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The rate of decline in ecosystem services has been exacerbated by inefficient and inequitable natural resource use and management. This study analyzes the natural capital stock and outflow in the Arid and Semi-Arid Northern Region of China (ASRNC) from 2000 to 2020. The Gini coefficient and coefficient of variation are used in the equity assessment of natural capital consumption. Over-appropriation of natural capital is a prerequisite for the inequitable distribution of natural resources, and all variables were accounted for through a geographic probe. Since most of the variables in this study have a nonlinear relationship, an in-depth analysis was conducted using NARDL. The results show that (1) natural capital flow occupancy generally shows an upward and downward trend and peaks in 2015. Natural capital stock occupancy was on a linear upward trend over the study period, rising from 14.580hm2/cap to 18.272hm2/cap. Depletion of natural capital is increasing and construction land has become the land type that leads to deep footprint changes (2) A city's consumption of natural capital matches its ecological carrying capacity to contribute to economic growth. However, the Gini coefficient for the depth of the ecological footprint from 2000 to 2020 is on a fluctuating upward trend. It reached its maximum in 2020 (1.457), indicating that the inequitable use of natural capital stock is increasing. (3) In the long run, population density and urbanization rate have different adverse effects on utilizing natural capital stock. In addition, the equity of planted forest area on natural capital use is heterogeneous in the long and short term. There is a negative effect of planted forest area on natural capital stock under long-term development. The study helps to judge the equity of regional consumption of natural capital and provides a scientific basis for the harmonious development between socio-economic systems and ecosystems. • The inequities in natural capital consumption are accounted for in a condition allowing nonlinear development. • Longitudinally, a chain of three aspects, natural capital accounting - equity measurement - imbalance tracing, is dissected. • In the long term, planted forests can exacerbate regional water shortages and lead to an imbalance in the use of natural capital. • Constructing an equity assessment framework for natural capital depletion can help guide the sustainable development of natural resources in arid and semi-arid regions. [ABSTRACT FROM AUTHOR]

• The achievement of regional sustainable development is at the core of PLES. • The quantitative identification of land use functions forms the foundation of territory spatial planning and management. • The COAL model provides a reference for determining future PLES development. Analysis of the dynamics of regional production-life-ecological space (PLES) can help to mitigate conflicts between economic development and the natural environment and can also promote sustainable and healthy regional development. However, the delineation and optimal integration of PLES at large scales, and predictions about its future, still lack sufficient scientific basis and reliable quantitative analysis. To fill this gap, this paper therefore chooses the city cluster as a research scale and the Lanzhou-Xining City Cluster (LXCC), an area typical of the "human-nature" conflict in northern China, as a case study. A collaborative optimal allocation of land-use (COAL) model was established to explore the future development of PLES in city clusters. In COAL, a morphological spatial pattern analysis (MSPA) and a minimum cumulative resistance model are used to determine the spatial functional areas of the country in 2020. Then, combined with the future land use simulation model, the PLES of LXCC is predicted in a multi-scenario perspective and differential control strategies are implemented for different land use functions. The results show that: (1) The identification and prioritization of source sites with important functions were the basis for enhancing the multiple functions of the land in the region. The ecological "source" of expansion accounts for 42% of the total area of LXCC, mainly in the mountains, forests, and ecological reserves, while the living "source" of expansion accounts for 58% of the total area of the city, mostly scattered on flat terrain. Based on this, five functional zones have been defined. The ecological protection zone was the largest, mainly in the western part of LXCC, and the agricultural buffer zone was the smallest. (2) The integration of different functional areas into the optimal allocation of land use is the premise of PLES delineation under the COAL framework. After a comparative analysis of multiple scenarios, the result of land use optimization under coordinated the city cluster scenario increased the area of productive land to 177,780.68 km2 and the area of living land to 13,947.33 km2. Based on this, the proportion of LXCC ecological, production, and living space were 77.20%, 18.23%, and 4.57% respectively. The optimized results have been proven to serve to meet the future spatial needs for food security and ecological conservation. The results of this study demonstrate that the COAL framework can help the government to determine the future development of PLES and promote balanced regional development in city clusters. [ABSTRACT FROM AUTHOR]

• A UGB scheme is proposed in which the ecological constraints are incorporated into a CA-Markov model. • Quantifies ecological resources and urban development in a complex environment. • The model and planning method can be applied to other ecologically fragile cities. Urban growth boundaries (UGBs) are seen as an effective tool to control urban sprawl and promote sustainable urban development. Existing methodologies related to urban boundary delineation focus mainly on increasing land intensification and compact urban development. However, it is not sufficient to focus on optimal urban development, especially in China. The delineation of UGBs should not only take into account the heterogeneity of regional natural resources but also further reconcile urban–ecological conflict. Therefore, this paper proposes a new framework for delineating UGBs in an ecologically sustainable manner. This study first uses the remote sensing ecological index (RSEI) and ecological sensitivity as a basis for ecological constraints (EC). Both the background state of the regional ecology and ecological stress from human activities are considered to be constraints on urban sprawl. These ecological constraints are then combined with a CA-Markov model to simulate future urban development. The framework is applied to the Linxia Hui Autonomous Prefecture, an ecologically fragile region in China, where UGB delineation can be used not only to reconcile ecological and land-use planning conflict but also to ensure sustainable resource development in individual zoning districts. The results suggest that a plan that only considers urban development may have a negative impact on the conservation of natural resources and ecological sustainability. The delineation of UGBs based on the proposed EC-CA-Markov model will thus help guide sustainable urban development. The conceptual and methodological advances in this study are applicable to other ecologically fragile cities and can help in the delineation of UGBs. [ABSTRACT FROM AUTHOR]