Bayesian inference to the genetic control of drought tolerance in spring wheat

Document Type : Research Paper


1 Department of Plant Breeding and Biotechnology, Faculty of Agriculture, University of Tabriz, Tabriz, Iran.

2 Department of Plant Breeding and Biotechnology, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

3 Department of Agronomy and Plant Breeding, Faculty of Agriculture Science, University of Guilan, Rasht, Iran.


Drought is the main abiotic stress seriously influencing wheat production and quality in the world. Information about the inheritance of drought tolerance is necessary to determine the type of breeding program and to develop tolerant cultivars. In this study, Bayesian inference was used to explore the nature and amount of gene effects controlling yield and its components under water deficit and normal conditions by assessment of contrasting bread wheat parents (Bam and Arta) and derived generations from them. Bayesian inference using the Gibbs Variable Selection (GVS) approach and the Deviance Information Criterion (DIC) were applied to identify the most important gene effects and to compare models including different gene effects. The GVS and DIC provided an efficient way to perform the analysis and to introduce the more appropriate models. It can be inferred from the results that the Bayesian analysis provides a robust inference of genetic architecture of yield and yield components in wheat. Since the additive, dominance and epistatic gene actions involved in the inheritance of agronomic characters under both water stress and normal conditions, methods which utilize all types of gene effects, such as hybrid seed production, may be useful in improving yield and its stability in wheat.


Article Title [فارسی]

استنباط بیزی برای کنترل ژنتیکی تحمل به تنش خشکی در گندم بهاره

Authors [فارسی]

  • پرویز صفری 1
  • محمد مقدم واحد 1
  • سیامک علوی کیا 2
  • مجید نوروزی 2
Abstract [فارسی]

خشکی تنش غیرزیستی اصلی است که به طور جدی بر تولید و کیفیت گندم در جهان تأثیر می­گذارد. اطلاعات مربوط به وراثت تحمل به خشکی برای تعیین نوع برنامه اصلاحی و تکوین ارقام متحمل ضروری است. در این مطالعه، استنباط بیزی برای بررسی ماهیت و میزان اثرهای ژنی کنترل کننده عملکرد و اجزای آن در شرایط کمبود آب و شرایط عادی با استفاده از ارزیابی ارقام گندم نان (بم و آرتا) و نسل های مشتق شده از آن­ها مورد استفاده قرار گرفت. استنباط بیزی با استفاده از روش گزینش متغیر گیبز (GVS) و معیار اطلاعات انحراف (DIC) برای شناسایی مهم ترین اثرهای ژنی و مقایسه مدل­هایی با اثرهای ژنی مختلف مورد استفاده قرار گرفت. GVS و DIC روشی کارآمد برای انجام تجزیه و تحلیل و معرفی مدل های مناسب ارایه کردند. می­توان نتیجه گرفت که تجزیه و تحلیل بیزی استنباط قوی از ساختار ژنتیکی عملکرد و اجزای عملکرد در گندم ارایه می دهد. از آن جا که اثرهای افزایشی، غالبیت و اپیستازی در وراثت صفات زراعی درگیر بودند، روش­هایی که از همه انواع اثرهای ژنی استفاده می­کنند مانند اصلاح ارقام هیبرید، در صورت رفع موانع تولید این ارقام، می­تواند در بهبود عملکرد و پایداری آن در گندم سودمند باشد.

Keywords [فارسی]

  • استنباط بیزی
  • روش­های زنجیر-مونت کارلو
  • کمبود آب
  • گزینش متغیر گیبز
  • گندم
  • معیار اطلاعات انحراف
Akaike H, 1973. Maximum likelihood identification of Gaussian autoregressive moving average models. Biometrika 60 (2): 255-265.
Balestre M, Von Pinho RG and Brito AH, 2012. Bayesian inference to study genetic control of resistance to gray leaf spot in maize. Genetics and Molecular Research 11(1): 17-29.
Dellaportas P, Forster JJ and Ntzoufras I, 2002. On Bayesian model and variable selection using MCMC. Statistics and Computing 12(1): 27-36.
Elster C and Wübbeler G, 2016. Bayesian regression versus application of least squares- an example. Metrologia 53(1): 10-16.
Fikse WF, Rekaya R and Weigel KA, 2003. Genotype × environment interaction for milk production in Guernsey cattle. Journal of Dairy Science 86(5): 1821-1827.
Fouskakis D, Ntzoufras I and Draper D, 2009. Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care. Annals of Applied Statistics 3(2): 663-690.
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(6): 721-741.
George EI and McCulloch RE, 1993. Variable selection via Gibbs sampling. Journal of the American Statistical Association 88(423): 881-889.
Hastings WK, 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1): 97-109.
Ijaz, US and Kashif M, 2013. Genetic study of quantitative traits in spring wheat through generation means analysis. American-Eurasian Journal of Agricultural and Environmental Sciences 13(2): 191-197.
Khattab SAM, Esmail RM and Al-Ansary AMF, 2010. Genetical analysis of some quantitative traits in bread wheat (Triticum aestivum L.). New York Science Journal 3(11): 152-157.
Longin CFH, Mühleisen J, Maurer HP, Zhang H, Gowda M and Reif JC, 2012. Hybrid breeding in autogamous cereals. Theoreticaland Applied Genetics 125:1087-1096.
Lynch SM, 2007. Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. Springer-Verlag, New York, USA.
Mather K and Jinks JL, 1971. Biometrical Genetics. 2nd ed. Chapman & Hall, London, UK.
Mathew B, Bauer AM, Koistinen P, Reetz TC, Léon J and Sillanpää MJ, 2012. Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters. Heredity 109(4): 235-245.
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH and Teller E, 1953. Equation of state calculations by fast computing machines. Journal of Chemical Physics 21(6): 1087-1092.
Mettle FO, Asiedu L, Quaye EN and Asare-Kumi AA, 2016. Comparison of least squares method and Bayesian with multivariate normal prior in estimating multiple regression parameters. British Journal of Mathematics and Computer Science 15(1): 1-8. 4th edition. WCB McGraw-Hill, New York, USA.
Nezhadahmadi A, Prodhan ZH and Faruq G, 2013. Drought tolerance in wheat.  Scientific World Journal 2013: 1-12.
Novoselovic D, Baric M, Drezner G, Gunjaca J and Lalic A, 2004. Quantitative inheritance of some wheat plant traits. Genetics and Molecular Biology 27(1): 92-98.
Ntzoufras I, 2002. Gibbs variable selection using BUGS. Journal of Statistical Software 7(7): 1-19.
Ntzoufras I, 2011. Bayesian Modeling Using WinBUGS. John Wiley & Sons, Hoboken, New Jersey, USA.
Omer SO, Abdalla AH, Ceccarelli S, Grando S and Singh M, 2014. Bayesian estimation of heritability and genetic gain for subsets of genotypes evaluated in a larger set of genotypes in a block design. European Journal of Experimental Biology 4(3): 566-575.
Rekaya R, Weigel KA and Gianola D, 2003. Bayesian estimation of parameters of a structural model for genetic covariances between milk yield in five regions of the United States. Journal of Dairy Science 86(5): 1837-1844.
SAS Institute, 2002. SAS User's Guide: Statistics Version 9 for Windows. SAS Institute, Carry, NC, USA.
Shriner D and Yi N, 2009. Deviance information criterion (DIC) in Bayesian multiple QTL mapping. Computational Statistics and Data Analysis 53(5): 1850-1860.
Spiegelhalter DJ, Best NG, Carlin BP and Van Der Linde A, 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society 64(4): 583-639.
Spiegelhalter DJ, Thomas A, Best NG and Lunn D, 2003. WinBUGS Version 1.4 User Manual. MRC Biostatistics Unit, Cambridge University, Cambridge, UK.
Waldmann P, Hallander J, Hoti F and Sillanpää MJ, 2008. Efficient Markov chain Monte Carlo implementation of Bayesian analysis of additive and dominance genetic variances in noninbred pedigrees. Genetics 179(2): 1101-1112.
Xu S, 2003. Estimating polygenic effects using markers of the entire genome. Genetics 163(2): 789-801.
Yi N, Shriner D, Banerjee S, Mehta T, Pomp D and Yandell BS, 2007. An efficient Bayesian model selection approach for interacting quantitative trait loci models with many effects. Genetics 176(3): 1865-1877.
Yi N, Yandell BS, Churchill GA, Allison DB, Eisen EJ and Pomp D, 2005. Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics 170(3): 1333-1344.