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A Novel Hybrid MARS Algorithm–Particle Swarm Optimization Approach for Predicting and Optimizing K+/Na+, Ca2+/Na+ Ratios and Salt Tolerance Index in Sorghum Seedlings Under Salinity
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DOI：10.1007/s42729-026-03492-2.png)
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Abstract
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Soil salinity severely limits crop establishment by disrupting ionic homeostasis and reducing biomass accumulation. Although potassium nitrate (KNO₃) seed priming is a well-known strategy for enhancing stress tolerance, the nonlinear response surfaces governing ion regulation in sorghum seedlings under combined KNO₃ and salinity treatments remain unexplored. With this aim, this pot experiment developed a hybrid modeling–optimization framework integrating multivariate adaptive regression splines (MARS) and particle swarm optimization (PSO) to predict and optimize Na⁺, K⁺, and Ca²⁺ levels, K⁺/Na⁺ and Ca²⁺/Na⁺ ratios, and the salt tolerance index (STI) in sorghum seedlings under varying soil salinity levels and KNO₃ priming doses. Increasing salinity severely disrupted ionic homeostasis, causing a 688.8% increase in shoot Na⁺ accumulation and 56.7% and 29.5% reductions in shoot K⁺ and Ca²⁺ contents, respectively, under non-primed conditions at 14.02 dS m⁻¹. However, priming with 25 and 50 mM KNO₃ reduced Na⁺ accumulation by 68.3% and 52.5%, respectively, while increasing STI by 44.1% and 49.0%, respectively, at the same salinity level. Moreover, MARS models showed strong predictive accuracy (R²: 0.844–0.978; RMSE: 0.021–7.670; MAE: 0.017–6.181) and identified a critical salinity threshold of 9.55 dS m⁻¹, beyond which ionic regulation deteriorated sharply. PSO-based multi-objective optimization identified 50 mM KNO₃ as the most favorable priming dose for maximizing combined ionic balance and salt tolerance across salinity levels. Finally, the integration of MARS and PSO advances salinity research from descriptive assessment toward a more prescriptive, data-driven framework for optimizing crop performance under saline conditions.
Keywords:
MARS
Mineral Uptake
Optimization
Salinity Stress
Sorghum Bicolor
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