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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.

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.

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.