An approximate theory of selection assuming a finite number of quantitative trait loci

An approximate theory of mid-term selection for a quantitative trait is developed for the case when a finite number of unlinked loci contribute to phenotypes. Assuming Gaussian distributions of phenotypic and genetic effects, the analysis shows that the dynamics of the response to selection is defined by one single additional parameter, the effective number Le of quantitative trait loci (QTL). This number is expected to be rather small (3-20) if QTLs have variable contributions to the genetic variance. As is confirmed by simulation, the change with time of the genetic variance and of the cumulative response to selection depend on this effective number of QTLs rather than on the total number of contributing loci. The model extends the analysis of Bulmer, and shows that an equilibrium structure arises after a few generations in which some amount of genetic variability is hidden by gametic disequilibria. The additive genetic variance VA and the genic variance Va remain linked by: (formula, see attached document) where K is the proportion of variance removed by selection, and h2 the current heritability of the trait. From this property, a complete approximate theory of selection can be developed, and modifications of correlations between relatives can be proposed. However, the model generally overestimates the cumulative response to selection except in early generations, which defines the time scale for which the present theory is of potential practical value.Une théorie approchée de la sélection est développée dans le cas d’un caractère quantitatif dont la variabilité génétique est due à un nombre fini de locus génétiquement indépendants. Le calcul est développé analytiquement en admettant que toutes les distributions statistiques peuvent être approchées par des lois normales. L’analyse montre que le comportement global du système génétique dépend essentiellement d’un «nombre efficace de locus», Le, dont les valeurs vraisemblables sont sans doute faibles (3 à 20). Des simulations confirment le rôle de ce paramètre pour caractériser la réponse cumulée à la sélection et la structure génétique de la population. Le modèle généralise l’analyse de M Bulmer. Après quelques générations d’un régime de sélection, une fraction de la variance génétique reste « cachée» sous la forme de covariances négatives, de sorte que la variance génétique additive VA et la variance génique Va demeurent liées par la relation :( formule, voir document attaché) où k est la fraction de variance réduite par la sélection, et h2 est l’héritabilité actuelle du caractère. Cette structuration de la variance génétique sous sélection permet de proposer des expressions modifiées des covariances entre apparentes issus de parents sélectionnés, et de développer une théorie complète de la sélection. Sauf à court et moyen terme, les prédictions quantitatives sont surestimées par le modèle gaussien, ce qui délimite le champ d’application pratique de la théorie

Contrainte de correspondance Document-Document pour la RI. Application à la Divergence de Kullback-Leibler

National audienceThis paper defines a new axiomatic constraint, namely DDMC (Document-DocumentMatching Constraint), for information retrieval that depicts the behavior of a matching if a corpusdocument is used as a query. The DDMC constraint is not verified by a classical IR modellike the Language Model based on Jelinek-Mercer smoothing and Kulback-Leibler Divergence.We introduce a modification of this model to validate DDMC. An experiment conducted on twocorpus show that the modification of the reference model does not degrade significantly theresults, and validates the DDMC.Cet article décrit une contrainte d'un modèle de recherche d'information décrivant les comportement attendu d'un système si un document du corpus est posé en requête, la contrainte DDMC (Document-Document Matching Constraint). Cette contrainte n'étant pas vérifiée par un modèle classique de recherche d'information (modèle de langue basé sur un calcul de néga-tive de Divergence de Kullback-Leibler avec lissage de Jelinek-Mercer), nous présentons une modification de ce dernier modèle qui permet de vérifier DDMC. Une dernière partie présente des expérimentations menées afin de vérifier que notre modification n'impacte pas la qualité des réponses d'un système, tout en garantissant la vérification de DDMC

Inbreeding depression and heterosis: Expected means and variances among inbred lines and their crosses

International audienc

On methods of estimation of maternal heterosis and recombination effects from a specific three breeds crossing system

International audienc

Identity coefficients and genetic variability in theoretical genetics

International audienc

Measuring genetic distances between breeds: use of some distances in various short term evolution models

Many works demonstrate the benefits of using highly polymorphic markers such as microsatellites in order to measure the genetic diversity between closely related breeds. But it is sometimes difficult to decide which genetic distance should be used. In this paper we review the behaviour of the main distances encountered in the literature in various divergence models. In the first part, we consider that breeds are populations in which the assumption of equilibrium between drift and mutation is verified. In this case some interesting distances can be expressed as a function of divergence time, t, and therefore can be used to construct phylogenies. Distances based on allele size distribution (such as (δμ)2 and derived distances), taking a mutation model of microsatellites, the Stepwise Mutation Model, specifically into account, exhibit large variance and therefore should not be used to accurately infer phylogeny of closely related breeds. In the last section, we will consider that breeds are small populations and that the divergence times between them are too small to consider that the observed diversity is due to mutations: divergence is mainly due to genetic drift. Expectation and variance of distances were calculated as a function of the Wright-Malécot inbreeding coefficient, F. Computer simulations performed under this divergence model show that the Reynolds distance [57]is the best method for very closely related breeds

Molecular approach to quantitative inheritance

International audienc

Calcul automatique des coefficients d'identité

International audienc