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Genomic evaluation methods assume that the reference population is genotyped and phenotyped. This is most often false and the generation of pseudo-phenotypes is uncertain and inaccurate. However, markers obey transmission rules and therefore the covariances of marker genotypes across individuals can be modelled using pedigree relationships. Based on this, an extension of the genomic relationship matrix can be constructed in which genomic relationships are propagated to all individuals, resulting in a combined relationship matrix, which can be used in a BLUP procedure called the Single Step Genomic BLUP. This procedure provides so far the most comprehensive option for genomic evaluation. Several extensions, options and details are described: compatibility of genomic and pedigree relationships, Bayesian regressions, multiple trait models, computational aspects, etc. Many details scattered …