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.

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.

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.

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 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.

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

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.

Genetic Response from Marker Assisted Selection in an Outbred Population for Differing Marker Bracket Sizes and with Two Identified Quantitative Trait Loci

Genetics ◽  
1998 ◽  
Vol 148 (3) ◽  
pp. 1389-1396 ◽  
Author(s):  
Richard Spelman ◽  
Henk Bovenhuis
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Marker Assisted Selection ◽  
Phenotypic Variance ◽  
Genetic Response ◽  
Breeding Scheme ◽  
Outbred Population ◽  
Trait Loci ◽  
Polygenic Component ◽  
Nucleus Breeding

AbstractEffect of flanking quantitative trait loci (QTL)-marker bracket size on genetic response to marker assisted selection in an outbred population was studied by simulation of a nucleus breeding scheme. In addition, genetic response with marker assisted selection (MAS) from two quantitative trait loci on the same and different chromosome(s) was investigated. QTL that explained either 5% or 10% of phenotypic variance were simulated. A polygenic component was simulated in addition to the quantitative trait loci. In total, 35% of the phenotypic variance was due to genetic factors. The trait was measured on females only. Having smaller marker brackets flanking the QTL increased the genetic response from MAS selection. This was due to the greater ability to trace the QTL transmission from one generation to the next with the smaller flanking QTL-marker bracket, which increased the accuracy of estimation of the QTL allelic effects. Greater negative covariance between effects at both QTL was observed when two QTL were located on the same chromosome compared to different chromosomes. Genetic response with MAS was greater when the QTL were on the same chromosome in the early generations and greater when they were on different chromosomes in the later generations of MAS.

scholarly journals A Generalization of the Mixture Model in the Mapping of Quantitative Trait Loci for Progeny From a Biparental Cross of Inbred Lines

Genetics ◽  
1996 ◽  
Vol 143 (1) ◽  
pp. 571-577
Author(s):  
R D Fisch ◽  
M Ragot ◽  
G Gay
Keyword(s):  
Molecular Markers ◽  
Quantitative Trait Loci ◽  
Molecular Marker ◽  
Mixture Model ◽  
Quantitative Trait ◽  
Doubled Haploids ◽  
Inbred Lines ◽  
Quantitative Inheritance ◽  
Trait Loci ◽  
Biometrical Models

Abstract The recent advent of molecular markers has created a great potential for the understanding of quantitative inheritance. In parallel to rapid developments and improvements in molecular marker technologies, biometrical models have been constructed, refined and generalized for the mapping of quantitative trait loci (QTL). However, current models present restricitions in terms of breeding designs to which they apply. In this paper, we develop an approach for the generalization of the mixture model for progeny from a single bi-parental cross of inbred lines. Detailed derivations are given for genetic designs involving populations developed by selfing, i.e., where marker genotypes are obtained from Fx (x ≤ 2) individuals and where phenotypes are measured on Fy (y ≥ x) individuals or families. Extensions to designs involving doubled-haploids, backcrossderived individuals and random matings are outlined. The derivations presented here can easily be combined with current QTL mapping approaches.

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