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Study areaWith an area of about 2.33 × 105 km2, the Western Sichuan Plateau (27.11°–34.31°N and 97.36°–104.62°E) is located in the transition zone between the Qinghai-Tibet Plateau and the Sichuan Basin, including all of Garze Prefecture and Aba Prefecture, and parts of Liangshan Yi Autonomous Prefecture28 (Fig. 1). With an altitude of 780–7556 m, this area is dominated by mountain and ravine areas and high mountain and plateau areas, and the terrain is high in the west and low in the east. The climate belongs to the subtropical plateau monsoon climate, with large temperature difference between day and night and abundant sunshine. The annual average temperature is about 9.01–10.5 °C, and the precipitation is about 556.8–730 mm28. The study area is rich in water resources, including the Yalong River, Minjiang River and other important river systems in the upper reaches of the Yangtze River, and the Baihe River, Heihe river and other river systems of the Yellow River. The main types of soil are plateau meadow soil dark brown soil, brown soil, cold frozen soil and cinnamon soil, and the main vegetation types are alpine meadow and scrub. With rich and diverse soil vegetation types and distinctive vertical zonal distribution characteristics, it is one of the global biodiversity conservation hotspots29.Figure 1Location of the study area. The map is created in the support of ArcGIS 10.2 (ESRI). The China map and Western Sichuan Plateau boundary data were collected from Resources and Environmental Science and Data Center (http://www.resdc.cn/). The Qinghai-Tibetan Plateau boundary data were collected from the Global Change Research Data Publishing & Repository (http://www.geodoi.ac.cn/WebCn/Default.aspx).Full size imageData source and processingMultisource archival data were used in this study (Table 1). The land use remote sensing monitoring data, administrative boundary data and geological disaster vector data were obtained from Resources and Environmental Science and Data Center. The spatial resolution of land use remote sensing monitoring data is 30 × 30 m, including 6 first-level classification and 26s-level classification. The first-level classification includes cropland, woodland, grassland, water body, built-up land, and unused land. The accuracy of remote sensing classification is not less than 95% for cropland and built-up land, not less than 90% for grassland, woodland, and water body, and not less than 85% for unused land, which meets the need of the research. Landsat remote sensing monitoring data is used as the main information resources, among which Landsat-TM/ETM remote sensing monitoring data is used in 2000, 2005, 2010 and Landsat 8 remote sensing monitoring data is used in 2015 and 2020. In light of actual conditions and the implementation of policies and philosophies including the natural forest protection project, return of farmland to forest, land remediation, ecological civilization, the period from 2000 to 2020 is selected as the study period, and the land use data of each period is cropped using ArcGIS 10.2 to reclassify the 26 secondary classifications into cropland, woodland, grassland, water body, built-up land and unused land.Table 1 Characteristics of data used for the study.Full size tableThe DEM data were obtained from SRTM (Shuttle Radar Topography Mission) of Resources and Environmental Science and Data Center, the spatial resolution of 30 × 30 m, absolute horizontal accuracy ± 20 m, absolute elevation accuracy ± 16 m, elevation and slope are extracted from the downloaded DEM. The Qinghai-Tibetan Plateau boundary data were collected from the Global Change Research Data Publishing & Repository. Data of carbon density of different land types were obtained from Chinese Ecosystem Research Network Data Center (http://www.nesdc.org.cn/).A total of 29,284 evaluation units were collected for spatial grid processing of the Western Sichuan Plateau according to 3 km × 3 km by ArcGIS 10.2. The impact factors obtained in this study include grid data per kilometer of GDP spatial distribution, grid data per kilometer of population spatial distribution, annual mean temperature spatial interpolation data, annual mean rainfall spatial interpolation data, long-term normalized difference vegetation index (NDVI) comes from Resources and Environmental Science and Data Center with a resolution of 1 km × 1 km. The Human Active Index (HAI), with a resolution of 30 m × 30 m, can be calculated by formula30,31, and the factors are discretized into the data type required for the geodetector by the natural breakpoint method.MethodsThe InVEST modelThe InVEST model was developed by Stanford University, the University of Minnesota, the Nature Conservancy and the World Wide Fund for Nature (WWF). The model’s terrestrial ecosystem services assessment includes four modules: soil conservation, water retention, carbon storage and biodiversity assessment, and provides an overall measurement of regional ecosystem services32. The carbon storage model of the InVEST model divides the carbon storage of the ecosystem into 4 basic carbon pools, namely above-ground carbon, underground carbon, soil carbon, dead organic matter carbon7.The calculation formula of total carbon storage in the Western Sichuan Plateau is as follows7:$$C_{total} = C_{above} + C_{below} + C_{soil} + C_{dead}$$
(1)
In formula (1), Ctotal is the total carbon storage; Cabove is the above-ground carbon storage; Cbelow is the underground carbon storage; Csoil is the soil carbon storage, and Cdead is the dead organic matter carbon storage.Based on the carbon density and land use data of different land use type, the carbon storage of each land use type in the Western Sichuan Plateau is calculated by the formula7:$$C_{{text{total}}i} = (C_{{text{above}}i} + C_{{text{below}}i} + C_{{text{soil}}i} + C_{{text{dead}}i}) times A_{i}$$
(2)
In formula (2), i is the average carbon density of each land use, and Ai is the area of this land used.The carbon density data of different land use types in this study were obtained from the shared date of the National Ecological Science Data Center and some documents33,34,35,36,37. Since the carbon density data were collected from the results of studies in different parts of China, the selected documents should be close to or similar to the study area as far as possible to avoid excessive data gap. At the same time, the carbon density varies with climate, soil properties and land use38, so the carbon density should be modified according to the climate characteristics and land use types of the Western Sichuan Plateau. Existing research results show that the carbon density is positively correlated with annual precipitation and weakly correlated with annual average temperature. The quantitative expression of the relationship between carbon density and temperature and precipitation is as follows39,40,41,42:$$C_{SP} = 3.3968 times P + 3996.1;;left( {{text{R}}^{{2}} = 0.{11}} right)$$
(3)
$$C_{BP} = 6.7981e^{0.00541p};;;left( {{text{R}}^{{2}} = 0.{7}0} right)$$
(4)
$$C_{BT} = 28 times {text{T}} + 398;;left( {{text{R}}^{{2}} = 0.{47,};{text{P}} < 0.0{1}} right)$$ (5) In these formula, CSP is the soil carbon density (kg m−2) based on the annual precipitation; CBP is the biomass carbon density (kg m−2) based on the annual precipitation; CBT is the biomass carbon density (kg m−2) based on annual average temperature; P is the average annual precipitation (mm), and T is the annual average temperature (°C). According to the data of China Meteorological Data Service Centre (http://data.cma.cn/), in the past 20 years, the average annual temperature of China and the Western Sichuan Plateau was 9.0 °C and 6.3 °C, and the average annual precipitation was 643.50 mm and 812.65 mm respectively.The modified formula of carbon density in the Western Sichuan Plateau is as follows7:$$K_{BP} = frac{C^{prime}{_{BP}}}{{C^{primeprime}{_{BP}}}}$$ (6) $$K_{BT} = frac{C^{prime}{_{BT}}}{{C^{primeprime}{_{BT}}}}$$ (7) $$C_{BT} = 28 times T + 398;;left( {{text{R}}^{{2}} = 0.{47,};{text{P}} < 0.0{1}} right)$$ (8) $$K_{S} = frac{C^{prime}{_{SP}}}{{C^{primeprime}{_{SP}}}}$$ (9) In these formula, KBP is the modified indices of precipitation factor in biomass carbon density; KBT is the modified indices of temperature factor; C'BP and C''BP are the biomass carbon density obtained from annual precipitation in the Western Sichuan Plateau and the whole country respectively. C'BT and C''BT are the biomass carbon density obtained from annual average temperature; C'SP and C''SP are the soil carbon density data obtained from annual average temperature; KB and KS are the biomass carbon density modified indices and soil carbon density modified indices respectively. The carbon density values of each land use type after modified in the Western Sichuan Plateau are shown in Table 2.Table 2 Carbon density values of different land use types in the Western Sichuan plateau (t hm−2).Full size tableExploratory spatial analysis methodGlobal spatial autocorrelationGlobal Moran’s I was used to describe the spatial differentiation characteristics of carbon storage in the study area, and the expression formula is as follows43:$$I = frac{{nsumnolimits_{i = 1}^{n} {sumnolimits_{j = 1}^{n} {w_{i,j} left( {x_{i} - overline{x} } right)left( {x_{j} - overline{x} } right)} } }}{{sumnolimits_{i = 1}^{n} {sumnolimits_{j = 1}^{n} {omega_{ij} } } sumnolimits_{i = 1}^{n} {left( {x_{i} - overline{x} } right)^{2} } }}$$ (10) wij is the spatial weight; x is the attribute mean; xi and xj are the attribute values of elements i, j, respectively; n is the number of cells, and the correlation is considered significant when |Z|  > 1.96.Local indications of spatial association (LISA)LISA reveals the local cluster characteristics of spatial unit attributes by analyzing the difference and significance between spatial units and surrounding units, and the expression formula is as follows42:$$I_{i} (d) = frac{{n(x_{i} – overline{x} )sumnolimits_{j = 1}^{n} {w_{ij} (x_{j} – overline{x} )} }}{{sumnolimits_{i = 1}^{n} {(x_{j} – overline{x} )^{2} } }}$$
(11)
Correlation analysisIn order to evaluate the influence of natural factors and socioeconomic factors on carbon storage in the study area, the correlation coefficients of temperature, rainfall, NDVI, GDP, population density (PD), HAI and carbon storage were calculated according to the Pearson correlation coefficient method. The calculation formula is as follows44:$$r_{xy} = frac{{sumnolimits_{i = 1}^{n} {(M_{i} – overline{x} )(y_{i} – overline{y} )} }}{{sqrt {sumnolimits_{i = 1}^{n} {(M_{i} – overline{x} )^{2} sumnolimits_{i = 1}^{n} {(y_{i} – overline{y} )} } } }}$$
(12)
rxy represents the correlation coefficient between x and y; Mi represents the carbon storage in the ith year; yi represents the value of the impact factor Y in the ith year, and ({overline{text{x}}}) and ({overline{text{y}}}) respectively represents the average value of carbon storage and impact factor in the research period over several years.Human influence index analysis methodLand use is significantly spatially clustered in the study area31, and LUCC changes will have a certain impact on the structure and process of the ecosystem. HAI has the characteristics of spatial variability, which can reflect the impact of human activities on land use and landscape composition changes. In this study, Human Influence Index Analysis Method (HAI) index was used to analyze the correlation between carbon storage and human interference intensity in the Western Sichuan Plateau. The calculation formula is as follows30,$$HAI = sumlimits_{i = 1}^{n} {left( {A_{i} P_{i} /TA} right)}$$
(13)
HAI is Human Active Index; Ai is the total area of the ith land use type; Pi The intensity parameter of human impact reflected by type i land use type; TA is the total final surface area of land use type in evaluation unit; n is the number of land use types. Combined with the land use type of this study, Pi is assigned by Delphi method, in which cropland is 0.67, woodland is 0.13, grassland is 0.12, water body is 0.10, built-up land is 0.96, and unused land is 0.0530,45.GeodetectorGeodetector is an algorithm that uses spatial heterogeneity principle to detect driving factors of carbon storage, which can quantitatively detect the influence of impact factors on carbon storage and explore the interaction between driving factors. Geodetector includes factor detection, risk detection, interaction detection and ecological detection46.Differentiation and factor detection: the influence factors were discretized, and then the significance test of the difference in the mean values of the impact factors was conducted to detect the relative importance among the factors. The statistical quantity q is used to measure the explanatory power of impact factors on the carbon storage spatial differentiation and the value range of q is between 0 and 1. The larger the value, the stronger the explanatory power of the factor47.$$q = 1{ – }frac{{sumnolimits_{h = 1}^{L} {N_{h} sigma_{h}^{2} } }}{{Nsigma^{2} }}$$
(14)
In this formula, h = 1, 2…, L is the classification or partition of variable (Y) or factor (X); Nh and N are layer h and regional number units respectively; and (sigma_{h}^{2}) and (sigma_{{}}^{2}) are the variance of the layer h and regional value Y respectively.The variance of the regional value Y is calculated as follows,$$sigma^{2} = frac{{sumnolimits_{i = 1}^{n} {(Y_{i} – overline{Y} )^{2} } }}{N – 1}$$
(15)
where, Yi and (overline{Y}) are the mean value of sample j and the region Y, respectively.$$sigma^{2} = frac{{sumnolimits_{i = 1}^{{n_{h} }} {(Y_{h,i} – overline{{Y_{h} }} )^{2} } }}{{N_{h} – 1}}$$
(16)
where, Y and (overline{Y}) are the value and mean value of sample i in layer h, respectively.Interaction detection: it is used to identify the interaction between different impact factors Xs, that is, to evaluate whether the combined action of X1 and X2 will increase or weaken the explanatory power of vegetation coverage Y, or the influence of these factors on Y is independent of each other. The evaluation method is to first calculate the value q of the two factors X1 and X2 for Y respectively: q(X1) and q(X2), and calculate the value q of their interaction (the new polygon distribution formed by the tangent of the two layers of the superimposed variables X1 and X2) : q(X1 ∩ X2) and compare q(X1) and q(X2) with q(X1 ∩ X2)46. More

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Synthesis and data extractionData were collected using a literature search of Web of Science for peer-reviewed journal articles published between 1970 and November 2019. We conducted two sets of searches to capture grazing with discrete comparisons (e.g., grazed/ungrazed, moderate vs. heavy intensity grazing) and a range of grazing intensities. The search terms used for each were as follows 1) (graz* OR livestock) AND (exclosure* OR exclusion OR exclude* OR ungrazed OR retire* OR fallow* OR fence* OR paddock*), 2) (“grazing intensity” OR “grazing gradient” OR “stocking rate” OR “rotation*grazing”). Our synthesis includes domesticated and wild grazer species, with the latter defined as an undomesticated species naturally occurring in the study area during the study. Wild grazers are typically native species to the region (e.g., the American bison in Western North America) but can include non-native species that are naturalized in the area (e.g., feral horses on Sable Island).We excluded any study that did not test the effect of grazing animals. A grazer was defined using the definition provided by the authors of the respective study to account for the proportion of forage types in a herbivore’s diet that varies between seasons and habitats. For example, we included animals where their diet is assumed to come from all (e.g., cattle, sheep), most (e.g., wapiti, kangaroos), or some (e.g., deer species) grass species. However, within the included studies, these animals were classified as grazers as most of their diet was grass for the duration of the study. For added clarity about the herbivore composition in each study, we extracted a list of any herbivores listed in the paper regardless of foraging type or if any data was provided.We only included studies that measured animal diversity or abundance as a response variable and included data we could extract or contact the author to obtain9. We included any study with a grazing treatment and included observations within these studies of any grazed and ungrazed sites. All studies with grazing included a comparison to either ungrazed sites, different grazing practices (e.g., cattle vs. sheep), and/or differences in intensities (e.g., heavy/light, extensive/intensive). Studies that only measured plants or soil biota were excluded because syntheses of grazing effects on these groups have already been conducted7,11,12, and our goal was to provide a robust inventory of animal diversity. However, if a study included plants, lichens, or fungi in addition to animals, we included this data. Studies discussing marine grazing or aquatic systems were also excluded. From these preliminary filters, we identified 3,489 published manuscripts. We reviewed these 3,489 published articles and found 245 studies that surveyed animals in grazed sites. In total, we extracted 16,105 observations for over 1,200 species.We extracted 28 variables that focus on management systems, assemblages of grazer species, ecosystem characteristics, and survey type (Table 1). The latitudes, longitudes, and elevations of each study were included when provided for use with geospatial data. In addition, we included variables about the study site’s disturbance history, including last time grazed, if a flood event or fire had occurred, if fertilization was used, if the area was open or fenced off, and if the area was publicly or privately owned. Furthermore, the timeline for the study (i.e., the years the authors initiated and completed the study) was also provided. Study initiation was described by the authors and could include when the grazing treatment started, another treatment was applied, and/or animal surveys began. These timeline columns can be useful in identifying long-term studies and differentiating single grazing events or multi-year experiments. Finally, we generalized the characteristics of the ecosystem of the sites used in each study based on the climate and dominant vegetation.Table 1 The attributes and description of the metadata.csv file that lists the general characteristics of each study.Full size tableWithin the grazing data, we included information about the grazer when provided, including any measurement of the intensity of grazing (e.g., animals per hectare, the height of residual vegetation). We also provided two columns that detailed whether the study tested grazing effects using a discrete comparison or gradient of intensities (Table 2). The value for the target specimens extracted may represent either a single observation or a summarized statistic (e.g., mean animals per site). We identify unique observations as “count” and summarized statistics by the metric used, such as mean, median, standard deviation (column stat in grazingData.csv). When possible, we also included any record of other grazers that co-occurred with the observed grazer species. The data for these variables were extracted from the papers by a single researcher who read through each paper and filled in available data on the mentioned variables.Table 2 The attributes and description of the grazingData.csv file that has the extracted data from each study.Full size tableWe extracted information about the target specimen, site, year, experimental replicate, and response estimate (Table 2). We included multiple categorizations of the target species to assist future users in synthesizing similar taxa (Table 2). When a species name or genus was provided, we conducted a search query (see detailedTaxa.r) through the global biodiversity information facility (GBIF.org) to determine the taxonomic classification of the species, including kingdom, phylum, order, class, and family. When a species name was not included, we provided the lowest taxonomic resolution available. We also included a broader classification of ‘higherTaxon’ to distinguish plants, fungi, vertebrates, and invertebrates. These columns may help group similar species together for community-level analyses. Lastly, we included the characteristic of the plant community (i.e., planted or self-assembled, tilled, and its vegetation class) when plant data was reported.Patterns among studiesMost of the studies took place in the United States (26%), Australia (9%), and the United Kingdom (7%) (Fig. 1). As expected, most studies were conducted in grasslands (n = 206), followed by forests (n = 92) and shrublands (n = 82) (Fig. 2). We included publications from the entire range of years (i.e., 1970–2019), but most were published after 2000 (76%). The number of sites in a study and the study duration showed a bimodal distribution with a long tail (Fig. 3). Most studies included one to eight different sites, and few were conducted longer than five years (Fig. 3). A few studies were highly replicated, while many were limited in their replication (Fig. 3).Fig. 1The locations of studies that measured the response of animals to domestic or wild grazing.Full size imageFig. 2The number of grazing studies conducted in ecosystems around the world. We generalized the characteristics of the ecosystem of the sites used in each study based on the climate and dominant vegetation community. We separated grassland communities into those that were (a) semi-natural without recent cultivation or seeding (self-assembled), (b) recently cultivated or had supplemental seeding (planted/cultivated), and (c) a combination of both. In most grasslands, the cultivation history was unclear.Full size imageFig. 3The number of independent sites surveyed and the duration of each study. Most studies were conducted at either a single site or with some replication (e.g., 6–8 sites). Similarly, most studies were either conducted in one year ( >30%) or over a few years (e.g., 3–6 years). Very few studies (32) or lasted longer than 15 years.Full size imageSite and management data were not reported in all studies, as found in other reviews of grazing impacts on ecological processes10. Of the studies that mentioned the ownership status of the land used, 46% were on private land, 42% were on public land, and 12% had a history of both public and private ownership. Most studies included binary comparisons (56%) of grazed vs. ungrazed plots or sites, though some also included a discrete (22%) or a continuous estimate of grazing intensities (18%).Of the studies that reported plant community origin, 76% were self-assembled, 17% were planted communities, and the remaining included sites were a combination of the two. Domesticated grazers as the focal herbivore made up 67% of the studies, with 12% of the studies having wild grazers as the focal herbivore, and 21% having both present. Domesticated livestock were the most frequently surveyed grazers including cattle (n = 164), sheep (n = 83), and horses (n = 21), but studies are included that examined wild grazers, such as kangaroos (n = 6), elephants (n = 5), and pronghorn (n = 5) (Fig. 4).Fig. 4The frequency in which a study reported herbivores. We included any mention of herbivores regardless of being a grazer, browser, granivore, or other class. This list was obtained by the text within the manuscript and is different than the representation of species in the database (i.e., the measured species).Full size image More