Identifying the genetic factors impacting the adaptation of crops to environmental conditions is of key interest for conservation and selection purposes. It can be achieved using population genomics, and evolutionary or quantitative genetics. Here we present a sorghum multireference back-cross nested association mapping population composed of 3,901 lines produced by crossing 24 diverse parents to 3 elite parents from West and Central Africa-back-cross nested association mapping. The population was phenotyped in environments characterized by differences in photoperiod, rainfall pattern, temperature levels, and soil fertility. To integrate the multiparental and multi-environmental dimension of our data we proposed a new approach for quantitative trait loci (QTL) detection and parental effect estimation. We extended our model to estimate QTL effect sensitivity to environmental covariates, which facilitated the integration of envirotyping data. Our models allowed spatial projections of the QTL effects in agro-ecologies of interest. We utilized this strategy to analyze the genetic architecture of flowering time and plant height, which represents key adaptation mechanisms in environments like West Africa. Our results allowed a better characterization of well-known genomic regions influencing flowering time concerning their response to photoperiod with Ma6 and Ma1 being photoperiod-sensitive and the region of possible candidate gene Elf3 being photoperiod-insensitive. We also accessed a better understanding of plant height genetic determinism with the combined effects of phenology-dependent (Ma6) and independent (qHT7.1 and Dw3) genomic regions. Therefore, we argue that the West and Central Africa-back-cross nested association mapping and the presented analytical approach constitute unique resources to better understand adaptation in sorghum with direct application to develop climate-smart varieties.

Agronomy Department University of Wisconsin Madison WI 53705 WI USA

CIRAD UMR AGAP Institut Montpellier F 34398 France

Crop Physiology Laboratory International Crops Research Institute for the Semi Arid Tropics Patancheru 502 324 India

Département d'Enseignement et de Recherche des Sciences et Techniques Agricoles Institut polytechnique rural de formation et de recherche appliquée de Katibougou Koulikoro BP 06 Mali

Department of Information Technologies Faculty of Economics and Management Czech University of Life Sciences Prague 165 00 Czech Republic

Dryland Crops Program International Maize and Wheat Improvement Center U C CERAAS Thiès Po Box 3320 Senegal

Faculté des Sciences et Techniques Université des Sciences des Techniques et des Technologies de Bamako Bamako BP E 3206 Mali

Institut d'Economie Rurale Bamako BP 262 Mali

Sorghum Program International Crops Research Institute for the Semi Arid Tropics Bamako BP 320 Mali

UMR AGAP Institut Univ Montpellier CIRAD INRAE Institut Agro Montpellier F 34398 France

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Genetics. 2024 Jun 5;227(2):iyae062. doi: 10.1093/genetics/iyae062. PubMed

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Altendorf  KR, Larson  SR, DeHaan  LR, Crain  J, Neyhart  J, Dorn  KM, Anderson  JA. 2021. Nested association mapping reveals the genetic architecture of spike emergence and anthesis timing in intermediate wheatgrass. G3 (Bethesda). 11(3):jkab025. doi:10.1093/g3journal/jkab025. PubMed DOI PMC

Andrews  DJ. 1973. Effects of date of sowing on photosensitive Nigerian sorghums. Exp Agric. 9(4):337–346. doi:10.1017/S0014479700010139. DOI

Annicchiarico  P. 2002. Genotype × Environment Interactions: Challenges and Opportunities for Plant Breeding and Cultivar Recommendations. FAO Plant Production and Protection Paper No. 174. Rome: FAO.

Bardol  N, Ventelon  M, Mangin  B, Jasson  S, Loywick  V, Couton  F, Derue  C, Blanchard  P, Charcosset  A, Moreau  L. 2013. Combined linkage and linkage disequilibrium QTL mapping in multiple families of maize (Zea mays L.) line crosses highlights complementarities between models based on parental haplotype and single locus polymorphism. Theor Appl Genet. 126(11):2717–2736. doi:10.1007/s00122-013-2167-9. PubMed DOI

Bauer  E, Falque  M, Walter  H, Bauland  C, Camisan  C, Campo  L, Meyer  N, Ranc  N, Rincent  R, Schipprack  W, et al.  2013. Intraspecific variation of recombination rate in maize. Genome Biol. 14(9):R103. doi:10.1186/gb-2013-14-9-r103. PubMed DOI PMC

Bernardo  R. 2016. Bandwagons I, too, have known. Theor Appl Genet. 129(12):2323–2332. doi:10.1007/s00122-016-2772-5. PubMed DOI

Bernardo  R. 2021. Multiparental populations in line development: genetic gain, diversity, and practical limitations. Crop Sci. 61(6):4139–4150. doi:10.1002/csc2.20632. DOI

Boer  MP, Wright  D, Feng  L, Podlich  DW, Luo  L, Cooper  M, van Eeuwijk  FA. 2007. A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize. Genetics. 177(3):1801–1813. doi:10.1534/genetics.107.071068. PubMed DOI PMC

Bouchet  S, Olatoye  MO, Marla  SR, Perumal  R, Tesso  T, Yu  J, Tuinstra  M, Morris  GP. 2017. Increased power to dissect adaptive traits in global Sorghum diversity using a nested association mapping population. Genetics. 206(2):573–585. doi:10.1534/genetics.116.198499. PubMed DOI PMC

Bradbury  PJ, Zhang  Z, Kroon  DE, Casstevens  TM, Ramdoss  Y, Buckler  ES. 2007. TASSEL: software for association mapping of complex traits in diverse samples. Bioinformatics. 23(19):2633–2635. doi:10.1093/bioinformatics/btm308. PubMed DOI

Broman  KW. 2022. A generic hidden Markov model for multiparent populations. G3 (Bethesda). 12(2):jkab396. doi:10.1093/g3journal/jkab396. PubMed DOI PMC

Brown  PJ, Rooney  WL, Franks  C, Kresovich  S. 2008. Efficient mapping of plant height quantitative trait loci in a Sorghum association population with introgressed dwarfing genes. Genetics. 180(1):629–637. doi:10.1534/genetics.108.092239. PubMed DOI PMC

Browning  BL, Zhou  Y, Browning  SR. 2018. A one-penny imputed genome from next-generation reference panels. Am J Hum Genet. 103(3):338–348. doi:10.1016/j.ajhg.2018.07.015. PubMed DOI PMC

Buckler  ES, Holland  JB, Bradbury  PJ, Acharya  CB, Brown  PJ, Browne  C, Ersoz  E, Flint-Garcia  S, Garcia  A, Glaubitz  JC, et al.  2009. The genetic architecture of maize flowering time. Science. 325(5941):714–718. doi:10.1126/science.1174276. PubMed DOI

Bustos-Korts  D, Malosetti  M, Chapman  S, van Eeuwijk  F. 2016. Modelling of genotype by environment interaction and prediction of complex traits across multiple environments as a synthesis of crop growth modelling, genetics and statistics. Crop Syst Biol. 55–82. doi:10.1186/s12918-016-0289-9 DOI

Campbell  DR, Waser  NM. 2001. Genotype‐by‐environment interaction and the fitness of plant hybrids in the wild. Evolution. 55(4):669–676. doi:10.1554/0014-3820(2001)055[0669:gbeiat]2.0.co;2. PubMed DOI

Cavanagh  C, Morell  M, Mackay  I, Powell  W. 2008. From mutations to MAGIC: resources for gene discovery, validation and delivery in crop plants. Curr Opin Plant Biol. 11(2):215–221. doi:10.1016/j.pbi.2008.01.002. PubMed DOI

CEDEAO-UEMOA-CILSS . 2016. Catalogue Régional des Espèces et Variétés Végétales CEDEAO-UEMOA-CILSS.

Chantereau  J, Ag Hamada  M, Bretaudeau  A, Tembely  S. 1998. Etude de Nouvelles Variétés de Sorgho en Milieu Paysan Dans la Zone Cotonnière Cmdt au Mali (1995–1996). Montpellier: CIRAD.

Chen  Q, Yang  CJ, York  AM, Xue  W, Daskalska  LL, DeValk  CA, Krueger  KW, Lawton  SB, Spiegelberg  BG, Schnell  JM, et al.  2019. TeoNAM: a nested association mapping population for domestication and agronomic trait analysis in maize. Genetics. 213(3):1065–1078. doi:10.1534/genetics.119.302594. PubMed DOI PMC

Childs  KL, Miller  FR, Cordonnier-Pratt  MM, Pratt  LH, Morgan  PW, Mullet  JE. 1997. The sorghum photoperiod sensitivity gene, Ma3, encodes a phytochrome B. Plant Physiol. 113(2):611–619. doi:10.1104/pp.113.2.611. PubMed DOI PMC

Christopher  M, Paccapelo  V, Kelly  A, Macdonald  B, Hickey  L, Richard  C, Verbyla  A, Chenu  K, Borrell  A, Amin  A, et al.  2021. QTL identified for stay-green in a multi-reference nested association mapping population of wheat exhibit context dependent expression and parent-specific alleles. Field Crops Res. 270:108181. doi:10.1016/j.fcr.2021.108181. DOI

Clément  JC, Leblanc  JM. 1980. Prospection des mils pénicillaires, sorghos et graminées mineures en Afrique de l’Ouest. Campagne 1978. République du Mali. Orstom editions. Paris: International Board for Plant Genetic Resources.

Cobb  JN, Biswas  PS, Platten  JD. 2019. Back to the future: revisiting MAS as a tool for modern plant breeding. Theor Appl Genet. 132(3):647–667. doi:10.1007/s00122-018-3266-4. PubMed DOI PMC

Costa-Neto  G, Galli  G, Carvalho  HF, Crossa  J, Fritsche-Neto  R. 2021. EnvRtype: a software to interplay enviromics and quantitative genomics in agriculture. G3 (Bethesda). 11(4):jkab040. doi:10.1093/g3journal/jkab040. PubMed DOI PMC

Crouse  WL, Kelada  SNP, Valdar  W. 2020. Inferring the allelic series at QTL in multiparental populations. Genetics. 216(4):957–983. doi:10.1534/genetics.120.303393. PubMed DOI PMC

Des Marais  DL, Hernandez  KM, Juenger  TE. 2013. Genotype-by-environment interaction and plasticity: exploring genomic responses of plants to the abiotic environment. Annu Rev Ecol Evol Syst. 44(1):5–29. doi:10.1146/annurev-ecolsys-110512-135806. DOI

De Walsche  A, Vergne  A, Rincent  R, Roux  F, Nicolas  SD, Welcker  C, Mezmouk  S, Charcosset  A, Mary-Huard  T. 2023. metaGE: Investigating Genotype-by-Environment interactions through meta-analysis. bioRxiv 530237. 10.1101/2023.03.01.530237, preprint: not peer reviewed. DOI

Diallo  C, Rattunde  HFW, Gracen  V, Touré  A, Nebié  B, Leiser  W, Dzidzienyo  DK, Sissoko  I, Danquah  EY, Diallo  AG, et al.  2019. Genetic diversification and selection strategies for improving Sorghum grain yield under phosphorous-deficient conditions in West Africa. Agronomy. 9(11):742. doi:10.3390/agronomy9110742. DOI

Diouf  I, Derivot  L, Koussevitzky  S, Carretero  Y, Bitton  F, Moreau  L, Causse  M. 2020. Genetic basis of phenotypic plasticity and genotype× environment interactions in a multi-parental tomato population. J Exp Bot. 71(18):5365–5376. doi:10.1093/jxb/eraa265. PubMed DOI PMC

Elshire  RJ, Glaubitz  JC, Sun  Q, Poland  JA, Kawamoto  K, Buckler  ES, Mitchell  SE. 2011. A robust, simple genotyping-by-sequencing (GBS) approach for high diversity Species. PLoS One. 6(5):e19379. doi:10.1371/journal.pone.0019379. PubMed DOI PMC

Falconer  DS, Mackay  TFC. 1996. Introduction to Quantitative Genetics. India: Pearson Education.

FAO . 2008. Catalogue ouest africain des espèces et variétés végétales. Rome. Available from http://www.insah.org/doc/pdf/catalogue_french.pdf.

FAO . 2023. Global Information System. FAO. 10.18730/NMYBY. DOI

Folkertsma  RT, Rattunde  HFW, Chandra  S, Raju  GS, Hash  CT. 2005. The pattern of genetic diversity of Guinea-race Sorghum bicolor (L.) Moench landraces as revealed with SSR markers. Theor Appl Genet. 111(3):399–409. doi:10.1007/s00122-005-1949-0. PubMed DOI

Folliard  A, Traoré  PCS, Vaksmann  M, Kouressy  M. 2004. Modeling of sorghum response to photoperiod: a threshold–hyperbolic approach. Field Crops Res. 89(1):59–70. doi:10.1016/j.fcr.2004.01.006. DOI

Fragoso  CA, Moreno  M, Wang  Z, Heffelfinger  C, Arbelaez  LJ, Aguirre  JA, Franco  N, Romero  LE, Labadie  K, Zhao  H, et al.  2017. Genetic architecture of a rice nested association mapping population. G3 (Bethesda). 7(6):1913–1926. doi:10.1534/g3.117.041608. PubMed DOI PMC

Gage  JL, Monier  B, Giri  A, Buckler  ES. 2020. Ten years of the maize nested association mapping population: impact, limitations, and future directions. Plant Cell. 32(7):2083–2093. doi:10.1105/tpc.19.00951. PubMed DOI PMC

Garin  V, Malosetti  M, van Eeuwijk  F. 2020. Multi-parent multi-environment QTL analysis: an illustration with the EU-NAM flint population. Theor Appl Genet. 133(9):2627–2638. doi:10.1007/s00122-020-03621-0. PubMed DOI PMC

Garin  V, Wimmer  V, Borchardt  D, Malosetti  M, van Eeuwijk  F. 2021. The influence of QTL allelic diversity on QTL detection in multi-parent populations: a simulation study in sugar beet. BMC Genomic Data. 22(1):4. doi:10.1186/s12863-021-00960-9. PubMed DOI PMC

Garin  V, Wimmer  V, Borchardt  D, Van Eeuwijk  FA, Malosetti  M. 2018. mppR: multi-parent population QTL analysis. Available from https://CRAN.R-project.org/package=mppR. R package version 1.3.0.

Garin  V, Wimmer  V, Mezmouk  S, Malosetti  M, van Eeuwijk  F. 2017. How do the type of QTL effect and the form of the residual term influence QTL detection in multi-parent populations? A case study in the maize EU-NAM population. Theor Appl Genet. 130(8):1753–1764. doi:10.1007/s00122-017-2923-3. PubMed DOI PMC

Giraud  H, Lehermeier  C, Bauer  E, Falque  M, Segura  V, Bauland  C, Camisan  C, Campo  L, Meyer  N, Ranc  N, et al.  2014. Linkage disequilibrium with linkage analysis of multiline crosses reveals different multiallelic QTL for hybrid performance in the flint and dent heterotic groups of maize. Genetics. 198(4):1717–1734. doi:10.1534/genetics.114.169367. PubMed DOI PMC

Glaubitz  JC, Casstevens  TM, Lu  F, Harriman  J, Elshire  RJ, Sun  Q, Buckler  ES. 2014. TASSEL-GBS: a high capacity genotyping by sequencing analysis pipeline. PLoS One. 9(2):e90346. doi:10.1371/journal.pone.0090346. PubMed DOI PMC

Goma  L, Mani  H, Tanimu  B, Aliyu  L, Garba  L, Jantar  H. 2012. Growth parameters of sorghum (Sorghum bicolor (L.) Moench) varieties as influenced by planting pattern and nitrogen rates. Agric Soc Niger. 609–618.

Gu  J, Yin  X, Zhang  C, Wang  H, Struik  PC. 2014. Linking ecophysiological modelling with quantitative genetics to support marker-assisted crop design for improved yields of rice (Oryza sativa) under drought stress. Ann Bot. 114(3):499–511. doi:10.1093/aob/mcu127. PubMed DOI PMC

Guindo  D, Teme  N, Vaksmann  M, Doumbia  M, Vilmus  I, Guitton  B, Sissoko  A, Mestres  C, Davrieux  F, Fliedel  G, et al.  2019. Quantitative trait loci for sorghum grain morphology and quality traits: toward breeding for a traditional food preparation of West-Africa. J Cereal Sci. 85:256–272. doi:10.1016/j.jcs.2018.11.012. DOI

Guitton  B, Théra  K, Tékété  ML, Pot  D, Kouressy  M, Témé  N, Rami  J-F, Vaksmann  M. 2018. Integrating genetic analysis and crop modeling: a major QTL can finely adjust photoperiod-sensitive sorghum flowering. Field Crops Res. 221:7–18. doi:10.1016/j.fcr.2018.02.007. DOI

Haussmann  B, Hess  D, Reddy  B, Mukuru  S, Kayentao  M, Welz  H, Geiger  H. 2001. Pattern analysis of genotype× environment interaction for striga resistance and grain yield in African sorghum trials. Euphytica. 122(2):297–308. doi:10.1023/A:1012909719137. DOI

Hemshrot  A, Poets  AM, Tyagi  P, Lei  L, Carter  CK, Hirsch  CN, Li  L, Brown-Guedira  G, Morrell  PL, Muehlbauer  GJ, et al.  2019. Development of a multiparent population for genetic mapping and allele discovery in six-row barley. Genetics. 213(2):595–613. doi:10.1534/genetics.119.302046. PubMed DOI PMC

Higgins  RH, Thurber  CS, Assaranurak  I, Brown  PJ. 2014. Multiparental mapping of plant height and flowering time QTL in partially isogenic Sorghum families. G3 (Bethesda). 4(9):1593–1602. doi:10.1534/g3.114.013318. PubMed DOI PMC

Holland  JB. 2007. Genetic architecture of complex traits in plants. Curr Opin Plant Biol. 10(2):156–161. doi:10.1016/j.pbi.2007.01.003. PubMed DOI

Hopkins  WG. 2008. Introduction to Plant Physiology. Hoboken (NJ): John Wiley & Sons.

Hung  HY, Browne  C, Guill  K, Coles  N, Eller  M, Garcia  A, Lepak  N, Melia-Hancock  S, Oropeza-Rosas  M, Salvo  S, et al.  2012. The relationship between parental genetic or phenotypic divergence and progeny variation in the maize nested association mapping population. Heredity (Edinb). 108(5):490–499. doi:10.1038/hdy.2011.103. PubMed DOI PMC

Jordan  DR, Mace  ES, Cruickshank  AW, Hunt  CH, Henzell  RG. 2011. Exploring and exploiting genetic variation from unadapted sorghum germplasm in a breeding program. Crop Sci. 51(4):1444–1457. doi:10.2135/cropsci2010.06.0326. DOI

Kadam  NN, Jagadish  SVK, Struik  PC, van der Linden  CG, Yin  X. 2019. Incorporating genome-wide association into eco-physiological simulation to identify markers for improving rice yields. J Exp Bot. 70(9):2575–2586. doi:10.1093/jxb/erz120. PubMed DOI PMC

Kante  M, Rattunde  F, Leiser  W, Nebié  B, Diallo  B, Diallo  A, Touré  A, Weltzien  E, Haussmann  B. 2017. Can tall Guinea-race Sorghum hybrids deliver yield advantage to smallholder farmers in West and Central Africa?  Crop Sci. 57(2):833–842. doi:10.2135/cropsci2016.09.0765. DOI

Kante  M, Rattunde  F, Nebié  B, Sissoko  I, Diallo  B, Diallo  A, Toure  A, Weltzien  E, Haussmann  B, Leiser  W. 2019. Sorghum hybrids for low-input farming systems in West Africa: quantitative genetic parameters to guide hybrid breeding. Crop Sci. 59(6):2544–2561. doi:10.2135/cropsci2019.03.0172. DOI

Kassam  AH, Andrews  DJ. 1975. Effects of sowing date on growth, development and yield of photosensitive sorghum at Samaru, Northern Nigeria. Exp Agric. 11(3):227–240. doi:10.1017/S0014479700006761. DOI

Kempton  RA. 1984. The design and analysis of unreplicated trials. Vortage fur Pflanzenzuchtung. 7:219–242.

Kidane  YG, Gesesse  CA, Hailemariam  BN, Desta  EA, Mengistu  DK, Fadda  C, Pè  ME, Dell’Acqua  M. 2019. A large nested association mapping population for breeding and quantitative trait locus mapping in Ethiopian durum wheat. Plant Biotechnol J. 17(7):1380–1393. doi:10.1111/pbi.13062. PubMed DOI PMC

Klasen  J, Piepho  H, Stich  B. 2012. QTL detection power of multi-parental RIL populations in Arabidopsis thaliana. Heredity (Edinb). 108(6):626–632. doi:10.1038/hdy.2011.133. PubMed DOI PMC

Klein  R, Rodriguez-Herrera  R, Schlueter  J, Klein  P, Yu  Z, Rooney  W. 2001. Identification of genomic regions that affect grain-mould incidence and other traits of agronomic importance in sorghum. Theor Appl Genet. 102:307–319. doi:10.1007/s001220051647. DOI

Kouressy  M, Dingkuhn  M, Vaksmann  M, Heinemann  AB. 2008. Adaptation to diverse semi-arid environments of sorghum genotypes having different plant type and sensitivity to photoperiod. Agric For Meteorol. 148(3):357–371. doi:10.1016/j.agrformet.2007.09.009. DOI

Kruijer  W, Boer  MP, Malosetti  M, Flood  PJ, Engel  B, Kooke  R, Keurentjes  JJB, van Eeuwijk  FA. 2015. Marker-Based estimation of heritability in immortal populations. Genetics. 199(2):379–398. doi:10.1534/genetics.114.167916. PubMed DOI PMC

Lehermeier  C, Krämer  N, Bauer  E, Bauland  C, Camisan  C, Campo  L, Flament  P, Melchinger  AE, Menz  M, Meyer  N, et al.  2014. Usefulness of multiparental populations of maize (Zea mays L.) for genome-based prediction. Genetics. 198(1):3–16. doi:10.1534/genetics.114.161943. PubMed DOI PMC

Leroy  T, Coumaré  O, Kouressy  M, Trouche  G, Sidibé  A, Sissoko  S, Touré  AO, Guindo  T, Sogoba  B, Dembélé  F. 2014. Inscription d’une variété de sorgho obtenue par sélection participative au Mali dans des projets multiacteurs.

Li  H, Bradbury  P, Ersoz  E, Buckler  ES, Wang  J. 2011. Joint QTL linkage mapping for multiple-cross mating design sharing one common parent. PLoS One. 6(3):e17573. doi:10.1371/journal.pone.0017573. PubMed DOI PMC

Li  J, Ji  L. 2005. Adjusting multiple testing in multilocus analyses using the eigenvalues of a correlation matrix. Heredity (Edinb). 95(3):221–227. doi:10.1038/sj.hdy.6800717. PubMed DOI

Li  W, Boer  MP, Zheng  C, Joosen  RV, Van Eeuwijk  FA. 2021. An IBD-based mixed model approach for QTL mapping in multiparental populations. Theor Appl Genet. 134(11):3643–3660. doi:10.1007/s00122-021-03919-7. PubMed DOI PMC

Li  X, Guo  T, Mu  Q, Li  X, Yu  J. 2018. Genomic and environmental determinants and their interplay underlying phenotypic plasticity. Proc Natl Acad Sci U S A. 115(26):6679–6684. doi:10.1073/pnas.1718326115. PubMed DOI PMC

Li  X, Li  X, Fridman  E, Tesso  TT, Yu  J. 2015. Dissecting repulsion linkage in the dwarfing gene Dw3 region for sorghum plant height provides insights into heterosis. Proc Natl Acad Sci U S A. 112(38):11823–11828. doi:10.1073/pnas.1509229112. PubMed DOI PMC

Mace  E, Innes  D, Hunt  C, Wang  X, Tao  Y, Baxter  J, Hassall  M, Hathorn  A, Jordan  D. 2019. The Sorghum QTL Atlas: a powerful tool for trait dissection, comparative genomics and crop improvement. Theor Appl Genet. 132(3):751–756. doi:10.1007/s00122-018-3212-5. PubMed DOI

Mace  ES, Cruickshank  AW, Tao  Y, Hunt  CH, Jordan  DR. 2021. A global resource for exploring and exploiting genetic variation in sorghum crop wild relatives. Crop Sci. 61(1):150–162. doi:10.1002/csc2.20332. DOI

Mace  ES, Hunt  CH, Jordan  DR. 2013. Supermodels: sorghum and maize provide mutual insight into the genetics of flowering time. Theor Appl Genet. 126(5):1377–1395. doi:10.1007/s00122-013-2059-z. PubMed DOI

Mace  ES, Jordan  DR. 2010. Location of major effect genes in sorghum (Sorghum bicolor (L.) Moench). Theor Appl Genet. 121(7):1339–1356. doi:10.1007/s00122-010-1392-8. PubMed DOI

Magalhaes  JV, Garvin  DF, Wang  Y, Sorrells  ME, Klein  PE, Schaffert  RE, Li  L, Kochian  LV. 2004. Comparative mapping of a major aluminum tolerance gene in sorghum and other species in the Poaceae. Genetics. 167(4):1905–1914. doi:10.1534/genetics.103.023580. PubMed DOI PMC

Mahalakshmi  V, Bidinger  F. 2002. Evaluation of stay-green sorghum germplasm lines at ICRISAT. Crop Sci. 42:965. doi:10.2135/cropsci2002.0965. DOI

Malosetti  M, Voltas  J, Romagosa  I, Ullrich  SE, van Eeuwijk  FA. 2004. Mixed models including environmental covariables for studying QTL by environment interaction. Euphytica. 137(1):139–145. doi:10.1023/B:EUPH.0000040511.46388.ef. DOI

Marla  SR, Burow  G, Chopra  R, Hayes  C, Olatoye  MO, Felderhoff  T, Hu  Z, Raymundo  R, Perumal  R, Morris  GP. 2019. Genetic architecture of chilling tolerance in sorghum dissected with a nested association mapping population. G3 (Bethesda). 9(12):4045–4057. doi:10.1534/g3.119.400353. PubMed DOI PMC

Maurer  A, Draba  V, Jiang  Y, Schnaithmann  F, Sharma  R, Schumann  E, Kilian  B, Reif  JC, Pillen  K. 2015. Modelling the genetic architecture of flowering time control in barley through nested association mapping. BMC Genomics. 16(1):290. doi:10.1186/s12864-015-1459-7. PubMed DOI PMC

McMullen  MD, Kresovich  S, Villeda  HS, Bradbury  P, Li  H, Sun  Q, Flint-Garcia  S, Thornsberry  J, Acharya  C, Bottoms  C, et al.  2009. Genetic properties of the maize nested association mapping population. Science. 325(5941):737–740. doi:10.1126/science.1174320. PubMed DOI

Moles  AT, Warton  DI, Warman  L, Swenson  NG, Laffan  SW, Zanne  AE, Pitman  A, Hemmings  FA, Leishman  MR. 2009. Global patterns in plant height. J Ecol. 97(5):923–932. doi:10.1111/j.1365-2745.2009.01526.x. DOI

Multani  DS, Briggs  SP, Chamberlin  MA, Blakeslee  JJ, Murphy  AS, Johal  GS. 2003. Loss of an MDR transporter in compact stalks of maize br2 and sorghum dw3 mutants. Science. 302(5642):81–84. doi:10.1126/science.1086072. PubMed DOI

Murphy  RL, Klein  RR, Morishige  DT, Brady  JA, Rooney  WL, Miller  FR, Dugas  DV, Klein  PE, Mullet  JE. 2011. Coincident light and clock regulation of pseudoresponse regulator protein 37 (PRR37) controls photoperiodic flowering in sorghum. Proc Natl Acad Sci USA. 108(39):16469–16474. doi:10.1073/pnas.1106212108. PubMed DOI PMC

Murphy  RL, Morishige  DT, Brady  JA, Rooney  WL, Yang  S, Klein  PE, Mullet  JE. 2014. Ghd7 (Ma6) represses sorghum flowering in long days: Ghd7 alleles enhance biomass accumulation and grain production. Plant Genome. 7(2). doi:10.3835/plantgenome2013.11.0040. DOI

Myles  S, Peiffer  J, Brown  PJ, Ersoz  ES, Zhang  Z, Costich  DE, Buckler  ES. 2009. Association mapping: critical considerations shift from genotyping to experimental design. Plant Cell. 21(8):2194–2202. doi:10.1105/tpc.109.068437. PubMed DOI PMC

Nakamichi  N. 2015. Adaptation to the local environment by modifications of the photoperiod response in crops. Plant Cell Physiol. 56(4):594–604. doi:10.1093/pcp/pcu181. PubMed DOI PMC

Paccapelo  MV, Kelly  AM, Christopher  JT, Verbyla  AP. 2022. WGNAM: whole-genome nested association mapping. Theor Appl Genet. 135(7):2213–2232. doi:10.1007/s00122-022-04107-x. PubMed DOI PMC

Paterson  AH, Bowers  JE, Bruggmann  R, Dubchak  I, Grimwood  J, Gundlach  H, Haberer  G, Hellsten  U, Mitros  T, Poliakov  A, et al.  2009. The Sorghum bicolor genome and the diversification of grasses. Nature. 457(7229):551–556. doi:10.1038/nature07723. PubMed DOI

Piepho  H-P, Pillen  K. 2004. Mixed modelling for QTL× environment interaction analysis. Euphytica. 137(1):147–153. doi:10.1023/B:EUPH.0000040512.84025.16. DOI

Rama Reddy  NR, Ragimasalawada  M, Sabbavarapu  MM, Nadoor  S, Patil  JV. 2014. Detection and validation of stay-green QTL in post-rainy sorghum involving widely adapted cultivar, M35-1 and a popular stay-green genotype B35. BMC Genomics. 15(1):909. doi:10.1186/1471-2164-15-909. PubMed DOI PMC

Ratnadass  A, Chantereau  J, Coulibaly  M, Cilas  C. 2002. Inheritance of resistance to the panicle-feeding bug eurystylus oldi and the sorghum midge stenodiplosis sorghicola in sorghum. Euphytica. 123(1):131–138. doi:10.1023/A:1014451103520. DOI

Reymond  M, Muller  B, Leonardi  A, Charcosset  A, Tardieu  F. 2003. Combining quantitative trait loci analysis and an ecophysiological model to analyze the genetic variability of the responses of maize leaf growth to temperature and water deficit. Plant Physiol. 131(2):664–675. doi:10.1104/pp.013839. PubMed DOI PMC

Rodríguez-Álvarez  MX, Boer  MP, van Eeuwijk  FA, Eilers  PH. 2018. Correcting for spatial heterogeneity in plant breeding experiments with P-splines. Spat Stat. 23:52–71. doi:10.1016/j.spasta.2017.10.003. DOI

Rooney  WL, Aydin  S. 1999. Genetic control of a photoperiod-sensitive response in Sorghum bicolor (L.) Moench. Crop Sci. 39(2):397–400. doi:10.2135/cropsci1999.0011183X0039000200016x. DOI

Sagnard  F, Deu  M, Dembélé  D, Leblois  R, Touré  L, Diakité  M, Calatalyud  C, Vaksmann  M, Bouchet  S, Mallé  Y, et al.  2011. Genetic diversity, structure, gene flow and evolutionary relationships within the Sorghum bicolor wild-weedy-crop complex in a western African region. Theor Appl Genet. 123(7):1231–1246. doi:10.1007/s00122-011-1662-0. PubMed DOI

Scott  MF, Ladejobi  O, Amer  S, Bentley  AR, Biernaskie  J, Boden  SA, Clark  M, Dell’Acqua  M, Dixon  LE, Filippi  CV, et al.  2020. Multi-parent populations in crops: a toolbox integrating genomics and genetic mapping with breeding. Heredity (Edinb). 125(6):396–416. doi:10.1038/s41437-020-0336-6. PubMed DOI PMC

Soumaré  M, Kouressy  M, Vaksmann  M, Maikano  I, Bazile  D, Traoré  PS, Traoré  S, Dingkuhn  M, Touré  A, Vom Brocke  K. 2008. Prévision de l’aire de diffusion des sorghos photopériodiques en Afrique de l’Ouest. Cah Agric. 17(2):160–164. doi:10.1684/agr.2008.0183. DOI

Sparks  AH. 2018. Nasapower: a NASA POWER global meteorology, surface solar energy and climatology data client for R. J Open Source Software. 3(30):1035. doi:10.21105/joss.01035. DOI

Takai  T, Yonemaru  J, Kaidai  H, Kasuga  S. 2012. Quantitative trait locus analysis for days-to-heading and morphological traits in an RIL population derived from an extremely late flowering F1 hybrid of sorghum. Euphytica. 187:411–420. doi:10.1007/s10681-012-0727-8. DOI

Tardieu  F. 2003. Virtual plants: modelling as a tool for the genomics of tolerance to water deficit. Trends Plant Sci. 8(1):9–14. doi:10.1016/S1360-1385(02)00008-0. PubMed DOI

Thera  K. 2017. Analyse des déterminants génétiques contrôlant la production et la composition de la tige chez le sorgho (Sorghum bicolor [L.] Moench). Intégration des approches bi-et multi-parentales. Thèse de doctorat: Sciences agronomiques et écologie. Montpellier: Montpellier SupAgro.

van Eeuwijk  FA, Bink  MC, Chenu  K, Chapman  SC. 2010. Detection and use of QTL for complex traits in multiple environments. Curr Opin Plant Biol. 13(2):193–205. doi:10.1016/j.pbi.2010.01.001. PubMed DOI

Van Oosterom  E, Carberry  P, Hargreaves  J, O’leary  G. 2001. Simulating growth, development, and yield of tillering pearl millet: II. Simulation of canopy development. Field Crops Res. 72(1):67–91. doi:10.1016/S0378-4290(01)00165-4. DOI

Verbeke  G, Molenberghs  G, Verbeke  G. 1997. Linear Mixed Models for Longitudinal Data. New York (NY): Springer.

Verbyla  AP, Cavanagh  CR, Verbyla  KL. 2014. Whole-Genome analysis of multienvironment or multitrait QTL in MAGIC. G3 (Bethesda). 4(9):1569–1584. doi:10.1534/g3.114.012971. PubMed DOI PMC

Vom Brocke  K, Trouche  G, Weltzien  E, Kondombo-Barro  CP, Sidibé  A, Zougmoré  R, Gozé  E. 2014. Helping farmers adapt to climate and cropping system change through increased access to sorghum genetic resources adapted to prevalent sorghum cropping systems in Burkina Faso. Exp Agric. 50(2):284–305. doi:10.1017/S0014479713000616. DOI

VSN International . 2022. Genstat for Windows 22nd Edition. Hemel Hempstead, UK: VSN International.

Wei  J, Xu  S. 2016. A random-model approach to QTL mapping in multiparent advanced generation intercross (MAGIC) populations. Genetics. 202(2):471–486. doi:10.1534/genetics.115.179945. PubMed DOI PMC

Wolabu  TW, Tadege  M. 2016. Photoperiod response and floral transition in sorghum. Plant Signal Behav. 11(12):e1261232. doi:10.1080/15592324.2016.1261232. PubMed DOI PMC

Wu  X-L, Jannink  J-L. 2004. Optimal sampling of a population to determine QTL location, variance, and allelic number. Theor Appl Genet. 108(7):1434–1442. doi:10.1007/s00122-003-1569-5. PubMed DOI

Xavier  A, Xu  S, Muir  WM, Rainey  KM. 2015. NAM: association studies in multiple populations. Bioinformatics. 31(23):3862–3864. doi:10.1093/bioinformatics/btv448. PubMed DOI

Xu  S. 1998. Mapping quantitative trait loci using multiple families of line crosses. Genetics. 148(1):517–524. doi:10.1093/genetics/148.1.517. PubMed DOI PMC

Xu  Y. 2016. Envirotyping for deciphering environmental impacts on crop plants. Theor Appl Genet. 129(4):653–673. doi:10.1007/s00122-016-2691-5. PubMed DOI PMC

Yang  S, Murphy  RL, Morishige  DT, Klein  PE, Rooney  WL, Mullet  JE. 2014. Sorghum phytochrome B inhibits flowering in long days by activating expression of SbPRR37 and SbGHD7, repressors of SbEHD1, SbCN8 and SbCN12. PLoS One. 9(8):e105352. doi:10.1371/journal.pone.0105352. PubMed DOI PMC

Yu  J, Holland  JB, McMullen  MD, Buckler  ES. 2008. Genetic design and statistical power of nested association mapping in maize. Genetics. 178(1):539–551. doi:10.1534/genetics.107.074245. PubMed DOI PMC

Zhang  Z, Wang  W, Valdar  W. 2014. Bayesian modeling of haplotype effects in multiparent populations. Genetics. 198(1):139–156. doi:10.1534/genetics.114.166249. PubMed DOI PMC

Zhang  J, Zhang  D, Fan  Y, Li  C, Xu  P, Li  W, Sun  Q, Huang  X, Zhang  C, Wu  L, et al.  2021. The identification of grain size genes by RapMap reveals directional selection during rice domestication. Nat Commun. 12:5673. doi:10.1038/s41467-021-25961-1. PubMed DOI PMC

Zheng  C, Boer  MP, van Eeuwijk  FA. 2015. Reconstruction of genome ancestry blocks in multiparental populations. Genetics. 200(4):1073–1087. doi:10.1534/genetics.115.177873. PubMed DOI PMC