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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.

The aim of this paper was to compare different methods for testing the presence of one versus multiple QTLs on a same chromosome. We describe different methods that have partially been taken out of the literature. We perform simulations covering different situations to compare the power of these methods for detecting more than one QTL. None of the tests considered appear to be similar; that is, the first-type error depends on the value of the parameters concerning the first QTL. The method starting with a two-QTL model is the most powerful in many situations.

Alfalfa (Medicago sativa L.) is a forage legume of world-wide importance whose both allogamous and autotetraploid nature maximizes the genetic diversity within natural and cultivated populations. This genetic diversity makes difficult the discrimination between two related populations. We analyzed this genetic diversity by screening DNA from individual plants of eight cultivated and natural populations of M. sativa and M. falcata using the RAPD method. A high level of genetic variation was found within and between populations. Using five primers, 64 intense bands were scored as present or absent across all populations. Most of the loci were revealed to be highly polymorphic whereas very few population-specific polymorphisms were identified. From these observations, we adopted a method based on the Roger's genetic distance between populations using the observed frequency of bands to discriminate populations pairwise. Except for one case, the between-population distances were all significantly different from zero. We have also determined the minimal number of bands and individuals required to test for the significance of between-population distances.

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.

In crop species, most QTL (quantitative trait loci) mapping strategies use segregating populations derived from an initial cross between two lines. However, schemes including more than two parents could also be used. We propose an approach using a high-density restriction fragment length polymorphism (RFLP) map established on six F 2 populations derived from diallel crosses among four inbred lines and the phenotypic performances of two types of replicated progenies (F 3 and topcross). The QTL is supposed to be on the marker locus considered. Three linear model tests for the detection of QTL effects (T 1, T 2 and T 3) are described and their power studied for the two types of progeny. T 1 tests the global genetic effects of the QTL (additivity and dominance) and T 2 tests only additive effects assuming dominance is absent when it could exist. The models of these two tests assume that the main effects of QTL alleles are constant in different genetic backgrounds. The additive model of test T 3 considers the six F 2 populations independently, and T 3 is the equivalent of the classical mean comparison test if we neglect dominance; it uses only contrasts between the homozygote marker classes. The results show that T 2 is much more powerful than T 3. The power of T 1 and T 2 depends on the relative sizes of the additive and dominance effects, and their comparison is not easy to establish. Nevertheless, T 2 seems to be the more powerful in most situations, indicating that it is often more interesting to ignore dominance when testing for a QTL effect. For a given size of genetic effects, the power is affected by the total number of individuals genotyped in F 2 and the recombination rate between the marker locus and the putative QTL. The approach presented in this paper has some drawbacks but could be easily generalized to other sizes of diallels and different progeny types.

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

We study the problem of estimating the density of a random variable G, given observations of a random variable Y = G + E. The random variable E is independent of G and its probability distribution function is considered as known. We build a family of estimators of the density of G using characteristic functions. We then derive a family of estimators of the density of Y based on the model for Y. The estimators are shown to be asymptotically unbiased and consistent. Simulations show that these estimators are better, as measured by integrated squared error, than the standard kernel estimators. Finally, we give an example of the use of this method for the detection of major genes in animal populations.

In order to develop improved fertilization strategies for fruit trees, it is necessary to have a quantitative understanding of the dynamics of N uptake. This study was conducted to select a mathematical model for describing N uptake in young peach trees (Prunus persica (L.) Batsch). In 1985 young peach trees were grown outdoors in Avignon, France, in sand-filled containers from late February to late September. At each of nine dates total tree N was measured by destructive sampling of three trees. The differences in total N between dates are related to N uptake. The models considered all take the form of a Michaelis-Menten equation, with maximum uptake expressed as the product of total root weight and uptake efficiency. The models differ in that they express the efficiency factor as different order polynomial functions of time. The criterion used for selecting a best model was related to the squared error of prediction integrated over time. The value of the criterion was estimated for each model, and it was found that the model that expressed efficiency as a third-order polynomial function of time had the smallest value of the criterion, and was therefore the model of choice. According to this model, N uptake efficiency increased from near zero in mid-April to a maximum of 3.1 pg N/g root/d in late May, and then decreased again to near zero in late September.

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.

L'estimation des parametres des modeles mecanistes de culture est un sujet important, mais peu etudie. Nous explorons ici la possibilite d'ajuster un petit nombre de combinaisons lineaires des parametres originaux. Nous esperons que cette methode evitera la surparametrisation tout en fournissant des valeurs des parametres realistes. Nous etudions tout d'abord un modele lineaire tres simple, et montrons les avantages d'ajuster une combinaison lineaire des parametres dans ce cas simple. Nous proposons ensuite une methode d'ajustement des combinaisons lineaires des parametres qui peut etre appliquee aux modeles mecanistes de culture. Le modele de culture est tout d'abord linearise et cette version linearisee est utilisee pour generer les combinaisons lineaires des parametres originaux selon la methode de la regression continue. Ensuite, ces combinaisons lineaires des parametres sont ajustees aux donnees en utilisant le modele de culture non lineaire original. Nous appliquons cette procedure a un exemple. La conclusion est que, globalement, cette approche semble prometteuse mais une etude supplementaire est necessaire afin de la rendre utilisable.

Des modeles de culture ont en general trop de parametres pour permettre de les ajuster tous aux donnees. On compense par l'utilisation d'information a priori sur les parametres, mais cette information est incertaine. Il est alors important d'evaluer l'importance de cette incertitude sur les modeles. On propose ici une telle evaluation dans le cas d'un modele de mais, ou un algorithme recent est utilise pour ajuster une partie des parametres. Pratiquement, on utilise l'algorithme avec des ensembles differents de valeurs initiales des parametres. L'algorithme determine automatiquement quels parametres devraient etre ajustes. On trouve que ce choix varie en fonction des valeurs initiales. Neanmoins, les deux premiers parametres choisis sont toujours les memes ou (pour le seul cas d'exception) ont essentiellement le meme effet dans le modele. La qualite de prediction et les predictions individuelles sont egalement relativement stables pour differentes valeurs initiales des parametres.

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.

We investigated protocol designs for gene mapping in livestock. The optimization of the population structure was based on the empirical variance of the recombination rate estimator. We concluded that a mixture of half-sib and full-sib families is preferred to half-sib families; a knowledge of parental phases does not improve the quality of the estimation for typical livestock families with five offspring or more; and measurements of the genotype of the mates in half-sib families are not useful. Graphs and algebraic approximations for the practical choice of family size and structure are given.

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.

The aim of this paper is to study the distribution of the likelihood ratio for testing whether or not one is sampling from a mixture of two distributions or from a single distribution. We study the case where some information is available on the variation range of the parameters of populations. First we study the simplest case in which the difference between the mean of the two populations is known. We show certain distortions between theoretical and simulation results. Secondly, we show how this distortion spreads to the situation where this difference belongs to an interval. Finally, we give an example concerning the detection of major genes in animal population.

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.

The adjustment of the parameters in mechanistic crop models to field data, using an automatic procedure, is essential to ensure efficient and objective use of measured data. However, it is in general numerically impossible, and in any case undoubtedly unwise, to adjust all the model parameters to the measured data. There is currently no widely accepted solution to this problem. This paper proposes a new approach to parameter adjustment, and applies it to a model of corn growth and development. One begins by defining a criterion of model goodness-of-fit, which should be adapted to the goal of the modeling exercise, and a corresponding criterion of model prediction error. For the latter we propose a cross validation version of the goodness-of-fit criterion. In Step 1 of the algorithm, one orders the parameters according to how much each improves the goodness-of-fit of the model. In the second step, the number of parameters actually adjusted is chosen to minimize the prediction error criterion. This approach has the advantage of explicitly using prediction quality as a criterion. As a by-product, it leads to adjusting relatively few parameters (in our example, 3 out of the 26 potentially adjustable parameters), which considerably reduces the numerical problems. The procedure is quite straightforward to apply, although it does require substantial computing time.

The mean squared error of prediction (MSEP) as a criterion for evaluating models used for studying ecological and agronomic systems is considered. It is shown that the different sources of error that have been discussed in the literature for such models can be rigorously defined in terms of the MSEP. A situation that occurs frequently for such models is that the model parameters are determined independently of data used to test the model, and the population of interest is structured in subpopulations. It is shown that in this case obtaining estimators of MSEP and of the individual error contributions can be reduced to the classic problem of estimating components of variance in a oneway random model. For comparison, the case where the parameters are estimated from the same data used to test the model is also addressed here.

Summary A Bayesian approach to map Quantitative Trait Loci (QTL) is compared to the flanking markers regression method (asymptotically equivalent to the traditional Interval Mapping method) using simulated backcross data. The main part consists of a comparison of the properties for a one QTL model. The Bayesian approach gives less biases and more accurate estimates of the genetic effect and significance thresholds close to χ2 quantiles when the number of individuals and markers become large. The behaviour of both approaches in the case of two linked QTL is mentioned. Zusammenfassung Eigenschaften eines BAYES Ansatz zur QTL Identifikation im Vergleich zur flankierende Marker Regressions-Methode. Der Bayes Ansatz zur Kartierung von Quantitativen Merkmals Loci (QTL) wurde mittels simulierter Ruckkreuzungsdaten mit der Flankierenden Marker Regressionsmethode (asymptotisch aquivalent mit der traditionellen Intervall Markierung) verglichen. Es werden hauptsachlich die Eigenschaften fur ein ein-QTL Modell gepruft. Der Bayes Ansatz ergibt weniger verzerrte und genauere Schatz-werte der genetischen Wirkung und Signifikanz Schwellen nahe den χ2 Quantilen bei grosen Individuen und Marker Zahlen. Die Eigenschaften beider Ansatze im Falle von zwei gekoppelten QTL werden erwahnt.