مدل‌های پیشرفته بیزی ammi برای تجزیه و تحلیل پایداری عملکرد دانه هیبرید‌های ذرت در آزمایش‌های چندمحیطی: مقایسه رویکردهای کلاسیک و بیزی

به‌نژاد گران 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 موثری 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 ایستگاه های 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 14 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 1 (ke79017/5111×k1264/5-1) بیشترین عملکرد دانه را داشت و با هیبریدهای شماره 3 (ke76009/311×b73) و 9 (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 1، 3 و 4  (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 اثرمعنی دار از غیرمعنی دار 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 1 و 3 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.

advanced ammi bayesian models for analysis of grain yield stability of maize hybrids in multi-environment trials: a comparison of classical and bayesian approaches

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.introductionmaize (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 methodsin 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 discussionthe 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. referencescrossa, 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/cropsci2010.06.0343nascimento, 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/csc2.70140olivoto, 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/agronj2019.03.0220shiri, 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