林木QTL功能作图统计方法
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摘要
QTL功能作图统计方法将动态性状的发育机制组装到QTL作图统计模型中,目前已经建立了近交群体(回交群体、F2群体等)的统计模型。林木属于异交群体,有许多自身的生物学特性,不能简单套用近交群体的作图方法,必须建立适合林木自身特性的QTL作图方法。
本文针对林木二倍体全同胞家系,考虑双亲的QTL基因型一个纯合,另一个杂合的情况,将全同胞家系所有的标记分离类型对和连锁相类型考虑到模型中,并将Logistic生长曲线组装到模型中,建立了林木F1代群体的QTL功能作图统计方法,使用EM算法获得模型未知参数向量的极大似然估计。
从模拟结果来看,即使在个体性状值向量的维数、遗传力和群体大小都较小的情况下,无论是QTL位置还是各个参数估计的均值都与真值非常接近,且误差均方根都比较小,这说明模型在定位QTL和参数估计方面有明显的效力;当个体性状值向量的维数、遗传力水平和群体大小任何一个因素提高时都能明显改善参数估计的精确度。通过分析一组杨树的实例数据,使用林木QTL功能作图的方法对影响杨树单株生根总数和最大根长两个性状的QTL进行定位来寻找与生根能力相关的QTL,总共搜索到三个显著的控制不定根发育轨迹的QTL。
我们编写了林木全同胞家系QTL功能作图软件——FsQtlFunMap 1.0,该软件在计算速度上有明显的优势,可进行相关的统计分析和图形绘制。
Functional mapping of quantitative trait loci (QTL) has embedded the biological mechanisms and processes of dynamic traits in the statistical method of QTL mapping. Although the functional mapping statistical model for mapping QTL has been well developed in inbred lines, it has not been proposed in outbred species, e.g. a full-sib family, in which the number of alleles may vary over loci and the linkage phases are usually unknown between loci. Since forest trees have several unique biological characteristics and most of them are outbred species, we should not directly apply the functional mapping model for inbred species to them.
The objective of this study is to develop a functional mapping statistical model for a full-sib family in forest trees. We suppose that the QTL genotype of one parent is heterozygous but the other is homozygous, and consider all pairwise combinations of marker segregation types and all possible linkage phases between mark loci in a diploid full-sib family into our model. A maximum likelihood approach based on a logistic-mixture model, implemented with EM algorithm, was developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories.
According to the results of a large number of simulations, we can infer that the estimation precision of the QTL effects and position is dependent on dimensions of measured variable, sample size and heritability. Even though when the dimension of measured variable, heritability and sample size are all smaller, the mean of the estimation of QTL location and each effective parameters approximates to the true value very closely and all the SMSEs of MLEs are also smaller, increased one of the factors (i.e. dimensions of measured variable, sample size and heritability) can decrease the SMSEs of MLEs of partial or all parameters obviously. All that indicate our model was robust for identifying the QTL position and estimating the parameters of QTL effects and residual (co)variance.
We use an example of poplar to demonstrate the validation of our functional mapping method for mapping QTL affecting growth trajectories in practice. The high-density genetic linkage map has been constructed with a mix of marker systems. Functional mapping identified two QTL affecting MRL (maximal root length) on the linkage 3 and one QTL affecting TNR (total root number per cutting) on the linkage 8.
We have developed Windows software, FsQtlFunMap 1.0, which was written in Visual C++ 6.0 to implement our functional mapping method for a full-sib family. FsQtlFunMap 1.0, which was used to map QTL in a full-sib family in forest trees, can do QTL statistical analysis and draw relevant figures. It has the remarkable advantage of speed for calculating.
本文针对林木二倍体全同胞家系,考虑双亲的QTL基因型一个纯合,另一个杂合的情况,将全同胞家系所有的标记分离类型对和连锁相类型考虑到模型中,并将Logistic生长曲线组装到模型中,建立了林木F1代群体的QTL功能作图统计方法,使用EM算法获得模型未知参数向量的极大似然估计。
从模拟结果来看,即使在个体性状值向量的维数、遗传力和群体大小都较小的情况下,无论是QTL位置还是各个参数估计的均值都与真值非常接近,且误差均方根都比较小,这说明模型在定位QTL和参数估计方面有明显的效力;当个体性状值向量的维数、遗传力水平和群体大小任何一个因素提高时都能明显改善参数估计的精确度。通过分析一组杨树的实例数据,使用林木QTL功能作图的方法对影响杨树单株生根总数和最大根长两个性状的QTL进行定位来寻找与生根能力相关的QTL,总共搜索到三个显著的控制不定根发育轨迹的QTL。
我们编写了林木全同胞家系QTL功能作图软件——FsQtlFunMap 1.0,该软件在计算速度上有明显的优势,可进行相关的统计分析和图形绘制。
Functional mapping of quantitative trait loci (QTL) has embedded the biological mechanisms and processes of dynamic traits in the statistical method of QTL mapping. Although the functional mapping statistical model for mapping QTL has been well developed in inbred lines, it has not been proposed in outbred species, e.g. a full-sib family, in which the number of alleles may vary over loci and the linkage phases are usually unknown between loci. Since forest trees have several unique biological characteristics and most of them are outbred species, we should not directly apply the functional mapping model for inbred species to them.
The objective of this study is to develop a functional mapping statistical model for a full-sib family in forest trees. We suppose that the QTL genotype of one parent is heterozygous but the other is homozygous, and consider all pairwise combinations of marker segregation types and all possible linkage phases between mark loci in a diploid full-sib family into our model. A maximum likelihood approach based on a logistic-mixture model, implemented with EM algorithm, was developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories.
According to the results of a large number of simulations, we can infer that the estimation precision of the QTL effects and position is dependent on dimensions of measured variable, sample size and heritability. Even though when the dimension of measured variable, heritability and sample size are all smaller, the mean of the estimation of QTL location and each effective parameters approximates to the true value very closely and all the SMSEs of MLEs are also smaller, increased one of the factors (i.e. dimensions of measured variable, sample size and heritability) can decrease the SMSEs of MLEs of partial or all parameters obviously. All that indicate our model was robust for identifying the QTL position and estimating the parameters of QTL effects and residual (co)variance.
We use an example of poplar to demonstrate the validation of our functional mapping method for mapping QTL affecting growth trajectories in practice. The high-density genetic linkage map has been constructed with a mix of marker systems. Functional mapping identified two QTL affecting MRL (maximal root length) on the linkage 3 and one QTL affecting TNR (total root number per cutting) on the linkage 8.
We have developed Windows software, FsQtlFunMap 1.0, which was written in Visual C++ 6.0 to implement our functional mapping method for a full-sib family. FsQtlFunMap 1.0, which was used to map QTL in a full-sib family in forest trees, can do QTL statistical analysis and draw relevant figures. It has the remarkable advantage of speed for calculating.
引文
[1]盖钧镒,章元明,王建康. 2003.植物数量性状遗传体系.北京:科学出版社.
[2]高会江,孙华,陈学辉,杨润清,徐士忠. 2006a. F2群体动态性状基因定位的极大似然分析.东北林业大学学报. 34(1): 72-77.
[3]高会江,杨润清. 2006b.动态性状基因座的复合区间定位.科学通报. 51(13): 1552-1557.
[4]刘杰,何德,李永红. 2008.林木遗传图谱构建的研究进展.生物技术通报, 1: 38-41.
[5]盛志廉,陈瑶生. 1999.数量遗传学.北京:科学出版社.
[6]施季森,童春发.2006.林木遗传图谱构建和QTL定位统计分析.北京:科学出版社.
[7]孙华. 2003.动态性状基因定位理论框架的初步构建[硕士学位论文].哈尔滨:东北农业大学.
[8]童春发,施季森. 2002.标记基因型中QTL基因型条件概率分布.生物数学学报. 17(4): 461-470.
[9]邬荣领,林敏,赵伟,侯伟,张博,诸葛强,黄敏仁,徐立安. 2006.动态复杂性状遗传结构研究的统计模(英文).南京林业大学学报(自然科学版). (03): 1-12.
[10]徐宁迎. 2000.量性状基因位点定位的常用试验设计方法.浙江畜牧兽医, 2: 42-43.
[11]杨润清,高会江,孙华,Shizhong Xu. 2004a.远交群体动态性状基因定位的似然分析Ⅰ.理论方法.遗传学报. 31(10): 1116-1122.
[12]杨润清,高会江,孙华,Shizhong Xu. 2004b.远交群体动态性状基因定位的似然分析Ⅱ.模拟研究.遗传学报. 31(11): 1254-1261.
[13]尹佟明,黄敏仁. 1995.林木遗传图谱构建和数量性状基因定位.世界林业研究, 3: 6-12.
[14]张博. 2005.杨树比较作图及重要性状QTLs定位[博士学位论文].南京:南京林业大学.
[15]朱军主编. 2002.遗传学.北京:中国农业出版社, 3: 311-313.
[16]朱军. 1999.运用混合线性模型定位复杂数量性状基因的方法.浙江大学学报(自然科学版), 33(3): 327-335.
[17] Banerjee S, Yandell B S, Yi N. 2008. Bayesian quantitative trait loci mapping for multiple traits. Genetics, 179(4): 2275-2289.
[18] Baret P V, Knott S A, Visscher P M. 1998. On the use of linear regression and maximum likelihood for QTL mapping in half-sib designs. Genet. Res., 72: 149-158.
[19] Bink M C, Janss L L, Quaas R L. 2000. Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations. Genet Res., 75(2): 231-241.
[20] Botstein D, White R L, Skolnick M, Davis R W. 1980. Construction of a genetic linkage map in man using restriction fragment length polymorphisms. Am. J. Hum. Genet., 32: 314-331.
[21] Broman K W, Wu H, Sen S, Churchill G A. 2003. R/qtl: QTL mapping in experimental crosses. Bioinformatics, 19: 889-890.
[22] Cockerham C C. 1954. An extension of the concept of partitioning hereditary variance for analysis of covariance among relatives when epistasis is present. Genetics, 39(6): 859-882.
[23] Cui Y H, Li S Y, Li G X. 2008. Functional mapping imprinted quantitative trait loci underlying developmental characteristics. Theoretical Biology and Medical Modelling, 6: 5.
[24] Cui Y H, Wu R L, Casella G, Zhu J. 2008. Nonparametric functional mapping quantitative trait loci underlyingprogrammed cell death. Statistical Applications in Genetics and Molecular Biology, 7: 1, Article 4.
[25] Cui Y H, Zhu J, Wu R L. 2006. Functional mapping for genetic control of programmed cell death. Physiol Genomics, 25: 458-469.
[26] de Koning D J, Visscher P M, Knott S A, Haley C S . 1998 . A strategy for QTL detection in half-sib populations. Animal Science, 67: 257-268.
[27] Dempster A P, Laird N M, Rubin D B. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Stattistival Society Series B, 39(1): 1-38.
[28] Doerge R W, Churchill G A. 1996. Permutation tests for multiple loci affecting a quantitative character. Genetics 142: 285-294.
[29] Donis-Keller H, Green P, Helms C, Cartinhour S, Weiffenbach B, Stephens K, Keith T, Bowden D, Smith D, Lander E, Botstein D, Akots G, Rediker K, Gra- vius T, Brown V, Rising M, Parker C, Powers J, Watt D, Kauffman E, Bricker A, Phipps P, Muller-Kahle H, Fulton T, Ng S, Schumm J, Braman J, Knowlton R, Barker D, Crooks S, Lincoln S, Daly M, Abrahamson J. 1987. A genetic linkage map of the human genome. Cell., 51: 319-337.
[30] Edwards M D, Stuber C W, Wendel J F. 1987. Molecular marker facilitated investigations of quantitative trait loci in maize. I. Numbers, genomic distribution and types of gene action. Genetics, 116(1): 113-125.
[31] Fulker D W, Cardon L R. 1994. A sib-pair approach to interval mapping of quantitative trait loci. Am. J. Hum. Genet., 54: 1092-1103.
[32] Green P J. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82: 711-732.
[33] Grignola F E, Hoeschele I, Tier B. 1996a. Mapping quantitative trait loci in outcross population via residual maximum likelihood. I: Methodology. Genet. Select. Evol., 28: 479-490.
[34] Grignola F E, Hoeschele I, Zhang Q, Thaller G. 1996b. Mapping quantitative trait loci in outcross populations via residual maximum likelihood. II: A simulation study. Genet. Sel. Evol., 28: 491-504.
[35] Grignola F E, Zhang Q, Hoeschele I. 1997. Mapping linked quantitative trait loci via Residual Maximum Likelihood. Genet. Sel. Evol., 22: 419-430.
[36] Jansen R C. 1993. Interval Mapping of Multiple Quantitative Trait Loci. Genetics, 135(1): 205-211.
[37] Jansen R C. 1996. A General Monte Carlo Method for Mapping Multiple Quantitative Trait Loci. Genetics, 142(1): 305-311.
[38] Jayakar S D. 1970. On the detection and estimation of linkage between a locus influencing a quantitative character and a maker locus. Biometrics, 26: 451- 464.
[39] Jiang C, Zeng Z B. 1995. Multiple trait analysis of genetic mapping for quantitative trait loci. Genetics, 140(3): 1111-1127.
[40] Kao C H, Zeng Z B, Teasdale R D. 1999. Multiple interval mapping for quantitative trait loci. Genetics, 152(3): 203-1216.
[41] Kao C H, Zeng Z B. 1997. General formulas for obtaining the MLEs and the asymptotic variance-covariance matrix in mapping quantitative trait loci when using the EM algorithm. Biometrics, 53: 359-371.
[42] Knott S A, Elsen J M, Haley C S. 1996. Methods for multiple-marker mapping of quantitative trait loci in half-sib populations. Theor. Appl. Genet., 93(1): 71-80.
[43] Lander E S, Botstein D. 1989. Mapping medelian factors underlying quantitative traits using RFLP linkage maps. Genetics, 121(1): 185-199.
[44] Lander E S, Green P, Abrahamson J, Barlow A, Daly M J, Lincoln S E, Newberg LA. 1987. MAPMAKER: an interactivecomputer package for constructing primary genetic linkage maps of experimental and natural populations. Genomics, 1(2): 174-81.
[45] Lin M, Aquilante C, Johnson J A, Wu R L. 2005a. Sequencing drug response with HapMap. Pharmacogenomics J., 5: 149-156.
[46] Lin M, Wu R L. 2005b. Theoretical basis for the identification of allelic variants that encode drug efficacy and toxicity. Genetics, 170(2): 919-928.
[47] Lin M, Wu R L. 2006. A joint model for nonparametric functional mapping of longitudinal trajectory and time-to-event. BMC Bioinformatics, 7(1):138.
[48] Liu J, Liu Y, Liu X, Deng H W. 2007. Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components. Am. J. Hum. Genet., 81(2): 304-320.
[49] Liu T, Johnson J A, Casella G, Wu R L. 2004. Sequencing complex diseases with HapMap. Genetics, 168(1): 503-511.
[50] Louis T A. 1982. Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical society, Series B, 44: 226-233.
[51] Luo Z W, Kearsey M J. 1989. Maximum likelihood estimation of linkage between a marker gene and a quantitative locus. Heredity, 63: 401-408.
[52] Ma C X , Casella G, Wu R L. 2002. Functional mapping of quantitative trait loci underlying the character process: A theoretical framework. Genetics, 161(4): 1751-1762.
[53] Ma C X, Wu R L, Casella G. 2004. FunMap: functional mapping of complex traits. Bioinformatics, 20: 1808-1811.
[54] Mackinnon M J, Weller J I. 1995. Methodology and accuracy of estimation of quantitative loci parameters in a half-sib design using maximum likelihood. Genetics, 141(2): 755-770.
[55] Maliepaard C, Jansen, J and Vanooijen J W. 1997. Linkage analysis in a full-sib family of an outbreeding plant species: overview and consequences for applications. Genet. Res., 70: 237-250.
[56] Manly K F, Cudmore R H Jr, Meer J M. 2001. Map Manager QTX, cross-platform software for genetic mapping. Mammalian Genome, 12(12): 930-2.
[57] Meuwissen T H, Goddard M E. 2004. Mapping multiple QTL using linkage disequilibrium and linkage analysis information and multitrait data. Genetics Selection Evolution, 363: 261-279.
[58] Nunez-Anton V, Zimmerman D L. 2000. Modeling nonstationary longitudinal data.Biometrics, 56: 699-705.
[59] Pearl R. 1925. The Biology of Population Growth. Knopf, New York.
[60] Rodriguez-Zas S L, Southey B R, Heyen D W, Lewin H A. 2002. Detection of quantitative trait loci influencing dairy traits using a model for longitudinal data. J. Dairy. Sci., 85: 2681-2691.
[61] Satagopan J M, Yandell B S, Newton M A, Osborn T C. 1996. A Bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo. Genetics, 144(2): 805-816.
[62] Seaton G, Haley C S, Knott S A, Kearsey M, Visscher P M. 2002. QTL Express: mapping quantitative trait loci in simple and complex pedigrees. Bioinformatics, 18: 339-340.
[63] Sillanp?? M A, Arjas E. 1999. Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics, 151(4): 1605-1619.
[64] Sollar M, Brody T, Genizi A. 1976. On the Power of Experimental Designs for the Detection of Linkage between Marker Loci and Quantitative Loci in Crosses between Inbred Lines. Theoretical and Applied Genetics, 47: 35-39.
[65] Spelman R J, Coppiters W, Karim L, Van Arendonk J A, Bocenhuis H. 1996. Quantitatice trait loci analysis for five milkproduction traits on chromosome six in the Dutch Holstein-Friesian population. Genetics, 144(4): 1799-1808.
[66] Uimari P, Hoeschele I. 1997. Mapping-Linked quantitative trait loci using Bayesian analysis and Markov Chain Monte Carlo algorithms. Genetics, 146(2): 735-743.
[67] van Ooijen J W. 2004. MapQTL 5: Software for the Mapping of Quantitative Trait Loci in Experimental Populations, Kyazma BV, Wageningen, The Netherlands.
[68] Visscher P M, Whittaker J C, Jansen R C. 2000. Mapping multiple QTL of different effects: comparison of a simple sequential testing strategy and multiple QTL mapping. Molecular Breeding, 6: 11-24.
[69] Wang D L, Zhu J, Li Z K, Paterson A H. 1999. Mapping QTL with epistatic effects and QTL environment interactions by mixed linear model approaches. Theor Appl Genet, 99: 1255-1264.
[70] Wang S, Basten C J, Zeng Z B. 2006. Windows QTL Cartographer 2.5. Department of Statistics, North Carolina State University, Raleigh, USA. (http://statgen.ncsu.edu/qtlcart/WQTLCart.htm).
[71] Weller J I. 1986. Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers. Biometrics, 42(3): 627-640.
[72] West G B, Brown J H, Enquist B J. 2001. A general model for ontogenetic growth. Nature, 413: 628-631.
[73] Wu R L, Ma C X, Chang M, Littell, R C, Wu S S, Yin T M, Huang M R, Wang M X, and Casella, G. 2002. A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories. Genet. Res., 19: 235-245.
[74] Wu R L, Ma C X, Yang, C K, Chang M, Littell R C, SANTRA U, Wu S S, Yin T M, Huang M R, Wang M X, Casella G. 2003a. Quantitative trait loci for growth trajectories in Populus. Genet. Res., 81: 51-64.
[75] Wu R L, Ma C X, Zhao W, Casella G. 2003b. Functional mapping of quantitative trait loci underlying growth rates: a parametric model. Physiol. Genomics, 14: 241-249.
[76] Wu R L, Ma C X, Lin M, Wang Z H, Casella G. 2004. Functional mapping of growth QTL using a transform-both-sides logistic model. Biometrics, 60: 729-738.
[77] Wu R L, Ma C X, Hou W, Corva P, Medrano J F. 2005. Functional Mapping of Quantitative Trait Loci That Interact With the hg Mutation to Regulate Growth Trajectories in Mice. Genetics, 171(1): 239-249
[78] Wu R L and Lin M. 2006. Functional mapping-How to map and study the genetic architecture of complex dynamic traits. Nat. Rev. Genet., 7(3): 229-237.
[79] Wu S, Yang J, Wu R L. 2007. Semiparametric functional mapping of quantitative trait loci governing long-term HIV dynamics. Bioinformatics, 23: i569-i576.
[80] Xu C W, Wang X F, Li Z K, Xu S Z. 2009. Mapping QTL for multiple traits using Bayesian statistics. Genetics Research, 91: 23-37.
[81] Xu S Z, Yi N J. 2000. Mixed model analysis of quantitative trait loci. Proc. Natl. Acad. Sci. USA 97: 14542-14547.
[82] Xu S Z, Atchley W R. 1995. A random model approach to interval mapping of quantitative trait loci. Genetics, 141(3): 1189-1197.
[83] Yandell B S, Mehta T, Banerjee S, Shriner D, Venkataraman R, Moon J Y, Neely W W, Wu H, von Smith R, Yi N J. 2007. R/qtlbim: QTL with Bayesian Interval Mapping in experimental crosses. Bioinformatics, 23(5): 641-643.
[84] Yang J, Wu R L, Casella G. 2009. Nonparametric Functional Mapping of Quantitative Trait Loci. Biometrics, 65: 30-39.
[85] Yang J, Hu C C, Hu H, Yu R D, Xia Z, Ye X Z, Zhu J. 2008. QTLNetwork: mapping and visualizing genetic architecture of complex traits in experimental populations. Bioinformatics, 24: 721-723.
[86] Yang R Q, Gao H J, Wang X, Zhang J, Zeng Z B, and Wu R L. (2007). A Semiparametric Approach for Composite Functional Mapping of Dynamic Quantitative Traits. Genetics, 177(3): 1859-1870.
[87] Yang R Q, Tian, Q, and Xu S Z. 2006. Mapping quantitative trait loci for longitudinal traits in line crosses. Genetics, 173: 2339-2356.
[88] Yang R Q, Xu S Z. 2007. Bayesian shrinkage analysis of quantitative trait loci for dynamic traits. Genetics, 2007: 1169-1185.
[89] Yi N J, Banerjee S. 2009. Hierarchical Generalized Linear Models for Multiple Quantitative Trait Locus Mapping. Genetics, 181: 1101-1113.
[90] Yi N J. 2004. A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics, 167(2): 967-975.
[91] Yi N J, Yandell B S, Churchill G A, Allison D B, Eisen E J, Pomp D. 2005. Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics, 170(3): 1333-1344.
[92] Yin T M, Zhang X Y, Huang M R, Wang M X, Zhuge Q, Tu S M, Zhu L H, Wu R L. 2002. Molecular linkage maps of the Populus genome. Genome, 45: 541-555.
[93] Zeng Z B. 1993. Theoretical basis of separation of multiple linked gene effects on mapping quantitative trait loci. Proc. Natl. Acad. Sci. USA, 90: 10972-10976.
[94] Zeng Z B. 1994. Precision mapping of quantitative trait loci. Genetics, 136(4): 1457-1468.
[95] Zhang Q, Boidhard D, Hoeschele I, et al. 1998. Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree. Genetics, 149(4): 1959-1973.
[96] Zhang Y M, Xu S. 2005a. Advanced statistical methods for detecting multiple quantitative trait loci. Rec. Res. Dev. Genet. Breed., 2(1): 1-23.
[97] Zhang Y M, Xu S. 2005b. A penalized maximum likelihood method for estimating epistatic effects of QTL. Heredity, 95(1): 96-104.
[98] Zhang Y M. 2006. Shrinkage estimation method for mapping multiple quantitative trait loci. Acta Genetica Sinica, 33(10): 861-869.
[99] Zhao W, Ma C X, Cheverud, M, Wu R L. 2003. A Unifying Statistical Model for QTL Mapping of Genotype×Sex Interaction for Developmental Trajectories. Physiological Genomics, 19: 218-227.
[100] Zhao W, Wu R L, Ma C X, Casella G. 2004. A fast algorithm for functional mapping of complex traits. Genetics 167(4): 2133-2137.
[101] Zhao W, Chen Y Q, Casella G, Cheverud J M, Wu R L. 2005. A non-stationary model for functional mapping of complex traits. Bioinformatics, 21(10): 2469-2477.
[102] Zhu J, Weir B S. 1998. Mixed model approaches for genetic analysis of quantitative traits. Chen L S, Ruan S G, Zhu J. Advanced topics in biomathematics procceedings of international conference on mathematics biology. Singapore: World Scientific Publishing Co., 321-330.
[103] Zimmerman D L, Nunez-Anton V. 2001. Parametric modelling of growth curve data: An overview. Test, 10: 1-73.
[2]高会江,孙华,陈学辉,杨润清,徐士忠. 2006a. F2群体动态性状基因定位的极大似然分析.东北林业大学学报. 34(1): 72-77.
[3]高会江,杨润清. 2006b.动态性状基因座的复合区间定位.科学通报. 51(13): 1552-1557.
[4]刘杰,何德,李永红. 2008.林木遗传图谱构建的研究进展.生物技术通报, 1: 38-41.
[5]盛志廉,陈瑶生. 1999.数量遗传学.北京:科学出版社.
[6]施季森,童春发.2006.林木遗传图谱构建和QTL定位统计分析.北京:科学出版社.
[7]孙华. 2003.动态性状基因定位理论框架的初步构建[硕士学位论文].哈尔滨:东北农业大学.
[8]童春发,施季森. 2002.标记基因型中QTL基因型条件概率分布.生物数学学报. 17(4): 461-470.
[9]邬荣领,林敏,赵伟,侯伟,张博,诸葛强,黄敏仁,徐立安. 2006.动态复杂性状遗传结构研究的统计模(英文).南京林业大学学报(自然科学版). (03): 1-12.
[10]徐宁迎. 2000.量性状基因位点定位的常用试验设计方法.浙江畜牧兽医, 2: 42-43.
[11]杨润清,高会江,孙华,Shizhong Xu. 2004a.远交群体动态性状基因定位的似然分析Ⅰ.理论方法.遗传学报. 31(10): 1116-1122.
[12]杨润清,高会江,孙华,Shizhong Xu. 2004b.远交群体动态性状基因定位的似然分析Ⅱ.模拟研究.遗传学报. 31(11): 1254-1261.
[13]尹佟明,黄敏仁. 1995.林木遗传图谱构建和数量性状基因定位.世界林业研究, 3: 6-12.
[14]张博. 2005.杨树比较作图及重要性状QTLs定位[博士学位论文].南京:南京林业大学.
[15]朱军主编. 2002.遗传学.北京:中国农业出版社, 3: 311-313.
[16]朱军. 1999.运用混合线性模型定位复杂数量性状基因的方法.浙江大学学报(自然科学版), 33(3): 327-335.
[17] Banerjee S, Yandell B S, Yi N. 2008. Bayesian quantitative trait loci mapping for multiple traits. Genetics, 179(4): 2275-2289.
[18] Baret P V, Knott S A, Visscher P M. 1998. On the use of linear regression and maximum likelihood for QTL mapping in half-sib designs. Genet. Res., 72: 149-158.
[19] Bink M C, Janss L L, Quaas R L. 2000. Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations. Genet Res., 75(2): 231-241.
[20] Botstein D, White R L, Skolnick M, Davis R W. 1980. Construction of a genetic linkage map in man using restriction fragment length polymorphisms. Am. J. Hum. Genet., 32: 314-331.
[21] Broman K W, Wu H, Sen S, Churchill G A. 2003. R/qtl: QTL mapping in experimental crosses. Bioinformatics, 19: 889-890.
[22] Cockerham C C. 1954. An extension of the concept of partitioning hereditary variance for analysis of covariance among relatives when epistasis is present. Genetics, 39(6): 859-882.
[23] Cui Y H, Li S Y, Li G X. 2008. Functional mapping imprinted quantitative trait loci underlying developmental characteristics. Theoretical Biology and Medical Modelling, 6: 5.
[24] Cui Y H, Wu R L, Casella G, Zhu J. 2008. Nonparametric functional mapping quantitative trait loci underlyingprogrammed cell death. Statistical Applications in Genetics and Molecular Biology, 7: 1, Article 4.
[25] Cui Y H, Zhu J, Wu R L. 2006. Functional mapping for genetic control of programmed cell death. Physiol Genomics, 25: 458-469.
[26] de Koning D J, Visscher P M, Knott S A, Haley C S . 1998 . A strategy for QTL detection in half-sib populations. Animal Science, 67: 257-268.
[27] Dempster A P, Laird N M, Rubin D B. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Stattistival Society Series B, 39(1): 1-38.
[28] Doerge R W, Churchill G A. 1996. Permutation tests for multiple loci affecting a quantitative character. Genetics 142: 285-294.
[29] Donis-Keller H, Green P, Helms C, Cartinhour S, Weiffenbach B, Stephens K, Keith T, Bowden D, Smith D, Lander E, Botstein D, Akots G, Rediker K, Gra- vius T, Brown V, Rising M, Parker C, Powers J, Watt D, Kauffman E, Bricker A, Phipps P, Muller-Kahle H, Fulton T, Ng S, Schumm J, Braman J, Knowlton R, Barker D, Crooks S, Lincoln S, Daly M, Abrahamson J. 1987. A genetic linkage map of the human genome. Cell., 51: 319-337.
[30] Edwards M D, Stuber C W, Wendel J F. 1987. Molecular marker facilitated investigations of quantitative trait loci in maize. I. Numbers, genomic distribution and types of gene action. Genetics, 116(1): 113-125.
[31] Fulker D W, Cardon L R. 1994. A sib-pair approach to interval mapping of quantitative trait loci. Am. J. Hum. Genet., 54: 1092-1103.
[32] Green P J. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82: 711-732.
[33] Grignola F E, Hoeschele I, Tier B. 1996a. Mapping quantitative trait loci in outcross population via residual maximum likelihood. I: Methodology. Genet. Select. Evol., 28: 479-490.
[34] Grignola F E, Hoeschele I, Zhang Q, Thaller G. 1996b. Mapping quantitative trait loci in outcross populations via residual maximum likelihood. II: A simulation study. Genet. Sel. Evol., 28: 491-504.
[35] Grignola F E, Zhang Q, Hoeschele I. 1997. Mapping linked quantitative trait loci via Residual Maximum Likelihood. Genet. Sel. Evol., 22: 419-430.
[36] Jansen R C. 1993. Interval Mapping of Multiple Quantitative Trait Loci. Genetics, 135(1): 205-211.
[37] Jansen R C. 1996. A General Monte Carlo Method for Mapping Multiple Quantitative Trait Loci. Genetics, 142(1): 305-311.
[38] Jayakar S D. 1970. On the detection and estimation of linkage between a locus influencing a quantitative character and a maker locus. Biometrics, 26: 451- 464.
[39] Jiang C, Zeng Z B. 1995. Multiple trait analysis of genetic mapping for quantitative trait loci. Genetics, 140(3): 1111-1127.
[40] Kao C H, Zeng Z B, Teasdale R D. 1999. Multiple interval mapping for quantitative trait loci. Genetics, 152(3): 203-1216.
[41] Kao C H, Zeng Z B. 1997. General formulas for obtaining the MLEs and the asymptotic variance-covariance matrix in mapping quantitative trait loci when using the EM algorithm. Biometrics, 53: 359-371.
[42] Knott S A, Elsen J M, Haley C S. 1996. Methods for multiple-marker mapping of quantitative trait loci in half-sib populations. Theor. Appl. Genet., 93(1): 71-80.
[43] Lander E S, Botstein D. 1989. Mapping medelian factors underlying quantitative traits using RFLP linkage maps. Genetics, 121(1): 185-199.
[44] Lander E S, Green P, Abrahamson J, Barlow A, Daly M J, Lincoln S E, Newberg LA. 1987. MAPMAKER: an interactivecomputer package for constructing primary genetic linkage maps of experimental and natural populations. Genomics, 1(2): 174-81.
[45] Lin M, Aquilante C, Johnson J A, Wu R L. 2005a. Sequencing drug response with HapMap. Pharmacogenomics J., 5: 149-156.
[46] Lin M, Wu R L. 2005b. Theoretical basis for the identification of allelic variants that encode drug efficacy and toxicity. Genetics, 170(2): 919-928.
[47] Lin M, Wu R L. 2006. A joint model for nonparametric functional mapping of longitudinal trajectory and time-to-event. BMC Bioinformatics, 7(1):138.
[48] Liu J, Liu Y, Liu X, Deng H W. 2007. Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components. Am. J. Hum. Genet., 81(2): 304-320.
[49] Liu T, Johnson J A, Casella G, Wu R L. 2004. Sequencing complex diseases with HapMap. Genetics, 168(1): 503-511.
[50] Louis T A. 1982. Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical society, Series B, 44: 226-233.
[51] Luo Z W, Kearsey M J. 1989. Maximum likelihood estimation of linkage between a marker gene and a quantitative locus. Heredity, 63: 401-408.
[52] Ma C X , Casella G, Wu R L. 2002. Functional mapping of quantitative trait loci underlying the character process: A theoretical framework. Genetics, 161(4): 1751-1762.
[53] Ma C X, Wu R L, Casella G. 2004. FunMap: functional mapping of complex traits. Bioinformatics, 20: 1808-1811.
[54] Mackinnon M J, Weller J I. 1995. Methodology and accuracy of estimation of quantitative loci parameters in a half-sib design using maximum likelihood. Genetics, 141(2): 755-770.
[55] Maliepaard C, Jansen, J and Vanooijen J W. 1997. Linkage analysis in a full-sib family of an outbreeding plant species: overview and consequences for applications. Genet. Res., 70: 237-250.
[56] Manly K F, Cudmore R H Jr, Meer J M. 2001. Map Manager QTX, cross-platform software for genetic mapping. Mammalian Genome, 12(12): 930-2.
[57] Meuwissen T H, Goddard M E. 2004. Mapping multiple QTL using linkage disequilibrium and linkage analysis information and multitrait data. Genetics Selection Evolution, 363: 261-279.
[58] Nunez-Anton V, Zimmerman D L. 2000. Modeling nonstationary longitudinal data.Biometrics, 56: 699-705.
[59] Pearl R. 1925. The Biology of Population Growth. Knopf, New York.
[60] Rodriguez-Zas S L, Southey B R, Heyen D W, Lewin H A. 2002. Detection of quantitative trait loci influencing dairy traits using a model for longitudinal data. J. Dairy. Sci., 85: 2681-2691.
[61] Satagopan J M, Yandell B S, Newton M A, Osborn T C. 1996. A Bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo. Genetics, 144(2): 805-816.
[62] Seaton G, Haley C S, Knott S A, Kearsey M, Visscher P M. 2002. QTL Express: mapping quantitative trait loci in simple and complex pedigrees. Bioinformatics, 18: 339-340.
[63] Sillanp?? M A, Arjas E. 1999. Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics, 151(4): 1605-1619.
[64] Sollar M, Brody T, Genizi A. 1976. On the Power of Experimental Designs for the Detection of Linkage between Marker Loci and Quantitative Loci in Crosses between Inbred Lines. Theoretical and Applied Genetics, 47: 35-39.
[65] Spelman R J, Coppiters W, Karim L, Van Arendonk J A, Bocenhuis H. 1996. Quantitatice trait loci analysis for five milkproduction traits on chromosome six in the Dutch Holstein-Friesian population. Genetics, 144(4): 1799-1808.
[66] Uimari P, Hoeschele I. 1997. Mapping-Linked quantitative trait loci using Bayesian analysis and Markov Chain Monte Carlo algorithms. Genetics, 146(2): 735-743.
[67] van Ooijen J W. 2004. MapQTL 5: Software for the Mapping of Quantitative Trait Loci in Experimental Populations, Kyazma BV, Wageningen, The Netherlands.
[68] Visscher P M, Whittaker J C, Jansen R C. 2000. Mapping multiple QTL of different effects: comparison of a simple sequential testing strategy and multiple QTL mapping. Molecular Breeding, 6: 11-24.
[69] Wang D L, Zhu J, Li Z K, Paterson A H. 1999. Mapping QTL with epistatic effects and QTL environment interactions by mixed linear model approaches. Theor Appl Genet, 99: 1255-1264.
[70] Wang S, Basten C J, Zeng Z B. 2006. Windows QTL Cartographer 2.5. Department of Statistics, North Carolina State University, Raleigh, USA. (http://statgen.ncsu.edu/qtlcart/WQTLCart.htm).
[71] Weller J I. 1986. Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers. Biometrics, 42(3): 627-640.
[72] West G B, Brown J H, Enquist B J. 2001. A general model for ontogenetic growth. Nature, 413: 628-631.
[73] Wu R L, Ma C X, Chang M, Littell, R C, Wu S S, Yin T M, Huang M R, Wang M X, and Casella, G. 2002. A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories. Genet. Res., 19: 235-245.
[74] Wu R L, Ma C X, Yang, C K, Chang M, Littell R C, SANTRA U, Wu S S, Yin T M, Huang M R, Wang M X, Casella G. 2003a. Quantitative trait loci for growth trajectories in Populus. Genet. Res., 81: 51-64.
[75] Wu R L, Ma C X, Zhao W, Casella G. 2003b. Functional mapping of quantitative trait loci underlying growth rates: a parametric model. Physiol. Genomics, 14: 241-249.
[76] Wu R L, Ma C X, Lin M, Wang Z H, Casella G. 2004. Functional mapping of growth QTL using a transform-both-sides logistic model. Biometrics, 60: 729-738.
[77] Wu R L, Ma C X, Hou W, Corva P, Medrano J F. 2005. Functional Mapping of Quantitative Trait Loci That Interact With the hg Mutation to Regulate Growth Trajectories in Mice. Genetics, 171(1): 239-249
[78] Wu R L and Lin M. 2006. Functional mapping-How to map and study the genetic architecture of complex dynamic traits. Nat. Rev. Genet., 7(3): 229-237.
[79] Wu S, Yang J, Wu R L. 2007. Semiparametric functional mapping of quantitative trait loci governing long-term HIV dynamics. Bioinformatics, 23: i569-i576.
[80] Xu C W, Wang X F, Li Z K, Xu S Z. 2009. Mapping QTL for multiple traits using Bayesian statistics. Genetics Research, 91: 23-37.
[81] Xu S Z, Yi N J. 2000. Mixed model analysis of quantitative trait loci. Proc. Natl. Acad. Sci. USA 97: 14542-14547.
[82] Xu S Z, Atchley W R. 1995. A random model approach to interval mapping of quantitative trait loci. Genetics, 141(3): 1189-1197.
[83] Yandell B S, Mehta T, Banerjee S, Shriner D, Venkataraman R, Moon J Y, Neely W W, Wu H, von Smith R, Yi N J. 2007. R/qtlbim: QTL with Bayesian Interval Mapping in experimental crosses. Bioinformatics, 23(5): 641-643.
[84] Yang J, Wu R L, Casella G. 2009. Nonparametric Functional Mapping of Quantitative Trait Loci. Biometrics, 65: 30-39.
[85] Yang J, Hu C C, Hu H, Yu R D, Xia Z, Ye X Z, Zhu J. 2008. QTLNetwork: mapping and visualizing genetic architecture of complex traits in experimental populations. Bioinformatics, 24: 721-723.
[86] Yang R Q, Gao H J, Wang X, Zhang J, Zeng Z B, and Wu R L. (2007). A Semiparametric Approach for Composite Functional Mapping of Dynamic Quantitative Traits. Genetics, 177(3): 1859-1870.
[87] Yang R Q, Tian, Q, and Xu S Z. 2006. Mapping quantitative trait loci for longitudinal traits in line crosses. Genetics, 173: 2339-2356.
[88] Yang R Q, Xu S Z. 2007. Bayesian shrinkage analysis of quantitative trait loci for dynamic traits. Genetics, 2007: 1169-1185.
[89] Yi N J, Banerjee S. 2009. Hierarchical Generalized Linear Models for Multiple Quantitative Trait Locus Mapping. Genetics, 181: 1101-1113.
[90] Yi N J. 2004. A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics, 167(2): 967-975.
[91] Yi N J, Yandell B S, Churchill G A, Allison D B, Eisen E J, Pomp D. 2005. Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics, 170(3): 1333-1344.
[92] Yin T M, Zhang X Y, Huang M R, Wang M X, Zhuge Q, Tu S M, Zhu L H, Wu R L. 2002. Molecular linkage maps of the Populus genome. Genome, 45: 541-555.
[93] Zeng Z B. 1993. Theoretical basis of separation of multiple linked gene effects on mapping quantitative trait loci. Proc. Natl. Acad. Sci. USA, 90: 10972-10976.
[94] Zeng Z B. 1994. Precision mapping of quantitative trait loci. Genetics, 136(4): 1457-1468.
[95] Zhang Q, Boidhard D, Hoeschele I, et al. 1998. Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree. Genetics, 149(4): 1959-1973.
[96] Zhang Y M, Xu S. 2005a. Advanced statistical methods for detecting multiple quantitative trait loci. Rec. Res. Dev. Genet. Breed., 2(1): 1-23.
[97] Zhang Y M, Xu S. 2005b. A penalized maximum likelihood method for estimating epistatic effects of QTL. Heredity, 95(1): 96-104.
[98] Zhang Y M. 2006. Shrinkage estimation method for mapping multiple quantitative trait loci. Acta Genetica Sinica, 33(10): 861-869.
[99] Zhao W, Ma C X, Cheverud, M, Wu R L. 2003. A Unifying Statistical Model for QTL Mapping of Genotype×Sex Interaction for Developmental Trajectories. Physiological Genomics, 19: 218-227.
[100] Zhao W, Wu R L, Ma C X, Casella G. 2004. A fast algorithm for functional mapping of complex traits. Genetics 167(4): 2133-2137.
[101] Zhao W, Chen Y Q, Casella G, Cheverud J M, Wu R L. 2005. A non-stationary model for functional mapping of complex traits. Bioinformatics, 21(10): 2469-2477.
[102] Zhu J, Weir B S. 1998. Mixed model approaches for genetic analysis of quantitative traits. Chen L S, Ruan S G, Zhu J. Advanced topics in biomathematics procceedings of international conference on mathematics biology. Singapore: World Scientific Publishing Co., 321-330.
[103] Zimmerman D L, Nunez-Anton V. 2001. Parametric modelling of growth curve data: An overview. Test, 10: 1-73.
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