A Mixture Model Approach to the Mapping of Quantitative Trait Loci in Complex Populations With an Application to Multiple Cattle Families

Genetics ◽  
1998 ◽  
Vol 148 (1) ◽  
pp. 391-399 ◽  
Author(s):  
Ritsert C Jansen ◽  
David L Johnson ◽  
Johan A M Van Arendonk
Keyword(s):  
Quantitative Trait Loci ◽  
Mixture Model ◽  
Quantitative Trait ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Data Set ◽  
Mixture Model Approach ◽  
Trait Loci ◽  
Monte Carlo Em ◽  
Model Approach

Abstract A mixture model approach is presented for the mapping of one or more quantitative trait loci (QTLs) in complex populations. In order to exploit the full power of complete linkage maps the simultaneous likelihood of phenotype and a multilocus (all markers and putative QTLs) genotype is computed. Maximum likelihood estimation in our mixture models is implemented via an Expectation-Maximization algorithm: exact, stochastic or Monte Carlo EM by using a simple and flexible Gibbs sampler. Parameters include allele frequencies of markers and QTLs, discrete or normal effects of biallelic or multiallelic QTLs, and homogeneous or heterogeneous residual variances. As an illustration a dairy cattle data set consisting of twenty half-sib families has been reanalyzed. We discuss the potential which our and other approaches have for realistic multiple-QTL analyses in complex populations.

scholarly journals Mapping quantitative trait loci in a selectively genotyped outbred population using a mixture model approach

1999 ◽  
Vol 73 (1) ◽  
pp. 75-83 ◽  
Author(s):  
DAVID L. JOHNSON ◽  
RITSERT C. JANSEN ◽  
JOHAN A. M. VAN ARENDONK
Keyword(s):  
Quantitative Trait Loci ◽  
Mixture Model ◽  
Quantitative Trait ◽  
Model Parameters ◽  
Outbred Population ◽  
Bivariate Model ◽  
Mixture Model Approach ◽  
Trait Loci ◽  
Unbiased Estimates ◽  
Model Approach

A mixture model approach is employed for the mapping of quantitative trait loci (QTL) for the situation where individuals, in an outbred population, are selectively genotyped. Maximum likelihood estimation of model parameters is obtained from an Expectation-Maximization (EM) algorithm facilitated by Monte Carlo sampling using a Gibbs sampler. All individuals with phenotypes, whether genotyped or not, are included in the analysis where both putative QTLs and missing marker genotypes are sampled conditional on known marker information and phenotype. A simulation of a half-sib family structure demonstrates that this mixture model approach will yield unbiased estimates of the allelic effects of a QTL affecting the trait on which selective genotyping is based. Unbiased estimates were also obtained for the QTL effect on a correlated trait provided both traits were analysed jointly in a bivariate model. The procedure is also compared with a standard linear model approach. The application of these methods is demonstrated for bovine chromosome six, the data arising from two Holstein–Friesian families selectively genotyped for protein yield in a daughter design.

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.

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 An Improved Approach for Mapping Quantitative Trait Loci in a Pseudo-Testcross: Revisiting a Poplar Mapping Study

2010 ◽  
Vol 4 ◽  
pp. BBI.S4153 ◽  
Author(s):  
Song Wu ◽  
Jie Yang ◽  
Youjun Huang ◽  
Yao Li ◽  
Tongming Yin ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Genetic Correlations ◽  
Published Data ◽  
Mapping Study ◽  
Data Set ◽  
Poplar Trees ◽  
Complete Identification ◽  
Trait Loci ◽  
Outcrossing Species

A pseudo-testcross pedigree is widely used for mapping quantitative trait loci (QTL) in outcrossing species, but the model for analyzing pseudo-testcross data borrowed from the inbred backcross design can only detect those QTLs that are heterozygous only in one parent. In this study, an intercross model that incorporates the high heterozygosity and phase uncertainty of outcrossing species was used to reanalyze a published data set on QTL mapping in poplar trees. Several intercross QTLs that are heterozygous in both parents were detected, which are responsible not only for biomass traits, but also for their genetic correlations. This study provides a more complete identification of QTLs responsible for economically important biomass traits in poplars.

scholarly journals A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines

2000 ◽  
Vol 75 (3) ◽  
pp. 345-355 ◽  
Author(s):  
YUEFU LIU ◽  
ZHAO-BANG ZENG
Keyword(s):  
Quantitative Trait Loci ◽  
Statistical Method ◽  
Mixture Model ◽  
Quantitative Trait ◽  
Genetic Model ◽  
General Procedure ◽  
Inbred Lines ◽  
Design Matrix ◽  
Trait Loci ◽  
Parental Lines

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.

A random model approach to interval mapping of quantitative trait loci.

Genetics ◽  
1995 ◽  
Vol 141 (3) ◽  
pp. 1189-1197 ◽  
Author(s):  
S Xu ◽  
W R Atchley
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Fixed Effects ◽  
Interval Mapping ◽  
Random Model ◽  
Likelihood Method ◽  
Mapping Procedure ◽  
Trait Loci ◽  
Outbred Populations ◽  
Model Approach

Abstract Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.

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 Multiple Interval Mapping for Quantitative Trait Loci

Genetics ◽  
1999 ◽  
Vol 152 (3) ◽  
pp. 1203-1216
Author(s):  
Chen-Hung Kao ◽  
Zhao-Bang Zeng ◽  
Robert D Teasdale
Keyword(s):  
Genetic Variation ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Genetic Parameters ◽  
Interval Mapping ◽  
Ratio Test ◽  
Data Set ◽  
Multiple Interval Mapping ◽  
Total Genetic Variation ◽  
Trait Loci

Abstract A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from ∼1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed ∼10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0.3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/~chkao/).

Enhanced Efficiency of Quantitative Trait Loci Mapping Analysis Based on Multivariate Complexes of Quantitative Traits

Genetics ◽  
2001 ◽  
Vol 157 (4) ◽  
pp. 1789-1803 ◽  
Author(s):  
Abraham B Korol ◽  
Yefim I Ronin ◽  
Alexander M Itskovich ◽  
Junhua Peng ◽  
Eviatar Nevo
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Broad Sense ◽  
Broad Sense Heritability ◽  
Qtl Detection ◽  
Data Set ◽  
Correlated Traits ◽  
Detection Power ◽  
Specific Calculation ◽  
Trait Loci

AbstractAn approach to increase the efficiency of mapping quantitative trait loci (QTL) was proposed earlier by the authors on the basis of bivariate analysis of correlated traits. The power of QTL detection using the log-likelihood ratio (LOD scores) grows proportionally to the broad sense heritability. We found that this relationship holds also for correlated traits, so that an increased bivariate heritability implicates a higher LOD score, higher detection power, and better mapping resolution. However, the increased number of parameters to be estimated complicates the application of this approach when a large number of traits are considered simultaneously. Here we present a multivariate generalization of our previous two-trait QTL analysis. The proposed multivariate analogue of QTL contribution to the broad-sense heritability based on interval-specific calculation of eigenvalues and eigenvectors of the residual covariance matrix allows prediction of the expected QTL detection power and mapping resolution for any subset of the initial multivariate trait complex. Permutation technique allows chromosome-wise testing of significance for the whole trait complex and the significance of the contribution of individual traits owing to: (a) their correlation with other traits, (b) dependence on the chromosome in question, and (c) both a and b. An example of application of the proposed method on a real data set of 11 traits from an experiment performed on an F2/F3 mapping population of tetraploid wheat (Triticum durum × T. dicoccoides) is provided.

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