Statistical modelling of growth using a mixed model with orthogonal polynomials

In statistical modelling, the effects of single-nucleotide polymorphisms (SNPs) are often regarded as time-independent. However, for traits recorded repeatedly, it is very interesting to investigate the behaviour of gene effects over time. In the analysis, simulated data from the 13th QTL-MAS Workshop (Wageningen, The Netherlands, April 2009) was used and the major goal was the modelling of genetic effects as time-dependent. For this purpose, a mixed model which describes each effect using the third-order Legendre orthogonal polynomials, in order to account for the correlation between consecutive measurements, is fitted. In this model, SNPs are modelled as fixed, while the environment is modelled as random effects. The maximum likelihood estimates of model parameters are obtained by the expectation–maximisation (EM) algorithm and the significance of the additive SNP effects is based on the likelihood ratio test, with p-values corrected for multiple testing. For each significant SNP, the percentage of the total variance contributed by this SNP is calculated. Moreover, by using a model which simultaneously incorporates effects of all of the SNPs, the prediction of future yields is conducted. As a result, 179 from the total of 453 SNPs covering 16 out of 18 true quantitative trait loci (QTL) were selected. The correlation between predicted and true breeding values was 0.73 for the data set with all SNPs and 0.84 for the data set with selected SNPs. In conclusion, we showed that a longitudinal approach allows for estimating changes of the variance contributed by each SNP over time and demonstrated that, for prediction, the pre-selection of SNPs plays an important role

Zirconium oxidation under high energy heavy ion irradiation

This paper concerns the study of zirconium oxidation under irradiation with high energetic Xe ions. The irradiations were performed on the IRRSUD beam line at GANIL (Caen). The oxygen partial pressure was fixed at 10$^{-3}$ Pa and two temperature conditions were used, either 480$\circ$C reached by Joule effect heating or 280$\circ$C due to Xe energy deposition. Zirconia was fully characterized by Rutherford Backscattering Spectrometry, Transmission Electron Microscopy and Grazing Angle X-ray Diffraction. Apparent diffusion coefficients of oxygen in ZrO2 were determined from these experiments by using a model which takes into account a surface exchange between oxygen gas and the ZrO2 surface. These results are compared with thermal oxidation data

Functional Mapping of Dynamic Traits with Robust t-Distribution

Functional mapping has been a powerful tool in mapping quantitative trait loci (QTL) underlying dynamic traits of agricultural or biomedical interest. In functional mapping, multivariate normality is often assumed for the underlying data distribution, partially due to the ease of parameter estimation. The normality assumption however could be easily violated in real applications due to various reasons such as heavy tails or extreme observations. Departure from normality has negative effect on testing power and inference for QTL identification. In this work, we relax the normality assumption and propose a robust multivariate -distribution mapping framework for QTL identification in functional mapping. Simulation studies show increased mapping power and precision with the distribution than that of a normal distribution. The utility of the method is demonstrated through a real data analysis

Use of structured antedependence models to estimate genotype by environment interaction

The objective of this research was to compare structured antedependence models (SAD) to random regression models (or reaction norm models) (RRM) in their ability to estimate genotype by environment interaction. In RRM, random effects for a trait are estimated as a regression on the environments and the (co)variances are modelled by a covariance function. In SAD, random effects for a trait are estimated as a function of the same trait in different environments and the (co)variances are modelled by so-called innovation variances and antedependence parameters. One of the major differences between the models is that the SAD allows the genetic correlations between a trait in different environment to be less than unity in situations where the genetic variance is constant across environments, whilst RRM implicitly model the change in covariances and variances simultaneously. Thus, SAD might be more flexible in estimating genetic correlations between a trait in different environments. Initial results from a simulation study indicate that genetic correlations between a trait expressed in different environments tend to be overestimated when using RRM and underestimated when using SAD