| تعداد نشریات | 285 |
| تعداد نشریات سازمان | 83 |
| تعداد شمارهها | 3,139 |
| تعداد مقالات | 34,918 |
| تعداد مشاهده مقاله | 50,383,224 |
| تعداد دریافت فایل اصل مقاله | 90,276,640 |
مدلهای پیشرفته بیزی AMMI برای تجزیه و تحلیل پایداری عملکرد دانه هیبریدهای ذرت در آزمایشهای چندمحیطی: مقایسه رویکردهای کلاسیک و بیزی | ||
| نهال و بذر | ||
| دوره 40، شماره 4، دی 1403، صفحه 624-599 اصل مقاله (791.23 K) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22092/spj.2026.371268.1455 | ||
| نویسندگان | ||
| محمدرضا شیری* 1؛ سجاد محرم نژاد2؛ حمید نجفی نژاد3؛ افشار استخر4؛ پیمان جعفری5؛ مجیدرضا کیانی6؛ مهدی متقی7؛ بهزاد احمدی8؛ لاله ابراهیمی9 | ||
| 1دانشیار، بخش تخقیقات ذرت و گیاهان علوفه ای، موسسه تحقیقات اصلاح و تهیه نهال و بذر، سازمان تحقیقات، آموزش و ترویج کشاورزی، کرج، ایران. | ||
| 2استادیار، بخش تحقیقات علوم زراعی و باغی، مرکز تحقیقات و آموزش کشاورزی و منابع طبیعی اردبیل، سازمان تحقیقات، آموزش و ترویج کشاورزی، اردبیل، ایران. | ||
| 3دانشیار، بخش تحقیقات علوم زراعی و باغی، مرکز تحقیقات و آموزش کشاورزی و منابع طبیعی کرمان، سازمان تحقیقات، آموزش و ترویج کشاورزی، کرمان، ایران. | ||
| 4استادیار، بخش تحقیقات علوم زراعی و باغی، مرکز تحقیقات و آموزش کشاورزی و منابع طبیعی فارس، سازمان تحقیقات، آموزش و ترویج کشاورزی، شیراز، ایران. | ||
| 5استادیار، بخش تحقیقات علوم زراعی و باغی، مرکز تحقیقات و آموزش کشاورزی و منابع طبیعی اصفهان، سازمان تحقیقات، آموزش و ترویج کشاورزی، اصفهان، ایران. | ||
| 6استادیار، بخش تحقیقات علوم زراعی و باغی، مرکز تحقیقات و آموزش کشاورزی و منابع طبیعی خراسان رضوی، سازمان تحقیقات، آموزش و ترویج کشاورزی، مشهد، ایران. | ||
| 7استادیار، بخش تحقیقات علوم زراعی و باغی، مرکز تحقیقات و آموزش کشاورزی و منابع طبیعی استان همدان، سازمان تحقیقات، آموزش و ترویج کشاورزی، همدان، ایران. | ||
| 8استادیار، بخش تحقیقات ذرت و گیاهان علوفه ای، موسسه تحقیقات اصلاح و تهیه نهال و بذر، سازمان تحقیقات، آموزش و ترویج کشاورزی، کرج، ایران. | ||
| 9دانشیار، بخش تحقیقات کنترل بیولوژیک، موسسه تحقیقات گیاهپزشکی کشور، سازمان تحقیقات، ترویج و آموزش کشاورزی، تهران، ایران. | ||
| چکیده | ||
| بهنژادگران گیاهی از مدل AMMI برای تجزیه و تحلیل دادههای آزمایشهای چندمحیطی و شناسایی الگوهای برهمکنش ژنوتیپ × محیط استفاده میکنند. شاخصهای مبتنی بر AMMI مانند میانگین وزنی قدر مطلق نمرات (WAAS) و میانگین وزنی قدر مطلق نمرات همراه با عملکرد (WAASY) ابزارهای مؤثری در ارزیابی و انتخاب ارقام برتر هستند، اما رویکرد کلاسیک AMMI در نمایش ناقابل اعتمادی و تفسیر آماری برهمکنشها محدودیتهایی دارد. در این پژوهش شش هیبرید امیدبخش ذرت به همراه سه شاهد تجاری (هیبریدهای کوشا، دهقان و طاها) در قالب طرح بلوکهای کامل تصادفی با سه تکرار در ایستگاههای تحقیقات کشاورزی کرج، مشهد، اصفهان، همدان، کرمان، مغان و شیراز در دو سال زراعی 1400 و 1402 ارزیابی شدند. عملکرد دانه هیبریدهای امیدبخش ذرت در ۱۴ محیط با استفاده از مدل بیزی AMMI و شاخصهای B-WAAS، B-WAASY و شاخص پایداری ماهالانوبیس (SM) تجزیه و تحلیل و با نتایج روش کلاسیک مقایسه شد. میانگین عملکرد دانه از 9/26تا 11/31تن در هکتار متغیر بود. هیبرید شماره ۱ (KE79017/5111×K1264/5-1) بیشترین عملکرد دانه را داشت و با هیبریدهای شماره ۳ (KE76009/311×B73) و ۹ (Taha=KE76009/311×K1264/5-1) تفاوت معنی دار نداشت. مدل بیزی 88/01درصد و مدل کلاسیک 74/10درصد از واریانس برهمکنش ژنوتیپ × محیط را توجیه کردند که بیانگر برآورد دقیقتر و تبیین قویتر در رویکرد بیزی است. شاخصهای بیزی B-WAAS و B-WAASY همراه با نمودار SMT هیبریدهای شماره ۱، ۳ و ۴ (KE77003/3×B73) را دارای عملکرد دانه و پایداری عملکرد مطلوب معرفی کردند که این یافته ها با نتایج شاخصهای کلاسیک WAAS و WAASY نیز همخوانی داشت. علاوه بر این، بایپلاتهای بیزی با استفاده از بازه چگالی بیشینه پسین (HPD) قابل اعتماد، امکان تفسیر دقیقتر اثر ژنوتیپ × محیط و تفکیک اثرمعنیدار از غیرمعنیدار را فراهم کردند، در حالی که بایپلات کلاسیک فاقد این قابلیت بود. در مجموع، رویکرد بیزی AMMI با ارائه اطلاعات آماری غنیتر و نمایش شفاف عدم قطعیت، روش قابل اعتمادتر و کارآمدتری نسبت به رویکرد کلاسیک بود. هیبریدهای شماره ۱ و ۳ به دلیل عملکرد دانه بالا و پایداری عملکرد مطلوب به عنوان گزینههای مناسبی برای استفاده در برنامههای بهنژادی و تولید هیبرید های تجاری ذرت شناسایی شدند. | ||
| کلیدواژهها | ||
| ذرت؛ برهمکنش ژنوتیپ × محیط؛ شاخصهای پایداری بیزی؛ سازگاری عمومی؛ سازگاری خصوصی | ||
| عنوان مقاله [English] | ||
| Advanced AMMI Bayesian Models for Analysis of Grain Yield Stability of Maize Hybrids in Multi-Environment Trials: A Comparison of Classical and Bayesian Approaches | ||
| نویسندگان [English] | ||
| M.R SHiri1؛ S. Moharramnejad2؛ H. Najafinezhad3؛ A. Estakhr4؛ P. Jafari5؛ M.R. Kiani6؛ M. Mottaghi7؛ B. Ahmadi8؛ L. Ebrahimi9 | ||
| 1Associate Professor, Maize and Forage Crops Research Department, Seed and Plant Improvement Institute, Agricultural Research, Education and Extension Organization, Karaj, Iran. | ||
| 2Assistant Professor, Field and Horticultural Crops Science Research Department, Ardabil Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization, Moghan, Iran. | ||
| 3Associate Professor, Field and Horticultural Crops Science Research Department, Kerman Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization, Kerman, Iran. | ||
| 4Assistant Professor, Field and Horticultural Crops Science Research Department, Fars Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization, Shiraz, Iran. | ||
| 5Assistant Professor, Field and Horticultural Crops Science Research Department, Isfahan Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization, Isfahan, Iran. | ||
| 6Assistant Professor, Field and Horticultural Crops Science Research Department, Khorasan Razavi Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization, Mashhad, Iran. | ||
| 7Assistant Professor, Field and Horticultural Crops Science Research Department, Hamedan Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization, Hamedan, Iran. | ||
| 8Assistant Professor, Maize and Forage Crops Research Department, Seed and Plant Improvement Institute, Agricultural Research Education and Extension Organization, Karaj, Iran. | ||
| 9Associate Professor, Biological Control Research Department, Iranian Research Institute of Plant Protection, Agricultural Research, Education and Extension Organization, Tehran, Iran. | ||
| چکیده [English] | ||
| Plant breeders commonly use the AMMI model to analyse multi-environment trials data and to identify genotype × environment interaction (GEI) patterns. AMMI-based indices such as the Weighted Average of Absolute Scores (WAAS) and the Weighted Average of Absolute Scores combined with yield (WAASY) help breeders to select superior genotypes across different environments. Despite its wide application, the classical AMMI model has limitations in statistically evaluating and representing the uncertainty of GEIs. In this study, six maize promising hybrids and three commercial checks (Kosha, Dehgan and Taha) were evaluated using randomized complete block design with three replications in seven agricutural research field stations; Karaj, Mashhad, Isfahan, Hamedan, Kerman, Moghan, and Shiraz in Iran over two cropping seasons 2021–2023. A Bayesian AMMI model and its indices, including B-WAAS, B-WAASY, and the Mahalanobis Stability Index (SM), were applied to for analyzing yield and yield stability of studied maize hybrids, and the results were compared with the classical AMMI model. The Bayesian AMMI model explained 88.01% of GEI variance, while the classical AMMI model explained 74.10%. Hybrids no. 3 and 4 were the most yield-stable, and hybrids no. 6 and 9 the least yield-stable. Combined indices and SMT plots identified hybrids no. 1, 3, and 4 as high-yielding and yild-stable. Therefore, hybrids no. 1 and 3 can be used in the maize breeding programs and recommended for being commercially released for target maize growing areas. Keywords: Maize, Bayesian stability indices, genotype × environment interaction, specific adaptation, wide adaptation. Introduction Maize (Zea mays L.) is one of the most important agricultural crops due to its high nutritional and commercial values, and is widely used for human food and animal feed. Plant breeding plays a crucial role in developing high-yielding and stress-tolerant genotypes (Shiri et al., 2024). Hybrid development, a major approach in genetic improvement, enables the combination of desirable phenotypes with superior genetics, leading to enhanced yield performance and stability, and adaptability. Since genotypes respond differently to environmental conditions, multi-environment trials (METs) are essential in final breeding stages to evaluate genotype performance and assess genotype × environment interactions (GEI). The AMMI (Additive Main Effects and Multiplicative Interaction) model is widely used for analysing METs data and identifying yield stability and mega-environments (Olivoto et al., 2019). However, the classical AMMI model has statistical limitations. The Bayesian AMMI model overcomes these by incorporating prior information and estimating full posterior distributions (Crossa et al., 2011). Recent study (Nascimento et al., 2025) has introduced Bayesian-based indices such as B-WAAS, B-WAASY, and the Mahalanobis Stability Measure (SM), which provide more accurate inference and visualization of uncertainty. Therefore, this study aimed to evaluate the yield performance and stability of maize promising hybrids using Bayesian AMMI and its indices compared with classical AMMI to support more informed maize hybrid breeding decisions. Materials and Methods In this study, six maize promising hybrids and three commercial checks (Kosha, Dehgan and Taha) were evaluated using randomized complete block design with three replications in seven Agricutural research field stations; Karaj, Mashhad, Isfahan, Hamedan, Kerman, Moghan, and Shiraz in Iran over two cropping seasons 2021–2023. Each plot consisted of four 5.44 m rows spaced 0.75 m apart, with 0.32 m between hills and two plants per hill, resulting in a density of about 83,000 plants ha⁻¹. Standard agronomic practices were applied, including irrigation, weed and pest management, and fertilization based on local soil tests. The Bayesian AMMI model was implemented as described by Crossa et al. (2011), where phenotypic responses followed a multivariate normal distribution with priors assigned to all parameters. Posterior distributions were estimated using Markov Chain Monte Carlo (MCMC) with 30,000 replications, a burn-in of 5,000 replications, and thinning every five samples via the Gibbs sampler. Convergence was assessed using Geweke and Raftery–Lewis diagnostics. Bayesian AMMI-based indices; B-WAAS, B-WAASY, and the Mahalanobis stability index (SM)—were derived directly from posterior samples. The Mahalanobis stability trait (SMT) plot was generated to visualize yield stability relationships and 90% HPD intervals. All analyses were conducted in R using the ChiDO framework (Nascimento et al., 2025). Results and Discussion The Bayesian AMMI model demonstrated satisfactory convergence, with 98.58% of parameters showing |Z| <1.96 and 92.63% having Raftery–Lewis <5, indicating stable MCMC chains. Posterior mean grain yield of nine maize hybrids in 14 environments ranged from 9.26 t ha⁻¹ (hybrid no. 7) to 11.31 t ha⁻¹ (hybrid no. 1), with hybrids no. 1, 3, and 9 performing the top-yielding group. Grain yields varied widely (3.20–15.08 t ha⁻¹) in different environments, reflecting high GEI. The Bayesian AMMI analysis explained 88.01% of the interaction variance outperforming the classical AMMI model (74.10%), and highlighting its effectiveness in capturing GEI patterns. Biplot analysis based on the Bayesian AMMI model, using posterior means and 90% HPD credible intervals, identified hybrids no. 3, 5, 6, and 9 and environments 5, 7, 11, and 12 as major contributors to GEI, indicating their strong influence on genotype-by-environment variability. HPD credible inetrvals visualized parameter uncertainty and confirmed genotype-specific adaptation. Stability indices ranked hybrids no. 3 and 4 as the most yield-stable, while hybrid no. 6 and 9 were least yield-stable. Combined indices, WAASY, B-WAASY and the SMT plot highlighted hybrids no. 1, 3, and 4 as both high-yielding and yiled-stable. Overall, the Bayesian AMMI approach provided a robust and informative framework for simultaneous evaluation of grain yield and yiled stability of the studied maize hybrids, and accounted for uncertainty and enabling more reliable selection of superior maize hybrids for being used in maize breeding programs and commercial release. References Crossa, J., Perez-Elizalde, S., Jarquín, D., Cotes, J. M., Viele, K., Liu, G. and Cornelius, P. L. 2011. Bayesian estimation of the additive main effects and multiplicative interaction model. Crop Science, 51, pp.1458–1469. DOI: 10.2135/cropsci2010.06.0343 Nascimento, A.C.C., Nascimento, M., Sagae, V.S., Destro, V., Nardino, M., Olivoto, T. and Jarquín, D. 2025. Bayesian AMMI‐based indexes for genotype selection: Integrating novel stability measures for enhanced G× E inference. Crop Science, 65(5), e70140. DOI: 10.1002/csc2.70140 Olivoto, T., Lúcio, A.D.C., Silva, J.A.G., Marchioro, V.S., Souza, V.Q. and Jost, E. 2019. Mean performance and stability in multi-environment trials I: Combining features of AMMI and BLUP techniques. Agronomy Journal, 111, pp.2949–2960. DOI: 10.2134/agronj2019.03.0220 Shiri, M.R., Estakhr, A., Najafinezhad, H., Hassanzadeh Moghaddam, H., Shirkhani, A. and Ataei, R. 2024. Employing Bayesian probabilistic approach for risk assessment in selection and recommendation of new maize (Zea mays L.) hybrids. Seed and Plant, 40, pp.295–320 (in Persian). DOI: 10.22092/spj.2025.368724.1410 | ||
| کلیدواژهها [English] | ||
| Maize, Bayesian stability indices, genotype × environment interaction, specific adaptation, wide adaptation | ||
| مراجع | ||
|
Annicchiarico, P. 2002. Genotype × environment interactions: Challenges and opportunities for plant breeding and cultivar recommendations. Volume 174 of FAO Plant Production and Protection Papers. 174. 115 pp.
Bernardo Júnior, L.A.Y., de Silva, C.P., de Oliveira, L.A., Nuvunga, J.J., Pires, L.P.M., Von Pinho, R.G. and Balestre, M. 2018. AMMI Bayesian models to study stability and adaptability in maize. Agronomy Journal, 110(5), pp.1765–1776. DOI: 10.2134/agronj2017.11.0668
Crossa, J., Perez-Elizalde, S., Jarquín, D., Cotes, J. M., Viele, K., Liu, G. and Cornelius, P. L. 2011. Bayesian estimation of the additive main effects and multiplicative interaction model. Crop Science, 51, pp.1458–1469. DOI: 10.2135/cropsci2010.06.0343
da Oliveira, L.A., da Silva, C.P., da Silva, A.Q., Mendes, C.T.E., Nuvunga, J.J., Nunes, J.A.R., Parrella, R.A.D.C., Baleste, M. and Filho, J.S.D.S.B. 2021. Bayesian GGE model for heteroscedastic multienvironmental trials. Crop Science, 62(3), pp.982–996. DOI: 10.1002/csc2.20696
da Silva, C.P., Mendes, C.T.E., Silva, A.Q.D., Oliveira, L.A.D., Von Pinho, R.G. and Balestre, M. 2023. Use of the reversible jump Markov Chain Monte Carlo algorithm to select multiplicative terms in the AMMI-Bayesian model. PLoS One, 18, e0279537. DOI:10.1371/journal.pone.0279537
da Silva, C.P., da Silva, A.Q., Nuvunga, J.J., Avelar, F.G., Braulio, R., Mendes, C.T.E., de Oliveira, L.A. and Bueno Filho, J.S.D.S. 2025a. Assessing the adaptability and stability of maize hybrids using a Bayesian factor analytic model. Crop Science, 65(5), e70162. DOI: 10.1002/csc2.70162
da Silva, E.V.P., Davide, L.M.C., Gianlup, C., de Oliveira, W.J.S., de Oliveira, L.A., da Silva, A.Q., da Silva, C.P., Mendes, C.T.E. and Khan, S. 2025b. Assessing the stability and adaptability of maize hybrid yield with the Bayesian AMMI model. Euphytica, 221(4), 43. DOI: 10.1007/s10681-025-03490-y
Denis, J.-B. and Pazman, A. 1999. Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models. Applied Mathematics, 44, pp.375–403. DOI: 10.1023/A:1023045028073
Ebrahimi, L. 2023. ‘Genotype by yield* trait’(GYT) biplot approach to evaluate resistance of soybean cultivars to Helicoverpa armigera Hübner under natural infestation conditions. Phytoparasitica, 51(4), pp.909–918. DOI: 10.1007/s12600-023-01078-7
Forkman, J. and Piepho, H.P. 2014. Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models. Biometrics, 70, pp.639–647. DOI: 10.1111/biom.12162
Gabriel, K.R. 1971. The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58, pp.453–467. DOI: 10.1093/biomet/58.3.453
Gamerman, D. and Lopes, H.F. 2006. Markov chain Monte Carlo: Stochastic simulation for Bayesian inference. Chapman and Hall. DOI: 10.1201/9781482296426
Gelman, A. and Rubin, D.B. 1992. Inference from iterative simulation using multiple sequences. Statistical Science, 7, pp.457–511. DOI: 10.1214/ss/1177011136
Geman, S. and Geman, D. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, pp.721–741. DOI: 10.1109/TPAMI.1984.4767596
Geweke, J. 1992. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Pp. 169–193. In: L. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith (eds.) Bayesian statistics. Oxford University Press.
Johnson, R.A. and Wichern, D.W. 2002. Applied multivariate statistical analysis. Fifth edition. Prentice Hall. 788 pp.
Josse, J., van Eeuwijk, F., Piepho, H.P. and Denis, J.-B. 2014. Another look at Bayesian analysis of AMMI models for genotype-environment data. Journal of Agricultural, Biological, and Environmental Statistics, 19, pp.240–257. DOI: 10.1007/s13253-014-0168-z
Khan, M.M.H., Rafii, M.Y., Ramlee, S.I., Jusoh, M. and Al Mamun, M. 2021. AMMI and GGE biplot analysis for yield performance and stability assessment of selected Bambara groundnut (Vigna subterranea L. Verdc.) genotypes under the multi-environmental trials (METs). Scientific Reports, 11, e22791. DOI: 10.1038/s41598-021-01411-2
Kona, P., Ajay, B. C., Gangadhara, K., Kumar, N., Choudhary, R.R., Mahatma, M.K., Singh, S., Reddy, K.K., Bera, S.K., Sangh, C., Rani, K., Chavada, Z. and Solanki, K.D. 2024. AMMI and GGE biplot analysis of genotype by environment interaction for yield and yield contributing traits in confectionery groundnut. Scientific Reports, 14, e2943. DOI: 10.1038/s41598-024-52938-z
Nascimento, A.C.C., Nascimento, M., Sagae, V.S., Destro, V., Nardino, M., Olivoto, T. and Jarquín, D. 2025. Bayesian AMMI‐based indexes for genotype selection: Integrating novel stability measures for enhanced G× E inference. Crop Science, 65(5), e70140. DOI: 10.1002/csc2.70140
Olivoto, T., Lúcio, A.D.C., Silva, J.A.G., Marchioro, V.S., Souza, V.Q. and Jost, E. 2019. Mean performance and stability in multi-environment trials I: Combining features of AMMI and BLUP techniques. Agronomy Journal, 111, pp.2949–2960. DOI: 10.2134/agronj2019.03.0220
Perez-Elizalde, S., Jarquín, D. and Crossa, J. 2012. A general Bayesian estimation method of linear-bilinear models applied to plant breeding trials with genotype × environment interaction. Journal of Agricultural, Biological, and Environmental Statistics, 17, pp.15–37. DOI: 10.1007/s13253-011-0063-9
R Core Team. 2024. R: the R project for statistical computing. https://www.r-project.org
Raftery, A.E. and Lewis, S.M. 1992. One long run with diagnostics: Implementation strategies for Markov chain Monte Carlo. Statistical Science, 7, pp.493–497. DOI: 10.1214/ss/1177011143
Shiri, M.R., Estakhr, A., Najafinezhad, H., Hassanzadeh Moghaddam, H., Shirkhani, A. and Ataei, R. 2024. Employing Bayesian probabilistic approach for risk assessment in selection and recommendation of new maize (Zea mays L.) hybrids. Seed and Plant, 40, pp.295–320 (in Persian). DOI: 10.22092/spj.2025.368724.1410
Shiri, M., Estakhr, A., Fareghi, Sh., Najafinezhad, H., Khorasani, S.K., Eshraghi-Nejad, M., Afarinesh, A., Anvari, K. and Ebrahimi, L. 2025a. Evaluating the efficiency of AMMI, GGE biplot, and HO-AMMI stability analysis models for selecting high-yielding and stable maize hybrids in multi-environment trials. Advanced Environmental Science, 23(2), pp.461–476 (in Persian). DOI: 10.48308/envs.2024.1421
Shiri, M., Estakhr, A., Shikhani, A., Mosavat, A. and Bahmankar, M. 2025b. The risk analysis for high-potential and stable cultivars recommendation in maize. Iranian Journal of Field Crop Science, 56(2), pp.77–90 (in Persian). DOI: 10.22059/ijfcs.2024.384144.655108
Shiri, M., Moharramnejad, S., Estakhr, A., Fareghi, S., Najafinezhad, H., Khavari Khorasani, S., Afarinesh, A. and Eshraghi-Nejad, M. 2025c. Strategic risk analysis for the selection of stable and high-potential maize genotypes in multi-environment trials. PLoS One, 20(6), e0325454. DOI: 10.1371/journal.pone.0325454
Smith, B. J. 2007. boa: An R package for MCMC output convergence assessment and posterior inference. Journal of Statistical Software, 21, pp.1-37. DOI: 10.18637/jss.v021.i11
Teodoro, P.E., Azevedo, C.F., Farias, F.J.C., Alves, R.S., de Azevedo Peixoto, L., Ribeiro, L.P., Paulo de Carvalho, L. and Bhering, L.L. 2019. Adaptability of cotton (Gossypium hirsutum) genotypes analysed using a Bayesian AMMI model. Crop and Pasture Science, 70(7), pp.615–621. DOI: 10.1071/CP18318
Viele, K. and Srinivasan, C. 2000. Parsimonious estimation of multiplicative interaction in analysis of variance using Kullback—Leibler information. Journal of Statistical Planning and Inference, 84, pp.201–219. DOI: 10.1016/S0378-3758(99)00151-2
Yang, R.-C., Crossa, J., Cornelius, P.L. and Burgueño, J. 2009. Biplot analysis of genotype × environment interaction: Proceed with caution. Crop Science, 49, pp.1564–1576. DOI: 10.2135/cropsci2008.11.0665
| ||
|
آمار تعداد مشاهده مقاله: 221 تعداد دریافت فایل اصل مقاله: 59 |
||