A Random Model Approach to Mapping Quantitative Trait Loci for Complex Binary Traits in Outbred Populations

Genetics ◽  
1999 ◽  
Vol 153 (2) ◽  
pp. 1029-1040 ◽  
Author(s):  
Nengjun Yi ◽  
Shizhong Xu
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Random Model ◽  
Monte Carlo Integration ◽  
Ratio Test ◽  
Outbred Population ◽  
Binary Traits ◽  
Trait Loci ◽  
Outbred Populations ◽  
Model Approach

Abstract Mapping quantitative trait loci (QTL) for complex binary traits is more challenging than for normally distributed traits due to the nonlinear relationship between the observed phenotype and unobservable genetic effects, especially when the mapping population contains multiple outbred families. Because the number of alleles of a QTL depends on the number of founders in an outbred population, it is more appropriate to treat the effect of each allele as a random variable so that a single variance rather than individual allelic effects is estimated and tested. Such a method is called the random model approach. In this study, we develop the random model approach of QTL mapping for binary traits in outbred populations. An EM-algorithm with a Fisher-scoring algorithm embedded in each E-step is adopted here to estimate the genetic variances. A simple Monte Carlo integration technique is used here to calculate the likelihood-ratio test statistic. For the first time we show that QTL of complex binary traits in an outbred population can be scanned along a chromosome for their positions, estimated for their explained variances, and tested for their statistical significance. Application of the method is illustrated using a set of simulated data.

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 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 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 On the Differences Between Maximum Likelihood and Regression Interval Mapping in the Analysis of Quantitative Trait Loci

Genetics ◽  
2000 ◽  
Vol 156 (2) ◽  
pp. 855-865 ◽  
Author(s):  
Chen-Hung Kao
Keyword(s):  
Quantitative Trait Loci ◽  
Maximum Likelihood ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Mean Squared Error ◽  
Interval Mapping ◽  
Size Difference ◽  
Ratio Test ◽  
Trait Loci ◽  
Variance Explained

AbstractThe differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.

scholarly journals Mapping quantitative trait loci in Gallus gallus using principal components

2010 ◽  
Vol 39 (11) ◽  
pp. 2434-2441 ◽  
Author(s):  
Luís Fernando Batista Pinto ◽  
Irineu Umberto Packer ◽  
Mônica Corrêa Ledur ◽  
Ana Silvia Alves Meira Tavares Moura ◽  
Kátia Nones ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Principal Components ◽  
Quantitative Trait ◽  
Live Weight ◽  
Gallus Gallus ◽  
Heart Weight ◽  
Ratio Test ◽  
Linear Combinations ◽  
Significant Qtls ◽  
Trait Loci

This study aimed at mapping QTL (quantitative trait loci) using linear combinations of characteristics of economical interest in Gallus gallus. A total of 350 F2 chickens from an initial crossing among males from a broiler line (TT) with females from a layer line (CC) were used. It was conducted a QTL mapping in chromosomes of Gallus gallus (GGA1, GGA3, GGA5, GGA8, GGA11, and GGA13) for 20 performance and carcass traits. For detecting QTL, it was used the likelihood ratio test between a reduced model (including fixed effects of sex, hatch and random effect of infinitesimal genetic value) and a full model (including all the previous effects plus QTL effects). When original characterists were analyzed, that is, before the formation of linear combinations, six significant QTLs were mapped at 1% in the genome, four in the GGA1 (live weight at 35 days of age and at 42 days of age, abdominal fat and heart weight); and two on GGA3 (live weight at 35 and 42 days of age); three significant QTLs at 5% in the genome, one on GGA1 (head weight), one on GGA3 (wings weight), and one on GGA8 (gizzard weight); besides seven suggestive linkages for several traits. When QTLs were mapped for principal components, many mapped QTLs were confirmed for original traits, in addition to finding three QTLs and eight suggestive linkages not mapped for the original traits.

scholarly journals A method for computing identity by descent probabilities and quantitative trait loci mapping with dominant (AFLP) markers

2002 ◽  
Vol 79 (3) ◽  
pp. 247-258 ◽  
Author(s):  
MIGUEL PÉREZ-ENCISO ◽  
ODILE ROUSSOT
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Cost Effective ◽  
Significant Loss ◽  
Outbred Population ◽  
Identity By Descent ◽  
Fluorescent Band ◽  
Length Polymorphisms ◽  
Trait Loci

Amplified fragment length polymorphisms (AFLPs) are a widely used marker system: the technique is very cost-effective, easy and rapid, and reproducibly generates hundreds of markers. Unfortunately, AFLP alleles are typically scored as the presence or absence of a band and, thus, heterozygous and dominant homozygous genotypes cannot be distinguished. This results in a significant loss of information, especially as regards mapping of quantitative trait loci (QTLs). We present a Monte Carlo Markov Chain method that allows us to compute the identity by descent probabilities (IBD) in a general pedigree whose individuals have been typed for dominant markers. The method allows us to include the information provided by the fluorescent band intensities of the markers, the rationale being that homozygous individuals have on average higher band intensities than heterozygous individuals, as well as information from linked markers in each individual and its relatives. Once IBD probabilities are obtained, they can be combined into the QTL mapping strategy of choice. We illustrate the method with two simulated populations: an outbred population consisting of full sib families, and an F2 cross between inbred lines. Two marker spacings were considered, 5 or 20 cM, in the outbred population. There was almost no difference, for the practical purpose of QTL estimation, between AFLPs and biallelic codominant markers when the band density is taken into account, especially at the 5 cM spacing. The performance of AFLPs every 5 cM was also comparable to that of highly polymorphic markers (microsatellites) spaced every 20 cM. In economic terms, QTL mapping with a dense map of AFLPs is clearly better than microsatellite QTL mapping and little is lost in terms of accuracy of position. Nevertheless, at low marker densities, AFLPs or other biallelic markers result in very inaccurate estimates of QTL position.

scholarly journals A genome scan for quantitative trait loci affecting cyanogenic potential of cassava root in an outbred population

BMC Genomics ◽  
2011 ◽  
Vol 12 (1) ◽  
Author(s):  
Sukhuman Whankaew ◽  
Supannee Poopear ◽  
Supanath Kanjanawattanawong ◽  
Sithichoke Tangphatsornruang ◽  
Opas Boonseng ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Genome Scan ◽  
Outbred Population ◽  
Cassava Root ◽  
A Genome ◽  
Trait Loci ◽  
Cyanogenic Potential

scholarly journals Testing the Robustness of the Likelihood-Ratio Test in a Variance-Component Quantitative-Trait Loci–Mapping Procedure

1999 ◽  
Vol 65 (2) ◽  
pp. 531-544 ◽  
Author(s):  
David B. Allison ◽  
Michael C. Neale ◽  
Raffaella Zannolli ◽  
Nicholas J. Schork ◽  
Christopher I. Amos ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Quantitative Trait ◽  
Variance Component ◽  
Ratio Test ◽  
Quantitative Trait Loci Mapping ◽  
Mapping Procedure ◽  
Trait Loci

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.

Sign in / Sign up

Export Citation Format

Share Document