Restricted maximum likelihood estimation for animal models using derivatives of the likelihood

International audienc

Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices

Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from k(k + 1)/2 to m(2k - m + 1)/2 for k effects and m principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given

High performance computing for large-scale genomic prediction

In the past decades genetics was studied intensively leading to the knowledge that DNA is the molecule behind genetic inheritance and starting from the new millennium next-generation sequencing methods made it possible to sample this DNA with an ever decreasing cost. Animal and plant breeders have always made use of genetic information to predict agronomic performance of new breeds. While this genetic information previously was gathered from the pedigree of the population under study, genomic information of the DNA makes it possible to also deduce correlations between individuals that do not share any known ancestors leading to so-called genomic prediction of agronomic performance. Nowadays, the number of informative samples that can be taken from a genome ranges from one thousand to one million. Using all this information in a breeding context where agronomic performance is predicted and optimized for different environmental conditions is not a straightforward task. Moreover, the number of individuals for which this information is available keeps on growing and thus sophisticated computational methods are required for analyzing these large scale genomic data sets. This thesis introduces some concepts of high performance computing in a genomic prediction context and shows that analyzing phenotypic records of large numbers of genotyped individuals leads to a better prediction accuracy of the agronomic performance in different environments. Finally, it is even shown that the parts of the DNA that influence the agronomic performance under certain environmental conditions can be pinpointed, and this knowledge can thus be used by breeders to select individuals that thrive better in the targeted environment