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This article presents a method to combine QTL results from different independent analyses. This method provides a modified Akaike criterion that can be used to decide how many QTL are actually represented by the QTL detected in different experiments. This criterion is computed to choose between models with one, two, three, etc., QTL. Simulations are carried out to investigate the quality of the model obtained with this method in various situations. It appears that the method allows the length of the confidence interval of QTL location to be consistently reduced when there are only very few “actual” QTL locations. An application of the method is given using data from the maize database available online at http://www.agron.missouri.edu/.

We present a general regression-based method for mapping quantitative trait loci (QTL) by combining different populations derived from diallel designs. The model expresses, at any map position, the phenotypic value of each individual as a function of the specific-mean of the population to which the individual belongs, the additive and dominance effects of the alleles carried by the parents of that population and the probabilities of QTL genotypes conditional on those of neighbouring markers. Standard linear model procedures (ordinary or iteratively reweighted least-squares) are used for estimation and test of the parameters.

This paper considers the use of an auxiliary variable X* to estimate quantiles of a test statistic X; X* may be an asymptotic expansion of X, or a simplified version which ignores some of the covariance structure. The proposed estimator involves three stages. First a large sample is drawn, and X* is evaluated. Then a first subsample is drawn, X and X* are evaluated and the conditional distribution of X given X* is estimated. Then a second subsample is drawn with weighting which is optimised for this conditional distribution, and for a particular quantile. From this subsample, an importance sampling estimator of the quantile is obtained. The resulting estimator is shown to have substantially lower mean squared error than the conventional estimator, and to be reasonably robust both to errors in the model for the conditional distribution and to the quantile assumed for the optimisation. An example in genetics is given.

"Chantier qualité spécifique "Auteurs Externes" département de Génétique animale : uniquement liaison auteur au référentiel HR-Access "; International audience

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.

International audience; Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.

The genetic diversity among strains in a worldwide collection of Ralstonia solanacearum, causal agent of bacterial wilt, was assessed by using three different molecular methods. PCR-RFLP analysis of the hrp gene region was extended from previous studies to include additional strains and showed that five amplicons were produced not only with all R. solanacearum strains but also with strains of the closely related bacteria Pseudomonas syzygii and the blood disease bacterium (BDB). However, the three bacterial taxa could be discriminated by specific restriction profiles. The PCR-RFLP clustering, which agreed with the biovar classification and the geographical origin of strains, was confirmed by AFLP. Moreover, AFLP permitted very fine discrimination between different isolates and was able to differentiate strains that were not distinguishable by PCR-RFLP. AFLP and PCR-RFLP analyses confirmed the results of previous investigations which split the species into two divisions, but revealed a further subdivision. This observation was further supported by 16S rRNA sequence data, which grouped biovar 1 strains originating from the southern part of Africa.

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.

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 example, Dans 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 donnée

Selective genotyping, i.e. increasing the size of the population phenotyped and genotyping only individuals from the high and low tails of the population, can considerably improve the efficiency of experiments aimed at detecting and locating quantitative trait loci (QTLs) affecting a single trait. In this paper we study how selective genotyping can increase the efficiency of multitrait QTL experiments. By selecting on an index combining the variables of interest and having the maximum correlation with each variable, the efficiency of QTL detection is increased for each trait. The efficiency of selective genotyping relative to random selection strongly depends on the correlation between the index and each variable. The optimum selection rate that minimizes costs for a given experimental power depends also on this correlation and on the genotyping costs relative to phenotyping costs. When the population segregating for the quantitative traits and the markers is not as simple as a backcross or an F2 population, but is composed of several connected or unconnected families, selective genotyping can be used to improve the efficiency of the QTL study. In this case, the extreme individuals should be selected within each family. A method is provided to choose the selection rates within each family in order to optimize the global power of the experiment when the family sizes are unequal.

Usually, experiments designed for mapping quantitative trait loci (QTL) involve the genotyping of all individuals of a segregating population but are not very efficient with populations of feasible sizes. The use of selective genotyping, i.e., genotyping only a selected sample of the population (the high and low phenotypic tails), can considerably increase the efficiency of an experiment, provided the size of the population phenotyped is increased. In this paper, we examine the consequences of the use of this method for backcross and similar populations. New formulas, derived from likelihood functions, are proposed to estimate easily, without numerical maximization of the likelihood function, the effect of a QTL on the selected trait and on other traits of interest. This estimation procedure is shown to be reliable and quite robust to nonnormality, at least when the selection rate is not too low. The effect of selection on the efficiency of QTL detection for a trait other than the trait selected on is also considered: we show that selective genotyping never results in a loss of accuracy compared to random selection. Formulas to estimate QTL effects in more complex segregating populations could be easily derived in the same way as those proposed here.

We compared the powers of two methods for detection of quantitative trait loci (QTL) using genetic markers, in the simple case of an interval between two codominant markers and a backcross population. The first method is the interval mapping approach, based on the use of likelihood ratio tests performed in many positions within the interval considered and the second is the classical analysis of variance (ANOVA) testing only on the positions of the two markers. For both approaches we took into account the correlation between tests performed at different markers or positions in the interval. Appropriate thresholds and powers of tests were then calculated using analytical formulations. Simulations were also done to check the validity of the approximations used to calculate the power of the interval mapping test. Results show that the interval mapping test is slightly more powerful (about 5%) than ANOVA for small intervals (less than 20 cM) and that, for quite large effects of the QTL, the advantage of interval mapping increases as the distance between markers increases. It is more than 30% for intervals of about 70 cM.

We describe a method for constructing the confidence interval of the QTL location parameter. This method is developed in the local asymptotic framework, leading to a linear model at each position of the putative QTL. The idea is to construct a likelihood ratio test, using statistics whose asymptotic distribution does not depend on the nuisance parameters and in particular on the effect of the QTL. We show theoretical properties of the confidence interval built with this test, and compare it with the classical confidence interval using simulations. We show in particular, that our confidence interval has the correct probability of containing the true map location of the QTL, for almost all QTLs, whereas the classical confidence interval can be very biased for QTLs having small effect.

A general method is proposed for calculating approximate thresholds of interval mapping tests for quantitative trait loci (QTL) detection. Simulation results show that this method, when applied to backcross and F2 populations, gives good approximations and is useful for any situation. Programs which calculate these thresholds for backcross, recombinant inbreds and F2 for any given level and any chromosome with any given distribution of codominant markers were written in Fortran 77 and are available under request. The approach presented here could be used to obtain, after suitable calculations, thresholds for most segregating populations used in QTL mapping experiments.

The aim of this paper is to study the behavior of the likelihood ratio test for the detection of a major gene in an F2 population. The model is a mixture of three normal distributions where the proportions are known. The information matrix is not positive definite, and therefore classical results cannot be used. An example concerning beans is given.

SUMMARY The paper shows that it is possible to pool departmental information to predict regional wheat yield. In an MSEP (mean squared error of prediction) context, shrinkage estimation in linear agrometeorological models improves regional prediction. Cross-validation is not precise enough to enable comparison between models. The authors calculate the MSEP using the hypothesis of a multinormal distribution in simple cases (the distribution parameters are estimated with data input) and simulations are used for complex cases. Stein-like estimators are shown to be a superior alternative to the conventional estimators usually applied for prediction.

SUMMARY The aim of this paper is to study the behaviour of the likelihood ratio test statistic in mixture models when the proportions of the distributions are known a priori. The results depend on the value of the proportion, the dimensionality of the problem and whether or not the variance of the distributions is known.

Background Integration of multiple results from Quantitative Trait Loci (QTL) studies is a key point to understand the genetic determinism of complex traits. Up to now many efforts have been made by public database developers to facilitate the storage, compilation and visualization of multiple QTL mapping experiment results. However, studying the congruency between these results still remains a complex task. Presently, the few computational and statistical frameworks to do so are mainly based on empirical methods (e.g. consensus genetic maps are generally built by iterative projection). Results In this article, we present a new computational and statistical package, called MetaQTL, for carrying out whole-genome meta-analysis of QTL mapping experiments. Contrary to existing methods, MetaQTL offers a complete statistical process to establish a consensus model for both the marker and the QTL positions on the whole genome. First, MetaQTL implements a new statistical approach to merge multiple distinct genetic maps into a single consensus map which is optimal in terms of weighted least squares and can be used to investigate recombination rate heterogeneity between studies. Secondly, assuming that QTL can be projected on the consensus map, MetaQTL offers a new clustering approach based on a Gaussian mixture model to decide how many QTL underly the distribution of the observed QTL. Conclusion We demonstrate using simulations that the usual model choice criteria from mixture model literature perform relatively well in this context. As expected, simulations also show that this new clustering algorithm leads to a reduction in the length of the confidence interval of QTL location provided that across studies there are enough observed QTL for each underlying true QTL location. The usefulness of our approach is illustrated on published QTL detection results of flowering time in maize. Finally, MetaQTL is freely available at http://bioinformatics.org/mqtl.

In this paper, we compare four different methods of dealing with the unknown linkage phase of sire markers which occurs in the detection of quantitative trait loci (QTL) in a half-sib family structure when no information is available on grand-parents. The methods are compared by considering a Gaussian approximation of the progeny likelihood instead of the mixture likelihood. In the first simulation study, the properties of the Gaussian model and of the mixture model were investigated, using the simplest method for sire gamete reconstruction. Both models lead to comparable results as regards the test power but the mean square error of sib QTL effect estimates was larger for the Gaussian likelihood than for the mixture likelihood, especially for maps with widely spaced markers. The second simulation study revealed that the simplest method for sire marker genotype estimation was as powerful as complicated methods and that the method including all the possible sire marker genotypes was never the most powerful., Dans ce papier, nous comparons quatre méthodes, qui permettent de résoudre le problème relatif à la phase inconnue des mâles aux marqueurs dans des familles de demi-germains, lorsque aucune information sur les grands-parents n’est disponible. Ces méthodes sont comparées, en utilisant l’approximation gaussienne de la vraisemblance à l’intérieur de chaque descendance à la place de la vraisemblance du mélange de distribution. Dans la première étude par simulation, les propriétés respectives du modèle gaussien et du modèle de mélange sont étudiées pour la méthode la plus simple de reconstruction des gamètes des mâles. Les deux modèles conduisent à des tests comparables au regard de leur puissance mais l’erreur quadratique moyenne d’estimation de l’effet de substitution du QTL intra-famille est plus grande pour le modèle gaussien que pour le modèle de mélange, en particulier pour les cartes génétiques très peu denses. La deuxième étude par simulation montre que la plus simple méthode d’estimation du génotype des mâles aux marqueurs est aussi puissante que les méthodes plus sophistiquées et que la méthode qui consiste à prendre en compte dans la vraisemblance tous les génotypes possibles d’un mâle aux marqueurs n’est jamais la plus puissante.

SUMMARY The use of major genes is a component of livestock improvement. This requires identification of the genotypes of reproducers, in particular progeny-tested sires after mating with homozygous females. Two test statistics derived from the nonnested test of Cox (1961, Proceedings of the Fouirth Berkeley Svmposium on Mathematical Statistics and Probability 1, 105-123; 1962, Journal of the Royal Statistical Society, Series B 24, 406-424) are proposed. For both tests, asymptotic normality is proved algebraically and the speed of convergence is studied through simulations. In the cases where a uniformly most powerful (UMP) test exists, the power of one of the tests is close to the power of that UMP test. Finally, the tests are applied to a population of poultry carrying the dwarf gene.

Model evaluation is an essential aspect of the process of development of system models. When the main purpose of the model is prediction, a reasonable criterion of model quality is the mean squared error of prediction. This criterion is defined here, and it is shown how it can be estimated from available data in a number of situations, including the situation where the parameters of the model are adjusted to the data. An example of the use of this criterion for choosing between alternative models is presented.