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Study siteThe field experiment was conducted at Namco Station (30°47’N, 90°58’E, altitude 4730 m) of the Institute of Tibetan Plateau Research, Chinese Academy of Sciences (ITPCAS), which is located in the alpine steppes of TP in China. The experiment was permitted by ITPCAS, complied with local and national guidelines and regulations. From 2006 to 2017, the mean annual temperature (MAT) and mean annual precipitation (MAP) was about − 0.6 °C and 406 mm, respectively. Monthly mean temperature varied from − 10.8 °C in January to 9.1 °C in July and most of the precipitation occurred from May to October37,38. During our six-year observations (2010, 2011, 2012, 2013, 2015 and 2017), climate change during the growing season from May to September varied differently, with the annual precipitation ranged from 255.9 mm to 493.8 mm and the MAT from 6.7 to 7.4 °C. Androsace tapete, Kobresia pygmaea, Stipa purpurea and Leontopodium pusillum were the dominant plant species at the alpine steppe.Experimental design and treatmentsThe long-term experiment began in May, 2010. Three homogenous plots were randomly arranged as replicates at the alpine steppe and six subplots (~ 13 m2) were distributed in each plot by a cycle, with a 2 m buffer zone between each adjacent subplot (Appendix S1: Fig. S1). In this experiment, six treatments of N fertilization rate (0, 1, 2, 4, 8, and 16 g N m−2 yr−1) were clockwise applied in each subplot. The subplots of 0 g N m−2 yr−1 were control group. We sprayed NH4NO3 solution on the first day of each month in the growing season (from May to September) each year. After fertilizing, we rinsed plant residual fertilizer with a little deionized water (no more than 2 mm rainfall). For the control groups, we added equivalent amount of water. The experiment was conducted from 2010 to 2017 (it should be pointed out that there was no fertilization in 2014 and 2016).Sampling and measurementsThe samples were collected with the training and permission of ITPCAS and involved plants that are common species and not endangered or protected. The identification of the plants was done by referring to a book of Chen and Yang39. Pictures of the corresponding specimens can be seen on the website of ITPCAS (http://itpcas.cas.cn/kxcb/kxtp/nmc_normal_plant/).Vegetation samples were collected in August in 2011 and repeated at the same time in 2012, 2013, 2015 and 2017. We established one 50 × 50 cm quadrat in each subplot, clipped aboveground biomass (AGB) and sorted species by families. The biomass was used to measure ANPP (g m−2 yr−1). Following aboveground portion collected, we used three soil cores (5 cm diameter) to collect the belowground roots at 0–30 cm depth and mixed into one sample, which were used to assess belowground net primary productivity (BNPP, g m−2 yr−1). The roots were cleaned with running water to remove sand and stones.Both plant and root samples were dried at 75 °C for 48 h and then ground into powder (particle size ~ 5 μm) by a laboratory mixer mill (MM400, Retsch). To determine N and C content of plants, we weighed the samples into tin capsules and measured with the elemental analyzer (MAT253, Finnigan MAT GmbH, Germany).Estimation of the critical N rate (Ncr), N retention fraction (NRF), N retention capacity and N-induced C gainAccording to the N saturation hypothesis, plant productivity increases gradually during N addition, reaches a maximum at the Ncr, and eventually declines16,17. We considered the Ncr to be the rate where ANPP no longer remarkably changed with N addition (Fig. 1).We defined plant N retention fraction (NRF, %; Eq. 1) as the aboveground N storage caused by unit N addition rate, and N retention capacity (g N m−2 yr−1; Eq. 2) was the increment of N storage due to exogenous N addition compared to the control40. The equations are as following:$$N;retention;fraction = frac{{ANPP_{tr} times N;content_{tr} – ANPP_{ck} times N;content_{ck} }}{N;rate}$$
(1)
$$N;retention;capacity = ANPP_{tr} times N;content_{tr} – ANPP_{ck} times N;content_{ck}$$
(2)
where ANPPtr and N contenttr (%) refer to those in the treatment (tr) groups, and ANPPck and N contentck refer to those in the control (ck) groups. These expressions are also used in the following equations (Eqs. 3–5).The N-induced C gain (g C m−2 yr−1; Eq. 3) was estimated by the increment of C storage owing to exogenous N addition compared to the control40. Maximum N retention capacity (MNRC, Eq. 4) and maximum N-induced C gain (Eq. 5) mean the maximum N and C storage increment in plant caused by exogenous N input at Ncr, respectively. The formulas are as following:$$N{text{-}}induced;C;gain = ANPP_{tr} times C;content_{tr} – ANPP_{ck} times C;content_{ck}$$
(3)
$$MNRC = ANPP_{max } times N;content_{max } – ANPP_{ck} times N;content_{ck}$$
(4)
$$Maximum;N{text{-}}induced;C;gain = ANPP_{max } times C;content_{max } – ANPP_{ck} times C;content_{ck}$$
(5)
where ANPPmax, N contentmax and C contentmax refer to the value of ANPP, N content and C content at Ncr, respectively.Data synthesisTo evaluate N limitation and saturation on the TP more accurately, we searched papers from the Web of Science (https://www.webofscience.com) and the China National Knowledge Infrastructure (https://www.cnki.net). The keywords used by article searching were: (a) N addition, N deposition or N fertilization, (b) grassland, steppe or meadow. Article selection was based on the following conditions. First, the experimental site must be conducted in a grassland ecosystem. Second, the experiment had at least three N addition levels and a control group. Third, if the experiment lasted for many years, we analyzed data with multi-year average. Based on the above, we collected 89 independent experimental cases. Among these, 27 cases were located on the TP alpine grasslands, 25 in the Inner Mongolia (IM) grasslands and 37 in other terrestrial grasslands (detailed information sees Appendix S2: Table S1).We extracted ANPP data and N addition rate of these cases and estimated Ncr and ANPPmax (Appendix S2: Fig. S2). We then calculated NRF, N retention and C gain of each group of data for further analysis (Appendix S2: Table S2). Most of the 89 cases did not have data on N and C content. To facilitate the calculation, we summarized N and C content from 40 articles in the neighboring areas of the cases and divided the N and C content into seven intervals according to the N addition rate (Appendix S2: Table S3 and Fig. S3). The unit of N addition rate was unified to “g N m−2 yr−1”. All the original data were obtained directly from texts and tables of published papers. If the data were displayed only in graphs, Getdata 2.20 was used to digitize the numerical data. For the estimation of N retention and C gain of the TP at current N deposition rates and future at Ncr, we fitted the exponential relationship to the data from 27 cases on the TP, and then substituted N rates into the fitted equations (Eq. 6):$$y = a times left[ {1 – exp left( { – bx} right)} right].$$
(6)
We also included MAT, MAP, soil C:N ratio, fencing management (fencing or grazing) and grassland type (meadow, steppe and desert steppe) of the experiment sites for exploring the drivers affecting N limitation (Appendix S2: Table S1). When climatic data were missing from the article, MAT and MAP were obtained from the WorldClim (http://www.worldclim.org).Species were usually divided into four functional groups (grasses, sedges, legumes and forbs) to study the response of species composition to N addition in previous study41. We synthesized 13 TP experimental cases (including our field experiment) from the data synthesis and each case included at least three functional groups (detailed references see Appendix S2).Statistical analysisThere were 42 species in our field experiment. We divided them by family into eleven groups: Asteraceae (forbs), Poaceae (grasses), Leguminosae (legumes), Rosaceae (forbs), Boraginaceae (forbs), Caryophyllaceae (forbs), Cyperaceae (sedges), Labiatae (forbs), Primulaceae (forbs), Scrophulariaceae (forbs) and Others. Due to species in the group of Others contributed only 1.22% of AGB, we analyzed AGB and foliar stoichiometry among other ten families (Appendix S1: Table S1). In Namco steppe, forbs, grasses, sedges and legumes accounted for 78.0%, 7.4%, 8.2% and 5.2% of the AGB respectively (Appendix S1: Table S1 and Fig. S2). Such a large number of forbs suggested that our experiment was conducted on a severely degraded grassland.For our field data, two-way ANOVAs were used to analyze the effects of year, N fertilization rate and their interactions on species AGB. One-way ANOVAs were used to test the response of ANPP, BNPP, root:shoot ratio, species foliar C content, N content and C:N ratio to N addition rate. Duncan’s new multiple range test was used to compare the fertilization influences at each rate in these ANOVAs. Prior to the above ANOVAs, we performed homogeneity of variance test and transformed the data logarithmically when necessary. Simple regression was used to estimate the relevance among ANPP, NRF, N retention capacity and C gain with N addition rates.Structural equation modeling (SEM) was used to explore complex relationships among multiple variables. To quantify the contribution of drivers such as climate and soil to Ncr, ANPP, NRF and MNRC, we constructed SEM based on existing ecological knowledge and the possible relationships between variables. We considered environmental factors (MAT, MAP and soil C:N) and ANPPck as explanatory variables, and Ncr, NRF and MNRC as response variables. We included the ANPPck in the SEM rather than the ANPPmax because we wonder whether there was a relationship between ANPP in the absence of exogenous N input and the ecosystem N retention in the presence of N saturation. This has important implications for assessing N input. Before constructing the SEM, we excluded collinearity between the factors. In addition, Student’s t-test and one-way ANOVAs were performed to explain the effect of fencing management and grassland type on above response variables, respectively. The SEM was constructed using the R package “piecewiseSEM”42. Fisher’s C was used to assess the goodness-of-model fit, and AIC was for model comparison.Given the influence of extreme values in the data synthesis, we calculated the geometric mean of Ncr, NRF, N retention and N-induced C gain. All statistical analyses were performed with SPSS 26.0 and RStudio (Version 1.2.1335) based on R version 3.6.2 (R Core Team, 2019). More

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