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

Genetics ◽  
2003 ◽  
Vol 165 (2) ◽  
pp. 867-883 ◽  
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.

scholarly journals Mapping quantitative trait loci with epistatic effects

2002 ◽  
Vol 79 (2) ◽  
pp. 185-198 ◽  
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.

scholarly journals Stochastic Search Variable Selection for Identifying Multiple Quantitative Trait Loci

Genetics ◽  
2003 ◽  
Vol 164 (3) ◽  
pp. 1129-1138 ◽  
Author(s):  
Nengjun Yi ◽  
Varghese George ◽  
David B Allison
Keyword(s):  
Quantitative Trait Loci ◽  
Variable Selection ◽  
Quantitative Trait ◽  
Complex Traits ◽  
Stochastic Search ◽  
Model Parameters ◽  
Data Set ◽  
Stochastic Search Variable Selection ◽  
Trait Loci ◽  
Search Variable

AbstractIn this article, we utilize stochastic search variable selection methodology to develop a Bayesian method for identifying multiple quantitative trait loci (QTL) for complex traits in experimental designs. The proposed procedure entails embedding multiple regression in a hierarchical normal mixture model, where latent indicators for all markers are used to identify the multiple markers. The markers with significant effects can be identified as those with higher posterior probability included in the model. A simple and easy-to-use Gibbs sampler is employed to generate samples from the joint posterior distribution of all unknowns including the latent indicators, genetic effects for all markers, and other model parameters. The proposed method was evaluated using simulated data and illustrated using a real data set. The results demonstrate that the proposed method works well under typical situations of most QTL studies in terms of number of markers and marker density.

scholarly journals Unconditional and Conditional Quantitative Trait Loci Mapping for Plant Height in Nonheading Chinese Cabbage

HortScience ◽  
2009 ◽  
Vol 44 (2) ◽  
pp. 268-273 ◽  
Author(s):  
Yan Cheng ◽  
Qian Wang ◽  
Qingyu Ban ◽  
Jianfeng Geng ◽  
Xiao Wei Zhang ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Plant Height ◽  
Chinese Cabbage ◽  
Qtl Analysis ◽  
Quantitative Trait ◽  
Genetic Model ◽  
Interval Mapping ◽  
Genetic Effects ◽  
Linkage Groups ◽  
Trait Loci

Quantitative trait loci (QTLs) identified so far in Brassica were mainly generated in the final stage of plant development, which did not apply to the exploitation of genetic effects that were expressed during a specific developmental stage. Thus, the objective of this study was to simultaneously identify unconditional and conditional QTL associated with plant height at various stages of nonheading Chinese cabbage. One hundred twelve doubled haploid (DH) lines developed from the cross between nonheading Chinese cabbage lines ‘SW-13’ and ‘SU-124’ were used for QTL analysis of plant height by the composite interval mapping method combined with mixed genetic model. The map we used for QTL analysis was an updated version of the first genetic map of nonheading Chinese cabbage with 48 additional markers to the same DH population. With data from 2 years, a total of 11 unconditional QTLs in six linkage groups and 23 conditional QTLs in eight linkage groups were identified for plant height. The results indicated that the number and type of QTLs and their genetic effects for plant height were different in a series of measuring stages. Each QTL can explain 7.92% to 28.25% of the total phenotypic variation. Two QTLs (ph8-4 and ph8-5) were identified to be associated with plant height using both unconditional and conditional mapping methods simultaneously in 2 years. These results demonstrated that it is highly effective for mapping QTL of developmental traits using the unconditional and conditional analysis methodology.

Epistatic Effects and Quantitative Trait Loci (QTL) x Environment (QE) Interaction Effects for Yield per Plot and Botanical Traits in Soybean

2014 ◽  
Vol 49 (3) ◽  
pp. 273
Author(s):  
Liang Huizhen ◽  
Yu Yongliang ◽  
Yang Hongqi ◽  
Zhang Haiyang ◽  
Dong Wei ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Interaction Effects ◽  
Epistatic Effects ◽  
Trait Loci

scholarly journals Bayesian Mapping of Quantitative Trait Loci for Complex Binary Traits

Genetics ◽  
2000 ◽  
Vol 155 (3) ◽  
pp. 1391-1403
Author(s):  
Nengjun Yi ◽  
Shizhong Xu
Keyword(s):  
Quantitative Trait Loci ◽  
Bayesian Statistics ◽  
Quantitative Trait ◽  
Data Augmentation ◽  
Threshold Model ◽  
Binary Trait ◽  
Monte Carlo Algorithm ◽  
Binary Traits ◽  
Trait Loci ◽  
Bayesian Mapping

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.

scholarly journals Is the Genotype-Phenotype Map Modular?: A Statistical Approach Using Mouse Quantitative Trait Loci Data

Genetics ◽  
2000 ◽  
Vol 156 (1) ◽  
pp. 305-311 ◽  
Author(s):  
Jason G Mezey ◽  
James M Cheverud ◽  
Günter P Wagner
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Statistical Approach ◽  
Genetic Effects ◽  
Statistical Distribution ◽  
Data Set ◽  
Alveolar Region ◽  
Phenotypic Characters ◽  
Statistical Support ◽  
Complex Characters

Abstract Various theories about the evolution of complex characters make predictions about the statistical distribution of genetic effects on phenotypic characters, also called the genotype-phenotype map. With the advent of QTL technology, data about these distributions are becoming available. In this article, we propose simple tests for the prediction that functionally integrated characters have a modular genotype-phenotype map. The test is applied to QTL data on the mouse mandible. The results provide statistical support for the notion that the ascending ramus region of the mandible is modularized. A data set comprising the effects of QTL on a more extensive portion of the phenotype is required to determine if the alveolar region of the mandible is also modularized.

Empirical Nonparametric Bootstrap Strategies in Quantitative Trait Loci Mapping: Conditioning on the Genetic Model

Genetics ◽  
1998 ◽  
Vol 148 (1) ◽  
pp. 525-535
Author(s):  
Claude M Lebreton ◽  
Peter M Visscher
Keyword(s):  
Quantitative Trait Loci ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Quantitative Trait ◽  
Genetic Factors ◽  
Genetic Model ◽  
Original Data ◽  
Nonparametric Bootstrap ◽  
Test Protocol ◽  
Trait Loci

AbstractSeveral nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.

scholarly journals A Rank-Based Nonparametric Method for Mapping Quantitative Trait Loci in Outbred Half-Sib Pedigrees: Application to Milk Production in a Granddaughter Design

Genetics ◽  
1998 ◽  
Vol 149 (3) ◽  
pp. 1547-1555 ◽  
Author(s):  
Wouter Coppieters ◽  
Alexandre Kvasz ◽  
Frédéric Farnir ◽  
Juan-Jose Arranz ◽  
Bernard Grisart ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Real Data ◽  
Interval Mapping ◽  
Mapping Method ◽  
Residual Variance ◽  
Data Set ◽  
Wilcoxon Rank Sum Test ◽  
Holstein Friesian ◽  
Trait Loci

Abstract We describe the development of a multipoint nonparametric quantitative trait loci mapping method based on the Wilcoxon rank-sum test applicable to outbred half-sib pedigrees. The method has been evaluated on a simulated dataset and its efficiency compared with interval mapping by using regression. It was shown that the rank-based approach is slightly inferior to regression when the residual variance is homoscedastic normal; however, in three out of four other scenarios envisaged, i.e., residual variance heteroscedastic normal, homoscedastic skewed, and homoscedastic positively kurtosed, the latter outperforms the former one. Both methods were applied to a real data set analyzing the effect of bovine chromosome 6 on milk yield and composition by using a 125-cM map comprising 15 microsatellites and a granddaughter design counting 1158 Holstein-Friesian sires.

scholarly journals Mapping of Quantitative Trait Loci Controlling Adaptive Traits in Coastal Douglas Fir. III. Quantitative Trait Loci-by-Environment Interactions

Genetics ◽  
2003 ◽  
Vol 165 (3) ◽  
pp. 1489-1506
Author(s):  
Kathleen D Jermstad ◽  
Daniel L Bassoni ◽  
Keith S Jech ◽  
Gary A Ritchie ◽  
Nicholas C Wheeler ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Complex Traits ◽  
Moisture Stress ◽  
Interval Mapping ◽  
Douglas Fir ◽  
Adaptive Traits ◽  
Growth Cessation ◽  
Trait Loci ◽  
Growth Initiation

Abstract Quantitative trait loci (QTL) were mapped in the woody perennial Douglas fir (Pseudotsuga menziesii var. menziesii [Mirb.] Franco) for complex traits controlling the timing of growth initiation and growth cessation. QTL were estimated under controlled environmental conditions to identify QTL interactions with photoperiod, moisture stress, winter chilling, and spring temperatures. A three-generation mapping population of 460 cloned progeny was used for genetic mapping and phenotypic evaluations. An all-marker interval mapping method was used for scanning the genome for the presence of QTL and single-factor ANOVA was used for estimating QTL-by-environment interactions. A modest number of QTL were detected per trait, with individual QTL explaining up to 9.5% of the phenotypic variation. Two QTL-by-treatment interactions were found for growth initiation, whereas several QTL-by-treatment interactions were detected among growth cessation traits. This is the first report of QTL interactions with specific environmental signals in forest trees and will assist in the identification of candidate genes controlling these important adaptive traits in perennial plants.

scholarly journals Bayesian Model Selection for Genome-Wide Epistatic Quantitative Trait Loci Analysis

Genetics ◽  
2005 ◽  
Vol 170 (3) ◽  
pp. 1333-1344 ◽  
Author(s):  
Nengjun Yi ◽  
Brian S. Yandell ◽  
Gary A. Churchill ◽  
David B. Allison ◽  
Eugene J. Eisen ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Model Selection ◽  
Quantitative Trait ◽  
Bayesian Model ◽  
Bayesian Model Selection ◽  
Genome Wide ◽  
Trait Loci ◽  
Selection For
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