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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.

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.

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.