Background Phosphorus (P) fixation on aluminum (Al) and iron (Fe) oxides in soil clays restricts P availability for crops cultivated on highly weathered tropical soils, which are common in developing countries. Hence, P deficiency becomes a major obstacle for global food security. We used multi-trait quantitative trait loci (QTL) mapping to study the genetic architecture of P efficiency and to explore the importance of root traits on sorghum grain yield on a tropical low-P soil. Results P acquisition efficiency was the most important component of P efficiency, and both traits were highly correlated with grain yield under low P availability. Root surface area was positively associated with grain yield. The guinea parent, SC283, contributed 58% of all favorable alleles detected by single-trait mapping. Multi-trait mapping detected 14 grain yield and/or root morphology QTLs. Tightly linked or pleiotropic QTL underlying the surface area of fine roots (1–2 mm in diameter) and grain yield were detected at positions 1–7 megabase pairs (Mb) and 71 Mb on chromosome 3, respectively, and a root diameter/grain yield QTL was detected at 7 Mb on chromosome 7. All these QTLs were near sorghum homologs of the rice serine/threonine kinase, OsPSTOL1 . The SbPSTOL1 genes on chromosome 3, Sb03g006765 at 7 Mb and Sb03g031690 at 60 Mb were more highly expressed in SC283, which donated the favorable alleles at all QTLs found nearby SbPSTOL1 genes. The Al tolerance gene, SbMATE , may also influence a grain yield QTL on chromosome 3. Another PSTOL1 -like gene , Sb07g02840 , appears to enhance grain yield via small increases in root diameter. Co-localization analyses suggested a role for other genes, such as a sorghum homolog of the Arabidopsis ubiquitin-conjugating E2 enzyme , phosphate 2 ( PHO2 ), on grain yield advantage conferred by the elite parent, BR007 allele. Conclusions Genetic determinants conferring higher root surface area and slight increases in fine root diameter may favor P uptake, thereby enhancing grain yield under low-P availability in the soil. Molecular markers for SbPSTOL1 genes and for QTL increasing grain yield by non-root morphology-based mechanisms hold promise in breeding strategies aimed at developing sorghum cultivars adapted to low-P soils. Electronic supplementary material The online version of this article (10.1186/s12870-019-1689-y) contains supplementary material, which is available to authorized users.

- F7, F14, F17, F20, F21, F24, F29, F31, F41, F42, F48, F51, F54 and F55 lines contributed to increase yield, while F29, F48 and F51 also

Key message A multiparental random mating population used in sorghum breeding is amenable for the detection of QTLs related to tropical soil adaptation, fine mapping of underlying genes and genomic selection approaches. Abstract Tropical soils where low phosphorus (P) and aluminum (Al) toxicity limit sorghum [Sorghum bicolor (L.) Moench] production are widespread in the developing world. We report on BRP13R, a multiparental random mating population (MP-RMP), which is commonly used in sorghum recurrent selection targeting tropical soil adaptation. Recombination dissipated much of BRP13R's likely original population structure and average linkage disequilibrium (LD) persisted up to 2.5 Mb, establishing BRP13R as a middle ground between biparental populations and sorghum association panels. Genome-wide association mapping (GWAS) identified conserved QTL from previous studies, such as for root morphology and grain yield under low-P, and indicated the importance of dominance in the genetic architecture of grain yield. By overlapping consensus QTL regions, we mapped two candidate P efficiency genes to a ~ 5 Mb region on chromosomes 6 (ALMT) and 9 (PHO2). Remarkably, we find that only 200 progeny genotyped with ~ 45,000 markers in BRP13R can lead to GWAS-based positional cloning of naturally rare, subpopulation-specific alleles, such as for SbMATE-conditioned Al tolerance. Genomic selection was found to be useful in such MP-RMP, particularly if markers in LD with major genes are fitted as fixed effects into GBLUP models accommodating dominance. Shifts in allele frequencies in progeny contrasting for grain yield indicated that intermediate to minor-effect genes on P efficiency, such as SbPSTOL1 genes, can be employed in pre-breeding via allele mining in the base population. Therefore, MP-RMPs such as BRP13R emerge as multipurpose resources for efficient gene discovery and deployment for breeding sorghum cultivars adapted to tropical soils.Communicated by Hai-Chun Jing.