Modélisation spatiale hiérarchique bayésienne de l'apparentement génétique et de l'héritabilité en milieu naturel à l'aide de marqueurs moléculaires

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Résumé La connaissance de l'apparentement génétique entre individus permet d'estimer l'héritabilité des caractères d'intérêt. La possibilité d'estimer l'héritabilité en milieu naturel suscite un intérêt croissant pour l'amélioration génétique des populations. Mais en milieu naturel, le pedigree n'est pas connu. L'utilisation des marqueurs moléculaires permet d'estimer l'apparentement puis d'estimer l'héritabilité. Néanmoins, les approches classiques ne permettent pas d'introduire une information exogène comme l'information spatiale. Or, nous pouvons supposer que deux individus proches géographiquement sont proches génétiquement. L'objectif de ce travail est de développer des modèles statistiques pour l'estimation de l'apparentement et de l'héritabilité à l'aide des marqueurs moléculaires en prenant en compte l'information spatiale. Premièrement, nous construisons un modèle spatial hiérarchique bayésien de l'apparentement. Comme la vraisemblance des observations, modes d'identité par état entre génotypes, est complexe, le modèle statistique pour l'apparentement considéré est celui de la vraisemblance composite. Le lien entre le mode d'identité par descendance et la distance spatiale se fait par l'intermédiaire d'un GLM probit ordinal. Deuxièmement, nous proposons une modélisation simultanée de l'apparentement et de l'héritabilité. Dans la troisième partie, nous proposons différents algorithmes MCMC pour l'inférence des paramètres des modèles. Finalement, l'intérêt du modèle spatial pour l'apparentement est illustré par une application à des données sur le karité (Vitellaria paradoxa).

Mots Clés Bayésien hiérarchique, MCMC, Vraisemblance Composite, Apparentement, Héritabilité, Spatial, Marqueurs Moléculaires, Karité

Spatial hierarchical Bayesian Model for relatedness and heritability based on
molecular markers.

Abstract The knowledge of genetic relatedness between individuals combined with phenotypic information enables us to estimate the heritability of character of interest. Estimating the heritability in natural populations remains a real challenge for the obvious reason that, in natural populations, the pedigree remains unknown. The use of molecular markers allows the assessment first of relatedness and then of heritability. However, classical approaches do not allow to introduce exogenous information such as geographical information. Nevertheless, we can assume that the closer two individuals are spatially, the more genetically close they are. The aim of this study is to develop statistical models allowing the simultaneous estimation of relatedness and heritability by using molecular markers as well as spatial information. In the first part, we develop a hierarchical spatial Bayesian model for relatedness taking into account spatial information. As the likelihood of the data given by the identity-by-state mode of pairs of genotypes, is not tractable, we propose the use of the composite likelihood approaches. The link between the identity-bydescent mode and the spatial distance is made using ordinal Probit models belonging to the generalized linear models. In the second part, we propose to model relatedness and heritability simultaneously. In the third part, we give different MCMC algorithms for model inference. Finally, the spatial model for relatedness is emphasized by an application on Shea tree (Vitellaria paradoxa) data.

Keywords Hierarchical Bayesian, MCMC, Composite Likelihood, Relatedness, Heritability, Spatial, Molecular Markers, Shea Tree.

Discipline : Biostatistiques

CIRAD, UR 39 : Diversité génétique et amélioration des espèces forestières.

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