Bayesian Mapping of Quantitative Trait Loci for Complex Binary Traits

Abstract A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.

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Mapping quantitative trait loci with epistatic effects

Genetics Research ◽

10.1017/s0016672301005511 ◽

2002 ◽

Vol 79 (2) ◽

pp. 185-198 ◽

Cited By ~ 50

Author(s):

NENGJUN YI ◽

SHIZHONG XU

Keyword(s):

Quantitative Trait Loci ◽

Quantitative Trait ◽

Complex Traits ◽

Quantitative Traits ◽

Threshold Model ◽

Monte Carlo Algorithm ◽

Epistatic Effects ◽

Trait Loci ◽

Robust Statistical Methods ◽

Qtl Effects

Epistatic variance can be an important source of variation for complex traits. However, detecting epistatic effects is difficult primarily due to insufficient sample sizes and lack of robust statistical methods. In this paper, we develop a Bayesian method to map multiple quantitative trait loci (QTLs) with epistatic effects. The method can map QTLs in complicated mating designs derived from the cross of two inbred lines. In addition to mapping QTLs for quantitative traits, the proposed method can even map genes underlying binary traits such as disease susceptibility using the threshold model. The parameters of interest are various QTL effects, including additive, dominance and epistatic effects of QTLs, the locations of identified QTLs and even the number of QTLs. When the number of QTLs is treated as an unknown parameter, the dimension of the model becomes a variable. This requires the reversible jump Markov chain Monte Carlo algorithm. The utility of the proposed method is demonstrated through analysis of simulation data.

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Bayesian Mapping of Quantitative Trait Loci Under the Identity-by-Descent-Based Variance Component Model

Genetics ◽

10.1093/genetics/156.1.411 ◽

2000 ◽

Vol 156 (1) ◽

pp. 411-422 ◽

Cited By ~ 6

Author(s):

Nengjun Yi ◽

Shizhong Xu

Keyword(s):

Quantitative Trait Loci ◽

Posterior Distribution ◽

Quantitative Trait ◽

Variance Component ◽

Threshold Model ◽

Variance Component Model ◽

Identity By Descent ◽

Mapping Procedure ◽

Trait Loci ◽

Bayesian Mapping

AbstractVariance component analysis of quantitative trait loci (QTL) is an important strategy of genetic mapping for complex traits in humans. The method is robust because it can handle an arbitrary number of alleles with arbitrary modes of gene actions. The variance component method is usually implemented using the proportion of alleles with identity-by-descent (IBD) shared by relatives. As a result, information about marker linkage phases in the parents is not required. The method has been studied extensively under either the maximum-likelihood framework or the sib-pair regression paradigm. However, virtually all investigations are limited to normally distributed traits under a single QTL model. In this study, we develop a Bayes method to map multiple QTL. We also extend the Bayesian mapping procedure to identify QTL responsible for the variation of complex binary diseases in humans under a threshold model. The method can also treat the number of QTL as a parameter and infer its posterior distribution. We use the reversible jump Markov chain Monte Carlo method to infer the posterior distributions of parameters of interest. The Bayesian mapping procedure ends with an estimation of the joint posterior distribution of the number of QTL and the locations and variances of the identified QTL. Utilities of the method are demonstrated using a simulated population consisting of multiple full-sib families.

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Bayesian Model Choice and Search Strategies for Mapping Interacting Quantitative Trait Loci

Genetics ◽

10.1093/genetics/165.2.867 ◽

2003 ◽

Vol 165 (2) ◽

pp. 867-883 ◽

Cited By ~ 19

Author(s):

Nengjun Yi ◽

Shizhong Xu ◽

David B Allison

Keyword(s):

Quantitative Trait Loci ◽

Quantitative Trait ◽

Complex Traits ◽

Bayesian Model ◽

Genetic Model ◽

Genetic Effects ◽

Monte Carlo Algorithm ◽

Data Set ◽

Epistatic Effects ◽

Trait Loci

AbstractMost complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.

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Mapping quantitative trait loci for binary trait in the F2:3 design

Journal of Genetics ◽

10.1007/s12041-008-0033-3 ◽

2008 ◽

Vol 87 (3) ◽

pp. 201-207

Author(s):

Chengsong Zhu ◽

Yuan-Ming Zhang ◽

Zhigang Guo

Keyword(s):

Quantitative Trait Loci ◽

Quantitative Trait ◽

Binary Trait ◽

Trait Loci

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Robust Bayesian mapping of quantitative trait loci using Student-t distribution for residual

Theoretical and Applied Genetics ◽

10.1007/s00122-008-0924-y ◽

2008 ◽

Vol 118 (3) ◽

pp. 609-617 ◽

Cited By ~ 1

Author(s):

Xin Wang ◽

Zhongze Piao ◽

Biye Wang ◽

Runqing Yang ◽

Zhixiang Luo

Keyword(s):

Quantitative Trait Loci ◽

Quantitative Trait ◽

Student T Distribution ◽

Trait Loci ◽

Bayesian Mapping ◽

T Distribution

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Bayesian Mapping of Quantitative Trait Loci Under Complicated Mating Designs

Genetics ◽

10.1093/genetics/157.4.1759 ◽

2001 ◽

Vol 157 (4) ◽

pp. 1759-1771 ◽

Cited By ~ 7

Author(s):

Nengjun Yi ◽

Shizhong Xu

Keyword(s):

Quantitative Trait Loci ◽

Quantitative Trait ◽

Mixed Model ◽

Inbred Lines ◽

Likelihood Method ◽

Mcmc Algorithm ◽

Model Framework ◽

Multiple Alleles ◽

Trait Loci ◽

Bayesian Mapping

AbstractQuantitative trait loci (QTL) are easily studied in a biallelic system. Such a system requires the cross of two inbred lines presumably fixed for alternative alleles of the QTL. However, development of inbred lines can be time consuming and cost ineffective for species with long generation intervals and severe inbreeding depression. In addition, restriction of the investigation to a biallelic system can sometimes be misleading because many potentially important allelic interactions do not have a chance to express and thus fail to be detected. A complicated mating design involving multiple alleles mimics the actual breeding system. However, it is difficult to develop the statistical model and algorithm using the classical maximum-likelihood method. In this study, we investigate the application of a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to QTL mapping under arbitrarily complicated mating designs. We develop the method under a mixed-model framework where the genetic values of founder alleles are treated as random and the nongenetic effects are treated as fixed. With the MCMC algorithm, we first draw the gene flows from the founders to the descendants for each QTL and then draw samples of the genetic parameters. Finally, we are able to simultaneously infer the posterior distribution of the number, the additive and dominance variances, and the chromosomal locations of all identified QTL.

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