Carrying capacity (potential) of food security can be assessed to align with the vision of the United Nations Sustainable Development Goal 2 (SDG 2) to 'end hunger, improve nutrition and promote sustainable agriculture.' This study aims to evaluate the maximum carrying potential of cultivated land, according to nutritional demands at different living standards and cultivated land productivity. Firstly, the evaluation models were applied to the production potential of cultivated land, including light-temperature production potential, climatic production potential, and the maximum yield of regional crops. The nutrient output model was combined after evaluation. The evaluation factor was conventionally transformed into a more reasonable output of nutrients using grain quantity. Taking the Shaanxi Province as the study area, the cultivated land production potential was evaluated under different scenarios. Subsequently, the nutrients and dietary structures (plant-only and plant-animal diet) under three living standards (subsistence, moderate prosperity, and affluent level) were selected to calculate the cultivated land carrying capacity and its index. Additionally, the improvement points of cultivated land production capacity were obtained to further clarify the pure grain and comprehensive output of cultivated land in 2023. Finally, the population of cultivated land was also evaluated under the living standards using the Bucket Theory. The results show: (1) The cultivated land provided 5 751.360 trillion kJ of energy, 39.82 trillion grams of protein, and 11.507 trillion grams of fat under the maximum yield of regional crops, which were 2.50 times, 2.88 times, and 1.55 times higher than the actual output level in 2023, respectively. The production potential of energy, protein, and fat shared the spatial agglomeration and hierarchical differentiation. (2) The maximum carrying capacity of cultivated land reached 672.36 million people at the subsistence level; there were 218.19 million people under the maximum yield of regional crops. Once the nutrient constraints were considered, the fat was served as the limiting factor for the maximum cultivated land carrying potential. There was great variation in the carrying capacity derived from cultivated land output and the limiting nutrient factors under the mixed plant-animal dietary structure. Specifically, the nutrient-restricting factor was shifted from fat to energy. The most attainable carrying potential of cultivated land was 50.1209 million people under the nutrient constraints at the affluent level, as calculated under Output Scenario III. (3) High carrying potential occurred in Northern and Central Shaanxi, with no overload over any living standard or dietary structure. Counties and districts in Yulin exhibited an increasing trend in carrying potential under nutrient constraints. This was attributed to the capacity of food to supply nutrients. (4) Cultivated Land Carrying Capacity Index shared the significant spatial heterogeneity with a Z-shaped distribution: A cluster with high values was found in Guanzhong, Southwestern Shaanxi, and Central Northern Shaanxi; a cluster with low values was concentrated in Western Shaanxi and Northern Yulin. The theoretical threshold was quantified for the carrying potential of cultivated land resources in Shaanxi Province, fully meeting the living standards and nutritional needs. The research findings can provide a strong reference to support food security in the stage of affluent life.

Prime farmland has been granted national protection as the high-quality, stable, concentrated, and contiguous cultivated land farmland with high productivity. It is required to accurately demarcate the prime farmland for the effective protection of farmland and national food security. In this article, the research area was taken as the Xianyang City, Shanxi Province, China. Firstly, evaluation indicators were selected as the ecological value and policy conditions, according to the natural endowment, socio-economic conditions, and stability of cultivated land. A factor analysis was implemented to fully evaluate the cultivated land quality. Secondly, spatial clustering was introduced to combine the local spatial autocorrelation, in order to identify the spatial clustering or discrete features of cultivated land quality. The matrix combination was utilized to clarify the quality levels of cultivated land and spatial clustering characteristics of each region in pairs. Four protection zones were then designated to identify the continuous levels of the cultivated land using Buffer analysis. Finally, the connectivity and protection zones of cultivated land were screened and sorted, according to "priority to contiguous areas, good quality, and quantity constraints". The prime farmland was classified to meet the requirements of the designated quantity constraints. The results show that: 1) The quality of cultivated land was divided into five levels: high, relative high, general, relative low, and low. More than half of the cultivated land shared the low and relative low levels (35.81% and 29.67%, respectively). The proportion of relative high and general level cultivated land only exceeded 10%. The terrain and regional economic development were dominated by the spatial distribution characteristics under the different quality levels of cultivated land. The overall quality level of cultivated land also showed a spatial distribution pattern of "high in the south and low in the north". The cultivated land quality presented the outstanding spatial agglomeration with the primary types of high-high and low-low adjacency agglomeration. 2) Four protection zones of cultivated land were divided into priority protection, suitable protection, key remediation, and comprehensive governance zone. Among them, the largest area was the comprehensive governance zone with an area of 107 904.92 hm², accounting for 35.50% of the total cultivated land area, whereas, the least area was the suitable protection zone, accounting for 11.81% of the total. 3) Six levels of contiguous cultivated land were divided into 49 713 contiguous cultivated land plots with an area of 289033.61 hm², accounting for 95.10% of the total arable land area. 4) The final demarcation of the prime farmland area was 266 420.85 hm², accounting for 87.66% of the total cultivated land area. The key demarcation areas were distributed in Qian County, Jingyang County, Binzhou City, and Yongshou County, with a cumulative demarcation area accounting for 51.64% of the total demarcation prime farmland area. The findings can provide new ideas to optimize the layout of cultivated land, particularly for the next stage of prime farmland adjustment and demarcation.

Rapid urbanization has exerted the considerable pressure on land resources and infrastructure, leading to urban sprawl. The delineation of urban growth boundaries (UGBs) has been one of the most crucial tools to manage and curb the urban sprawl. The delineation can also be optimized to alleviate the land-use conflicts for the sustainable urban development. The second-largest city in Shaanxi Province, Xianyang City is similar to the most middle-sized cities in China, indicating the rapid development with the land-use conflicts and ecological crises. In this study, according to the "Dual-Evaluation" framework, the ecological protection areas of the high importance, the agricultural production and urban construction suitability areas were delineated.The "top-down" policy constraints were served as the delineation of UGBs. Concurrently, the patch-generating land use simulation (PLUS) model was employed to conduct to meet the resource requirements and development potential in the study area. Future demands were forecasted and simulated for the land use. A "bottom-up" demand-driven approach was used to promote the rational use of land resources in the sustainable development of the environment. The delineation of UGBs was also in line with the local needs of actual development. Additionally, the erosion-dilation test was also employed to remove the noise points from the UGBs, particularly for the smoother and easier to manage. The results showed that: 1) The southern region was predominantly focused on urban development, where the area of 1 368.98 km² was designated as the urban construction. Meanwhile, the northern was prioritized the ecological protection, where the area of 3 853.04 km² was unsuitable for construction. 2) The PLUS model was used to simulate the urban construction land in 2040, which was 133.86 km² under the constraints of suitability evaluation. Compared with the natural development scenario, there was a significant reduction in the unused land area, along with an increase in the areas of arable land, forest land, and construction land, in order to facilitate the efficient use of land. 3) The erosion and dilation were integrated to exclude the unsuitable area for urban construction. The bottom-line UGBs was delineated as 3 863.39 km²; The alternate UGBs was 852.28 km², which was composed of the suitable urban construction zones; The priority UGBs was 134.84 km² in the distribution range of urban construction land by 2040. The triple functional boundaries were established to promote the more compact and continuous urban pattern after morphological adjustments, thus guiding the direction of urban development. This approach can offer a novel perspective and scientific rationale to delineate the UGBs in the urbanization, in order to balance the development and protection. The conflicts among urban development, farmland protection and ecological conservation can also be determined to enable the coordinated development among population, resources and the environment.