Abstract
The development of lines with high performance and stability for synthesis of superior hybrids is the most expensive and time-consuming phase in maize hybrid breeding. Several times, due to available resources, only a part of possible hybrid combinations is tested. Therefore, the breeder needs methods that allow the evaluation of genotypes untested in the field. This work was carried out with the objective of proposing a prediction model of general and specific (SCA) combining ability, and interactions with environments, associated with the use of credible regions in biplots obtained through Additive Main Effects and Multiplicative Interaction Bayesian model. Two analyses were done, in which the first one was conducted with simulated data, and the second one with real data. Credible ellipses were constructed in biplot in order to evaluate the stability of interaction effects for GCA and SCA. For the analysis of simulated data, the predictions obtained had high correlation with the real values. For the effects of GCA and SCA, the predictions kept the standard of signals and rank. The model was efficient to provide credible intervals which covered the simulated values. For the analysis of real data, estimates of GCA and SCA for all genotypes evaluated do not differ from zero. The biplots for GCA × E and SCA × E interactions allowed evaluate the genotype stability in a more accurate way and the uncertainty about interaction estimates. The model is shown as a promising tool for helping the breeder to select and recommend genotypes.
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References
Abera W, Hussein S, Derera J, Worku M, Laing M (2016) Heterosis and combining ability of elite maize inbred lines under northern corn leaf blight disease prone environments of the mid-altitude tropics. Euphytica 208(2):391–400. https://doi.org/10.1007/s10681-015-1619-5
Acosta-Pech R, Crossa J, de los Campos G, Teyssèdre S, Claustres B, Pérez-Elizalde S, Pérez-Rodríguez P (2017) Genomic models with genotype x environment interaction for predicting hybrid performance: an application in maize hybrids. Theor Appl Genet 130(7):1431–1440. https://doi.org/10.1007/s00122-017-2898-0
Adebayo MA, Menkir A, Blay E, Gracen V, Danquah E (2017) Combining ability and heterosis of elite drought-tolerant maize inbred lines evaluated in diverse environments of lowland tropics. Euphytica 213(2):43. https://doi.org/10.1007/s10681-017-1840-5
Amegbor IK, Badu-Apraku B, Annor B (2017) Combining ability and heterotic patterns of extra-early maturing white maize inbreds with genes from Zea diploperennis under multiple environments. Euphytica 213(1):24. https://doi.org/10.1007/s10681-016-1823-y
Balestre M, Machado JC, Lima JL, Souza JC, Nóbrega Filho L (2008) Genetic distance estimates among single cross hybrids and correlation with specific combining ability and yield in corn double cross hybrids. Genet Mol Res 7(1):65–73. https://doi.org/10.4238/vol7-1gmr403
Beck DL, Vasal SK, Crossa J (1990) Heterosis and combining ability of CIMMYT’s tropical early and intermediate maturity maize (Zea mays L.) germplasm. Maydica 35(3):279–285
Bernardo Júnior LAY, da Silva CP, de Oliveira LA, Nuvunga JJ, Pires LPM, Von Pinho RG, Balestre M (2018) AMMI bayesian models to study stability and adaptability in maize. Agron J 110(5):1765–1776
Bradu D, Gabriel KR (1978) The biplot as a diagnostic tool for models of two-way tables. Technometrics 20(1):47–68
Burgueño J, de los Campos G, Weigel K, Crossa J (2012) Genomic prediction of breeding values when modeling genotype × environment interaction using pedigree and dense molecular markers. Crop Sci 52(2):707–719. https://doi.org/10.2135/cropsci2011.06.0299
Camargos RB, Von Pinho RG, Balestre M, Ferreira RADC, Dias KOG, Pires LPM, Souza VF (2017) Efficiency of selection per se and in single-cross hybrids for disease resistance in maize. Genet Mol Res. https://doi.org/10.4238/gmr16039716
Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8(1):69–92. https://doi.org/10.1080/10618600.1999.10474802
Cornelius PL, Crossa J (1999) Prediction assessment of shrinkage estimators of multiplicative models for multi-environment cultivar trials. Crop Sci 39(4):998–1009. https://doi.org/10.2135/cropsci1999.0011183x003900040007x
Crossa J, Perez-Elizalde S, Jarquin D, Cotes JM, Viele K, Liu G, Cornelius PL (2011) Bayesian estimation of the additive main effects and multiplicative interaction model. Crop Sci 51(4):1458–1469. https://doi.org/10.2135/cropsci2010.06.0343
Cruz CD, Regazzi, AJ, Carneiro PCS (2012) Modelos biométricos aplicados ao melhoramento genético. Viçosa: Ed. UFV
da Silva CP, de Oliveira LA, Nuvunga JJ, Pamplona AKA, Balestre M (2015) A Bayesian shrinkage approach for AMMI models. PLoS ONE 10(7):1–27. https://doi.org/10.1371/journal.pone.0131414
de Figueiredo AG, Von Pinho RG, Silva HD, Balestre M (2015) Application of mixed models for evaluating stability and adaptability of maize using unbalanced data. Euphytica 202(3):393–409. https://doi.org/10.1007/s10681-014-1301-3
de Oliveira LA, da Silva CP, Nuvunga JJ, da Silva AQ, Balestre M (2015) Credible intervals for scores in the AMMI with random effects for genotype. Crop Sci 55(2):465–476. https://doi.org/10.2135/cropsci2014.05.0369
Derera J, Tongoona P, Vivek BS, Laing MD (2008) Gene action controlling grain yield and secondary traits in southern African maize hybrids under drought and non-drought environments. Euphytica 162(3):411–422. https://doi.org/10.1007/s10681-007-9582-4
Gabriel KR (1971) The biplot graphic display of matrices with application to principal component analysis. Biometrika 58(3):453–467. https://doi.org/10.1093/biomet/58.3.453
Giraud H, Bauland C, Falque M, Madur D, Combes V, Jamin P, Monteil C, Laborde J, Palaffre C, Gaillard A, Blanchard P, Charcosset A, Moreau L (2017) Reciprocal genetics: Identifying QTL for general and specific combining abilities in hybrids between multiparental populations from two maize (Zea mays L.) heterotic groups. Genetics 207(3):1167–1180. https://doi.org/10.1534/genetics.117.300305
Griffing B (1956) A generalised treatment of the use of diallel crosses in quantitative inheritance. Heredity 10(1):31. https://doi.org/10.1038/hdy.1956.2
Guedes FL (2012) Desempenho de híbridos de milho a partir de progênies contrastantes em relação ao uso de nitrogênio (Doctoral thesis). Retrieved from Federal University of Lavras Digital Repository http://repositorio.ufla.br/jspui/handle/1/374
Heidelberger P, Welch PD (1983) Simulation run length control in the presence of an initial transient. Oper Res 31(6):1109–1144. https://doi.org/10.1287/opre.31.6.1109
Heslot N, Akdemir D, Sorrells ME, Jannink JL (2014) Integrating environmental covariates and crop modeling into the genomic selection framework to predict genotype by environment interactions. Theor Appl Genet 127(2):463–480. https://doi.org/10.1007/s00122-013-2231-5
Holland JB, Nyquist WE, Cervantes-Martínez CT (2003) Estimating and interpreting heritability for plant breeding: an update. Plant Breed Rev, 22
Jarquín D, Crossa J, Lacaze X, Du Cheyron P, Daucourt J, Lorgeou J, Piraux F, Guerreiro L, Pérez P, Calus M, Burgueño J, De Los Campos G (2014) A reaction norm model for genomic selection using high-dimensional genomic and environmental data. Theor Appl Genet 127(3):595–607. https://doi.org/10.1007/s00122-013-2243-1
Jumbo MB, Carena MJ (2008) Combining ability, maternal, and reciprocal effects of elite early-maturing maize population hybrids. Euphytica 162(3):325–333. https://doi.org/10.1007/s10681-007-9618-9
Kadam DC, Potts SM, Bohn MO, Lipka AE, Lorenz AJ (2016) Genomic prediction of single crosses in the early stages of a maize hybrid breeding pipeline. G3 Genes Genomes Genet 6(11):3443–3453. https://doi.org/10.1534/g3.116.031286
Kulka VP, da Silva TA, Contreras-Soto RI, Maldonado C, Mora F, Scapim CA (2018) Diallel analysis and genetic differentiation of tropical and temperate maize inbred lines. Crop Breed Appl Biotechnol 18(1):31–38. https://doi.org/10.1590/1984-70332018v18n1a5
Lopez-Cruz M, Crossa J, Bonnett D, Dreisigacker S, Poland J, Jannink JL, Singh RP, Autrique E, De Los Campos G (2015) Increased prediction accuracy in wheat breeding trials using a marker × environment interaction genomic selection model. G3 Genes Genomes Genet 5(4):569–582. https://doi.org/10.1534/g3.114.016097
Massman JM, Gordillo A, Lorenzana RE, Bernardo R (2013) Genomewide predictions from maize single-cross data. Theor Appl Genet 126(1):13–22. https://doi.org/10.1007/s00122-012-1955-y
Matzinger DF, Sprague GF, Cockerham CC (1959) Diallel crosses of maize in experiments repeated over locations and years. Agron J 51(3):346–350. https://doi.org/10.2134/agronj1959.00021962005100060012x
Melo WMC, Balestre M, Von Pinho RG, Bueno Filho JSS (2014) Genetic control of the performance of maize hybrids using complex pedigrees and microsatellite markers. Euphytica 195(3):331–344. https://doi.org/10.1007/s10681-013-0999-7
Nass LL, Lima M, Vencovsky R, Gallo PB (2000) Combining ability of maize inbred lines evaluated in three environments in Brazil. Sci Agric 57(1):129–134. https://doi.org/10.1590/S0103-90162000000100021
Nuvunga JJ, da Silva CP, de Oliveira LA, de Lima RR, Balestre M (2019) Bayesian factor analytic model: an approach in multiple environment trials. PLoS ONE 14(8):1–26. https://doi.org/10.1371/journal.pone.0220260
Pires LPM (2017) Predição genômica do desempenho de híbridos de milho considerando a interação genótipos por ambientes (Doctoral thesis). Retrieved from Federal University of Lavras Digital Repository http://repositorio.ufla.br/jspui/handle/1/29463
R Development Core Team (2018) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2018
Raftery AE, Lewis SM (1992) Comment: one long run with diagnostics: implementation strategies for Markov Chain Monte Carlo. Stat Sci 7:493–497. https://doi.org/10.1214/ss/1177011143
Rojas BA, Sprague GF (1952) A comparison of variance components in corn yield trials: III. General and specific combining ability and their interaction with locations and years. Agron J 44(9):462. https://doi.org/10.2134/agronj1952.00021962004400090002x
SAS Institute Inc (2002) SAS/STAT® software: version 9
Schmidt P, Hartung J, Rath J, Piepho HP (2019) Estimating broad-sense heritability with unbalanced data from agricultural cultivar trials. Crop Sci 59(2):525–536. https://doi.org/10.2135/cropsci2018.06.0376
Schrag TA, Möhring J, Maurer HP, Dhillon BS, Melchinger AE, Piepho HP, Sorensen AP, Frisch M (2009) Molecular marker-based prediction of hybrid performance in maize using unbalanced data from multiple experiments with factorial crosses. Theor Appl Genet 118(4):741–751. https://doi.org/10.1007/s00122-008-0934-9
Smith BJ (2007) boa: an R package for MCMC output convergence assessment and posterior inference. J Stat Softw 21(11):1–37. https://doi.org/10.18637/jss.v021.i11
Viele K, Srinivasan C (2000) Parsimonious estimation of multiplicative interaction in analysis of variance using Kullback-Leibler information. J Stat Plan Inference 84(1–2):201–219. https://doi.org/10.1016/S0378-3758(99)00151-2
Yang RC, Crossa J, Cornelius PL, Burgueño J (2009) Biplot analysis of genotype × environment interaction: proceed with caution. Crop Sci 49(5):1564–1576. https://doi.org/10.2135/cropsci2008.11.0665
Zobel RW, Wright MJ, Gauch HG (1988) Statistical analysis of a yield trial. Agron J 80(3):388–393. https://doi.org/10.2134/agronj1988.00021962008000030002x
Acknowledgements
The authors dedicate this paper to the memory of our dear friend and colleague, Dr. Marcio Balestre, a brilliant mind. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.
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LAYBJ was responsible for investigation, interpretation of statistical analysis as well as manuscript writing. RGVP and MB were responsible for project conceptualization, supervision, funding and data set acquisition. CPS and LAO were responsible for performing the statistical analysis. ICVJ and EVVS were responsible for manuscript editing, reviewing and submission.
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Bernardo Júnior, L.A.Y., Von Pinho, R.G., da Silva, C.P. et al. AMMI-Bayesian models and use of credible regions in the study of combining ability in maize. Euphytica 217, 173 (2021). https://doi.org/10.1007/s10681-021-02903-y
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DOI: https://doi.org/10.1007/s10681-021-02903-y