Methods for the detection of multiple linked QTL applied to a mixture of full and half sib families

A new multiple trait strategy based on discriminant analysis was studied for efficient detection of linked QTL in outbred sib families, in comparison with a multivariate likelihood technique. The discriminant analysis technique describes the segregation of a linear combination of the traits in a univariate likelihood. This combination is calculated for each pair of positions depending on the inheritance of the pairs of QTL haplotypes in the progeny. The gains in power and accuracy for position estimations of multiple trait methods in grid searches were evaluated in reference to single trait detections of linked QTL. The methods were applied to simulated designs with two correlated traits submitted to various effects from the linked QTL. Multiple trait strategies were generally more powerful and accurate than the single trait technique. Linked QTL were distinguished when they were separated enough to identify informative recombinations: at least two genetic markers and 25 cM between the QTL under the simulated conditions. Except in a particular case, discriminant analysis was at least as powerful as the multivariate technique and its implementation was five times faster. Combining the advantages from both methodologies, we finally propose a complete strategy for rapid and efficient systematic multivariate detections in outbred populations

Power of three multitrait methods for QTL detection in crossbred populations

The multitrait detections of QTL applied to a mixture of full- and half-sib families require specific strategies. Indeed, the number of parameters estimated by the multivariate methods is excessive compared with the size of the population. Thus, only multitrait methods based on a univariate analysis of a linear combination (LC) of the traits can be extensively performed. We compared three strategies to obtain the LC of the traits. Two linear transformations were performed on the overall population. The last one was performed within each half-sib family. Their powers were compared on simulated data depending on the frequency of the two QTL alleles in each of the grand parental populations of an intercross design. The transformations from the whole population did not lead to a large loss of power even though the frequency of the QTL alleles was similar in the two grand parental populations. In these cases, applying the within-sire family transformation improved the detection when the number of progeny per sire was greater than 100

QTL detection for a medium density SNP panel: comparison of different LD and LA methods

Background: New molecular technologies allow high throughput genotyping for QTL mapping with dense genetic maps. Therefore, the interest of linkage analysis models against linkage disequilibrium could be questioned. As these two strategies are very sensitive to marker density, experimental design structures, linkage disequilibrium extent and QTL effect, we propose to investigate these parameters effects on QTL detection.[br/] Methods: The XIIIth QTLMAS workshop simulated dataset was analysed using three linkage disequilibrium models and a linkage analysis model. Interval mapping, multivariate and interaction between QTL analyses were performed using QTLMAP.[br/] Results: The linkage analysis models identified 13 QTL, from which 10 mapped close of the 18 which were simulated and three other positions being falsely mapped as containing a QTL. Most of the QTLs identified by interval mapping analysis are not clearly detected by any linkage disequilibrium model. In addition, QTL effects are evolving during the time which was not observed using the linkage disequilibrium models.[br/] Conclusions: Our results show that for such a marker density the interval mapping strategy is still better than using the linkage disequilibrium only. While the experimental design structure gives a lot of power to both approaches, the marker density and informativity clearly affect linkage disequilibrium efficiency for QTL detection

A statistical model for genotype determination at a major locus in a progeny test design

Considering a normally distributed quantitative trait whose genetic variation is controlled by both an autosomal major locus and a polygenic component, and whose expression is influenced by environmental factors, a mixed model was developed to classify sires and daughters for their genotypes at the major locus in a progeny test design. Repeatability and genetic parameters reflecting the polygenic variation were assumed to be known. Posterior distribution of the sire genotypes and that of the daughters given the sire genotypes were derived. A method was proposed to estimate these posterior probabilities as well as the unknown parameters, and a method using the likelihood ratios to test specific genetic hypotheses was suggested. An iterative two-step procedure similar to the EM (expectation-maximization) algorithm was used to estimate the posterior probabilities and the unknown parameters. The operational value of this approach was tested with simulated data.S’appliquant à un caractère quantitatif à distribution normale, dont la variabilité génétique est contrôlée à la fois par un locus majeur autosomal et par une composante polygénique et dont l’expression est influencée par des facteurs de milieu, un modèle mixte est développé afin de déterminer le génotype (au locus majeur) des pères et de leurs filles dans un test sur descendance. La répétabilité et les paramètres génétiques relatifs à la composante polygénique sont supposés connus. La loi a posteriori des génotypes des pères et celles des génotypes de leurs filles, conditionnellement aux génotypes des pères, sont établies. Une méthode est proposée pour estimer ces probabilités a posteriori, ainsi que les paramètres inconnus, et une méthode utilisant les rapports de vraisemblance est suggérée afin de tester des hypothèses génétiques spécifiques. Une procédure itérative en deux étapes, similaire à l’algorithme EM (expectation-maximization), est présentée afin d’estimer les probabilités a posteriori et les paramètres inconnus. L’intérêt opérationnel de cette approche est éprouvé sur des données simulées

Comparison of analyses of the XVth QTLMAS common dataset III: Genomic Estimations of Breeding Values

<p>Abstract</p> <p>Background</p> <p>The QTLMAS XV^thdataset consisted of pedigree, marker genotypes and quantitative trait performances of animals with a sib family structure. Pedigree and genotypes concerned 3,000 progenies among those 2,000 were phenotyped. The trait was regulated by 8 QTLs which displayed additive, imprinting or epistatic effects. The 1,000 unphenotyped progenies were considered as candidates to selection and their Genomic Estimated Breeding Values (GEBV) were evaluated by participants of the XV^thQTLMAS workshop. This paper aims at comparing the GEBV estimation results obtained by seven participants to the workshop.</p> <p>Methods</p> <p>From the known QTL genotypes of each candidate, two "true" genomic values (TV) were estimated by organizers: the genotypic value of the candidate (TGV) and the expectation of its progeny genotypic values (TBV). GEBV were computed by the participants following different statistical methods: random linear models (including BLUP and Ridge Regression), selection variable techniques (LASSO, Elastic Net) and Bayesian methods. Accuracy was evaluated by the correlation between TV (TGV or TBV) and GEBV presented by participants. Rank correlation of the best 10% of individuals and error in predictions were also evaluated. Bias was tested by regression of TV on GEBV.</p> <p>Results</p> <p>Large differences between methods were found for all criteria and type of genetic values (TGV, TBV). In general, the criteria ranked consistently methods belonging to the same family.</p> <p>Conclusions</p> <p>Bayesian methods - A<B<C<Cπ - were the most efficient whatever the criteria and the True Value considered (with the notable exception of the MSEP of the TBV). The selection variable procedures (LASSO, Elastic Net and some adaptations) performed similarly, probably at a much lower computing cost. The TABLUP, which combines BayesB and GBLUP, generally did well. The simplest methods, GBLUP or Ridge Regression, and even worst, the fixed linear model, were much less efficient.</p

Alternative models for QTL detection in livestock. I. General introduction

In a series of papers, alternative models for QTL detection in livestock are proposed and their properties evaluated using simulations. This first paper describes the basic model used, applied to independent half-sib families, with marker phenotypes measured for a two or three generation pedigree and quantitative trait phenotypes measured only for the last generation. Hypotheses are given and the formulae for calculating the likelihood are fully described. Different alternatives to this basic model were studied, including variation in the performance modelling and consideration of full-sib families. Their main features are discussed here and their influence on the result illustrated by means of a numerical exampleDans une série d’articles scientifiques, des modèles alternatifs pour la détection de (QTLs chez les animaux de ferme sont proposés et leurs propriétés sont évaluées par simulation. Ce premier article décrit le modèle de base utilisé, qui concerne des familles indépendantes de demi-germains de père, avec des phénotypes marqueurs mesurés sur deux ou trois générations et des phénotypes quantitatifs mesurés seulement sur la dernière génération. Les hypothèses sont données et l’expression de la vraisemblance décrite en détail. À partir de ce modèle de base, différentes alternatives ont été étudiées, incluant diverses modélisations des performances et la prise en compte de structures familiales avec de vrais germains. Leurs principales caractéristiques sont décrites et une illustration est donné

Alternative models for QTL detection in livestock. III. Heteroskedastic model and models corresponding to several distributions of the QTL effect

This paper describes two kinds of alternative models for QTL detection in livestock: an heteroskedastic model, and models corresponding to several hypotheses concerning the distribution of the QTL substitution effect among the sires: a fixed and limited number of alleles or an infinite number of alleles. The power of different tests built with these hypotheses were computed under different situations. The genetic variance associated with the QTL was shown in some situations. The results showed small power differences between the different models, but important differences in the quality of the estimations. In addition, a model was built in a simplified situation to investigate the gain in using possible linkage disequilibrium.Ce papier décrit deux types de modèles alternatifs pour la détection de QTL dans les populations animales : un modèle hétéroscédastique d’une part, et des modèles correspondants à différentes hypothèses sur la distribution de l’effet de substitution du QTL pour chaque mâle : un nombre fixe et limité d’allèles ou au contraire un nombre infini d’allèles. Les puissances des différents tests construits avec ces hypothèses sont calculées dans différentes situations. L’estimation de la variance génétique liée au QTL est donnée dans certaines situations. Les résultats montrent de faibles différences de puissance entre les différents modèles, mais des différences importantes dans la qualité des estimations. De plus, on construit un modèle dans une situation simplifiée pour étudier le gain que l’on peut obtenir en utilisant un éventuel déséquilibre de liaison

Selection for reduced muscle glycolytic potential in Large White pigs I. Direct responses

International audienc

Statistical properties of interval mapping methods on quantitative trait loci location: impact on QTL/eQTL analyses

<p>Abstract</p> <p>Background</p> <p>Quantitative trait loci (QTL) detection on a huge amount of phenotypes, like eQTL detection on transcriptomic data, can be dramatically impaired by the statistical properties of interval mapping methods. One of these major outcomes is the high number of QTL detected at marker locations. The present study aims at identifying and specifying the sources of this bias, in particular in the case of analysis of data issued from outbred populations. Analytical developments were carried out in a backcross situation in order to specify the bias and to propose an algorithm to control it. The outbred population context was studied through simulated data sets in a wide range of situations.</p> <p>The likelihood ratio test was firstly analyzed under the "one QTL" hypothesis in a backcross population. Designs of sib families were then simulated and analyzed using the QTL Map software. On the basis of the theoretical results in backcross, parameters such as the population size, the density of the genetic map, the QTL effect and the true location of the QTL, were taken into account under the "no QTL" and the "one QTL" hypotheses. A combination of two non parametric tests - the Kolmogorov-Smirnov test and the Mann-Whitney-Wilcoxon test - was used in order to identify the parameters that affected the bias and to specify how much they influenced the estimation of QTL location.</p> <p>Results</p> <p>A theoretical expression of the bias of the estimated QTL location was obtained for a backcross type population. We demonstrated a common source of bias under the "no QTL" and the "one QTL" hypotheses and qualified the possible influence of several parameters. Simulation studies confirmed that the bias exists in outbred populations under both the hypotheses of "no QTL" and "one QTL" on a linkage group. The QTL location was systematically closer to marker locations than expected, particularly in the case of low QTL effect, small population size or low density of markers, i.e. designs with low power. Practical recommendations for experimental designs for QTL detection in outbred populations are given on the basis of this bias quantification. Furthermore, an original algorithm is proposed to adjust the location of a QTL, obtained with interval mapping, which co located with a marker.</p> <p>Conclusions</p> <p>Therefore, one should be attentive when one QTL is mapped at the location of one marker, especially under low power conditions.</p

Likelihood and Bayesian analyses reveal major genes affecting body composition, carcass, meat quality and the number of false teats in a Chinese European pig line

Segregation analyses were performed using both maximum likelihood – via a Quasi Newton algorithm – (ML-QN) and Bayesian – via Gibbs sampling – (Bayesian-GS) approaches in the Chinese European Tiameslan pig line. Major genes were searched for average ultrasonic backfat thickness (ABT), carcass fat (X2 and X4) and lean (X5) depths, days from 20 to 100 kg (D20100), Napole technological yield (NTY), number of false (FTN) and good (GTN) teats, as well as total teat number (TTN). The discrete nature of FTN was additionally considered using a threshold model under ML methodology. The results obtained with both methods consistently suggested the presence of major genes affecting ABT, X2, NTY, GTN and FTN. Major genes were also suggested for X4 and X5 using ML-QN, but not the Bayesian-GS, approach. The major gene affecting FTN was confirmed using the threshold model. Genetic correlations as well as gene effect and genotype frequency estimates suggested the presence of four different major genes. The first gene would affect fatness traits (ABT, X2 and X4), the second one a leanness trait (X5), the third one NTY and the last one GTN and FTN. Genotype frequencies of breeding animals and their evolution over time were consistent with the selection performed in the Tiameslan line