考虑基因与基因间的交互作用的基因组选择方法研究
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摘要
综合考虑主基因效应以及基因间的交互效应对植物选育种的作用是基因组选择研究关注的热点问题之一.目前已有的研究大多忽略了基因的交互效应,这主要是由于考虑交互效应会大大增加备选基因的数目,从而导致已有的统计建模方法不稳定.本文将基因效应与基因间的交互效应同时引入模型,提出三步模型构建方法以达到简化计算和提高模型预测精度的目标.第一步,不考虑具体模型,通过距离相关筛除方法删掉与响应变量显著无关的基因;第二步,在剩下的基因中,利用贝叶斯方法筛选可能的基因;第三步,基于选出的基因,同时考虑单基因效应和交互效应,利用惩罚方法选择模型并估计参数.通过模拟计算说明我们提出的方法与已有的一步模型选择方法相比具有计算简单、稳健、运行时间少并且预测精度高等优点.最后,将本文的方法应用于油菜花数据,实证分析表明,我们提出的方法显著地提高花期性状的预测精度.
It is one of the hot topics in genome selection research to comprehensively consider the effects of main gene and intergenic interaction on plant breeding.At present,most existing studies ignore the interaction effect of genes,which is mainly because the interaction effect will greatly increase the number of candidate genes,resulting in the instability of existing statistical modeling methods.In this paper,gene effect and interaction effect between genes are introduced into the model at the same time,and a three-step model construction method is proposed to simplify the calculation and improve the prediction accuracy of the model.In the first step,genes significantly unrelated to response variables were deleted by distance correlation screening without considering the specific model;in the second step,the remaining genes were screened for possible genes by Bayes method;the third step is to select the model and estimate the parameters based on the selected genes and considering the single gene effect and interaction effect.Compared with the existing one-step model selection method,the proposed method has the advantages of simple calculation,robustness,low running time and high prediction accuracy.Finally,the method of this paper is applied to the data of rape flower,and the empirical analysis shows that the proposed method can significantly improve the prediction accuracy of flowering traits.
It is one of the hot topics in genome selection research to comprehensively consider the effects of main gene and intergenic interaction on plant breeding.At present,most existing studies ignore the interaction effect of genes,which is mainly because the interaction effect will greatly increase the number of candidate genes,resulting in the instability of existing statistical modeling methods.In this paper,gene effect and interaction effect between genes are introduced into the model at the same time,and a three-step model construction method is proposed to simplify the calculation and improve the prediction accuracy of the model.In the first step,genes significantly unrelated to response variables were deleted by distance correlation screening without considering the specific model;in the second step,the remaining genes were screened for possible genes by Bayes method;the third step is to select the model and estimate the parameters based on the selected genes and considering the single gene effect and interaction effect.Compared with the existing one-step model selection method,the proposed method has the advantages of simple calculation,robustness,low running time and high prediction accuracy.Finally,the method of this paper is applied to the data of rape flower,and the empirical analysis shows that the proposed method can significantly improve the prediction accuracy of flowering traits.
引文
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[21]Hao N,Zhang H H.Interaction Screening for Ultra-High Dimensional Data.Journal of the American Statistical Association,2014,109(507):1285-1301
[22]Li J,Zhong W,Li R,Wu R.A Fast Algorithm for Detecting Gene-gene Interactions in Genome-wide Association Studies.Ann Appl Stat,2014,8(4):2292-2318
[23]Kong Y,Li D,Fan Y,et al.Interaction pursuit in high-dimensional multi-response regression via distance correlation.Annals of Statistics,2017,45(2):897-922
[24]Zhang Y,Thomas C L,Xiang J,et al.QTL meta-analysis of root traits in Brassica napus under contrasting phosphorus supply in two growth systems.Sci.Rep.,2016,6:33113
[25]Li R,Zhong W,Zhu L.Feature Screening via Distance Correlation Learning.Journal of the American Statistical Association,2012,107(499):1129
[26]Li L,Long Y,Zhang L,et al.Genome Wide Analysis of Flowering Time Trait in Multiple Environments via High-throughput Genotyping Technique in Brassica napus L.Plos One,2015,10(3):e0119425
[2]Lipka A E,Kandianis C B,Hudson M E,et al.From association to prediction:statistical methods for the dissection and selection of complex traits in plants.J.Current Opinion in Plant Biology,2015,24:110-118
[3]Xu S,Zhu D,Zhang Q.Predicting hybrid performance in rice using genomic best linear unbiased prediction.J.Proceedings of the National Academy of Sciences of the United States of America,2014,111(34):12456
[4]W(u|")rschum T,Abel S,Zhao Y.Potential of genomic selection in rapeseed(Brassica napus,L.)breeding.J.Plant Breeding,2013,133(1):45-51
[5]Wientjes Y C,Veerkamp R F,Bijma P,et al.Empirical and deterministic accuracies of acrosspopulation genomic prediction.J.Genetics Selection Evolution,2015,47(1):1-14
[6]Wheeler H E,Aquino Michaels K,Gamazon E R,et al.Poly Omic Prediction of Complex Traits:OmicKriging.J.Genetic Epidemiology,2016,38(5):402-415
[7]袁志凯,熊思灿.带环境效应的基因组选择方法研究.应用数学,2016,29(1):225-232)(Yuan Z K,Xiong S C.The Study of Genomic Selection Methods with Environmental Effects.Mathematica Applicata,2016,29(1):225-232)
[8]Henderson C R.Best linear unbiased estimation and prediction under a selection model.Biometrics,1975,31(2):423-447
[9]Liu X Q,Rong J Y,Liu X Y.Best linear unbiased prediction for linear combinations in general mixed linear models.Journal of Multivariate Analysis,2008,99(8):1503-1517
[10]Tibshirani R.Regression Shrinkage and Selection via the Lasso.Journal of the Royal Statistical Society,1996,58(1):267-288
[11]Leo Breiman.Better Subset Regression Using the Nonnegative Garrote.American Society for Quality Control and American Statistical Association,1995
[12]Breiman L.Better Subset Regression Using the Nonnegative Garrote.Technometrics,1995,37(4):373-384
[13]Henderson C R.Applications of linear models in animal breeding.Applications of Linear Models in Animal Breeding,1984
[14]Piepho H P.Ridge Regression and Extensions for Genomewide Selection in Maize.Crop Science,2009,49(4):1165-1176
[15]Whittaker J C,Thompson R,Denham M C.Marker-assisted selection using ridge regression.Annals of Human Genetics,1999,63(4):249
[16]Berlinet A,Thomas-Agnan C.Reproducing Kernel Hilbert Spaces in Probability and Statistics.Springer US,2004
[17]Steinwart I.Mercer's Theorem on General Domains:On the Interaction between Measures,Kernels,and RKHSs.Constructive Approximation,2012,35(3):363-417
[18]Franklin J.The elements of statistical learning:data mining,inference and prediction.Mathematical Intelligencer,2010,99(466):567-567
[19]Cortes C,Vapnik V.Support-vector networks.Machine Learning,1995,20(3):273-297
[20]Flannery B P,Flannery B P,Teukolsky S A,et al.Numerical recipes:the art of scientific computing.Cambridge University Press,1986
[21]Hao N,Zhang H H.Interaction Screening for Ultra-High Dimensional Data.Journal of the American Statistical Association,2014,109(507):1285-1301
[22]Li J,Zhong W,Li R,Wu R.A Fast Algorithm for Detecting Gene-gene Interactions in Genome-wide Association Studies.Ann Appl Stat,2014,8(4):2292-2318
[23]Kong Y,Li D,Fan Y,et al.Interaction pursuit in high-dimensional multi-response regression via distance correlation.Annals of Statistics,2017,45(2):897-922
[24]Zhang Y,Thomas C L,Xiang J,et al.QTL meta-analysis of root traits in Brassica napus under contrasting phosphorus supply in two growth systems.Sci.Rep.,2016,6:33113
[25]Li R,Zhong W,Zhu L.Feature Screening via Distance Correlation Learning.Journal of the American Statistical Association,2012,107(499):1129
[26]Li L,Long Y,Zhang L,et al.Genome Wide Analysis of Flowering Time Trait in Multiple Environments via High-throughput Genotyping Technique in Brassica napus L.Plos One,2015,10(3):e0119425
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