This study aimed to identify nutritional limitations in melon (Cucumis melo L.) production by integrating two complementary diagnostic frameworks, Diagnosis and Recommendation Integrated System (DRIS) and Compositional Nutrient Diagnosis (CND), with machine learning, and to characterize the functional shape of the nutrient–yield relationship using parametric and nonparametric regression. Leaf tissue from 106 commercial fields was analyzed for ten macro- and micronutrients and partitioned by median yield into low- (n = 53) and high-yield (n = 53) reference populations. DRIS and CND indices were calculated, and multiple linear regression (MLR), generalized additive models (GAM), natural splines, Random Forest, gradient boosting (GBM), and extreme gradient boosting (XGBoost) were evaluated for yield prediction. Model assumptions were verified through Shapiro–Wilk, Anderson–Darling, Breusch–Pagan, Durbin–Watson, variance-inflation, Cook’s distance, and DFBETAS diagnostics; heteroscedasticity-consistent (HC3) standard errors were reported alongside classical SEs. DRIS identified calcium as the most deficient nutrient in low-yield plants (mean DRIS_Ca = − 8.03 ± 4.41 vs. 0 ± 7.01 in the high-yield reference; p < 0.001) and nitrogen as the most excessive (mean DRIS_N = + 7.59 ± 5.03 vs. 0 ± 6.49; p < 0.001); CND independently confirmed the same pattern. Repeated tenfold cross-validation across six model families showed multiple linear regression performed best, with CV-R2 = 0.88, held-out test R2 = 0.90, and the smallest train-test gap of any model (ΔR2 = 0.07); tree ensembles (XGBoost, GBM, Random Forest) reached comparable CV-R2 but exhibited substantially larger overfit gaps (ΔR2 = 0.19–0.22). The final MLR achieved adjusted R2 = 0.622 on the full 106-sample dataset (F₈,₉₇ = 22.64, p < 2.2 × 10⁻1⁶) with residuals that were normally distributed (Shapiro–Wilk p = 0.58; Anderson–Darling p = 0.59), independent (Durbin–Watson p = 0.255), and free of multicollinearity (maximum VIF = 2.1). A mild but statistically detectable heteroscedasticity (Breusch–Pagan p = 0.001) was addressed using HC3 robust standard errors, under which DRIS_Ca (β = + 0.153, p = 0.004) and DRIS_N (β = − 0.194, p < 0.0001) remained the two strongest predictors. Univariate GAM analysis revealed that the yield–Ca relationship was significantly nonlinear (effective degrees of freedom = 3.6–3.8, p < 0.001), exhibiting a saturating response consistent with the Mitscherlich–Liebig paradigm: yield increased with Ca balance up to the optimum and then plateaued, with univariate linear R2 = 0.40 for DRIS_Ca improving to GAM R2 = 0.60. Sensitivity refits with eight influential observations removed left the sign and significance of every key predictor unchanged. Convergent evidence from DRIS, CND, and ensemble learning identifies calcium as the dominant yield-limiting nutrient in melon under the hyper-arid, calcareous conditions of the Sistan Plain. The novel finding that the response is saturating rather than strictly linear reconciles the additive structure assumed by compositional diagnostics with the biological reality of Liebig-type limitation and refines the management implication: yield gains from calcium supplementation are expected only in plants below the saturation threshold, with diminishing returns beyond it.

Calcium Deficiency as a Saturating Yield Constraint in Melon: A Machine Learning Analysis of Compositional Leaf-Tissue Diagnostics

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发表日期：

2026年6月22日

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Hamed Arfania,
Jehangir Bhadha

摘要

This study aimed to identify nutritional limitations in melon (Cucumis melo L.) production by integrating two complementary diagnostic frameworks, Diagnosis and Recommendation Integrated System (DRIS) and Compositional Nutrient Diagnosis (CND), with machine learning, and to characterize the functional shape of the nutrient–yield relationship using parametric and nonparametric regression. Leaf tissue from 106 commercial fields was analyzed for ten macro- and micronutrients and partitioned by median yield into low- (n = 53) and high-yield (n = 53) reference populations. DRIS and CND indices were calculated, and multiple linear regression (MLR), generalized additive models (GAM), natural splines, Random Forest, gradient boosting (GBM), and extreme gradient boosting (XGBoost) were evaluated for yield prediction. Model assumptions were verified through Shapiro–Wilk, Anderson–Darling, Breusch–Pagan, Durbin–Watson, variance-inflation, Cook’s distance, and DFBETAS diagnostics; heteroscedasticity-consistent (HC3) standard errors were reported alongside classical SEs. DRIS identified calcium as the most deficient nutrient in low-yield plants (mean DRIS_Ca = − 8.03 ± 4.41 vs. 0 ± 7.01 in the high-yield reference; p < 0.001) and nitrogen as the most excessive (mean DRIS_N = + 7.59 ± 5.03 vs. 0 ± 6.49; p < 0.001); CND independently confirmed the same pattern. Repeated tenfold cross-validation across six model families showed multiple linear regression performed best, with CV-R² = 0.88, held-out test R² = 0.90, and the smallest train-test gap of any model (ΔR² = 0.07); tree ensembles (XGBoost, GBM, Random Forest) reached comparable CV-R² but exhibited substantially larger overfit gaps (ΔR² = 0.19–0.22). The final MLR achieved adjusted R² = 0.622 on the full 106-sample dataset (F₈,₉₇ = 22.64, p < 2.2 × 10⁻1⁶) with residuals that were normally distributed (Shapiro–Wilk p = 0.58; Anderson–Darling p = 0.59), independent (Durbin–Watson p = 0.255), and free of multicollinearity (maximum VIF = 2.1). A mild but statistically detectable heteroscedasticity (Breusch–Pagan p = 0.001) was addressed using HC3 robust standard errors, under which DRIS_Ca (β = + 0.153, p = 0.004) and DRIS_N (β = − 0.194, p < 0.0001) remained the two strongest predictors. Univariate GAM analysis revealed that the yield–Ca relationship was significantly nonlinear (effective degrees of freedom = 3.6–3.8, p < 0.001), exhibiting a saturating response consistent with the Mitscherlich–Liebig paradigm: yield increased with Ca balance up to the optimum and then plateaued, with univariate linear R² = 0.40 for DRIS_Ca improving to GAM R² = 0.60. Sensitivity refits with eight influential observations removed left the sign and significance of every key predictor unchanged. Convergent evidence from DRIS, CND, and ensemble learning identifies calcium as the dominant yield-limiting nutrient in melon under the hyper-arid, calcareous conditions of the Sistan Plain. The novel finding that the response is saturating rather than strictly linear reconciles the additive structure assumed by compositional diagnostics with the biological reality of Liebig-type limitation and refines the management implication: yield gains from calcium supplementation are expected only in plants below the saturation threshold, with diminishing returns beyond it.