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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Sustain. Food Syst.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Sustainable Food Systems</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Sustain. Food Syst.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2571-581X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fsufs.2026.1767684</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Optimization and driving mechanisms of agricultural resilience measurement based on XGBoost-SHAP model: Evidence from China</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Zhou</surname>
<given-names>Dapeng</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/3181027"/>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Data curation" vocab-term-identifier="https://credit.niso.org/contributor-roles/data-curation/">Data curation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing &#x2013; original draft</role>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Jing</given-names>
</name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Data curation" vocab-term-identifier="https://credit.niso.org/contributor-roles/data-curation/">Data curation</role>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Zou</surname>
<given-names>Fan</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing &#x2013; original draft</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Zixuan</given-names>
</name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &#x0026; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-review-editing/">Writing &#x2013; review &#x0026; editing</role>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Huan</surname>
<given-names>Honghua</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x002A;</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Funding acquisition" vocab-term-identifier="https://credit.niso.org/contributor-roles/funding-acquisition/">Funding acquisition</role>
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</contrib-group>
<aff id="aff1"><label>1</label><institution>Jiangsu Academy of Agricultural Sciences</institution>, <city>Nanjing</city>, <country country="cn">China</country></aff>
<aff id="aff2"><label>2</label><institution>Jiangsu Rural Revitalization Research Institute</institution>, <city>Nanjing</city>, <country country="cn">China</country></aff>
<aff id="aff3"><label>3</label><institution>Institute of Agricultural Economy and Science Information, Fujian Academy of Agricultural Sciences</institution>, <city>Fuzhou</city>, <country country="cn">China</country></aff>
<aff id="aff4"><label>4</label><institution>Department of Economics, Iowa State University</institution>, <city>Ames</city>, <state>IA</state>, <country country="us">United States</country></aff>
<author-notes>
<corresp id="c001"><label>&#x002A;</label>Correspondence: Honghua Huan, <email xlink:href="mailto:20230048@jaas.ac.cn">20230048@jaas.ac.cn</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-02-09">
<day>09</day>
<month>02</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>10</volume>
<elocation-id>1767684</elocation-id>
<history>
<date date-type="received">
<day>15</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>04</day>
<month>01</month>
<year>2026</year>
</date>
<date date-type="accepted">
<day>12</day>
<month>01</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2026 Zhou, Zhang, Zou, Li and Huan.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Zhou, Zhang, Zou, Li and Huan</copyright-holder>
<license>
<ali:license_ref start_date="2026-02-09">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>As agricultural systems face increasingly intertwined and recurrent external risks, strengthening the resilience of China&#x2019;s agricultural industry has become a strategic priority for ensuring national food security and agricultural sustainability. A robust and systematic measurement of the resilience of China&#x2019;s agricultural industry (RCAI), together with an examination of its principal drivers, is therefore essential. This study develops a comprehensive RCAI evaluation framework for 31 provincial-level regions in China, characterizes the spatiotemporal evolution of RCAI from 2000 to 2022, and employs an XGBoost&#x2013;SHAP analytical framework to refine the index and uncover underlying driving mechanisms. The results show that: (1) the resilience of China&#x2019;s agricultural industry exhibits a clear upward trend over time and a pronounced spatial pattern of &#x201C;higher in the east and lower in the west&#x201D;; (2) the XGBoost model optimizes the RCAI evaluation framework, yielding an index that is more robust and representative; (3) agricultural fixed-asset investment contributes 30.6% to RCAI, making it the most influential determinant of resilience enhancement. In addition, rural consumption expenditure and transportation infrastructure are positively associated with RCAI and display threshold effects. Overall, the findings demonstrate that the XGBoost&#x2013;SHAP framework can effectively capture complex nonlinear relationships between RCAI and its determinants and can improve the precision of resilience measurement.</p>
</abstract>
<kwd-group>
<kwd>agricultural industry</kwd>
<kwd>machine learning</kwd>
<kwd>resilience</kwd>
<kwd>SHAP analysis</kwd>
<kwd>XGBoost</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This paper was supported by Jiangsu Province Key Research and Development Program [No. BE2023352].</funding-statement>
</funding-group>
<counts>
<fig-count count="7"/>
<table-count count="4"/>
<equation-count count="5"/>
<ref-count count="80"/>
<page-count count="17"/>
<word-count count="11762"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Land, Livelihoods and Food Security</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="sec1">
<label>1</label>
<title>Introduction</title>
<p>In recent years, the compounded effects of extreme climate events, resource constraints, and market volatility have made the stability, efficiency, and sustainability of agricultural production a top priority for governments and agricultural sectors worldwide (<xref ref-type="bibr" rid="ref60">Xie and Wang, 2017</xref>; <xref ref-type="bibr" rid="ref15">Davis et al., 2023</xref>; <xref ref-type="bibr" rid="ref22">Guo et al., 2024</xref>). Such risks can trigger yield reductions and farm losses, thereby amplifying the vulnerability of agricultural systems (<xref ref-type="bibr" rid="ref1">Altieri and Nicholls, 2017</xref>; <xref ref-type="bibr" rid="ref47">Raza et al., 2019</xref>). Accordingly, resilience has become a central concept for assessing agricultural systems under uncertainty. The concept of resilience originated in physics and was later extended to economics (<xref ref-type="bibr" rid="ref25">Huggins and Thompson, 2015</xref>). In an agricultural context, resilience can be defined as the capacity of an agricultural system to resist, recover from, and rebuild after external disturbances. That is, it reflects the ability of a regional agricultural system to maintain its functioning under shocks arising from climate, ecology, or resource constraints, and to return to normal performance levels thereafter (<xref ref-type="bibr" rid="ref9">Cellini and Torrisi, 2014</xref>; <xref ref-type="bibr" rid="ref40">Martin and Sunley, 2015</xref>; <xref ref-type="bibr" rid="ref41">Meuwissen et al., 2019</xref>). Following this understanding, we examine the resilience of China&#x2019;s agricultural industry from an industry-wide perspective, adopting a comprehensive lens to evaluate regional capabilities to withstand and rebound from risks. This provides evidence to support risk assessment and management, as well as policy formulation (<xref ref-type="bibr" rid="ref53">Wang et al., 2025</xref>).</p>
<p>Existing studies, however, largely construct resilience indices from a single dimension such as economic or ecological aspects, apply entropy-based weighting or TOPSIS for measurement, and then examine spatial and temporal heterogeneity (<xref ref-type="bibr" rid="ref59">Xiao et al., 2020</xref>; <xref ref-type="bibr" rid="ref61">Xie et al., 2024</xref>; <xref ref-type="bibr" rid="ref14">Das et al., 2025</xref>; <xref ref-type="bibr" rid="ref64">Yang et al., 2025</xref>). This prevailing research paradigm presents two notable challenges: First, conventional index-construction methods primarily assign weights and may yield biased results when handling high-dimensional data (<xref ref-type="bibr" rid="ref21">Greco et al., 2019</xref>; <xref ref-type="bibr" rid="ref65">Yang et al., 2022</xref>). Second, the mechanisms linking the composite index to its constituent indicators remain difficult to interpret, and traditional econometric approaches often offer limited insights into nonlinear relationships among variables (<xref ref-type="bibr" rid="ref2">Athey and Imbens, 2019</xref>). To address these gaps, we introduce an explainable machine-learning framework based on eXtreme Gradient Boosting (XGBoost) to measure and refine the resilience of China&#x2019;s agricultural industry, and employ SHapley Additive exPlanations (SHAP) to interpret key drivers. This approach aims to produce a more refined and interpretable resilience index, thereby advancing measurement and mechanism identification in this field.</p>
<p>China provides a representative setting for resilience research because its agricultural system faces pronounced and multifaceted pressures (<xref ref-type="bibr" rid="ref35">Liu et al., 2024</xref>). With about 7% of the world&#x2019;s arable land, China must feed roughly 22% of the global population (<xref ref-type="bibr" rid="ref33">Li et al., 2023</xref>; <xref ref-type="bibr" rid="ref36">L&#x00FC; et al., 2023</xref>). Moreover, agricultural heterogeneity across regions is substantial: climatic conditions, resource endowments, and binding constraints differ markedly, complicating policy design and implementation (<xref ref-type="bibr" rid="ref61">Xie et al., 2024</xref>; <xref ref-type="bibr" rid="ref48">Sui and Dai, 2025</xref>). Historical evidence further shows that agriculture in many regions has been repeatedly exposed to external shocks such as climate extremes, natural disasters, and epidemics (<xref ref-type="bibr" rid="ref68">Yu et al., 2018</xref>; <xref ref-type="bibr" rid="ref13">Cheng et al., 2023</xref>; <xref ref-type="bibr" rid="ref33">Li et al., 2023</xref>). Under a fragmented production structure dominated by smallholders, China&#x2019;s agricultural sector often lacks the capacity to absorb such shocks, which can further exacerbate systemic vulnerability (<xref ref-type="bibr" rid="ref49">Sundstrom et al., 2023</xref>; <xref ref-type="bibr" rid="ref69">Yu et al., 2023</xref>). These features make China an informative case for studying agricultural resilience.</p>
<p>This study contributes in three ways. First, it introduces a machine-learning approach to refine resilience index construction, offering a novel methodological perspective for measurement and evaluation. Second, by leveraging the interpretability of XGBoost and SHAP, it moves beyond the linear assumptions of conventional econometrics and shifts resilience assessment from simple measurement toward mechanism-oriented diagnosis, revealing nonlinear relationships and marginal contributions of indicators. Third, it documents the spatiotemporal evolution of the resilience of China&#x2019;s agricultural industry through three core capacities and uncovers the deeper logic underlying resilience dynamics.</p>
<p>The remainder of the paper is organized as follows. Section 2 reviews the literature on agricultural resilience and presents the analytical framework. Section 3 describes the data, models, and methods, and reports the measurement and spatiotemporal patterns of the resilience index. Section 4 applies the explainable machine-learning framework to identify nonlinear relationships and driving mechanisms. Section 5 conducts robustness checks. Section 6 concludes and discusses policy implications.</p>
</sec>
<sec id="sec2">
<label>2</label>
<title>Literature review</title>
<sec id="sec3">
<label>2.1</label>
<title>Research trajectory of agricultural resilience</title>
<p>Agriculture has long been regarded as a high-risk sector, and early studies attributed vulnerability to seasonal climate variability, pest and disease outbreaks, and price uncertainty (<xref ref-type="bibr" rid="ref26">Ifejika Speranza, 2013</xref>). Over time, interacting risks have exposed agricultural systems to multiple shocks, including extreme weather, supply-chain reconfiguration, and institutional change (<xref ref-type="bibr" rid="ref4">Berardi et al., 2011</xref>; <xref ref-type="bibr" rid="ref20">Gasc&#x00F3;n and Mamani, 2022</xref>; <xref ref-type="bibr" rid="ref49">Sundstrom et al., 2023</xref>). Disruptions to global food supply chains during the COVID-19 pandemic highlighted a critical point: conventional risk-resistance frameworks are often insufficient to explain collapse and delayed recovery under successive shocks. Agriculture should not be viewed as a passive recipient of risk; rather, it is a dynamic system with capacities for adaptation, reorganization, and transformation (<xref ref-type="bibr" rid="ref72">Zampieri et al., 2020</xref>; <xref ref-type="bibr" rid="ref46">Quandt, 2023</xref>). Accordingly, resilience assessment should incorporate resistance capacity, adaptation capacity, and innovation capacity (<xref ref-type="bibr" rid="ref73">Zeng et al., 2025</xref>), which are discussed in detail in Section 3.</p>
<p>Consequently, maintaining stability, facilitating recovery, and enabling adaptation under uncertainty has become a central agenda in resilience research (<xref ref-type="bibr" rid="ref50">Sundstrom et al., 2025</xref>). The literature can be broadly grouped into two strands. The first emphasizes deepening vulnerability driven by external shocks, focusing primarily on climatic hazards such as droughts and floods that frequently reduce yields and generate economic losses (<xref ref-type="bibr" rid="ref8">Carter et al., 2018</xref>). The magnitude of these impacts depends on the resources and technologies that agricultural systems can mobilize in response to emerging risks (<xref ref-type="bibr" rid="ref57">Ward, 2022</xref>; <xref ref-type="bibr" rid="ref14">Das et al., 2025</xref>). The second strand highlights resilience deficits arising from internal resource or structural constraints&#x2014;for example, population pressure, limited land resources, fragmented sectoral organization, and pronounced regional heterogeneity in China (<xref ref-type="bibr" rid="ref5">Bizikova et al., 2019</xref>; <xref ref-type="bibr" rid="ref34">Li and He, 2025</xref>). While documenting China&#x2019;s vulnerabilities, existing studies also underscore potential pathways to strengthen resilience, including technological innovation and agricultural digitalization, infrastructure investment, subsidy and disaster insurance programs, and industrial restructuring (<xref ref-type="bibr" rid="ref38">Luo et al., 2024</xref>; <xref ref-type="bibr" rid="ref74">Zhang et al., 2025</xref>; <xref ref-type="bibr" rid="ref16">Dong et al., 2025</xref>).</p>
</sec>
<sec id="sec4">
<label>2.2</label>
<title>Assessment of mainstream measurement approaches</title>
<p>Quantifying agricultural industry resilience is a prerequisite for uncovering its underlying mechanisms. Three approaches dominate the literature: the core-variable approach, composite index construction, and systemic risk methods. First, the core-variable approach follows the tradition of <xref ref-type="bibr" rid="ref9003">Rose (2007)</xref> and <xref ref-type="bibr" rid="ref9001">Martin (2012)</xref> by tracking the relative deviation of key variables that are highly sensitive to shocks before and after events. While straightforward and conducive to cross-country and intertemporal comparisons, it oversimplifies system complexity and may fail to capture overall elasticity under complex economic fundamentals (<xref ref-type="bibr" rid="ref3">Belhadi et al., 2024</xref>). Second, composite index methods are widely used. They integrate multidimensional sub-capacities into a unified framework via entropy&#x2013;TOPSIS, principal component analysis, or factor analysis to provide static measurement and cross-sectional comparisons (<xref ref-type="bibr" rid="ref59">Xiao et al., 2020</xref>; <xref ref-type="bibr" rid="ref61">Xie et al., 2024</xref>; <xref ref-type="bibr" rid="ref53">Wang et al., 2025</xref>). Although useful for synthesizing key macro variables and offering a systematic perspective (<xref ref-type="bibr" rid="ref6">Bolson et al., 2022</xref>), such methods often overlook nonlinear responses of micro-level agents (e.g., households and firms) near thresholds (<xref ref-type="bibr" rid="ref24">Huang et al., 2023</xref>). Third, systemic risk methods employ impulse-response analysis and complex networks to characterize contagion intensity, duration, and cascading pathways (<xref ref-type="bibr" rid="ref77">Zhou et al., 2020</xref>; <xref ref-type="bibr" rid="ref10">Chen Y. et al., 2025</xref>). Overall, existing measurement frameworks remain relatively narrow and often cannot identify which indicators matter most or how indicators mechanistically relate to resilience, leaving apparent paradoxes (e.g., &#x201C;high index&#x2013;low recovery&#x201D; or &#x201C;high risk&#x2013;high innovation&#x201D;) insufficiently explained.</p>
</sec>
<sec id="sec5">
<label>2.3</label>
<title>Machine learning applications in resilience research</title>
<p>The rise of big data and artificial intelligence has accelerated the use of algorithms such as random forests, backpropagation neural networks, and support vector machines (SVM) in resilience research (<xref ref-type="bibr" rid="ref52">Tang et al., 2025</xref>). Compared with traditional approaches, these tools can identify latent patterns in high-dimensional data with complex nonlinearities and interaction effects without imposing <italic>a priori</italic> functional forms (<xref ref-type="bibr" rid="ref44">Peters et al., 2014</xref>; <xref ref-type="bibr" rid="ref55">Wang et al., 2020</xref>). They have achieved notable progress in ecological applications (e.g., forests and wetlands) and urban resilience assessment (<xref ref-type="bibr" rid="ref58">Wu et al., 2025</xref>; <xref ref-type="bibr" rid="ref67">Yin et al., 2025</xref>). Building on this, XGBoost improves predictive performance through iterative residual learning and regularization, while mitigating overfitting, and has been shown to be particularly suitable for agricultural contexts characterized by &#x201C;small samples and high-dimensional features&#x201D; (<xref ref-type="bibr" rid="ref9002">Alam et al., 2025</xref>). Nonetheless, the black-box nature of many machine-learning models has limited researchers&#x2019; ability to interpret internal mechanisms (<xref ref-type="bibr" rid="ref30">Kim and Kim, 2022</xref>). The integration of SHAP with machine-learning models addresses this challenge by combining predictive accuracy with process transparency (<xref ref-type="bibr" rid="ref37">Lundberg and Lee, 2017</xref>). The resulting framework can identify key thresholds and quantify heterogeneous responses across regions and agents, providing an interpretable evidence base for targeted interventions. Although this approach has been applied to crop yield prediction and risk-factor diagnostics in agriculture (<xref ref-type="bibr" rid="ref39">Martin et al., 2024</xref>), it has not yet been systematically extended to agricultural resilience, leaving substantial room for methodological and empirical advancement.</p>
</sec>
<sec id="sec6">
<label>2.4</label>
<title>Identification of research gaps</title>
<p>Despite significant advancements in defining and measuring agricultural resilience, two critical issues remain largely overlooked in the literature. First, existing evaluation frameworks are often predicated on linear assumptions, utilizing mainstream measurement methods such as entropy-weighting to measure and rank resilience (<xref ref-type="bibr" rid="ref59">Xiao et al., 2020</xref>; <xref ref-type="bibr" rid="ref61">Xie et al., 2024</xref>; <xref ref-type="bibr" rid="ref53">Wang et al., 2025</xref>). However, simple linear weighting approaches face substantial challenges in accurately reflecting high-dimensional and structurally complex resilience data. Second, regarding the identification of driving mechanisms, existing literature frequently relies on pre-specifying mechanism variables for verification and interpretation (<xref ref-type="bibr" rid="ref38">Luo et al., 2024</xref>; <xref ref-type="bibr" rid="ref74">Zhang et al., 2025</xref>; <xref ref-type="bibr" rid="ref16">Dong et al., 2025</xref>). There is a notable lack of tools capable of automatically traversing feature importance and discovering latent mechanisms within the data.</p>
<p>Consequently, this study aims to address the following research gaps. First, to construct a measurement framework capable of handling high-dimensional, non-linear data without sacrificing accuracy, applied to the estimation of complex and diverse agricultural resilience data across China&#x2019;s 31 provinces. Second, to reveal the non-linear relationships and threshold effects of key driving factors, thereby fully explaining how these factors influence variations in agricultural resilience. Third, to comprehensively and systematically assess the changes in resilience across different geographical regions in China over a long period, identifying regional imbalances and dynamic trends.</p>
<p>In summary, this study constructs a comprehensive analytical framework integrating XGBoost and SHAP methods. This framework optimizes the measurement of high-dimensional structured data while simultaneously elucidating the non-linear relationships and threshold effects between resilience and its driving mechanisms, thereby providing a more accurate measurement standard and a deeper, mechanism-oriented explanation for the disaster resistance capability of China&#x2019;s agricultural industry.</p>
</sec>
<sec id="sec7">
<label>2.5</label>
<title>Overall analytical framework</title>
<p><xref ref-type="fig" rid="fig1">Figure 1</xref> summarizes the research procedure. First, we preprocess and validate the data, establish a three-capacity indicator system, and conduct outlier treatment, Pearson correlation tests, and dataset partitioning. Second, we measure the resilience index using a combined &#x201C;entropy-weighting and coefficient of variation&#x201D; method and examine its spatiotemporal evolution. Third, we feed high-dimensional structured data into multiple machine-learning models, select the best-performing XGBoost specification, and refine the resilience index accordingly. Finally, we apply SHAP to identify key drivers and nonlinear relationships, thereby providing a mechanism-based interpretation of the observed spatiotemporal patterns.</p>
<fig position="float" id="fig1">
<label>Figure 1</label>
<caption>
<p>Article framework structure and method flowchart.</p>
</caption>
<graphic xlink:href="fsufs-10-1767684-g001.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">The flowchart illustrates the measurement, optimization and analysis process of RCAI, involving three main steps. Step 1: Use the entropy weight and coefficient of variation method to measure RCAI and draw the temporal and spatial evolution trend. Step 2: Select and validate the superiority of the XGBoost model in fitting the RCAI dataset, and optimize the RCAI index. Step 3: Use SHAP to explore the nonlinear relationship between RCAI and driving factors. Data processing includes constructing the index system, outlier detection, dataset division, and correlation heat map.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec id="sec8">
<label>3</label>
<title>Model method and resilience measurement</title>
<sec id="sec9">
<label>3.1</label>
<title>Model and method introduction</title>
<sec id="sec10">
<label>3.1.1</label>
<title>Machine learning model and evaluation basis</title>
<p>Among machine learning models, XGBoost model has the characteristics of fast prediction speed and high prediction accuracy, and offers distinct advantages in addressing structural and high-dimensional data problems. It is well-suited for addressing the research questions regarding RCAI and index system in this paper, so it is used as the main model of this study. XGBoost is an efficient gradient boosting tree algorithm that integrates gradient boosting with regularization techniques to enhance predictive performance (<xref ref-type="bibr" rid="ref11">Chen T. et al., 2025</xref>). XGBoost constructs a strong predictive model by combining multiple weak learners (decision trees). It calculates both the gradient and the second derivative of the loss function to determine the weight of each decision tree. And it also introduce a regularization term to suppress overfitting and improve generalization (<xref ref-type="bibr" rid="ref32">Lee et al., 2023</xref>). The optimal model is obtained by minimizing the following objective function (<xref ref-type="disp-formula" rid="EQ1">Equation 1</xref>):</p>
<disp-formula id="EQ1">
<mml:math id="M1">
<mml:mi mathvariant="italic">Obj</mml:mi>
<mml:mo stretchy="true">(</mml:mo>
<mml:mi>&#x03B8;</mml:mi>
<mml:mo stretchy="true">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:munderover>
<mml:mo movablelimits="false">&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>M</mml:mi>
</mml:munderover>
<mml:mi>l</mml:mi>
<mml:mo stretchy="true">(</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mover accent="true">
<mml:mi>y</mml:mi>
<mml:mo stretchy="true">&#x0302;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo stretchy="true">)</mml:mo>
<mml:mo>+</mml:mo>
<mml:munderover>
<mml:mo movablelimits="false">&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>t</mml:mi>
</mml:munderover>
<mml:mi>&#x03A9;</mml:mi>
<mml:mo stretchy="true">(</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:mo stretchy="true">)</mml:mo>
</mml:math>
<label>(1)</label>
</disp-formula>
<p>where <italic>M</italic> denotes the number of samples, <inline-formula>
<mml:math id="M2">
<mml:mi>l</mml:mi>
<mml:mo stretchy="true">(</mml:mo>
<mml:mo>&#x22C5;</mml:mo>
<mml:mo stretchy="true">)</mml:mo>
</mml:math>
</inline-formula> represents the loss between predicted and actual values, <italic>t</italic> denotes the number of trees, <inline-formula>
<mml:math id="M3">
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:math>
</inline-formula> denotes the k-th regression tree, and <inline-formula>
<mml:math id="M4">
<mml:mi>&#x03A9;</mml:mi>
<mml:mo stretchy="true">(</mml:mo>
<mml:mo>&#x22C5;</mml:mo>
<mml:mo stretchy="true">)</mml:mo>
</mml:math>
</inline-formula> represents the regularization term that controls model complexity and prevents overfitting.</p>
</sec>
<sec id="sec11">
<label>3.1.2</label>
<title>Evaluation of model performance and efficiency</title>
<p>Model evaluation: The performance and efficiency of the models were assessed using the coefficient of determination (<italic>R</italic><sup>2</sup>), root mean square error (RMSE), and mean absolute error (MAE). <italic>R</italic><sup>2</sup> measures the goodness of fit, generally ranging between [0, 1], with values closer to 1 indicating better fit (<xref ref-type="bibr" rid="ref56">Wang et al., 2023</xref>). RMSE and MAE capture prediction errors, with lower values reflecting higher predictive accuracy (<xref ref-type="bibr" rid="ref70">Yuan et al., 2024</xref>). The calculation of the evaluation indicators is as shown in (<xref ref-type="disp-formula" rid="EQ2">Equations 2</xref>&#x2013;<xref ref-type="disp-formula" rid="EQ4">4</xref>).</p>
<disp-formula id="EQ2">
<mml:math id="M5">
<mml:msup>
<mml:mi>R</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:munderover>
<mml:mo movablelimits="false">&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="true">(</mml:mo>
<mml:msub>
<mml:mover accent="true">
<mml:mi>y</mml:mi>
<mml:mo stretchy="true">&#x0302;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:mi>y</mml:mi>
<mml:mo stretchy="true">&#x00AF;</mml:mo>
</mml:mover>
<mml:mo stretchy="true">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:munderover>
<mml:mo movablelimits="false">&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="true">(</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:mi>y</mml:mi>
<mml:mo stretchy="true">&#x00AF;</mml:mo>
</mml:mover>
<mml:mo stretchy="true">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="EQ3">
<mml:math id="M6">
<mml:mtext mathvariant="italic">RMSE</mml:mtext>
<mml:mo>=</mml:mo>
<mml:msqrt>
<mml:mrow>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mi>n</mml:mi>
</mml:mfrac>
<mml:munderover>
<mml:mo movablelimits="false">&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="true">(</mml:mo>
<mml:mi>y</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mover accent="true">
<mml:mi>y</mml:mi>
<mml:mo stretchy="true">&#x0302;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo stretchy="true">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:msqrt>
</mml:math>
<label>(3)</label>
</disp-formula>
<disp-formula id="EQ4">
<mml:math id="M7">
<mml:mi mathvariant="italic">MAE</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mi>n</mml:mi>
</mml:mfrac>
<mml:munderover>
<mml:mo movablelimits="false">&#x2211;</mml:mo>
<mml:mrow>
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<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
<mml:mo>&#x2223;</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
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</mml:msub>
<mml:mo>&#x2212;</mml:mo>
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</mml:mover>
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<mml:mo>&#x2223;</mml:mo>
</mml:math>
<label>(4)</label>
</disp-formula>
</sec>
<sec id="sec12">
<label>3.1.3</label>
<title>Basic principles of SHAP analysis</title>
<p>Traditional machine learning models have the feature of &#x201C;black box,&#x201D; which is difficult to explain the decision formation process of the model. SHAP, derived from the Shapley value in cooperative game theory, is an algorithm designed to interpret machine learning models (<xref ref-type="bibr" rid="ref37">Lundberg and Lee, 2017</xref>). Its core principle is to quantify the contribution of each feature to model prediction by calculating its marginal contribution when added to the model (<xref ref-type="bibr" rid="ref63">Yang et al., 2021</xref>). Specifically, SHAP evaluates the marginal contributions of a feature across all possible feature orderings and averages them to obtain the SHAP value. In this study, SHAP provides both global and local interpretations of the XGBoost model&#x2019;s decision process. At the global level, the average absolute SHAP values are computed to generate the ranking of feature importance and their overall contributions. At the local level, the sign of the SHAP values is used to identify whether a feature exerts a positive or negative effect on the prediction. The calculation of the SHAP value for feature <italic>i</italic> is shown in (<xref ref-type="disp-formula" rid="EQ5">Equation 5</xref>):</p>
<disp-formula id="EQ5">
<mml:math id="M8">
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<mml:mi>i</mml:mi>
</mml:msub>
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<mml:mo>,</mml:mo>
<mml:mi>x</mml:mi>
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<mml:mo>=</mml:mo>
<mml:munder>
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<mml:mi>S</mml:mi>
<mml:mo>&#x2286;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo>\</mml:mo>
<mml:mo stretchy="true">{</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo stretchy="true">}</mml:mo>
</mml:mrow>
</mml:munder>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x2223;</mml:mo>
<mml:mi>S</mml:mi>
<mml:mo>&#x2223;</mml:mo>
<mml:mo>!</mml:mo>
<mml:mo stretchy="true">(</mml:mo>
<mml:mo>&#x2223;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo>&#x2223;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mo>&#x2223;</mml:mo>
<mml:mi>S</mml:mi>
<mml:mo>&#x2223;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo stretchy="true">)</mml:mo>
<mml:mo>!</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2223;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo>&#x2223;</mml:mo>
<mml:mo>!</mml:mo>
</mml:mrow>
</mml:mfrac>
<mml:mo stretchy="true">[</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mo stretchy="true">(</mml:mo>
<mml:mi>S</mml:mi>
<mml:mo>&#x222A;</mml:mo>
<mml:mo stretchy="true">{</mml:mo>
<mml:mi>i</mml:mi>
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<mml:mo stretchy="true">)</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mo stretchy="true">(</mml:mo>
<mml:mi>S</mml:mi>
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<mml:mo stretchy="true">]</mml:mo>
</mml:math>
<label>(5)</label>
</disp-formula>
<p>Where <italic>F</italic> denotes the set of all features, <italic>S</italic> denotes a subset of F that excludes feature <italic>i</italic>, <inline-formula>
<mml:math id="M9">
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mo stretchy="true">(</mml:mo>
<mml:mi>S</mml:mi>
<mml:mo stretchy="true">)</mml:mo>
</mml:math>
</inline-formula> represents the prediction based on the feature subset <italic>S</italic>, and <inline-formula>
<mml:math id="M10">
<mml:mo stretchy="true">[</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mo stretchy="true">(</mml:mo>
<mml:mi>S</mml:mi>
<mml:mo>&#x222A;</mml:mo>
<mml:mo stretchy="true">{</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo stretchy="true">}</mml:mo>
<mml:mo stretchy="true">)</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mo stretchy="true">(</mml:mo>
<mml:mi>S</mml:mi>
<mml:mo stretchy="true">)</mml:mo>
<mml:mo stretchy="true">]</mml:mo>
</mml:math>
</inline-formula> is the marginal contribution of feature <italic>i</italic>.</p>
</sec>
</sec>
<sec id="sec13">
<label>3.2</label>
<title>Evaluation system and measurement of resilience of China&#x2019;s agricultural industry</title>
<sec id="sec14">
<label>3.2.1</label>
<title>Construction and measurement of the resilience indicator system</title>
<p>Drawing on existing studies (<xref ref-type="bibr" rid="ref34">Li and He, 2025</xref>), this paper develops a comprehensive evaluation framework for agricultural industry resilience in China from three dimensions: resistance, adaptation, and innovation. The indicator system is presented in <xref ref-type="table" rid="tab1">Table 1</xref>. The rationale for selecting indicators in each dimension is as follows:</p>
<table-wrap position="float" id="tab1">
<label>Table 1</label>
<caption>
<p>The RCAI indicator system and calculation weights.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Primary indicator</th>
<th align="left" valign="top">Dimension</th>
<th align="left" valign="top">Factor index</th>
<th align="left" valign="top">Code</th>
<th align="left" valign="top">Unit</th>
<th align="center" valign="top">Property</th>
<th align="left" valign="top">Reference</th>
<th align="left" valign="top">Combination weight</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle" rowspan="17">Resilience of China&#x2019;s Agricultural Industry (RCAI)</td>
<td align="left" valign="middle" rowspan="5">Resistance Capacity</td>
<td align="left" valign="middle">Total grain output/grain sown area</td>
<td align="left" valign="middle">GOGA</td>
<td align="left" valign="middle">%</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref29">Jing et al. (2024)</xref>
</td>
<td align="char" valign="middle" char=".">0.0646</td>
</tr>
<tr>
<td align="left" valign="middle">Regional Agricultural GDP/Regional Total GDP</td>
<td align="left" valign="middle">RATG</td>
<td align="left" valign="middle">%</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref54">Wang et al. (2024)</xref>; <xref ref-type="bibr" rid="ref11">Chen T. et al. (2025)</xref></td>
<td align="char" valign="middle" char=".">0.0393</td>
</tr>
<tr>
<td align="left" valign="middle">Regional Agricultural Labor Force/Total Regional Labor Force</td>
<td align="left" valign="middle">RATF</td>
<td align="left" valign="middle">%</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref77">Zhou et al. (2020)</xref>; <xref ref-type="bibr" rid="ref34">Li and He (2025)</xref></td>
<td align="char" valign="middle" char=".">0.0258</td>
</tr>
<tr>
<td align="left" valign="middle">Area of Crops Seriously Damaged/Area of Crops Affected by Disasters</td>
<td align="left" valign="middle">ACSD</td>
<td align="left" valign="middle">%</td>
<td align="center" valign="middle">&#x2212;</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref12">Cheng et al. (2024)</xref>
</td>
<td align="char" valign="middle" char=".">0.0288</td>
</tr>
<tr>
<td align="left" valign="middle">Effective Irrigated Farmland Area/Total Sown Area</td>
<td align="left" valign="middle">EIFA</td>
<td align="left" valign="middle">%</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref31">Lankford et al. (2023)</xref>
</td>
<td align="char" valign="middle" char=".">0.0425</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="6">Adaptation Capacity</td>
<td align="left" valign="middle"><italic>Per Capita</italic> Net Income of Rural Residents</td>
<td align="left" valign="middle">PCIR</td>
<td align="left" valign="middle">CNY per person</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref34">Li and He (2025)</xref>
</td>
<td align="char" valign="middle" char=".">0.0698</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>Per Capita</italic> Consumption Expenditure of Rural Residents</td>
<td align="left" valign="middle">PCCE</td>
<td align="left" valign="middle">CNY per person</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref34">Li and He (2025)</xref>
</td>
<td align="char" valign="middle" char=".">0.0703</td>
</tr>
<tr>
<td align="left" valign="middle">Total Agricultural Machinery Power</td>
<td align="left" valign="middle">TAMP</td>
<td align="left" valign="middle">10 thousand kilowatts</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref18">Fang et al. (2024)</xref>
</td>
<td align="char" valign="middle" char=".">0.0819</td>
</tr>
<tr>
<td align="left" valign="middle">Fertilizer Application Amount</td>
<td align="left" valign="middle">FAA</td>
<td align="left" valign="top">Tons</td>
<td align="center" valign="middle">&#x2212;</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref71">Zahm et al. (2008)</xref>; <xref ref-type="bibr" rid="ref7">Bux et al. (2024)</xref></td>
<td align="char" valign="middle" char=".">0.0138</td>
</tr>
<tr>
<td align="left" valign="middle">Pesticide Usage</td>
<td align="left" valign="middle">PU</td>
<td align="left" valign="top">Tons</td>
<td align="center" valign="middle">&#x2212;</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref75">Zhang et al. (2021)</xref>
</td>
<td align="char" valign="middle" char=".">0.0197</td>
</tr>
<tr>
<td align="left" valign="middle">Agricultural Plastic Film Usage</td>
<td align="left" valign="middle">APFU</td>
<td align="left" valign="top">Tons</td>
<td align="center" valign="middle">&#x2212;</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref75">Zhang et al. (2021)</xref>
</td>
<td align="char" valign="middle" char=".">0.0125</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="6">Innovation Capacity</td>
<td align="left" valign="middle">Investment in Agricultural Fixed Assets</td>
<td align="left" valign="middle">IAFA</td>
<td align="left" valign="middle">100 million CNY</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref51">Szymanska and Dziwulski (2021)</xref>; <xref ref-type="bibr" rid="ref76">Zhou et al. (2025)</xref></td>
<td align="char" valign="middle" char=".">0.1789</td>
</tr>
<tr>
<td align="left" valign="middle">Disaster Relief Subsidies</td>
<td align="left" valign="middle">DRS</td>
<td align="left" valign="middle">10 thousand CNY</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top">
<xref ref-type="bibr" rid="ref17">dos Santos et al. (2024)</xref>
</td>
<td align="char" valign="middle" char=".">0.2156</td>
</tr>
<tr>
<td align="left" valign="middle">Average Years of Education</td>
<td align="left" valign="middle">AYE</td>
<td align="left" valign="middle">/</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref39">Martin et al. (2024)</xref>; <xref ref-type="bibr" rid="ref64">Yang et al. (2025)</xref></td>
<td align="char" valign="middle" char=".">0.0091</td>
</tr>
<tr>
<td align="left" valign="middle">Total Postal and Telecommunication Services/Regional GDP</td>
<td align="left" valign="middle">PTRG</td>
<td align="left" valign="middle">%</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref51">Szymanska and Dziwulski (2021)</xref>; <xref ref-type="bibr" rid="ref16">Dong et al. (2025)</xref></td>
<td align="char" valign="middle" char=".">0.0588</td>
</tr>
<tr>
<td align="left" valign="middle">R&#x0026;D Internal Expenditure/Regional GDP</td>
<td align="left" valign="middle">RDRD</td>
<td align="left" valign="middle">%</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref39">Martin et al. (2024)</xref>; <xref ref-type="bibr" rid="ref64">Yang et al. (2025)</xref></td>
<td align="char" valign="middle" char=".">0.0598</td>
</tr>
<tr>
<td align="left" valign="middle">Transportation Infrastructure Level</td>
<td align="left" valign="middle">TIL</td>
<td align="left" valign="middle">/</td>
<td align="center" valign="middle">+</td>
<td align="left" valign="top"><xref ref-type="bibr" rid="ref51">Szymanska and Dziwulski (2021)</xref>; <xref ref-type="bibr" rid="ref16">Dong et al. (2025)</xref></td>
<td align="char" valign="middle" char=".">0.0088</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>Average years of education&#x202F;=&#x202F;(number of people with primary school education &#x002A;6&#x202F;+&#x202F;number of people with junior high school education &#x002A;9&#x202F;+&#x202F;number of people with senior high school and technical secondary school education &#x002A;12&#x202F;+&#x202F;number of people with junior college and bachelor degree or above &#x002A;16)/total population aged 6 or above; Transportation Infrastructure Level&#x202F;=&#x202F;Ln (highway mileage).</p>
</table-wrap-foot>
</table-wrap>
<p>Resistance capacity. For agricultural systems, resistance capacity is defined as the ability to maintain existing functions and quickly return to normal levels after external disturbances (<xref ref-type="bibr" rid="ref41">Meuwissen et al., 2019</xref>). The collapse of agricultural systems is often accompanied by severe losses in production, farmer livelihoods, and food security; hence, previous studies have frequently linked resilience to production targets (<xref ref-type="bibr" rid="ref50">Sundstrom et al., 2025</xref>). At the production level, Land productivity and the proportion of effective irrigated area are selected to reflect the system&#x2019;s physical buffer against shocks. High land productivity ensures food security under stress (<xref ref-type="bibr" rid="ref29">Jing et al., 2024</xref>), while irrigation facilities significantly mitigate yield volatility caused by droughts (<xref ref-type="bibr" rid="ref31">Lankford et al., 2023</xref>). At the economic and social stability level, The ratio of agricultural value-added to regional GDP serves as a macro-economic stabilizer. A strong agricultural economic base effectively buffers regional economic fluctuations and ensures the continuity of supply chains (<xref ref-type="bibr" rid="ref54">Wang et al., 2024</xref>; <xref ref-type="bibr" rid="ref11">Chen T. et al., 2025</xref>). The share of agricultural employment is adopted as a proxy for social resistance. In China, the agricultural sector functions as a vital &#x201C;employment reservoir&#x201D; during crises. A stable workforce prevents social structural collapse and ensures rapid post-disaster recovery efficiency (<xref ref-type="bibr" rid="ref77">Zhou et al., 2020</xref>; <xref ref-type="bibr" rid="ref34">Li and He, 2025</xref>). At the disaster Response level, the extent of damage is captured by the ratio of seriously damaged crop area, which inversely reflects the system&#x2019;s vulnerability to climate extremes (<xref ref-type="bibr" rid="ref12">Cheng et al., 2024</xref>).</p>
<p>Adaptation capacity. This dimension emphasizes the ability of agricultural subjects to adjust resource allocation and production behaviors in response to changing conditions. At the livelihood capital level, Per capita net income and consumption expenditure of rural residents represent financial adaptability. Higher household liquidity enables farmers to finance diverse livelihood strategies and adopt risk-mitigation measures (<xref ref-type="bibr" rid="ref34">Li and He, 2025</xref>). At the production flexibility level, total agricultural machinery power is used to measure technological adaptability. Mechanization enhances the timeliness of farming operations, allowing producers to flexibly adjust planting and harvesting windows in response to climate variability (<xref ref-type="bibr" rid="ref18">Fang et al., 2024</xref>). At the ecological sustainability level, the intensity of chemical inputs&#x2014;fertilizers, pesticides, and plastic film&#x2014;reflects the sustainability of adaptation practices. Excessive reliance on these inputs degrades soil health and weakens the long-term adaptive potential of the agroecosystem (<xref ref-type="bibr" rid="ref71">Zahm et al., 2008</xref>; <xref ref-type="bibr" rid="ref75">Zhang et al., 2021</xref>; <xref ref-type="bibr" rid="ref7">Bux et al., 2024</xref>).</p>
<p>Innovation capacity. This dimension highlights the potential for structural change and long-term innovation in agriculture (<xref ref-type="bibr" rid="ref64">Yang et al., 2025</xref>). In terms of financial support for innovation, Investment in agricultural fixed assets acts as the primary driver for upgrading production conditions. Sustained capital accumulation is essential for crossing resilience thresholds and fostering high-quality development (<xref ref-type="bibr" rid="ref51">Szymanska and Dziwulski, 2021</xref>; <xref ref-type="bibr" rid="ref76">Zhou et al., 2025</xref>). Disaster relief subsidies represent institutional innovation in risk transfer, providing a financial safety net that encourages producers to engage in higher-risk, higher-return agricultural activities (<xref ref-type="bibr" rid="ref17">dos Santos et al., 2024</xref>). In terms of the construction level of key areas, the level of transportation infrastructure and postal/telecom services reflects the system&#x2019;s connectivity. Efficient networks facilitate the flow of technology, information, and market resources, which are prerequisites for innovative decision-making (<xref ref-type="bibr" rid="ref51">Szymanska and Dziwulski, 2021</xref>; <xref ref-type="bibr" rid="ref16">Dong et al., 2025</xref>). In terms of the potential of technological innovation, R&#x0026;D internal expenditure and average years of education measure the intellectual and financial support for innovation. These &#x201C;slow variables&#x201D; determine the system&#x2019;s long-term capacity to develop stress-tolerant varieties and adopt smart agricultural technologies (<xref ref-type="bibr" rid="ref39">Martin et al., 2024</xref>; <xref ref-type="bibr" rid="ref64">Yang et al., 2025</xref>).</p>
</sec>
<sec id="sec15">
<label>3.2.2</label>
<title>Data sources and preprocessing</title>
<p>This study uses panel data for 31 provincial-level regions in China (provinces, autonomous regions, and municipalities) from 2000 to 2022. Due to data availability and completeness, the statistics exclude Hong Kong, Macao, and Taiwan, and the same convention applies throughout the paper. The selection of the research period from 2000 to 2022 is grounded in both data availability and the analytical need for a long-term perspective. As of the current analysis, 2022 represents the most recent year for which complete and verified official statistics are available across all 31 provincial-level regions. Furthermore, this 23-year span covers critical phases of China&#x2019;s agricultural transformation, enabling the study to capture the full trajectory of resilience evolution&#x2014;from early-stage fluctuations to recent stability&#x2014;and ensuring that the machine learning model has sufficient historical depth to identify robust structural regularities. The data are primarily drawn from the National Bureau of Statistics of China, the China Rural Statistical Yearbook, and provincial statistical yearbooks. A small number of missing observations are imputed using linear interpolation to ensure dataset integrity. Prior to index construction, all indicators are directionally aligned (i.e., transformed so that higher values consistently indicate stronger resilience) and standardized using <italic>Z</italic>-scores, thereby addressing differences in indicator orientation and measurement units.</p>
</sec>
<sec id="sec16">
<label>3.2.3</label>
<title>Index construction method</title>
<p>To address the limitations of relying on a single weighting scheme in prior research, we construct the resilience index using a combined weighting approach, integrating the entropy method and the coefficient of variation method to compute RCAI. Specifically, we first estimate weights separately using the entropy method and the coefficient of variation method, and then derive an optimized composite weight to calculate the index. Following this procedure, we obtain the initial target variable used to train the machine-learning models. The key advantage of this approach is that the secondary calibration embedded in the composite weighting reduces potential bias introduced by any single method and yields a more plausible weight structure. The weights for the indicator calculation are shown in <xref ref-type="table" rid="tab1">Table 1</xref>.</p>
</sec>
</sec>
<sec id="sec17">
<label>3.3</label>
<title>Spatiotemporal heterogeneity of the resilience of China&#x2019;s agricultural industry</title>
<sec id="sec18">
<label>3.3.1</label>
<title>Dynamic evolution of RCAI and the three capacity dimensions</title>
<p>Based on the composite weights, we compute three sub-dimensions&#x2014;resistance, adaptation and innovation capacity&#x2014;to examine the extent to which RCAI co-evolves with these capacities. <xref ref-type="fig" rid="fig2">Figure 2</xref> illustrates the interannual trends of RCAI and the three dimensions. Three patterns emerge. First, both RCAI and the three capacities exhibit an overall upward trajectory, indicating a sustained improvement in the resilience level. Second, variations in RCAI are most closely aligned with changes in innovation capacity, with synchronous upswings and downswings observed during periods such as 2007&#x2013;2010 and 2017&#x2013;2021. Third, the three capacities evolve at different rates: resistance capacity remains relatively stable over time; adaptation capacity starts from a relatively low level in 2000 but increases steadily thereafter; and innovation capacity shows the fastest and largest growth.</p>
<fig position="float" id="fig2">
<label>Figure 2</label>
<caption>
<p>Inter-annual trends of the resilience and three-dimensional capacity of China&#x2019;s agricultural industry.</p>
</caption>
<graphic xlink:href="fsufs-10-1767684-g002.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">The line chart shows the evolution trend of resilience index, resistance, adaptation and innovation capacity of China's agricultural industry from 2000 to 2022. The resilience of China's agricultural industry and the capacity of the three dimensions continue to rise, and the resilience and innovation capacity maintain a high correlation.</alt-text>
</graphic>
</fig>
<p>Since RCAI is a composite index jointly determined by three capacity dimensions, an excessive contribution from any single dimension may mask deficiencies in the others and potentially induce a &#x201C;resilience illusion.&#x201D; To mitigate this risk, we decompose resilience into its three constituent capacities and examine them separately. We further visualize the spatial distributions of these capacities using GIS maps (<xref rid="SM1" ref-type="supplementary-material">Supplementary Appendix Figures A1&#x2013;A3</xref>). Indicators within the resistance dimension, such as crop yield and disaster-affected area, are largely lagging measures that reflect realized outcomes after shocks occur. By contrast, adaptation capacity dimension captures contemporaneous responses to risk and is characterized by variables such as mechanization level, rural income and consumption capacity, and the use of fertilizers and pesticides. Both resistance and adaptation capacity exhibit clear upward trends as well as pronounced regional heterogeneity. Provinces along the southeastern coast&#x2014;such as Shandong, Zhejiang, and Fujian&#x2014;as well as major grain-producing regions such as Heilongjiang, show relatively rapid improvements in risk resistance and adaptive capacity. In contrast, northwestern provinces including Gansu and Qinghai improve more slowly, which is closely associated with constraints in infrastructure upgrading and mechanization. In the innovation dimension, indicators such as transport and communication conditions and R&#x0026;D capability are leading measures of risk preparedness. Improvements in this capacity are concentrated in major agricultural and economically advanced provinces, including Heilongjiang, Shandong, and Henan. A higher level of innovation capacity implies stronger potential for resilience upgrading and regime shifts.</p>
</sec>
<sec id="sec19">
<label>3.3.2</label>
<title>Spatiotemporal evolution of RCAI</title>
<p>Building on the three-capacity analysis, we construct GIS maps of RCAI for 2001, 2008, 2015, and 2022 to characterize its spatiotemporal evolution (<xref ref-type="fig" rid="fig2">Figures 2</xref>, <xref ref-type="fig" rid="fig3">3</xref>). Across provinces, RCAI ranges from 0.011 to 0.212. Overall, the resilience of China&#x2019;s agricultural industry exhibits an upward trajectory, albeit with clear interannual differences. During 2001&#x2013;2008, resilience increased slowly and high-resilience areas were spatially fragmented. During 2008&#x2013;2015, resilience growth accelerated and high-resilience regions expanded outward, largely anchored around major grain-producing areas. During 2015&#x2013;2022, resilience strengthened more comprehensively, with high-resilience areas becoming increasingly contiguous.</p>
<p>Furthermore, we interpret the logic linking China&#x2019;s agricultural transformation to the resilience of China&#x2019;s agricultural industry from three perspectives: policy, technology, and structural change. On the policy front, resilience has been strengthened through successive legal and institutional arrangements. The revised Agriculture Law in 2002 explicitly emphasized, for the first time, the need to enhance agriculture&#x2019;s capacity to withstand risks, alongside reinforced investment in agricultural and rural infrastructure. The 2004 Central No. 1 Document proposed the construction of farmland with stable yields under both drought and flood conditions, aiming to secure output and stabilize production. This institutional trajectory was further consolidated by the issuance of the Technical Code for High-Standard Farmland Construction (Trial) in 2011 and the implementation of the Regulations on Agricultural Insurance in 2012, which jointly formalized infrastructure upgrading and risk protection as long-term policy instruments. Since the launch of the Rural Revitalization Strategy in 2017, resilience-oriented agriculture has been increasingly embedded in national priorities, with greater attention paid to the interaction between climate risks and agricultural development.</p>
<p>Technological support has also expanded in a staged and cumulative manner. Before 2005, public investment focused primarily on water-saving irrigation and hydraulic infrastructure. Between 2005 and 2010, China increased support for germplasm innovation and breeding R&#x0026;D, improving both crop yields and stress tolerance. After 2011, efforts accelerated toward the development of intelligent agricultural equipment, raising mechanization and automation levels. Since 2016, the strategic emphasis has shifted toward digital technologies such as big data, fostering a broader transition toward data-driven and digitally enabled agriculture. Together, these technological upgrades have provided intrinsic momentum for the observed improvements in RCAI.</p>
<fig position="float" id="fig3">
<label>Figure 3</label>
<caption>
<p>Analysis of the dynamic evolution of RCAI.</p>
<p>Note: In 2008, due to the Wenchuan earthquake, the cost of natural disaster relief in Sichuan was extremely high, resulting in the overall values being relatively high during this period.</p>
</caption>
<graphic xlink:href="fsufs-10-1767684-g003.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Four-panel data visualization map illustrating changes in regional resilience across provinces in China in 2001, 2008, 2015, and 2022. Maps use a color gradient from brown (high resilience) to light yellow (low resilience). In 2008, one central province displays markedly higher resilience, while in 2022, resilience levels appear more varied across provinces, especially in northeastern and southeastern regions. Insets show China&#x2019;s outlying islands for context.</alt-text>
</graphic>
</fig>
<p>Finally, regional structural change has shaped heterogeneous resilience trajectories. Infrastructure expansion and the renovation of medium- and low-yield farmland have contributed to resilience gains in traditional major grain-producing areas. With advances in technology diffusion and application, refined and efficiency-oriented agricultural development has become an increasingly important lever for resilience breakthroughs in many regions. However, in western China, structural adjustment remains constrained by ecological fragility and climatic limitations, which restrict the feasibility and speed of transformation. As a result, the eastern region generally exhibits faster and more readily achievable transformation than the western frontier provinces, reinforcing the observed east&#x2013;west gradient in the resilience of China&#x2019;s agricultural industry.</p>
</sec>
</sec>
</sec>
<sec id="sec20">
<label>4</label>
<title>Empirical analysis</title>
<p>The preceding analysis of the spatiotemporal evolution of RCAI reveals two issues. First, the RCAI constructed using conventional index methods may be sensitive to extreme observations; in the presence of outliers, measurement bias can arise and may obscure the true contemporaneous patterns in other regions. Second, the spatiotemporal analysis remains largely descriptive and does not sufficiently address the determinants of RCAI dynamics. To overcome these limitations, this section applies a machine-learning framework to refine the RCAI and to further elucidate the mechanisms underlying changes in the resilience of China&#x2019;s agricultural industry.</p>
<sec id="sec21">
<label>4.1</label>
<title>Machine-learning models</title>
<sec id="sec22">
<label>4.1.1</label>
<title>Data preprocessing</title>
<p>The machine-learning dataset contains 714 observations. Following an 8:1:1 split, the full sample is divided into a training set, a validation set, and a test set to facilitate model development and evaluation. We first conduct outlier detection to reduce the influence of extreme values on model fitting. Specifically, we employ an Isolation Forest to characterize the distribution of the dataset and set an anomaly threshold. Observations exceeding the threshold are removed to prevent abnormal data from degrading model performance. The anomaly threshold is set to 0.5375, and 36 observations are excluded accordingly.</p>
</sec>
<sec id="sec23">
<label>4.1.2</label>
<title>Correlation analysis</title>
<p>Before fitting machine-learning models, we assess the association between candidate features and the target variable to understand feature&#x2013;outcome relevance and to inform subsequent modeling. Because the RCAI indicator system is constructed based on prior literature and theoretical considerations, we primarily examine the overall strength of association between each indicator and RCAI, rather than conducting aggressive feature elimination at this stage. We apply Pearson correlation analysis, and the resulting heatmap is reported in <xref ref-type="fig" rid="fig4">Figure 4</xref>. Several variables&#x2014;GOGA (land productivity), PCIR (rural residents&#x2019; income), PCCE (rural residents&#x2019; expenditure), IAFA (agricultural fixed-asset investment), and TIL (transportation infrastructure level)&#x2014;exhibit correlations above 0.5 with RCAI. These variables span the resistance, adaptation, and innovation dimensions, providing additional support for the internal coherence of the indicator system. The results also suggest that higher agricultural fixed-asset investment, stronger rural income and consumption capacity, and higher land productivity are associated with a higher level of the resilience of China&#x2019;s agricultural industry.</p>
<fig position="float" id="fig4">
<label>Figure 4</label>
<caption>
<p>Correlation heatmap of indicator characteristics and RCAI.</p>
</caption>
<graphic xlink:href="fsufs-10-1767684-g004.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">The thermogram demonstrates the degree of correlation between the indicator variables and the RCAI. The values -1 to 1 reflect the degree of correlation, ranging from negative to positive. At the same time, it is equipped with significance markers, &#x002A;&#x002A;&#x002A; means p &#x003C; 0.001, &#x002A;&#x002A; means p &#x003C; 0.01, and &#x002A; means p &#x003C; 0.05.</alt-text>
</graphic>
</fig>
</sec>
<sec id="sec24">
<label>4.1.3</label>
<title>Evaluation of multiple machine-learning models</title>
<p>We benchmark a range of machine-learning algorithms, including Gaussian kernel regression, Decision Tree, Random Forest, GAM, GRNN, LightGBM, LSBoost, and XGBoost. Prior to training, all variables are normalized to improve numerical stability and ensure comparability across features. <xref ref-type="fig" rid="fig5">Figure 5</xref> reports the prediction errors by comparing fitted values with observed RCAI. Among the competing models, XGBoost exhibits the narrowest error band, indicating that its test-set predictions are the closest to the observed values.</p>
<fig position="float" id="fig5">
<label>Figure 5</label>
<caption>
<p>Prediction effects of different machine learning models.</p>
</caption>
<graphic xlink:href="fsufs-10-1767684-g005.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">The violin plot compares the prediction results of GAM, GRNN, LightGBM, LSBoost, XGBoost, GS, TREE and RF. Each model exhibits a range distribution of differences between its predicted and true values. The data are represented by blue dots, where the XGBoost model has a more concentrated distribution of error ranges.</alt-text>
</graphic>
</fig>
<p>We further evaluate model performance using standard metrics, with results reported in <xref ref-type="table" rid="tab2">Table 2</xref>. MAE and RMSE quantify prediction errors, while <italic>R</italic><sup>2</sup> measures goodness of fit. Across the eight models, XGBoost achieves the lowest MSE (<inline-formula>
<mml:math id="M11">
<mml:mn>5.0932</mml:mn>
<mml:mo>&#x00D7;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
</inline-formula>) and RMSE (0.002), together with the highest <italic>R</italic><sup>2</sup> (0.9239), indicating that it demonstrates superior performance compared to the alternatives in both predictive accuracy and explanatory power. Random Forest and GRNN rank second, with <italic>R</italic><sup>2</sup> values of 0.9095 and 0.9007 and RMSE values of 0.0023 and 0.0024, respectively, which are close to those of XGBoost. In contrast, LSBoost performs poorly, with an <italic>R</italic><sup>2</sup> of only 0.5401. Except for LSBoost, all other models yield <italic>R</italic><sup>2</sup> values above 0.8, albeit with slightly larger errors than XGBoost. Taken together, XGBoost is selected for subsequent analysis due to its dual advantage in minimizing prediction errors and maximizing explained variance.</p>
<table-wrap position="float" id="tab2">
<label>Table 2</label>
<caption>
<p>Reference indicators for performance evaluation of machine learning model.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Model</th>
<th align="center" valign="top">MAE</th>
<th align="center" valign="top">MAPE</th>
<th align="center" valign="top">MSE</th>
<th align="center" valign="top">RMSE</th>
<th align="center" valign="top">
<italic>R</italic>
<sup>2</sup>
</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">Gaussian kernel</td>
<td align="char" valign="top" char=".">0.0022</td>
<td align="char" valign="top" char=".">0.1033</td>
<td align="center" valign="top">8.2563&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0028</td>
<td align="char" valign="top" char=".">0.8608</td>
</tr>
<tr>
<td align="left" valign="top">Decision tree</td>
<td align="char" valign="top" char=".">0.0021</td>
<td align="char" valign="top" char=".">0.0925</td>
<td align="center" valign="top">9.2673&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0030</td>
<td align="char" valign="top" char=".">0.8438</td>
</tr>
<tr>
<td align="left" valign="top">Random forest</td>
<td align="char" valign="top" char=".">0.0019</td>
<td align="char" valign="top" char=".">0.0845</td>
<td align="center" valign="top">5.3676&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0023</td>
<td align="char" valign="top" char=".">0.9095</td>
</tr>
<tr>
<td align="left" valign="top">GAM</td>
<td align="char" valign="top" char=".">0.0019</td>
<td align="char" valign="top" char=".">0.0808</td>
<td align="center" valign="top">7.6119&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0027</td>
<td align="char" valign="top" char=".">0.8717</td>
</tr>
<tr>
<td align="left" valign="top">GRNN</td>
<td align="char" valign="top" char=".">0.0015</td>
<td align="char" valign="top" char=".">0.0651</td>
<td align="center" valign="top">5.8909&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0024</td>
<td align="char" valign="top" char=".">0.9007</td>
</tr>
<tr>
<td align="left" valign="top">LightGBM</td>
<td align="char" valign="top" char=".">0.0022</td>
<td align="char" valign="top" char=".">0.1021</td>
<td align="center" valign="top">7.4937&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0027</td>
<td align="char" valign="top" char=".">0.8737</td>
</tr>
<tr>
<td align="left" valign="top">LSBoost</td>
<td align="char" valign="top" char=".">0.0029</td>
<td align="char" valign="top" char=".">0.1270</td>
<td align="center" valign="top">2.7289&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0052</td>
<td align="char" valign="top" char=".">0.5401</td>
</tr>
<tr>
<td align="left" valign="top">XGBoost</td>
<td align="char" valign="top" char=".">0.0018</td>
<td align="char" valign="top" char=".">0.0806</td>
<td align="center" valign="top">5.0932&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;6</sup></td>
<td align="char" valign="top" char=".">0.0022</td>
<td align="char" valign="top" char=".">0.9239</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="sec25">
<label>4.2</label>
<title>XGBoost hyperparameter configuration</title>
<p>The XGBoost model is configured as follows: max_depth&#x202F;=&#x202F;5, learning_rate&#x202F;=&#x202F;0.1, min_child_weight&#x202F;=&#x202F;1, and subsample&#x202F;=&#x202F;0.95, while colsample and num_parallel_tree are kept at their default values of 1. These hyperparameters are chosen to balance model flexibility and generalization. The learning rate controls the step size of parameter updates during boosting; a smaller value typically requires more boosting iterations to achieve comparable performance. Tree depth determines the complexity of each base learner: deeper trees can capture richer nonlinear patterns but require more data and computation and may increase the risk of overfitting. The number of boosting iterations governs overall model complexity; an appropriate number of rounds improves learning capacity without excessive variance.</p>
<p>To examine the model&#x2019;s performance on the full dataset under this configuration, we apply five-fold cross-validation (<xref ref-type="bibr" rid="ref66">Ye et al., 2023</xref>). The sample is split into five subsets; in each fold, four subsets are used for training and the remaining subset is used for testing, repeated five times so that each subset serves as the test fold once. The MAE values across folds are 0.0012, 0.0010, 0.0011, 0.0009, and 0.0011, with an average MAE of 0.0011. The consistently low errors indicate that XGBoost performs well and generalizes favorably in this dataset.</p>
</sec>
<sec id="sec26">
<label>4.3</label>
<title>Refining the RCAI using XGBoost predictions</title>
<p>Based on the trained XGBoost model, we input the resilience indicators for 2000&#x2013;2022 as features to predict RCAI. The rationale for this optimization lies in the generalization capability of machine learning algorithms. Unlike the static calculation of the composite weighting method, XGBoost captures the complex, non-linear mapping relationships between the multidimensional input indicators and the resilience capacity through iterative residual learning. By generating predictions from this trained model, we obtain a &#x201C;re-estimated&#x201D; index that reflects the structural regularities of the agricultural system rather than raw arithmetic aggregations. This process effectively filters out random noise and anomalies inherent in the initial data, ensuring that the index represents the systematic resilience level.</p>
<p>The resulting predictions constitute the refined index for the resilience of China&#x2019;s agricultural industry, as reported in <xref ref-type="table" rid="tab3">Table 3</xref>. Two features are noteworthy. First, the refinement mainly involves local adjustments rather than wholesale changes: the predicted values represent modest numerical corrections, and provincial rankings by resilience remain broadly stable. Second, the refined RCAI effectively mitigates bias induced by extreme values. For instance, in Sichuan in 2008, disaster relief-related variables surged following the Wenchuan earthquake, yielding an abnormally high value of 0.2124 under the original composite-weight method. In contrast, the XGBoost-based prediction is 0.0319&#x2014;still relatively high, but no longer inflated by orders of magnitude relative to other provinces. This demonstrates that the XGBoost-refined RCAI is less sensitive to outliers and provides a more reliable measure when high-dimensional indicators and extreme observations coexist.</p>
<table-wrap position="float" id="tab3">
<label>Table 3</label>
<caption>
<p>China&#x2019;s agricultural industry resilience index optimized based on XGBoost model.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" rowspan="2">Province</th>
<th align="center" valign="top" colspan="4">Entropy weight&#x2014;coefficient of variation</th>
<th align="center" valign="top" colspan="4">XGBoost model prediction</th>
</tr>
<tr>
<th align="center" valign="top">2001</th>
<th align="center" valign="top">2008</th>
<th align="center" valign="top">2015</th>
<th align="center" valign="top">2022</th>
<th align="center" valign="top">2001</th>
<th align="center" valign="top">2008</th>
<th align="center" valign="top">2015</th>
<th align="center" valign="top">2022</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle">Anhui</td>
<td align="char" valign="middle" char=".">0.0153</td>
<td align="char" valign="bottom" char=".">0.0216</td>
<td align="char" valign="bottom" char=".">0.0257</td>
<td align="char" valign="middle" char=".">0.0315</td>
<td align="char" valign="middle" char=".">0.0150</td>
<td align="char" valign="bottom" char=".">0.0214</td>
<td align="char" valign="bottom" char=".">0.0255</td>
<td align="char" valign="middle" char=".">0.0313</td>
</tr>
<tr>
<td align="left" valign="middle">Beijing</td>
<td align="char" valign="middle" char=".">0.0191</td>
<td align="char" valign="bottom" char=".">0.0246</td>
<td align="char" valign="bottom" char=".">0.0323</td>
<td align="char" valign="middle" char=".">0.0403</td>
<td align="char" valign="middle" char=".">0.0192</td>
<td align="char" valign="bottom" char=".">0.0236</td>
<td align="char" valign="bottom" char=".">0.0318</td>
<td align="char" valign="middle" char=".">0.0312</td>
</tr>
<tr>
<td align="left" valign="middle">Fujian</td>
<td align="char" valign="middle" char=".">0.0135</td>
<td align="char" valign="bottom" char=".">0.0176</td>
<td align="char" valign="bottom" char=".">0.0243</td>
<td align="char" valign="middle" char=".">0.0322</td>
<td align="char" valign="middle" char=".">0.0141</td>
<td align="char" valign="bottom" char=".">0.0181</td>
<td align="char" valign="bottom" char=".">0.0244</td>
<td align="char" valign="middle" char=".">0.0318</td>
</tr>
<tr>
<td align="left" valign="middle">Gansu</td>
<td align="char" valign="middle" char=".">0.0131</td>
<td align="char" valign="bottom" char=".">0.0224</td>
<td align="char" valign="bottom" char=".">0.0227</td>
<td align="char" valign="middle" char=".">0.0259</td>
<td align="char" valign="middle" char=".">0.0135</td>
<td align="char" valign="bottom" char=".">0.0221</td>
<td align="char" valign="bottom" char=".">0.0221</td>
<td align="char" valign="middle" char=".">0.0262</td>
</tr>
<tr>
<td align="left" valign="middle">Guangdong</td>
<td align="char" valign="middle" char=".">0.0149</td>
<td align="char" valign="bottom" char=".">0.0207</td>
<td align="char" valign="bottom" char=".">0.0268</td>
<td align="char" valign="middle" char=".">0.0316</td>
<td align="char" valign="middle" char=".">0.0153</td>
<td align="char" valign="bottom" char=".">0.0206</td>
<td align="char" valign="bottom" char=".">0.0265</td>
<td align="char" valign="middle" char=".">0.0307</td>
</tr>
<tr>
<td align="left" valign="middle">Guangxi</td>
<td align="char" valign="middle" char=".">0.0140</td>
<td align="char" valign="bottom" char=".">0.0203</td>
<td align="char" valign="bottom" char=".">0.0241</td>
<td align="char" valign="middle" char=".">0.0338</td>
<td align="char" valign="middle" char=".">0.0137</td>
<td align="char" valign="bottom" char=".">0.0202</td>
<td align="char" valign="bottom" char=".">0.0237</td>
<td align="char" valign="middle" char=".">0.0339</td>
</tr>
<tr>
<td align="left" valign="middle">Guizhou</td>
<td align="char" valign="middle" char=".">0.0129</td>
<td align="char" valign="bottom" char=".">0.0176</td>
<td align="char" valign="bottom" char=".">0.0227</td>
<td align="char" valign="middle" char=".">0.0305</td>
<td align="char" valign="middle" char=".">0.0134</td>
<td align="char" valign="bottom" char=".">0.0180</td>
<td align="char" valign="bottom" char=".">0.0227</td>
<td align="char" valign="middle" char=".">0.0306</td>
</tr>
<tr>
<td align="left" valign="middle">Hainan</td>
<td align="char" valign="middle" char=".">0.0147</td>
<td align="char" valign="bottom" char=".">0.0184</td>
<td align="char" valign="bottom" char=".">0.0210</td>
<td align="char" valign="middle" char=".">0.0337</td>
<td align="char" valign="middle" char=".">0.0146</td>
<td align="char" valign="bottom" char=".">0.0180</td>
<td align="char" valign="bottom" char=".">0.0210</td>
<td align="char" valign="middle" char=".">0.0320</td>
</tr>
<tr>
<td align="left" valign="middle">Hebei</td>
<td align="char" valign="middle" char=".">0.0189</td>
<td align="char" valign="bottom" char=".">0.0255</td>
<td align="char" valign="bottom" char=".">0.0319</td>
<td align="char" valign="middle" char=".">0.0350</td>
<td align="char" valign="middle" char=".">0.0181</td>
<td align="char" valign="bottom" char=".">0.0244</td>
<td align="char" valign="bottom" char=".">0.0308</td>
<td align="char" valign="middle" char=".">0.0342</td>
</tr>
<tr>
<td align="left" valign="middle">Henan</td>
<td align="char" valign="middle" char=".">0.0182</td>
<td align="char" valign="bottom" char=".">0.0252</td>
<td align="char" valign="bottom" char=".">0.0430</td>
<td align="char" valign="middle" char=".">0.0609</td>
<td align="char" valign="middle" char=".">0.0185</td>
<td align="char" valign="bottom" char=".">0.0260</td>
<td align="char" valign="bottom" char=".">0.0429</td>
<td align="char" valign="middle" char=".">0.0566</td>
</tr>
<tr>
<td align="left" valign="middle">Heilongjiang</td>
<td align="char" valign="middle" char=".">0.0124</td>
<td align="char" valign="bottom" char=".">0.0194</td>
<td align="char" valign="bottom" char=".">0.0364</td>
<td align="char" valign="middle" char=".">0.1039</td>
<td align="char" valign="middle" char=".">0.0131</td>
<td align="char" valign="bottom" char=".">0.0189</td>
<td align="char" valign="bottom" char=".">0.0368</td>
<td align="char" valign="middle" char=".">0.0594</td>
</tr>
<tr>
<td align="left" valign="middle">Hubei</td>
<td align="char" valign="middle" char=".">0.0141</td>
<td align="char" valign="bottom" char=".">0.0213</td>
<td align="char" valign="bottom" char=".">0.0247</td>
<td align="char" valign="middle" char=".">0.0296</td>
<td align="char" valign="middle" char=".">0.0153</td>
<td align="char" valign="bottom" char=".">0.0214</td>
<td align="char" valign="bottom" char=".">0.0248</td>
<td align="char" valign="middle" char=".">0.0296</td>
</tr>
<tr>
<td align="left" valign="middle">Hunan</td>
<td align="char" valign="middle" char=".">0.0150</td>
<td align="char" valign="bottom" char=".">0.0224</td>
<td align="char" valign="bottom" char=".">0.0265</td>
<td align="char" valign="middle" char=".">0.0321</td>
<td align="char" valign="middle" char=".">0.0149</td>
<td align="char" valign="bottom" char=".">0.0221</td>
<td align="char" valign="bottom" char=".">0.0262</td>
<td align="char" valign="middle" char=".">0.0314</td>
</tr>
<tr>
<td align="left" valign="middle">Jilin</td>
<td align="char" valign="middle" char=".">0.0142</td>
<td align="char" valign="bottom" char=".">0.0181</td>
<td align="char" valign="bottom" char=".">0.0217</td>
<td align="char" valign="middle" char=".">0.0243</td>
<td align="char" valign="middle" char=".">0.0143</td>
<td align="char" valign="bottom" char=".">0.0181</td>
<td align="char" valign="bottom" char=".">0.0212</td>
<td align="char" valign="middle" char=".">0.0239</td>
</tr>
<tr>
<td align="left" valign="middle">Jiangsu</td>
<td align="char" valign="middle" char=".">0.0150</td>
<td align="char" valign="bottom" char=".">0.0194</td>
<td align="char" valign="bottom" char=".">0.0274</td>
<td align="char" valign="middle" char=".">0.0331</td>
<td align="char" valign="middle" char=".">0.0149</td>
<td align="char" valign="bottom" char=".">0.0196</td>
<td align="char" valign="bottom" char=".">0.0278</td>
<td align="char" valign="middle" char=".">0.0323</td>
</tr>
<tr>
<td align="left" valign="middle">Jiangxi</td>
<td align="char" valign="middle" char=".">0.0138</td>
<td align="char" valign="bottom" char=".">0.0192</td>
<td align="char" valign="bottom" char=".">0.0243</td>
<td align="char" valign="middle" char=".">0.0368</td>
<td align="char" valign="middle" char=".">0.0138</td>
<td align="char" valign="bottom" char=".">0.0192</td>
<td align="char" valign="bottom" char=".">0.0251</td>
<td align="char" valign="middle" char=".">0.0365</td>
</tr>
<tr>
<td align="left" valign="middle">Liaoning</td>
<td align="char" valign="middle" char=".">0.0140</td>
<td align="char" valign="bottom" char=".">0.0204</td>
<td align="char" valign="bottom" char=".">0.0253</td>
<td align="char" valign="middle" char=".">0.0282</td>
<td align="char" valign="middle" char=".">0.0146</td>
<td align="char" valign="bottom" char=".">0.0199</td>
<td align="char" valign="bottom" char=".">0.0250</td>
<td align="char" valign="middle" char=".">0.0283</td>
</tr>
<tr>
<td align="left" valign="middle">Neimenggu</td>
<td align="char" valign="middle" char=".">0.0143</td>
<td align="char" valign="bottom" char=".">0.0179</td>
<td align="char" valign="bottom" char=".">0.0260</td>
<td align="char" valign="middle" char=".">0.0397</td>
<td align="char" valign="middle" char=".">0.0144</td>
<td align="char" valign="bottom" char=".">0.0180</td>
<td align="char" valign="bottom" char=".">0.0258</td>
<td align="char" valign="middle" char=".">0.0391</td>
</tr>
<tr>
<td align="left" valign="middle">Ningxia</td>
<td align="char" valign="middle" char=".">0.0125</td>
<td align="char" valign="bottom" char=".">0.0143</td>
<td align="char" valign="bottom" char=".">0.0184</td>
<td align="char" valign="middle" char=".">0.0214</td>
<td align="char" valign="middle" char=".">0.0131</td>
<td align="char" valign="bottom" char=".">0.0148</td>
<td align="char" valign="bottom" char=".">0.0179</td>
<td align="char" valign="middle" char=".">0.0228</td>
</tr>
<tr>
<td align="left" valign="middle">Qinghai</td>
<td align="char" valign="middle" char=".">0.0112</td>
<td align="char" valign="bottom" char=".">0.0148</td>
<td align="char" valign="bottom" char=".">0.0185</td>
<td align="char" valign="middle" char=".">0.0237</td>
<td align="char" valign="middle" char=".">0.0123</td>
<td align="char" valign="bottom" char=".">0.0147</td>
<td align="char" valign="bottom" char=".">0.0182</td>
<td align="char" valign="middle" char=".">0.0238</td>
</tr>
<tr>
<td align="left" valign="middle">Shandong</td>
<td align="char" valign="middle" char=".">0.0189</td>
<td align="char" valign="bottom" char=".">0.0267</td>
<td align="char" valign="bottom" char=".">0.0405</td>
<td align="char" valign="middle" char=".">0.0553</td>
<td align="char" valign="middle" char=".">0.0190</td>
<td align="char" valign="bottom" char=".">0.0271</td>
<td align="char" valign="bottom" char=".">0.0353</td>
<td align="char" valign="middle" char=".">0.0490</td>
</tr>
<tr>
<td align="left" valign="middle">Shanxi</td>
<td align="char" valign="middle" char=".">0.0130</td>
<td align="char" valign="bottom" char=".">0.0154</td>
<td align="char" valign="bottom" char=".">0.0249</td>
<td align="char" valign="middle" char=".">0.0467</td>
<td align="char" valign="middle" char=".">0.0134</td>
<td align="char" valign="bottom" char=".">0.0155</td>
<td align="char" valign="bottom" char=".">0.0250</td>
<td align="char" valign="middle" char=".">0.0461</td>
</tr>
<tr>
<td align="left" valign="middle">Shaanxi</td>
<td align="char" valign="middle" char=".">0.0154</td>
<td align="char" valign="bottom" char=".">0.0312</td>
<td align="char" valign="bottom" char=".">0.0245</td>
<td align="char" valign="middle" char=".">0.0271</td>
<td align="char" valign="middle" char=".">0.0152</td>
<td align="char" valign="bottom" char=".">0.0306</td>
<td align="char" valign="bottom" char=".">0.0237</td>
<td align="char" valign="middle" char=".">0.0268</td>
</tr>
<tr>
<td align="left" valign="middle">Shanghai</td>
<td align="char" valign="middle" char=".">0.0131</td>
<td align="char" valign="bottom" char=".">0.0204</td>
<td align="char" valign="bottom" char=".">0.0247</td>
<td align="char" valign="middle" char=".">0.0341</td>
<td align="char" valign="middle" char=".">0.0137</td>
<td align="char" valign="bottom" char=".">0.0203</td>
<td align="char" valign="bottom" char=".">0.0249</td>
<td align="char" valign="middle" char=".">0.0314</td>
</tr>
<tr>
<td align="left" valign="middle">Sichuan</td>
<td align="char" valign="middle" char=".">0.0153</td>
<td align="char" valign="bottom" char=".">0.2124</td>
<td align="char" valign="bottom" char=".">0.0379</td>
<td align="char" valign="middle" char=".">0.0664</td>
<td align="char" valign="middle" char=".">0.0148</td>
<td align="char" valign="bottom" char=".">0.0319</td>
<td align="char" valign="bottom" char=".">0.0349</td>
<td align="char" valign="middle" char=".">0.0518</td>
</tr>
<tr>
<td align="left" valign="middle">Tianjin</td>
<td align="char" valign="middle" char=".">0.0134</td>
<td align="char" valign="bottom" char=".">0.0188</td>
<td align="char" valign="bottom" char=".">0.0290</td>
<td align="char" valign="middle" char=".">0.0408</td>
<td align="char" valign="middle" char=".">0.0140</td>
<td align="char" valign="bottom" char=".">0.0181</td>
<td align="char" valign="bottom" char=".">0.0276</td>
<td align="char" valign="middle" char=".">0.0297</td>
</tr>
<tr>
<td align="left" valign="middle">Xizang</td>
<td align="char" valign="middle" char=".">0.0143</td>
<td align="char" valign="bottom" char=".">0.0177</td>
<td align="char" valign="bottom" char=".">0.0178</td>
<td align="char" valign="middle" char=".">0.0219</td>
<td align="char" valign="middle" char=".">0.0140</td>
<td align="char" valign="bottom" char=".">0.0152</td>
<td align="char" valign="bottom" char=".">0.0171</td>
<td align="char" valign="middle" char=".">0.0236</td>
</tr>
<tr>
<td align="left" valign="middle">Xinjiang</td>
<td align="char" valign="middle" char=".">0.0149</td>
<td align="char" valign="top" char=".">0.0197</td>
<td align="char" valign="top" char=".">0.0229</td>
<td align="char" valign="top" char=".">0.0266</td>
<td align="char" valign="top" char=".">0.0153</td>
<td align="char" valign="top" char=".">0.0202</td>
<td align="char" valign="top" char=".">0.0231</td>
<td align="char" valign="top" char=".">0.0283</td>
</tr>
<tr>
<td align="left" valign="top">Yunnan</td>
<td align="char" valign="top" char=".">0.0146</td>
<td align="char" valign="top" char=".">0.0235</td>
<td align="char" valign="top" char=".">0.0286</td>
<td align="char" valign="top" char=".">0.0398</td>
<td align="char" valign="top" char=".">0.0165</td>
<td align="char" valign="top" char=".">0.0232</td>
<td align="char" valign="top" char=".">0.0283</td>
<td align="char" valign="top" char=".">0.0368</td>
</tr>
<tr>
<td align="left" valign="top">Zhejiang</td>
<td align="char" valign="top" char=".">0.0145</td>
<td align="char" valign="top" char=".">0.0203</td>
<td align="char" valign="top" char=".">0.0284</td>
<td align="char" valign="top" char=".">0.0358</td>
<td align="char" valign="top" char=".">0.0146</td>
<td align="char" valign="top" char=".">0.0200</td>
<td align="char" valign="top" char=".">0.0311</td>
<td align="char" valign="top" char=".">0.0318</td>
</tr>
<tr>
<td align="left" valign="top">Chongqing</td>
<td align="char" valign="top" char=".">0.0113</td>
<td align="char" valign="top" char=".">0.0158</td>
<td align="char" valign="top" char=".">0.0221</td>
<td align="char" valign="top" char=".">0.0268</td>
<td align="char" valign="top" char=".">0.0129</td>
<td align="char" valign="top" char=".">0.0165</td>
<td align="char" valign="top" char=".">0.0237</td>
<td align="char" valign="top" char=".">0.0308</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Accordingly, this step addresses the first concern raised in the Introduction: conventional index-construction approaches may struggle to maintain robustness and plausibility in the presence of high-dimensional data and extreme values. Having obtained the refined RCAI, we next use it to identify key drivers and interpret the mechanisms underlying resilience dynamics.</p>
</sec>
<sec id="sec27">
<label>4.4</label>
<title>Driving mechanisms of RCAI</title>
<p>To address the black-box nature of machine-learning models, we employ SHAP to identify the key determinants of RCAI and to interpret their underlying mechanisms. <xref ref-type="fig" rid="fig6">Figure 6</xref> presents (a) the SHAP feature-importance (contribution) plot and (b) the SHAP summary plot. As shown in <xref ref-type="fig" rid="fig6">Figure 6a</xref>, IAFA (agricultural fixed-asset investment) accounts for 30.6% of the total contribution and ranks first among all indicators, indicating that IAFA plays a pivotal role in shaping RCAI and is the most influential driver of variation in the resilience of China&#x2019;s agricultural industry. A plausible explanation is that fixed-asset investment accelerates the construction and upgrading of agricultural infrastructure, thereby directly strengthening system-wide risk resistance (<xref ref-type="bibr" rid="ref76">Zhou et al., 2025</xref>). In particular, investment in irrigation and water conservancy facilities can mitigate yield losses from droughts and floods, while investment in high-standard farmland construction enhances overall production capacity (<xref ref-type="bibr" rid="ref28">Jiao et al., 2025</xref>). Together, these investments improve production stability and continuity and reduce production disruptions induced by external shocks such as natural hazards and market fluctuations.</p>
<fig position="float" id="fig6">
<label>Figure 6</label>
<caption>
<p>SHAP analysis results. <bold>(a)</bold> SHAP feature importance graph; <bold>(b)</bold> SHAP feature value summary graph.</p>
</caption>
<graphic xlink:href="fsufs-10-1767684-g006.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">SHAP analysis diagram shows the feature contribution and feature SHAP value distribution of RCAI. The left side shows the percentage contribution of each feature, and the right side shows the distribution of SAHP values of each feature as well as the positive and negative effects.</alt-text>
</graphic>
</fig>
<p>PCCE and PCIR (rural residents&#x2019; expenditure and income) are also highly influential, contributing 14.3 and 10.4%, respectively. Increases in household income and consumption capacity enhance farmers&#x2019; ability to finance production inputs and facilitate technology adoption and innovation. Higher rural income enables greater investment in modern machinery, improved seed varieties, and other productivity-enhancing inputs, and increases both willingness and capacity to adopt new technologies, thereby improving efficiency and output quality. Rising income may also strengthen risk-management capacity by supporting agricultural insurance uptake and encouraging income diversification, which reduces exposure to shocks affecting a single production activity.</p>
<p>Other indicators also contribute substantially to RCAI. Ranked by contribution, GOGA (land productivity) accounts for 10.2%, directly capturing output efficiency per unit of land. Higher land productivity implies greater agricultural output under the same resource endowment, which not only strengthens economic performance but also enhances the capacity to absorb external shocks. Improvements in land productivity are typically associated with technological progress and more efficient resource use, supporting a transition toward more efficient and sustainable agricultural development. DRS (disaster relief expenditure for rural residents) contributes 6.9% and reflects public financial assistance provided in response to disaster-related agricultural losses. Such support can help affected households resume production more rapidly and reduce income losses associated with production interruptions. TIL (transportation infrastructure; 6.1%) and PTRG (postal and telecommunications service volume; 5.0%) further highlight the importance of connectivity and information flows. Under natural hazards or market fluctuations, better transport infrastructure facilitates timely resource mobilization and stabilizes production and distribution. Higher postal and telecommunications activity implies improved access to market, technical, and policy information, enabling producers to make more informed decisions.</p>
<p>The SHAP summary plot in <xref ref-type="fig" rid="fig6">Figure 6b</xref> further illustrates the direction of each feature&#x2019;s effect on RCAI. Each point represents an observation, with color indicating feature value; SHAP values above (below) zero imply positive (negative) contributions relative to the baseline prediction (<xref ref-type="bibr" rid="ref19">Gao et al., 2025</xref>; <xref ref-type="bibr" rid="ref45">Pinichka et al., 2025</xref>). Overall, IAFA, PCCE, PCIR, GOGA, DRS, TIL, and PTRG exhibit predominantly positive effects, indicating a generally positive association between these indicators and RCAI, though the magnitude of this effect varies nonlinearly. Taken together, improvements in these factors can enhance production efficiency and quality, strengthen disaster recovery capacity, improve circulation efficiency, and promote information diffusion and market integration, thereby raising the resilience of China&#x2019;s agricultural industry. Notably, some observations display negative SHAP values, suggesting the presence of threshold effects or other nonlinearities, which motivates a more detailed variable-specific investigation in the subsequent analysis.</p>
<p>We further select the six most influential features and use SHAP dependence plots to examine the complex nonlinear relationships between these factors and RCAI (<xref ref-type="fig" rid="fig7">Figure 7</xref>). The analysis reveals that the enhancement of agricultural resilience is governed by distinct structural thresholds, where different factors specifically activate the system&#x2019;s capacities for resistance, adaptation, and innovation in non-uniform ways.</p>
<fig position="float" id="fig7">
<label>Figure 7</label>
<caption>
<p>Dependency diagram of the main influencing characteristics of RCAI.</p>
</caption>
<graphic xlink:href="fsufs-10-1767684-g007.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">The PDP plot shows the nonlinear relationship between six indicators (IAFA, PCIR, PCCE, GOGA, TIL, DRS) and RCAI. Each plot shows the data points in a color gradient from purple to orange. The dashed black line represents the median, and the dashed red line represents the threshold for each indicator. The distribution of the scatter points in the picture demonstrates the nonlinear relationship between the indicator and RCAI, as well as the threshold effect.</alt-text>
</graphic>
</fig>
<p>Agricultural Fixed Asset Investment (IAFA) demonstrates characteristics of increasing marginal returns. The dependence plot indicates that below a threshold of 475.20, the contribution of capital investment to resilience is negligible, likely because low-level investments are absorbed by basic depreciation and maintenance. However, surpassing this inflection point triggers a qualitative leap in system capability (<xref ref-type="bibr" rid="ref62">Xue et al., 2025</xref>). High-intensity investment serves as a dual driver: it fortifies resistance capacity through the construction of high-standard farmland and robust infrastructure, while simultaneously unlocking innovation capacity by providing the material basis for technological upgrading and equipment renewal (<xref ref-type="bibr" rid="ref27">Jiang and Peng, 2026</xref>).</p>
<p>Similarly, rural consumption (PCCE) and income (PCIR) exhibit threshold behaviors consistent with the relaxation of liquidity constraints. Both variables show a distinct &#x201C;hockey-stick&#x201D; trajectory, with resilience gains accelerating sharply only after exceeding thresholds of 5653.60 and 5944.06, respectively. This suggests that below these levels, household resources are primarily allocated to subsistence. Once income crosses this safety threshold, the financial buffer allows farmers to diversify livelihoods and adopt climate-smart practices, thereby significantly boosting their adaptation capacity to market and climatic volatility, as well as supporting post-disaster recovery (<xref ref-type="bibr" rid="ref42">Mnukwa et al., 2025</xref>).</p>
<p>Transportation Infrastructure (TIL) displays a pattern indicative of network externalities. The impact on resilience remains limited until the index reaches 11.94, implying that fragmented road networks contribute little to systemic stability. Surpassing this critical density enables the rapid release of resilience benefits. A connected network coordinates the system&#x2019;s defenses: it enhances adaptation capacity by ensuring efficient market circulation during fluctuations and strengthens resistance capacity by facilitating the rapid mobilization of emergency resources during extreme events (<xref ref-type="bibr" rid="ref23">Hossain and Kashem, 2025</xref>; <xref ref-type="bibr" rid="ref43">Mthembu et al., 2025</xref>).</p>
<p>In contrast, Land Productivity (GOGA) and Disaster Relief Subsidies (DRS) show signs of diminishing returns or passive effects. GOGA exhibits a ceiling effect, indicating that relying solely on yield maximization provides only baseline resistance but cannot sustain long-term resilience growth without structural transformation. Meanwhile, DRS functions primarily as an ex-post compensatory mechanism. While positively correlated with RCAI, it supports short-term recovery but contributes less to active, ex-ante adaptive or innovative capabilities compared to proactive investments.</p>
<p>Overall, these findings provide a supplement to the traditional linear narrative about the construction of resilience. They suggest that resilience enhancement is not a continuous linear accumulation but a step-wise evolution. Achieving higher resilience requires key capacities&#x2014;specifically capital stock, financial liquidity, and physical connectivity&#x2014;to accumulate beyond critical tipping points. Only by crossing these thresholds can the agricultural system structurally activate its intrinsic abilities to resist shocks, adapt to changes, and innovate for the future.</p>
</sec>
</sec>
<sec id="sec28">
<label>5</label>
<title>Robustness checks</title>
<sec id="sec29">
<label>5.1</label>
<title>Alternative measurement of RCAI</title>
<p>To assess the robustness of the empirical results, we reconstruct the resilience index using two alternative composite methods&#x2014;entropy&#x2013;TOPSIS and entropy&#x2013;VIKOR&#x2014;and then refit XGBoost using the newly computed RCAI as the target variable. The results are reported in <xref ref-type="table" rid="tab4">Table 4</xref>. Under the two alternative indices, the test-set <italic>R</italic><sup>2</sup> values are 0.9342 and 0.9536, respectively, indicating that model fit remains strong after replacing the index-construction method. The corresponding test-set RMSE values are 0.0001 and 0.0248, suggesting that prediction errors remain low. In addition, five-fold cross-validation yields mean MAE values of <inline-formula>
<mml:math id="M12">
<mml:mn>9.8796</mml:mn>
<mml:mo>&#x00D7;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
</inline-formula> and 0.0136, confirming that the model performs well when applied to the full dataset.</p>
<table-wrap position="float" id="tab4">
<label>Table 4</label>
<caption>
<p>Training results of XGBoost model after replacing the index system measurement method.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" rowspan="2">Method</th>
<th align="center" valign="top" colspan="3">Training set</th>
<th align="center" valign="top" colspan="3">Testing set</th>
</tr>
<tr>
<th align="center" valign="top">MAE</th>
<th align="center" valign="top">RMSE</th>
<th align="center" valign="top">
<italic>R</italic>
<sup>2</sup>
</th>
<th align="center" valign="top">MAE</th>
<th align="center" valign="top">RMSE</th>
<th align="center" valign="top">
<italic>R</italic>
<sup>2</sup>
</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle">Entropy weight-topsis-xgboost</td>
<td align="center" valign="middle">5.0680&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;5</sup></td>
<td align="center" valign="middle">7.4570&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;5</sup></td>
<td align="char" valign="middle" char=".">0.9925</td>
<td align="center" valign="middle">9.5149&#x202F;&#x00D7;&#x202F;10<sup>&#x2212;5</sup></td>
<td align="char" valign="middle" char=".">0.0001</td>
<td align="char" valign="middle" char=".">0.9342</td>
</tr>
<tr>
<td align="left" valign="middle">Entropy weight-vikor-xgboost</td>
<td align="center" valign="middle">0.0048</td>
<td align="center" valign="middle">0.0065</td>
<td align="char" valign="middle" char=".">0.9983</td>
<td align="center" valign="middle">0.0202</td>
<td align="char" valign="middle" char=".">0.0248</td>
<td align="char" valign="middle" char=".">0.9536</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="sec30">
<label>5.2</label>
<title>Feature screening</title>
<p>We further examine whether the results are sensitive to indicator selection. Based on the feature-importance ranking from the Pearson correlation analysis, we remove indicators with correlations below 0.3, reconstruct RCAI, and refit the XGBoost model. The resulting MAE (0.0016) and RMSE (0.0905) are lower than those of the baseline specification, and <italic>R</italic><sup>2</sup> increases to 0.9553, indicating improved predictive accuracy and overall fit. These findings suggest that the main results are not driven by indicator-selection bias.</p>
</sec>
</sec>
<sec id="sec31">
<label>6</label>
<title>Conclusions and policy implications</title>
<sec id="sec32">
<label>6.1</label>
<title>Conclusion</title>
<p>This study measures and evaluates the resilience of China&#x2019;s agricultural industry over the period 2000&#x2013;2022, refines the resilience index using XGBoost, and employs SHAP to identify key drivers and nonlinear relationships. The main findings are as follows.</p>
<p>First, the resilience of China&#x2019;s agricultural industry exhibits pronounced spatiotemporal heterogeneity. It shows an overall upward trajectory over time, alongside substantial regional disparities. The evolution of resilience follows a clear pattern of &#x201C;fragmentation&#x2013;regional clustering&#x2013;spatial contiguity.&#x201D; Driven jointly by policy reforms, technological upgrading, and agricultural structural adjustment, China&#x2019;s overall capacity to withstand risks has improved markedly. High-resilience regions are concentrated in North China and the southeastern coastal provinces, whereas resilience improvement is relatively limited in the northwest due to constraints such as climate and resource endowments. Among the three dimensions, resistance and adaptation capacity contribute to gradual resilience enhancement, while innovation capacity acts as the key force behind resilience upgrading.</p>
<p>Second, comparative evaluation across multiple machine-learning models indicates that XGBoost demonstrates robust performance in fitting and predicting the relationship between RCAI and the underlying indicator system. Using the trained XGBoost model to reconstruct the index yields a refined RCAI that is more coherent and reliable. This refinement mitigates shortcomings of conventional index-construction methods in handling high-dimensional structured data and provides a more robust treatment of extreme observations, thereby reducing the risk of overall measurement bias induced by outliers. Consequently, the proposed &#x201C;index construction&#x2013;XGBoost&#x2013;SHAP&#x201D; framework not only improves measurement plausibility but also addresses the interpretability challenge of machine-learning models, offering strong potential for broader application in other evaluation and composite-index studies.</p>
<p>Third, the explainable machine-learning framework effectively identifies key determinants and nonlinearities of RCAI. SHAP results show that agricultural fixed-asset investment, rural residents&#x2019; income and expenditure, transportation infrastructure, and disaster relief expenditure contribute most to RCAI. These factors improve regional agricultural infrastructure, production capacity, and adaptive capability, thereby promoting resilience enhancement. At the same time, the effects of several drivers display clear threshold behavior, indicating that resilience gains may accelerate only after certain capacity levels are reached.</p>
</sec>
<sec id="sec33">
<label>6.2</label>
<title>Policy implications</title>
<p>Based on the identification of key drivers and threshold mechanisms, this study proposes three targeted policy implications to enhance the resilience of China&#x2019;s agricultural industry.</p>
<p>First, investment strategies should focus on reaching the &#x201C;critical mass&#x201D; of capital accumulation to trigger scale effects. Since agricultural fixed-asset investment exhibits a distinct threshold effect, scattered or insufficient investments may fail to generate observable resilience gains. Policymakers should prioritize high-intensity investments in key infrastructure&#x2014;such as high-standard farmland and water conservancy projects&#x2014;ensuring that regional investment levels surpass the effective threshold to trigger a qualitative leap in resistance and innovation capacities.</p>
<p>Second, enhancing the financial adaptability of rural households is essential for bottom-up resilience. The findings reveal that rural income and consumption must cross specific safety thresholds to unlock significant improvements in adaptation capacity. Therefore, policies should go beyond post-disaster relief to focus on ex-ante capacity building. This includes diversifying rural income sources and strengthening financial support systems, enabling farmers to overcome liquidity constraints and invest in resilience-enhancing technologies and diversified livelihoods.</p>
<p>Third, differentiated resilience-building pathways should be adopted based on regional endowments. Recognizing the &#x201C;East&#x2013;West&#x201D; disparity, the eastern regions should leverage their advantages to foster transformation and innovation, focusing on digital agriculture and structural upgrading. Conversely, the western regions, constrained by ecological fragility, should prioritize resistance and adaptation. Interventions in these areas should focus on overcoming binding constraints (e.g., water scarcity) through region-specific technologies (e.g., water-saving irrigation) rather than blindly replicating the capital-intensive models of the eastern plains.</p>
</sec>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="sec34">
<title>Data availability statement</title>
<p>The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/<xref rid="SM1" ref-type="supplementary-material">Supplementary material</xref>.</p>
</sec>
<sec sec-type="author-contributions" id="sec35">
<title>Author contributions</title>
<p>DZ: Data curation, Methodology, Writing &#x2013; original draft, Writing &#x2013; review &#x0026; editing. JZ: Data curation, Writing &#x2013; review &#x0026; editing. FZ: Writing &#x2013; original draft. ZL: Writing &#x2013; review &#x0026; editing. HH: Funding acquisition, Supervision, Writing &#x2013; review &#x0026; editing.</p>
</sec>
<sec sec-type="COI-statement" id="sec36">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="sec37">
<title>Generative AI statement</title>
<p>The author(s) declared that Generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="sec38">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec sec-type="supplementary-material" id="sec39">
<title>Supplementary material</title>
<p>The Supplementary material for this article can be found online at: <ext-link xlink:href="https://www.frontiersin.org/articles/10.3389/fsufs.2026.1767684/full#supplementary-material" ext-link-type="uri">https://www.frontiersin.org/articles/10.3389/fsufs.2026.1767684/full#supplementary-material</ext-link></p>
<supplementary-material xlink:href="A1.png" id="SM1" mimetype="image/png" xmlns:xlink="http://www.w3.org/1999/xlink">
<label>SUPPLEMENTARY APPENDIX A1</label>
<caption>
<p>Dynamic evolution trend of resistance capacity from 2000 to 2022.</p>
</caption>
</supplementary-material>
<supplementary-material xlink:href="A2.png" id="SM2" mimetype="image/png" xmlns:xlink="http://www.w3.org/1999/xlink">
<label>SUPPLEMENTARY APPENDIX A2</label>
<caption>
<p>Dynamic evolution trend of adaptation capacity from 2000 to 2022.</p>
</caption>
</supplementary-material>
<supplementary-material xlink:href="A3.png" id="SM3" mimetype="image/png" xmlns:xlink="http://www.w3.org/1999/xlink">
<label>SUPPLEMENTARY APPENDIX A3</label>
<caption>
<p>Dynamic evolution trend of innovation capacity from 2000 to 2022.</p>
</caption>
</supplementary-material>
<supplementary-material xlink:href="Table_1.XLSX" id="SM4" mimetype="application/vnd.openxmlformats-officedocument.spreadsheetml.sheet" xmlns:xlink="http://www.w3.org/1999/xlink"/>
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<fn fn-type="custom" custom-type="edited-by" id="fn0001">
<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1038100/overview">Jiawei Liu</ext-link>, Xi&#x2019;an Jiaotong-Liverpool University, China</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by" id="fn0002">
<p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2223899/overview">Yingjie Dai</ext-link>, Northeast Agricultural University, China</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3326439/overview">Jingting Yu</ext-link>, Lanzhou University, China</p>
</fn>
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