1 Introduction

Zhejiang Province is one of China’s comparatively strong vegetable-producing regions, with an average comprehensive advantage index above 1 and one of the highest annual competitiveness rankings among major winter and spring vegetable production areas, indicating that vegetable production has substantial economic and strategic importance in the province (Hou and Wang, 2024). At the same time, Zhejiang represents a distinctive agricultural setting shaped by rapid urbanization, limited land resources, and increasingly fragmented farmland, conditions that have promoted diversification of agricultural production while also complicating land management and input allocation (Qiu et al., 2020). This regional context makes vegetable productivity in Zhejiang more than a simple question of expanding cultivated area. Across China, vegetable supply has historically depended heavily on harvested area, but current evidence shows a transition toward yield-dependent growth, with future gains expected to come more from productivity improvement and better management than from further area expansion (Tang et al., 2023). For Zhejiang, therefore, improving the efficiency and stability of vegetable production requires closer attention to the soil conditions that sustain intensive cultivation, especially because fragmented and highly managed production systems can magnify both agronomic opportunity and environmental risk.

Among the factors controlling vegetable productivity, soil nutrients are central because they directly determine soil fertility and the capacity of crops to grow, accumulate biomass, and form marketable yield (Wang et al., 2024). Nitrogen, phosphorus, and potassium are especially important macronutrients in vegetable systems, and field evidence from lettuce shows that, within suitable application ranges, increasing N, P, and K inputs raises plant height, stem diameter, yield, and some quality traits relative to unfertilized conditions. The same study also found clear quadratic relationships between fertilizer application rates and yield, indicating that nutrient effects are not simply linear and that both deficiency and excess can reduce production efficiency (Hong et al., 2022). Broader evidence from Chinese vegetable systems reinforces this pattern: soil nutrients are positively correlated with vegetable yield, and balanced substitution of mineral fertilizer with manure can increase soil organic carbon, total nitrogen, available phosphorus, and yield, with medium substitution ratios producing the largest average yield gain of 18.6%. These findings show that vegetable yield formation depends not only on the presence of nutrients, but also on their balance, availability, and management over time.

Because nutrient effects vary across fields and management histories, statistical assessment is necessary to move from general agronomic knowledge to region-specific diagnosis. Soil nutrients are not uniformly distributed in farmland; in a hilly agricultural region of southern China, coefficients of variation for topsoil nutrients ranged from 47.88% to 76.91%, and different nutrients showed distinct spatial patterns across the landscape (Wang et al., 2024). In a vegetable production area of Hebei, geostatistical analysis likewise showed distinct semivariance structures for soil nitrate-N, available P, K, and Zn, with spatial correlation ranges of 204-348 m, confirming that nutrient heterogeneity can be substantial even within relatively concentrated production zones. That study further showed that nutrient distributions were associated with vegetable production history and fertilizer application rates, suggesting that current soil fertility reflects both natural variation and cumulative farmer management. For Zhejiang, where vegetable production occurs under diverse topographic and land-use conditions, this kind of statistical and spatial evidence supports the need to analyze soil data quantitatively rather than relying on uniform fertilizer assumptions. A statistically grounded evaluation can identify limiting nutrients, reveal spatial variability, and provide the basis for more precise nutrient management in vegetable fields.

Accordingly, the purpose of the present study is to statistically evaluate how key soil nutrients affect vegetable productivity in the Zhejiang region and to build an analytical framework that links soil fertility indicators with observed variation in crop performance. Such a framework is justified by evidence that nutrient application rate is one of the strongest predictors of vegetable yield variation, while related factors such as planting years, precipitation, initial soil pH, and soil organic carbon also shape the availability and productivity effects of soil nutrients (Wang et al., 2024). At the national scale, improved soil-crop system management combined with more efficient fertilizer use has already demonstrated that vegetable yields can increase by 17% while nitrogen application falls by 38%, indicating that better nutrient management can simultaneously support productivity and sustainability. On this basis, the study can reasonably be structured around three analytical tasks: first, describing the status and variability of major soil nutrients; second, testing their statistical relationships with vegetable productivity; and third, identifying the nutrient factors most relevant for regionally adapted management. In this way, the paper addresses both an empirical question-how soil nutrients influence vegetable yield in Zhejiang-and a practical one-how statistical evidence can inform efficient, high-yield, and environmentally sound vegetable production.

2 Characteristics of Soil Nutrients and Vegetable Production Systems in Zhejiang Region

2.1 Soil nutrient distribution and spatial variability across vegetable-growing areas

Soil nutrient conditions in Zhejiang show clear spatial heterogeneity, which is highly relevant for vegetable production because nutrient availability is not uniform across the province. At the provincial scale, topsoil total nitrogen averaged 1.48 g/kg and displayed a marked north-south gradient, with higher values in northern Zhejiang and lower values in the south; random-forest analysis further identified nitrogen deposition, pH, and mean annual precipitation as major drivers of this variability (Tian et al., 2024). Spatial evidence from the Hangzhou-Jiaxing-Huzhou Plain in Zhejiang likewise showed that soil organic matter and total nitrogen had moderate spatial dependence with long correlation distances, indicating that nutrient management zones can be defined at broader landscape scales rather than treated as spatially uniform fields.

Within vegetable-growing landscapes, nutrient variability is also shaped by management history, fertilizer inputs, and land-use patterns rather than by inherent soil properties alone. In Chinese vegetable production areas, geostatistical studies found that N, P, K, and Zn can all act as limiting nutrients and that these variables often show coherent spatial clustering, with nutrient-rich and nutrient-poor zones occurring side by side across farmer plots. Evidence from an intensive agricultural area in the Yangtze River Delta similarly showed high variability in soil organic matter, total nitrogen, available P, and K, while principal-component analysis linked part of this variation to land use and pH, reinforcing the need for statistically explicit spatial assessment in regions such as Zhejiang where vegetable production is highly diversified and fragmented.

2.2 Major vegetable cropping systems and productivity characteristics

Vegetable production systems in Zhejiang have become increasingly diversified, intensive, and commercially oriented, with vegetables now occupying a central place in the province’s agricultural structure. Provincial evidence from 1995 to 2015 shows that Zhejiang experienced profound diversification of agricultural production, and vegetable production increased by 89.33%, reflecting a broader shift away from traditional grain cultivation toward higher-value crops such as vegetables, fruits, and tea (Qiu et al., 2020). This structural change is consistent with broader comparative analyses showing that Zhejiang is one of China’s stronger winter and spring vegetable regions, with an average comprehensive advantage index above 1 and the second-highest annual average competitiveness score among the major producing provinces assessed.

A second defining characteristic is the growing importance of facility-based and intensive vegetable systems, especially plastic sheds and other protected cultivation modes that support high yields and year-round supply. Zhejiang has followed the national shift toward large-scale and facility agriculture, and facility farming is characterized by high efficiency, quality, and profitability, making it increasingly significant for modern crop production in the province (Wang et al., 2024). Evidence from intensive vegetable systems in the Yangtze River Basin further shows that integrated soil-crop system management can raise pepper yield by 17% relative to farmers’ current practice, indicating that productivity differences among cropping systems depend not only on structure but also on how nutrient, crop, and soil management are coordinated within intensive production environments (Wu et al., 2024).

2.3 Current challenges in soil nutrient management

The main nutrient-management challenge in intensive vegetable systems is over-fertilization, which raises yields only inefficiently while creating large nutrient surpluses and soil degradation risks. Greenhouse vegetable cultivation is widely characterized by high fertilizer input, and over-fertilization remains common because farmers pursue high yields, even though vegetable nitrogen recovery can be extremely low, reported as less than 20% in southern greenhouse systems and 10% in northern ones (Wu et al., 2024). At the national level, this management pattern has major environmental implications: Chinese vegetable production uses only 1.7% of global crop harvest area yet accounts for 7.8% of chemical fertilizer use worldwide, underscoring how nutrient inefficiency has become a structural issue rather than an isolated farm problem (Wang et al., 2024).

A related challenge is that long-term nutrient imbalance often produces acidification, salinization, and uneven accumulation of N, P, and K across vegetable fields. Studies from the Yangtze River Delta found that soil acidification and phosphorus enrichment were major problems in intensive vegetable fields, with vegetable-field N surplus exceeding 170 kg/ha/crop and P surplus exceeding 40 kg/ha/crop, while some fields still showed insufficient potassium supplementation. Similar greenhouse evidence showed that excessive nutrient surpluses rapidly increased soil total N, Olsen P, and exchangeable K, while also reducing topsoil pH and increasing electrical conductivity, confirming that current nutrient management can simultaneously create accumulation, acidification, and salinity problems that threaten long-term vegetable productivity (Bai et al., 2020).

3 Data Collection and Statistical Methodology for Soil Nutrient Analysis

3.1 Soil sampling design and nutrient measurement approaches

Soil sampling design must account for the strong spatial variability of agricultural soils, because sampling strategy directly determines whether nutrient measurements represent field conditions well enough for later statistical analysis. Reviews of soil sampling methods distinguish between design-based sampling and model-based geostatistical sampling, and they note that practical recommendations on sample size, depth, and layout remain highly variable across studies, which makes explicit protocol design especially important in heterogeneous vegetable-growing areas. For field studies aimed at mean nutrient estimation and routine fertilizer recommendation, design-based sampling is often preferred because it is simpler, less costly, and more objective than full geostatistical sampling. However, structured point allocation within fields, strata, or management zones improves representativeness compared with simple zig-zag compositing, which is not sufficiently randomized for all soil variables (Lawrence et al., 2020).

For vegetable systems, nutrient measurement should combine conventional soil analysis with crop-sensitive monitoring indicators when nitrogen dynamics are important. A representative example from a Chinese vegetable production area collected 217 soil samples on a 50 × 50 m grid at 0-20 cm depth and measured pH, organic matter, nitrate-N, available P, K, Zn, and particle size, while also recording crop history, rotations, and fertilizer use. That design is methodologically useful because vegetable production history and fertilizer practice can shape observed nutrient levels as strongly as inherent soil properties. For nitrogen assessment during crop growth, plant and soil monitoring methods can complement baseline soil tests: leaf N content and petiole sap nitrate are established plant-based indicators, whereas soil solution nitrate can be sampled using suction samplers and rapid on-farm analysis systems. Broader sensing reviews further support using laboratory methods alongside ion-selective, biosensor, spectroscopic, and portable field-deployable systems when high-resolution nutrient monitoring is needed for precision agriculture (Figure 1) (Kashyap and Kumar, 2021).

Figure 1 Conceptual framework illustrating soil spatial variability and the influence of different sampling designs on nutrient estimation accuracy in agricultural fields. Structured grid-based and stratified sampling approaches improve spatial representation compared with non-randomized sampling patterns by capturing heterogeneous nutrient distributions

3.2 Statistical methods for evaluating nutrient-productivity relationships

The first stage of statistical assessment usually relies on correlation and regression methods to identify which soil variables are associated with vegetable productivity and how strongly they explain yield variation. Linear analytical workflows commonly begin by testing variables such as soil pH, organic matter, total nitrogen, available phosphorus, potassium, and texture against crop yield using Pearson correlation and then building multiple regression models to estimate the apparent strength of those relationships. This approach is valuable for identifying dominant nutrients because some variables are often strongly intercorrelated, and multivariable regression helps separate their partial contributions to yield variation. In smallholder and plot-based systems, statistically significant relationships between available soil nutrients and crop yield have already been reported, supporting the use of regression-based nutrient diagnosis for site-specific management.

Where soil variables are numerous and correlated, multivariate statistical methods are more informative than simple linear screening. Principal component analysis has been used to reduce multiple soil properties into a smaller number of derived indicators, and in one yield study three principal components explained 89.471% of total soil variance before being entered into principal-component regression. That approach outperformed regression on simple indicators alone, explaining mean relative yield with an adjusted R² of 0.771, which suggests that combined nutrient and soil-condition gradients are often more meaningful than single nutrient variables analyzed separately. For nutrient-efficiency analysis at broader scales, stepwise multiple linear regression has also been paired with explanatory variables spanning management, climate, topography, economy, soil, and crop type, showing that statistical assessment can be extended beyond plot chemistry to county-scale agricultural systems (Liu et al., 2025).

3.3 Advanced statistical and computational approaches

Advanced soil-nutrient analysis increasingly combines geostatistics, digital soil mapping, and machine learning to capture nonlinear patterns and spatial dependence that conventional regression may miss. Modern soil mapping reviews note that conventional survey approaches often oversimplify soil variability, whereas geostatistics can interpolate soil properties across space by accounting for spatial autocorrelation and quantifying prediction uncertainty. This is especially relevant for Zhejiang vegetable systems, where nutrient variation is unlikely to be random across landscapes and management histories. Digital soil mapping extends this logic by combining soil sensing data with environmental covariates to generate nutrient maps, and robust workflows typically include model training, cross-validation, independent validation in similar regions, and then testing transferability to different geographic areas (Folorunso et al., 2023).

Machine-learning methods are attractive because they can model nonlinear relationships and handle many cross-correlated predictors without the distributional assumptions required by classical geostatistics (Wadoux et al., 2020). Reviews consistently report that advanced ML approaches often outperform simpler models for soil prediction, although gains depend on data quality, parameter tuning, and careful validation (Folorunso et al., 2023). In agricultural nutrient analysis, Random Forest has shown higher explanatory performance than stepwise linear regression for nitrogen use efficiency at county scale, with model efficiencies reaching 0.84 for PFPN and 0.89 for PNBN and highlighting the importance of soil and climate covariates (Liu et al., 2025). At the same time, newer soil-science-informed ML frameworks argue that prediction alone is not enough, and that more reliable and generalizable models should incorporate pedological knowledge, observational priors, and soil-informed constraints to improve interpretability and scientific credibility.

4 Effects of Individual Soil Nutrients on Vegetable Productivity

4.1 Influence of nitrogen availability on vegetable growth and yield

Nitrogen availability strongly regulates vegetable growth because it determines whether crop demand is met during rapid biomass accumulation while avoiding excessive soil nitrate supply. Reviews of vegetable nitrogen management show that fertilizer N is often applied in excess of actual crop demand, largely because growers treat N as insurance against yield loss in high-value systems, even though optimal management requires fertilizer to supplement other N sources rather than simply maximize application rates. This matters for productivity because N deficiency constrains growth, but excessive application does not proportionally increase yield and instead reflects low recovery efficiency and weak synchrony between supply and crop uptake.

Evidence from intensive Chinese vegetable systems further indicates that yield can be maintained or increased when nitrogen is managed dynamically rather than applied uniformly. Knowledge-based optimization and integrated strategies are designed to match root-zone N supply to vegetable demand across growth stages, and combined organic-mineral N fertilization has been identified as an effective way to maintain yield while reducing. A recent greenhouse study also showed that partial organic substitution can reduce mineral N input without sacrificing productivity when kept at moderate levels, whereas excessive substitution reduced annual vegetable yield by 23.29-32.81%, indicating that both insufficient and poorly balanced N supply can depress output (Liu et al., 2025).

4.2 Effects of phosphorus and potassium on yield formation and quality improvement

Phosphorus and potassium contribute to vegetable productivity by supporting yield formation, nutrient uptake, and market-quality traits, but their effects are strongest when supplied in balance with nitrogen rather than in isolation. In lettuce, increasing P and K within an appropriate range raised yield by 15.15%~42.42% and 7.14%~10.32%, respectively, while also improving traits such as vitamin C and soluble sugar; the responses followed significant quadratic relationships, indicating clear optima rather than indefinite gains from higher rates (Hong et al., 2022). Similar evidence from potato showed that combined NPK fertilization increased tuber yield, chlorophyll, carotenoids, starch, sucrose, and sucrose enzyme activity more than individual nutrient applications, supporting the principle that balanced macronutrient supply improves both yield and quality formation (Wang et al., 2024).

Potassium also appears particularly important for product quality and nutrient-use sustainability in vegetable systems. An early field and pot study on Chinese cabbage reported that rational P and K fertilization increased yield and improved quality, and that potassium application markedly reduced nitrate accumulation in plants, which is relevant for leafy vegetables where excessive nitrate can lower market value (Hong et al., 2022). More recent work in Chinese cabbage further showed that integrated potassium management increased uptake of both macro- and micronutrients and improved available soil N and K, with multivariate analysis identifying the treatment that combined reduced mineral K with FYM, PGPR, and foliar nano-K as the more sustainable option.

4.3 Contribution of organic matter and micronutrients to soil productivity

Soil organic matter contributes to vegetable productivity by serving as both a nutrient reservoir and a regulator of nutrient transformations in soil. Reviews consistently show that decomposition of organic matter releases macronutrients, micronutrients, and secondary nutrients, while loss of soil organic matter is detrimental to crop productivity because it degrades physical, chemical, and biological soil properties. Organic matter build-up is also positively associated with the availability of nitrogen, phosphorus, potassium, zinc, manganese, iron, and sulfur, indicating that its contribution to productivity extends beyond carbon supply to broader fertility regulation (Dhaliwal et al., 2024).

Micronutrient availability is closely tied to soil organic matter because organic inputs modify the reactions that control whether Zn, Cu, Fe, Mn, B, and Mo remain plant-accessible. Soil organic matter can increase water-soluble and exchangeable micronutrient forms and convert adsorbed fractions into more available pools, which tends to support uptake, although the effects differ by element and redox sensitivity. In vegetable systems, this broader soil-quality effect is reflected in meta-analytic and field evidence showing that moderate manure substitution increases SOC, total N, available P, and microbial activity while improving yields, whereas excessive substitution or excessive SOM accumulation can reduce productivity, so the benefit of organic enrichment depends on maintaining an optimal range rather than maximizing soil organic matter alone (Wang et al., 2024).

5 Multivariate Statistical Analysis of Soil Nutrient Effects on Vegetable Productivity

5.1 Identification of dominant nutrient factors affecting vegetable yield

Multivariate analysis consistently shows that the dominant nutrient factors affecting yield cannot be identified reliably from single-variable comparisons alone, because soil and plant variables are intercorrelated and act jointly. In regression-based field studies spanning multiple crops, plant nutrient uptake often emerged as a stronger predictor of yield than soil macronutrient levels by themselves; for example, tomato yield was significantly associated with phosphorus uptake, while maize yield was mainly influenced by plant and soil nitrogen in specific transects. This emphasis on uptake-based indicators is methodologically important for Zhejiang vegetable systems, where apparent soil fertility does not necessarily translate directly into productivity unless nutrients are captured effectively by the crop (Sathish and Siddu, 2026).

Principal-component approaches reach a similar conclusion by showing that dominant yield factors are usually composite soil-property gradients rather than isolated nutrients. In one widely cited pedological analysis, simple stepwise regressions using individual soil indicators were inadequate, whereas PCA reduced the system to three interpretable components explaining 89.471% of total variance, and these components explained mean relative yield with an adjusted R² of 0.771. Related work also showed that principal components or minimum data sets can capture the essential soil dimensions that govern productivity, with PCA-based indicator selection producing strong yield relationships in intensive cropping systems (Ghosh et al., 2025).

5.2 Modeling nutrient interactions and productivity responses

Modeling nutrient effects on vegetable productivity increasingly focuses on interactions among N, P, K, pH, management, and environmental context, rather than estimating the independent effect of each nutrient in isolation. Machine-learning analysis of 157 multi-environment vegetable fertilizer trials found that soil and managerial features were the most important predictors of marketable yield, and that N and P offtakes were especially influenced by P-related features, indicating substantive N-P interactions. This interaction-based view is reinforced by response-surface studies in leafy vegetables, where optimal N-P-K ratios differed across spinach, bok choy, and Chinese cabbage, demonstrating that productivity responses are species-specific and depend on nutrient balance rather than universal dosage rules (Figure 2) (Yang et al., 2025).

Figure 2 Workflow of multivariate and machine-learning approaches for predicting vegetable productivity from integrated soil, management, and environmental variables

From a statistical standpoint, several multivariate frameworks are used to model these interaction effects. Reviews of soil-yield analysis note that simple linear functions are often inappropriate because multicollinearity among soil properties obscures interpretation, whereas PLS, PCA-derived regression, and tree-based methods are better suited to capturing structured covariance and nonlinear responses. Spatially explicit studies also show that combining PCA with clustering or factor analysis can identify latent dimensions such as fertility, nutrient availability, or chemical composition, which then explain differences in productivity across fields or management zones more effectively than raw nutrient variables alone (Tomaz et al., 2022).

6. Case Study: Statistical Evaluation of Soil Nutrient Drivers Affecting Greenhouse Vegetable Productivity in Zhejiang Region

6.1 Experimental design and soil-crop data collection

The Zhejiang case study should be structured as a field-based greenhouse vegetable survey combined with plot-level soil and crop measurements, because intensive protected vegetable systems in China are characterized by high fertilizer inputs, strong nutrient accumulation, and marked variation in soil chemical conditions across production settings. A suitable sampling design would stratify greenhouses by production intensity, vegetable type, and cultivation history, then collect baseline topsoil samples before planting and post-harvest samples from the 0-20 cm layer for analysis of available N, P, and K, pH, electrical conductivity, soil organic matter, and related fertility indicators (Fan et al., 2020).

Crop observations should be recorded simultaneously with soil sampling to support nutrient-productivity modeling at the greenhouse scale. Yield, biomass, and plant nutrient uptake are especially important because productivity responses often reflect both soil nutrient supply and crop nutrient acquisition, while greenhouse soils in China commonly show declining pH and increasing soluble salts under long-term intensive fertilization. Accordingly, plot records should also include fertilizer source, application rate, irrigation practice, cropping duration, and vegetable species so that nutrient effects can be separated from management effects in later statistical analysis (Rangaiah et al., 2025).

6.2 Statistical analysis of nutrient effects on productivity

The statistical analysis should begin with descriptive statistics and correlation screening, followed by multivariate methods that reduce redundancy among strongly related soil indicators. Principal component analysis is especially appropriate because soil fertility datasets often contain collinear variables such as available nutrients, organic matter, pH, and salinity, and earlier work showed that a minimal dataset can be selected by combining univariate tests, correlation analysis, and PCA with varimax rotation. For Zhejiang greenhouse vegetables, the extracted components can then be entered into regression models to identify the dominant nutrient-related factors controlling yield variation across sampled sites (Rangaiah et al., 2025).

To quantify productivity responses more directly, multiple regression or principal component regression should be used with vegetable yield as the dependent variable and nutrient, soil, and management variables as predictors. This approach is justified because simple single-indicator models are often inadequate, whereas multivariate regressions and component-based models better capture site-specific yield responses and explain a larger share of variability. If spatially referenced greenhouse data are available, spatial regression or random-forest-based approaches can be added as robustness checks, but the core interpretation should remain focused on statistically significant effects of available N, P, K, pH, and soil organic matter on productivity (Paccioretti et al., 2021).

6.3 Implications for nutrient management optimization

The expected management implication for Zhejiang is not simply to increase fertilizer rates, but to optimize nutrient supply relative to existing soil reserves and crop demand. Chinese greenhouse vegetable systems frequently receive excessive nutrient inputs, and evidence from intensive systems shows that such practices can sustain large nutrient surpluses while accelerating acidification, salinization, and nutrient imbalance. Therefore, the statistical identification of yield-limiting nutrients should be used to support soil-test-based recommendations that reduce unnecessary N and P inputs in fields where residual fertility is already high (Fan et al., 2020).

A more effective optimization strategy is integrated nutrient management, combining mineral fertilizer adjustment with organic amendments, improved timing, and soil-remediation practices where needed. This is consistent with greenhouse studies showing that integrated soil-crop system management increased pepper yield by 17% over farmers’ practice while reducing apparent N losses, and with broader evidence that coordinated use of mineral and organic nutrient sources can maintain or increase vegetable yields while improving soil function and nutrient cycling efficiency. For Zhejiang greenhouses, this implies that nutrient management should be guided by statistical diagnosis of local soil constraints and implemented through balanced, site-specific, and seasonally adjusted fertilization programs (Wu et al., 2024; Himanshu et al., 2026).

7 Application of Statistical Analysis in Precision Soil Nutrient Management

7.1 Development of data-driven fertilization strategies

Statistical analysis underpins data-driven fertilization by converting heterogeneous soil measurements into site-specific recommendations rather than uniform input rates. Precision agriculture frameworks use remote sensing, GPS guidance, and data analytics to support localized decisions on fertilizer and water use, while site-specific interventions such as variable-rate application are designed to match input levels to within-field nutrient demand and reduce waste (Xing and Wang, 2024). In parallel, machine-learning-based nutrient management systems have been developed to estimate fertilizer needs and nutrient status from large, multi-platform datasets, reflecting a broader shift from descriptive soil testing to predictive decision support.

For Zhejiang vegetable systems, the practical statistical goal is to translate spatial nutrient variability into management zones and fertilizer prescriptions that differ across fields and seasons. Geostatistical analysis combined with principal component analysis and fuzzy c-means clustering has been used to delineate five nutrient management zones for variable-rate fertilization, showing how multivariate classification can support balanced fertilizer use and higher profitability than farmer-uniform practice. More advanced fertilization models now encode climatic, soil nutrient, and yield data into spatio-temporal tensors to predict both the amount and timing of base fertilizer and topdressing, and these multi-task learning systems have shown better accuracy and stability than standard regression models (Zhang et al., 2023).

7.2 Integration of digital technologies in vegetable production management

Digital technologies extend statistical analysis from periodic diagnosis to real-time nutrient management by continuously monitoring soil and crop conditions and feeding those data into decision systems. IoT-enabled platforms combine sensors for soil moisture, pH, NPK, temperature, and humidity with cloud storage so that time-stamped field data can be analyzed continuously rather than only after laboratory sampling (Senapaty et al., 2023). Broader reviews of smart agriculture similarly show that electrochemical and optical sensors, IoT connectivity, and AI-driven nutrient modeling are becoming central tools for site-specific nutrient management and variable-rate fertilization.

In vegetable production management, these digital systems are most useful when they integrate sensing, interpretation, and farmer-facing recommendations within a single workflow. Real-time IoT systems have already been coupled to AI-driven mobile applications that generate recommendations for fertilization, irrigation, and crop management from live soil data, demonstrating how statistical inference can be embedded directly in field operations (Shahab et al., 2025). At a wider production scale, digital agriculture also incorporates sensors, drones, satellites, and artificial intelligence to monitor crop growth and soil conditions, and these tools support more informed decisions on irrigation and fertilization across open-field, greenhouse, and horticultural systems.

7.3 Future perspectives for sustainable vegetable production in zhejiang

Future precision nutrient management in Zhejiang will likely depend on linking statistical diagnosis with integrated agronomic strategies that improve both productivity and environmental performance. In Chinese vegetable systems, inappropriate nitrogen management has caused low nutrient-use efficiency and high reactive nitrogen losses, whereas knowledge-based optimization, innovative products, and integrated knowledge-and-products strategies are presented as the main pathway to maintaining yield while reducing losses. Evidence from national field experiments further shows that such integrated strategies can reduce nitrogen application by 38%, cut nitrogen surplus by 65%, lower greenhouse gas emissions by 28%, and still increase vegetable yield by 17%, which makes them especially relevant for Zhejiang’s intensive vegetable sector (Wang et al., 2024).

A second priority is to combine digital precision management with broader sustainability measures and stronger evidence infrastructure. Large-scale Chinese evidence indicates that management practices such as combining organic and chemical fertilizers, straw recycling, and deep fertilizer placement increased crop yields by 10%, reduced nitrogen pollution by 8%, and raised nitrogen-use efficiency by 18%, suggesting that statistical nutrient management should be embedded within wider green-development policy rather than treated as a stand-alone technical tool. At the same time, digital agriculture reviews emphasize that adoption still faces barriers from high upfront costs, data-management demands, and skill requirements, so future implementation in Zhejiang will depend not only on better models but also on training, standardization, and accessible decision platforms for vegetable growers (Xing and Wang, 2024).

8 Conclusions

The evidence indicates that vegetable productivity is regulated by both the absolute supply and the balance of soil nutrients, with nitrogen and phosphorus generally exerting stronger yield effects than potassium when deficiencies occur. Long-term omission experiments showed that balanced NPK fertilization improved yield primarily by increasing soil organic carbon, total and available N, total and available P, and available K, while edaphic variables explained more yield variation than phenological factors). Complementary deficiency experiments further showed that nitrogen deficiency significantly reduced crop yield, and phosphorus deficiency had a greater effect than potassium deficiency on nutrient absorption and accumulation, supporting the conclusion that N and P are the dominant macronutrient constraints in intensive cropping systems.

In vegetable systems specifically, yield responses are closely tied to broader soil quality indicators rather than to mineral fertilizer inputs alone. A meta-analysis of Chinese vegetable fields found that soil organic carbon, total nitrogen, microbial biomass carbon, microbial biomass nitrogen, available phosphorus, and available potassium were all positively related to vegetable yield, indicating that productivity depends on integrated fertility status. At the same time, intensive vegetable production in the Yangtze River Delta has generated substantial N and P surpluses, together with soil acidification and phosphorus enrichment, showing that nutrient excess can undermine long-term sustainability even where short-term yields remain high.

Statistical approaches have been central to identifying which soil variables matter most, reducing dimensionality in highly correlated datasets, and translating complex fertility information into usable management indicators. Principal component regression has been shown to handle large soil datasets effectively by reducing correlated predictors into a smaller number of principal components, and one study found that three components captured 78% of the information while preserving high classification accuracy. Related work combining PCA, discriminant analysis, and partial least squares regression showed that multivariate feature selection can isolate a reduced set of informative indicators, including organic carbon, Olsen P, water-extractable nitrogen, and physical quality variables, thereby improving soil-status interpretation under different management systems.

Spatial and predictive statistics have further expanded soil fertility management from diagnosis to site-specific intervention. Geostatistical and multivariate mapping studies showed that soil fertility can be translated into spatially explicit indices and management zones, with regression kriging achieving R² = 0.68 in fertility prediction and zone-specific recommendations for nutrient replacement, phosphorus regulation, and soil amendment (Poma-Chamana et al., 2025). Similarly, geostatistics combined with PCA and fuzzy clustering successfully delineated distinct management zones from gridded soil samples, demonstrating that statistical zoning can support site-specific nutrient management while reducing the environmental risks of excessive fertilization.

Future research should move beyond single-nutrient assessment toward integrated, site-specific nutrient management systems that protect soil health while sustaining vegetable output. Recent reviews emphasize that site-specific nutrient management is a critical strategy for raising crop production, maintaining soil health, and reducing environmental pollution, but they also note major research gaps in adoption, nutrient-prediction accuracy, and the inability of any single sensing technology to capture all soil properties. More broadly, sustainable soil management now requires a holistic framework that integrates scientific, technological, environmental, and socio-economic dimensions rather than treating fertilizer optimization as an isolated technical problem.

For Zhejiang, the most promising direction is to combine statistical nutrient analysis with digital sensing, integrated nutrient management, and conservation-oriented production systems. Reviews of smart nutrient sensing identify IoT integration, AI-driven nutrient modeling, and variable-rate management as key future tools, but they also highlight unresolved challenges in sensor standardization and technology integration. In parallel, integrated nutrient management research shows that combining organic inputs, soil- and plant-based nutrient management, and conservation practices can improve fertilizer-use efficiency, soil health, and crop performance, making this a strong framework for future sustainable vegetable production in Zhejiang.

Acknowledgments

I extend my sincere gratitude to the anonymous reviewers for their valuable and insightful comments, which have greatly strengthened this paper.

Conflict of Interest Disclosure

The author affirms that this research was conducted without any commercial or financial relationships that could be construed as a potential conflict of interest.

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