Correction: Revealing urban-rural sustainability dynamics based on multi-source data and machine learning: spatio-temporal hotspots, driving mechanisms, and non-linear thresholds in Suzhou, China

Urbanisation is one of the primary drivers of land-use transformation in contemporary society, reshaping both urban and rural landscapes throughout the 20th century (Nuissl and Siedentop, 2021). Although urbanisation drives economic growth and infrastructure advancement, it simultaneously leads to extensive transitions from rural to urban land uses, inevitably posing profound challenges to the sustainable development of land-use systems, particularly in peri-urban areas (Fu et al., 2021). These transitional zones, situated between urban and rural systems, integrate land, ecological resources, and human activities related to production and living. They are critical components of regional development (Zhang et al., 2020) and have significant impacts on human health and well-being (Barton, 2009). In the Chinese context, these processes unfold against a longstanding institutional separation between urban and rural areas, shaped by the household registration (hukou) system, differentiated land-use practices, economic structures and socio-cultural characteristics (Li, 2012).Rapid urbanisation has accelerated land-use transformations in peri-urban areas, shifting landscapes from primarily agricultural functions toward residential, industrial, and commercial uses. Development models focused on economic growth, to some extent, overlook the land-use conflicts resulting from such expansion and exacerbate their negative impacts (He et al., 2020).Existing studies on urban-rural land-use transitions can be broadly categorised into two perspectives. The first perspective examines how land-use change in peri-urban areas reshapes economic, ecological and social outcomes. Empirical work has assessed the efficiency and effectiveness of land-use transformation (Fu et al., 2021), the ecological consequences of land-use changes and land-use intensity (Wu et al., 2024;Xu et al., 2020), and broader sustainability implications, including environmental degradation, habitat fragmentation and the loss of cultural landscape identity (Shao et al., 2020;Xu et al., 2020). International research further highlights that unsustainable land-use transformations in rural areas during urbanisation can lead to displacement (Salem et al., 2020), infrastructure deficits, and widening socioeconomic disparities (Dadashpoor and Ahani, 2019). Taken together, this perspective demonstrates that peri-urban land-use transitions are crucial to the sustainability of urban-rural regions and have a direct impact on human well-being. However, most studies address economic, ecological and social dimensions separately or treat them as loosely connected outcome indicators, paying limited attention to how these dimensions interact and co-evolve over time. As a result, the coupled dynamics of "coordination-conflict" between land-use transitions and multi-dimensional sustainability outcomes remain insufficiently understood, particularly in rapidly urbanising contexts such as China.A second perspective focuses on governance arrangements, planning instruments and assessment frameworks for managing land-use change in urban-rural interfaces. Scholars have highlighted that current landuse transformation processes are often governed by fragmented and overlapping institutional regimes, leading to overlapping jurisdictions, inefficient decision-making and weak coordination across administrative boundaries (Perrin et al., 2018). Additionally, Follmann et al. (2021) and Ahani and Dadashpoor (2021) note that existing peri-urban land-use assessment and management frameworks fail to address the dynamic realities of urbanisation, creating loopholes for informal land speculation, unauthorised urban expansion, and environmental degradation. Although this line of research has significantly advanced the understanding of governance deficits and institutional complexity, it tends to emphasise qualitative institutional analysis or singledimensional indicators. However, the foundation of sustainable development lies in the coordination between economic, social, and environmental factors, with the core being the balance between ecological considerations and other dimensions (Gan et al., 2020;Li et al., 2022). There is a lack of attention to operational, quantitative frameworks that can systematically link land-use structures to economic vitality, ecological quality, and social well-being, and that can identify when and how urban-rural systems shift from coordinated development to conflictual outcomes (Buzási and Csete, 2017;Keith et al., 2023). Consequently, despite a substantial body of work on land-use transformation, ecological impacts, planning and control mechanisms, a comprehensive evaluation framework that integrates these dimensions to support sustainable development remains lacking (Salem et al., 2025).In addition to these theoretical gaps, there are notable limitations in the methodological approaches employed in the existing research. Currently, three categories of quantitative approaches are commonly used to evaluate urban-rural sustainability and land-use dynamics. The first category comprises statistical and spatial econometric models, including fixed-effects and random-effects models, as well as spatial panel specifications.The Spatial Durbin Model (SDM) has been widely used to identify spatial spillover effects and the impacts of neighbouring areas, serving as a key tool for evaluating the efficiency and driving factors of land use structure. (Luge et al., 2025). These models offer clear parameter interpretations and a solid theoretical foundation for analysing directional relationships and spillover effects. However, their reliance on linearity and global stationarity limits their capacity to capture non-linear interactions, high-order effects and complex spatial heterogeneity, and model stability can be compromised when the underlying processes are strongly nonstationary.The second category centres on geographically weighted regression (GWR) and its extensions, such as multi-scale regression methods (MGWR), which are used to address spatial non-stationarity by allowing coefficient estimates to vary across space (Wu et al., 2025). These approaches are effective for uncovering localised spatial mechanisms and scale-dependent relationships and have been used to explore the spatial heterogeneity of land-use drivers in urban-rural regions. Yet, they are less suited to handling high-dimensional variables and intricate interaction structures, and their performance often depends on subjective choices of bandwidths and kernel functions. As noted by Lessani and Li (2024), many extensions of GWR still have these limitations and thus only partially resolve the challenges of modelling complex, multi-dimensional land systems.The third category encompasses predictive models based on remote sensing and machine learning, including random forests, support vector machines, XGBoost, and deep learning. These models have demonstrated strong capabilities in extracting complex spatiotemporal patterns from large-scale remote sensing and multi-source big data, and can achieve high predictive accuracy in land-use classification, change detection and risk However, they often from limited and weak to theoretical frameworks in land-use and sustainability research and 2025). in including and have the of such models by global and and interactions, leading to frameworks such as These approaches have to to some extent, the between and et al., et al., 2025). their in urban-rural sustainability assessment remains and have been evaluation frameworks that integrate economic, ecological and social existing approaches statistical or emphasise predictive performance the of with to integrate their into a on the it is clear that existing research has significant to understanding the spatial structures, and efficiency of urban-rural land as well as the governance challenges of peri-urban However, key the and there is a lack of of the mechanisms between land-use transitions and their impacts on economic vitality, ecological quality, and social well-being. in of a quantitative for evaluating the dynamic transformation processes of "coordination-conflict" outcomes in urban-rural and for when development remain sustainable or the non-linear relationships and interaction effects urban-rural land-use factors have been it to how land use structures and sustainability and critical changes in landuse can the methodological the of multi-source spatial and machine models into urban-rural sustainability research frameworks remains methods have been there is a lack of that can simultaneously capture multi-dimensional spatial heterogeneity and non-linear and these into for sustainable land-use to these and the this the core research land-use transitions in urban-rural systems interact and co-evolve across the economic, ecological and social and critical these processes shift from coordination to this three research are that integrates economic, and social the multi-dimensional characteristics of urban-rural the and the Model to the spatial coordination mechanisms between human intensity and ecological and to identify the effects of land use and structures on urban-rural a quantitative framework for urban-rural sustainability on on the of panel models, the framework a Model with to a that statistical non-linear and the three the theoretical it framework that the mechanisms of and non-linear urban-rural framework existing effects to and critical the methodological it a quantitative that statistical models and random effects models, with machine models and for relationships and effects in complex land the as the land use and key driving and that spatial and sustainable governance in rapidly urbanising with to other urban-rural land-use transformation is both a of urbanisation and a critical of urban and rural development et al., 2020). 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