compared with models lacking autocorrelation structure. Second, we used bivariate analyses and linear models to test the effect of fertilization and period of experimental duration on biodiversity–stability relationships at the two scales investigated. Again, models including an autocorrelation structure gave substantial improvement in model fit (Supplementary Table 1)46,47,48. We ran similar models based on nutrient-induced changes in diversity, stability, and asynchrony. For each site, relative changes in biodiversity, stability, and asynchrony at the two scales considered were calculated, as the natural logarithm of the ratio between the variable in the fertilized and unmanipulated plots (Supplementary Fig. 9). Because plant diversity, asynchronous dynamics, and temporal stability may be jointly controlled by interannual climate variability22, we ran similar analyses on the residuals of models that included the coefficient of variation among years for each of temperature and precipitation. Results of our analyses controlling for interannual climate variability did not differ qualitatively from the results presented in the text (Supplementary Fig. 4). In addition, to test for temporal trends in stability and diversity responses to fertilization, we used data on overlapping intervals of four consecutive years. Results of our analyses using temporal trends did not differ qualitatively from the results presented in the text (Supplementary Fig. 6). Inference was based on 95% CIs.
Second, we used SEM29 with linear models, to evaluate multiple hypothesis related to key predictions from theories (Table 1). The path model shown in Fig. 1e was evaluated for each treatment (control and fertilized), and we ran separate SEMs for each period of experimental duration (from 4 to 9 years of duration). We generated a summary SEM by performing a meta-analysis of the standardized coefficients across all durations for each treatment. We then tested whether the path coefficients for each model differed by treatment by testing for a model-wide interaction with the “treatment” factor. A positive interaction for a given path implied that effects of one variable on the other are significantly different between fertilized and unfertilized treatments. We used the R functions “psem” to fit separate piecewise SEMs49 for each duration and combined the path coefficients from those models, using the “metagen” function50.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article. More

Credit: Tad Theimer

Joseph (Joe) Connell altered both what and how ecologists study. Tree by tree, coral by coral, barnacle by barnacle, he saw patterns and processes across diverse ecosystems. Simply and with incontrovertible evidence, he demonstrated that interactions such as competition and predation could determine where species lived.
Before his classic experiments on Scotland’s rocky shores, field ecology was mainly descriptive, focusing on physical conditions such as temperature or moisture in determining where species lived. Connell, who died last month aged 96, inspired thousands of ecologists to test their hypotheses by manipulating conditions in the field.
Connell established long-term studies of coral reefs at Heron Island in the Great Barrier Reef and of tropical rainforests in Queensland, Australia, that spanned more than three and five decades, respectively. Monitoring revealed the dynamic nature of plant and animal communities that had long been considered stable. He discovered that natural variability in biological interactions and physical factors maintains diversity in these and other endangered ecosystems.
Born in 1923, Connell grew up just outside Pittsburgh, Pennsylvania. When the United States entered the Second World War in 1941, he enlisted in the Army Air Corps and was trained in meteorology. Later, conducting weather surveillance in the Azores — the Portuguese Atlantic archipelago — in support of army operations in Europe, he spent his free time birdwatching and identifying trees. Meeting army recruits who worked as wildlife managers, he realized it was possible to have a career as a biologist. After the war, and a degree in meteorology at the University of Chicago, Illinois, he headed to the University of California, Berkeley, for a master’s in zoology.
Connell produced what he described as a dull, unsatisfying thesis on brush rabbits (Sylvilagus bachmani) in the Berkeley Hills. Discouraged by the difficulties of conducting a population study (he trapped only 40 rabbits in 2 years), he adopted a rule of thumb — never again to study anything bigger than his thumb. As a doctoral student at the University of Glasgow, UK, he gleefully discovered what Charles Darwin had found a century before: that thousands of barnacles could easily be studied on the seashore, no traps required.
Connell realized that he could test his hypotheses about what factors determined where on the shore certain species lived by removing, adding or transplanting barnacles and their snail predators. Classic papers ensued, inspiring other ecologists to rethink distribution patterns, and, importantly, to test their ideas with controlled field experiments.
After a postdoc at the Woods Hole Oceanographic Institution in Massachusetts, Connell joined the faculty at the University of California, Santa Barbara, where he remained for the rest of his career. He was curious about processes that affected distribution and abundance, and those that might keep biodiversity high. Shifting to species that live for hundreds or thousands of years on coral reefs and in rainforests, he set up his Australian long-term monitoring studies in 1962 and 1963. Both recorded the demography and interactions of organisms in permanent plots, tracking community dynamics and the impact of disturbances, ranging from fallen trees to cyclones.
Visiting Connell’s sites with him in the 1970s and 1990s, we were impressed with his foresight and inspired by his insights. On the reef, he explained, physical disturbance by large waves associated with recurring cyclones intermittently reduced the cover of dominant species such as staghorn coral (Acropora aspera). This prompted recolonization by a diverse assemblage of weaker competitors such as encrusting or mound-like species. Connell coined the term ‘intermediate disturbance hypothesis’ to describe this process.
We strolled through the larger of his rainforest plots, avoiding stinging trees, biting flies, ticks and leeches, and relishing the richness — more than 300 tree species and about 100,000 individual plants. Connell outlined another hypothesis, that forests are more diverse when rarer species such as the conifer Sundacarpus amarus are favoured over more common ones such as the flowering tree Planchonella sp. Patterns of seedling establishment, growth or survival depend on that difference in frequency. Because common species grow more densely than rare ones, they are more vulnerable to specialist herbivores or pathogens.
This pattern of density-dependent predation or infection thins out common species, enabling a richer mix to coexist. It is a central component of the Janzen–Connell hypothesis (independently proposed by US ecologist Daniel Janzen in 1970), which predicts that seedlings are more likely to die under the canopies of their parent trees than farther away, ensuring diversity.
Connell was unfailingly kind, generous and devoted to his family. He never lost his profound curiosity about the natural world or his delight in exploring ideas with students and colleagues. He loved to be challenged and, if proven wrong, he gladly moved on to a new hypothesis or question. He sought truth, not fame. Moreover, he empowered everyone around him to think critically by focusing on ideas and evidence, not personalities. Fortunately for the world, his way of exploring science proved powerful, infectious, fun and enduringly productive. More

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Sediment reduction analysis method
This section presents the methods used to calculate sediment reduction caused by the major contributors, i.e., reservoir works, water diversion works, soil and water conservation works, and rainfall.
Sediment reduction by reservoir works
Reservoir works reduce sediment by impounding and retaining the sediment. Recent variations in sediment reduction due to reservoir works were analysed according to the variations in the average annual sediment deposition in the reservoirs of the basin during different periods.
The average annual sediment reduction by various reservoirs can be calculated by dividing the accumulated sediment in each reservoir during a certain period by the number of years:

$$ WS_{r} = sumlimits_{1}^{n} {D_{i} /N} , $$
(1)

where (D_{i}) is the accumulated sediment (100,000,000 t) in a reservoir during a certain period, N is the number of years in the period, and WSr is the average annual sediment reduction (100,000,000 t) in the period by all reservoirs in the basin.
The Hydrological Bureau under the Yellow River Water Conservancy Commission annually measures and calculates the deposition of sediment in all reservoirs in the Yellow River Basin. Two methods can be used, namely, the topographic method and the section method. In the topographic method, the area enclosed by contour lines on the topographic map of the reservoir area is measured to calculate the reservoir volume. The cumulative deposition of sediment during a specific period is the difference between the current and the previous reservoir volume. The topographic method requires closed contour lines on the map. In reality, however, the contour lines cannot be closed due to the presence of farmland, houses, and other artificial structures in the reservoir area, resulting in measurement errors. Therefore, the section method is mainly used at present. Here, M test sections were deployed in the reservoir area, and the test section data were used to calculate the total storage capacity of the reservoir in sections by period, as follows:

$$ V_{i} = sumlimits_{m = 1}^{M – 1} {V_{i,m} } . $$
(2)

The difference in the storage capacity measured twice is the cumulative deposition of sediment in reservoir (D_{i}):

$$ D_{i} = V_{i – 1} – V_{i} , $$
(3)

where Vi is the storage capacity measured at the end of period i and Vi,m is the storage capacity measured in section m – 1.
Sediment reduction by water diversion works
During water diversion, a certain amount of sediment is diverted, along with water, and is deposited in irrigation areas, resulting in a decrease in the volume of the sediment in the river channel. The average annual sediment reduction by water diversion works can be calculated by multiplying the average annual water diversion in different periods in the Jinghe River Basin by the average annual sediment concentration in the water diversion period, as follows:

$$ WS_{d} = sumlimits_{1}^{n} {W_{di} /N times overline{S}} /{1}000, $$
(4)

where (W_{di}) is the cumulative water diversion (100,000,000 m3) in the basin in the water diversion period, N is the number of years in the period, (overline{S}) is the average annual sediment concentration in the period (kg/m3), and (WS_{d}) is the average annual sediment reduction (100,000,000 t) in the basin during the period. Recent variations in sediment discharge caused by water diversion works were analysed according to the variations in the average annual water diversion in the basin in different periods.
Sediment reduction by soil and water conservation works
A commonly used method to compute the sediment reduction by soil and water conservation works is to multiply the area subject to the soil and water conservation works, such as terracing, forestation, grassing, creating enclosures, and constructing silt-arrester dams, by the sediment reduction by each measure per unit area, followed by their summation, as follows:

$$ WS_{SC} = sumlimits_{1}^{n} {F_{i} times S_{j} /10^{8} ,} $$
(5)

where Sj is the sediment reduction due to each soil and water conservation measure (t/hm2), published by the soil and water conservation monitoring institutions in each basin based on the analysis of the long-term observation data, Fi is the area subjected to each measure (hm2), and WSSC is the comprehensive sediment concentration for each measure (100,000,000 t). The variations in sediment reduction by soil and water conservation works were analysed based on the variations in the soil and water conservation areas in the basin during different periods.
Analysis of rainfall-induced sediment yield
The deduction method was adopted to analyse the rainfall-induced variations in the sediment yield. Recent variations in sediment reduction attributable to reservoirs, water diversion, and soil and water conservation works were computed and deducted from the measured sediment reduction in recent years (2000–2015):

$$ Delta WS_{p} = Delta WS_{t} – Delta WS_{r} – Delta WS_{d} – Delta WS_{sc} , $$
(6)

where (Delta WS_{t}) is the recently measured sediment reduction (100,000,000 t), (Delta WS_{r}) is the recent variation in the sediment reduction (100,000,000 t) caused by variations in the sediment retention due to reservoir works, (Delta WS_{d}) is the recent variation in sediment reduction (100,000,000 t) caused by variations in water diversion, (Delta {text{WS}}_{{{text{SC}}}}) is the recent variation in sediment reduction (100,000,000 t) caused by variations in the soil and water conservation area, and (Delta WS_{p}) is the recent variation in the rainfall-induced sediment yield caused by variations in rainfall.
Sediment yield calculation method
Figure 6 depicts the computational process for the sediment calculation. First, a reduction calculation of the natural runoff was performed as follows:

$$ W_{0} = W_{m} + W_{cum} + W_{s} + W_{e} + W_{SC} , $$
(7)

where W0 is the natural runoff, Wm is the measured runoff, Wcuw is the industrial water consumption in the basin, Ws is the water retention by reservoirs, We is the water evaporation and seepage losses, Wsc is the water reduction by soil and water conservation, and W0 is the natural water volume in the basin. All these terms are in 100,000,000 m3.
Second, the runoff-sediment relationship in the natural state was established based on the measured runoff and sediment data in periods with negligible human activity, as well as when the underlying surface was in a nearly natural state. Natural sediment discharge was calculated using the relationship between runoff and sediment discharge. According to the observation data from the basin for the past 35 years, runoff was closely related to sediment discharge. Given China’s climatic conditions and economic growth, the basin was nearly in a natural state up to 1960 because human activity had a minor impact on runoff and sediment discharge. Based on the runoff and sediment discharge measurements at Zhangjiashan Station from 1932 to 1960, the relationship between the natural runoff and sediment discharge was established as WS0 = f(W0). Natural sediment discharge in the basin was calculated considering the restored natural runoff.
Third, the natural sediment discharge was calculated using the natural runoff results and the runoff-sediment relationship. Based on the major contributors to sediment reduction in the basin, the future sustainable sediment reduction was calculated as the sum of sediment reduction due to reservoirs, water diversion, and soil and water conservation measures. Sediment reduction caused by variations in rainfall was limited to certain periods. For example, recent reduced heavy rainfall has led to a decreased rainfall-induced sediment yield and consequently a decreased sediment discharge. However, according to forecasts by the Intergovernmental Panel on Climate Change (2014)50, extreme weather and heavy rainfall events are likely to increase in the future. The reduction in sediment due to variations in rainfall was calculated as follows:

$$ WS_{d} = WS_{r} + WS_{d} + W_{SC} , $$
(8)

where WSr is the future sediment reduction caused by reservoir works, i.e., the sum of the sediment retention potential of the remaining capacity of the existing reservoirs and that of planned future reservoirs; WSd is the sediment reduction caused by future water diversion works, which can be obtained by multiplying the water diversion in the basin forecasted according to the social and economic development by the average sediment concentration in the water diversion period; WSsc is the future sediment reduction caused by soil and water conservation, obtained from areas subject to existing and planned soil and water conservation works and the corresponding sediment reduction rates; and WSd is the forecasted value of sediment reduction in the basin. All these terms are in 100,000,000 t.
Fourth, the sustainable sediment reduction in the basin was calculated considering variations in the contributions to sediment reduction in a future period and their effect. Future sediment discharge in the basin is the difference between the natural and future sediment reduction, as follows:

$$ WS_{f} = WS_{0} – WS_{d} , $$
(9)

where WS0 is the natural sediment discharge in the basin, WSd is the forecasted sediment reduction in the basin, and WSf is the forecasted sediment discharge in the basin. All these terms are in 100,000,000 t.
Finally, future river sediment discharge was obtained by subtracting the future sustainable sediment reduction from the natural sediment discharge.
Data acquisition
Hydrological data
A total of 28 hydrometric stations and 190 rainfall stations are located along the main stream and tributaries of the Jinghe River to effectively monitor rainfall, runoff, and sediment in the basin.
Zhangjiashan Station, located at the outlet of the Jinghe River Basin, has a catchment area of 432,160,000 km2, covering 95% of the total area of the basin. Few hydrometric and rainfall stations were operational in this basin before 1956, and hence incomplete data were collected. Analyses in this study were based on data from the Zhangjiashan Station from 1956–2015. At this station, the cross-sections in the main stream and Jinghui Canal (a water diversion canal) were hydrologically measured to determine the discharge, sediment transport rate, and sediment concentration.
Engineering data
Data on sediment reduction due to reservoir works and terraces, forests, grasslands, enclosures, and dams in the basin were based on the results of the National Water Resources Census and official data collated by the Upper and Middle Yellow River Bureau of the Yellow River Conservancy Commission. These data are thus accurate and reliable.
For data collection and erosion–deposition calculations, DL/T 5089–1999 “Specification for Sediment Design of Hydropower and Water Conservancy Projects” provided that “The calculated results of erosion and deposition should be compared with the measured data for several years of operation. If the amount and location of sedimentation are 70% consistent, and the elevation of sedimentation in the reservoir differs by 1 to 2 m, then the calculated results are deemed reliable. For erosion–deposition calculation results, only reliability is considered”.
Relevant data from the stations were systematically verified and collated by the Hydrological Bureau of the Yellow River Conservancy Commission and are therefore accurate and reliable. More

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