Salt stress shifts wild tomato root systems toward transport efficiency along a gravitropism-constrained Pareto front

- Root system architecture balances the carbon cost of building roots (wiring cost) against transport speed to the shoot (conduction delay). Wild tomato (S. Pimpinellifolium) roots lie near the Pareto front, but existing models treat lateral roots as straight, misrepresenting curved architectures. - We extended the Pareto model to account for lateral-root curvature, estimating curvature parameter G and trade-off weight for 1,597 root systems from 240 accessions grown with or without 100mM NaCl. We also measured root angles and conducted a GWAS. This is the first Pareto model of root architecture to incorporate lateral-root curvature and the first study to demonstrate heritability of position on the Pareto front and identify an associated locus. - Curvature improved model fit in 80% of root systems after penalizing the additional parameter. Salt shifted root systems toward conduction-delay minimization (lower ) across all four architectural types. Lateral roots grew 10{degrees} closer to vertical, while main-root angle was unchanged. was more heritable under salt, and a chromosome~6 locus within an intron of the ISOAMYLASE~3 ortholog explained approximately 11% of its variation. - Salt reorganizes lateral roots, but not the main root, toward faster transport, with a heritable, mappable component.