{'fraction_non_alphanumeric': 0.036451301832208294, 'fraction_numerical': 0.03972999035679846, 'mean_word_length': 4.886492622020431, 'pattern_counts': {'":': 0, '<': 4, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Evolution and effects of the social-ecological system over a millennium in China’s Loess Plateau

The evolutionary phases of the social-ecological system in China’s Loess Plateau over a millennium are identified.


Section S1. Changes of the components of the SES in the LP
The population (Fig. 4A)

Section S2. Changes of interactions between system components
The correlation relationship between population and cropland area went through five periods ( Fig. 3A). During the period 1100 to 1750, the population was positively correlated with cropland area (p<0.001), meaning that the increase of population was accompanied by the expansion of cropland. During 1750 to 1951, the relationship was non-significant, the cropland area changed little with the increase of population. Between 1952 and 1980, the relationship transformed to a negative correlation (p<0.001), meaning that as the population increased, the area of cropland fell. From 1981 to 2000, population was still negatively correlated to cropland area (p=0.065), but the regression slope is less than during the third period. In the fifth period, 2001-2018, the relationship between population and cropland area transformed to no statistical significance.
The relationship between population and forest coverage can be divided into three periods (Fig.   3B). From 1100 to 1949, population was negatively correlated to forest coverage (p<0.001), indicating that the population increased as the forest area decreased. The relationship transformed to a positive correlation during 1950 to 1993 (p=0.01). From 1994 to 2018, the relationship was still positive (p<0.001), but the regression slope is higher than the second period, meaning that population increased with forest restoration.
Due to the competition for land between cropland and forest, cropland area was negatively correlated with forest coverage throughout our study period (Fig. 3C). However, the regression slope increased from the first period, 1100-1750, to the second period, 1750-1993. The slope of the third period, 1994-2018, is higher than that of the first two periods, but it is non-significant.

Section S3. Changes of drivers and effects of social-ecological interactions in the SES
Our study period climatically covers the Medieval Climate Anomaly, the Little Ice Age, and  5D). There were two peaks of war frequency in North China during our study period: the early 17 th century and the late 19 th century (Fig. 5E). The farming-grazing boundary on the LP shifted southwards from the Northern Song to the Yuan and Ming dynasties, but moved northwards in the Qing dynasty (36).
As for the indicators of effects, grain production in the LP changed in line with population and increased steadily after 1949 (Fig. 6A); annual sediment load of the YR increased from 1100 to 1950s, and peaking at 29.65×10 8 t in 1958, after that, it decreased steadily (Fig. 6B); annual natural runoff of the YR varied over time but decreased after the 1990s (Fig. 6C); the area change of the YR delta changed with the sediment load of the YR, becoming negative after 2000 (Fig. 6D); the frequency of natural breaches of the lower YR increased during historical times, but has remained at zero since 1956 due to the raising and reinforcement of the levee structure and construction of the Sanmenxia and Xiaolangdi Dams (19) (Fig. 6E).

Section S4. Limitations of historical data
Due to the long study period, the datasets we used are combinations of historical records, reconstructed data, and inferred data for historical periods, together with observational and statistical data after 1949. Historical records and reconstructed data are highly reliant on the accuracy of historical archives and documents. There may be some errors and uncertainties in the historical archives for several reasons -such as lost or deliberate hiding of records (25). The inferred data were estimated based on historical archives and documents, and other relevant materials (e.g., sedimentation rates) in each original study. Although the temporal coverages of inferred data are poor, they still reflect the overall trends. In addition, most of these datasets are the only sources of the indicators (see Methods). Being cautious about the reliability of these datasets, we are confident that our study reflected the general trends (Supplementary Table S1).
However, some regime shifts may be masked or subdued because of lower temporal resolution and data quality, and reliability constraints. For example, climate change is a possible major driver of regime shift (10). A previous study found that due to the shortening of the growing season and increase of frost days and cold spells in cold climatic periods, agricultural yields in China in the period 1840-1890 (cold period) was reduced by 10-25% in comparison with 1730-1770 (warm period) (30), which may affect the relationship between population and cropland area. However, due to the coarse temporal resolution and data availability, the changes of relationships between SES components caused by climate change could not be captured in our analysis.   Change in area of the YR delta (km 2 yr -1 ) Published literature (52,62)