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"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.