Nitrogen and plant density reshape the allometric basis of morphological lodging resistance potential in maize

Abstract Lodging remains a major constraint to maize ( Zea mays L.) productivity worldwide. Stem diameter (D) and plant height (H) jointly determine stalk mechanical stability through an allometric relationship rooted in Euler buckling theory, yet how nitrogen and plant density reshape this allometric basis across commercial hybrids remains poorly quantified. We analyzed a TerraSentia robot-based phenotyping data from a nitrogen × density × hybrid field experiment and computed the morphological lodging resistance index (MLRI = D 4 /H 2 ) for 370 plant-level observations from six commercial hybrids across four nitrogen rates (0–336kg N∙ha − 1 ) and three plant density classes. Linear mixed-effects models with hybrid as random intercept were used to partition the effects of ln (D), nitrogen, density, and their interactions, with model comparison by AIC/BIC on a common sample. The best model ( ln (D) × N + density, marginal R 2 = 0.946, conditional R 2 = 0.980, LOOCV R 2 = 0.923) revealed a dominant positive effect of stem diameter ( β = 3.729, p < 2×10 − 16 ) and significant negative nitrogen main effects (− 0.88 to − 1.07, all p < 0.001) that were partially reversed by positive ln (D) × N interactions ( 0.232 to 0.293, all p < 0.01). Plant density showed contrasting patterns: simple group means declined from 12.4 (low) to 7.6 (high), yet the partial coefficient was positive (+ 0.077, p < 2×10 − 16 ), indicating two independent pathways—an indirect one via reduced stem diameter and a direct one via suppressed plant height. Hybrid identity explained 67% of unexplained variance (ICC = 0.671), with 13 of 15 pairwise comparisons significant after Tukey adjustment. Three MLRI formulations (D 4 /H 2 , D 3 /H, D 2 /H) yielded nearly identical rankings (Spearman ρ ≥ 0.994) and qualitatively identical coefficients, confirming robustness. The result demonstrate that nitrogen and plant density shift the allometric balance of morphological lodging resistance through partially independent pathways, and that D 4 /H 2 provides a rapid, robot-phenotyping-compatible morphological proxy that may complement mechanical and field-based lodging assessments.