Genetic progress by selection and mating is based on prediction of the ability of the parents

19 Genomic evaluation methods assume that the reference population is genotyped and 20 phenotyped. This is most often false and the generation of pseudo-phenotypes is uncertain and 21 inaccurate. However, markers obey transmission rules and therefore the covariances of 22 marker genotypes across individuals can be modelled using pedigree relationships. Based on 23 this, an extension of the genomic relationship matrix can be constructed in which genomic 24 relationships are propagated to all individuals, resulting in a combined relationship matrix, 25 which can be used in a BLUP procedure called the Single Step Genomic BLUP. This 26 procedure provides so far the most comprehensive option for genomic evaluation. Several 27 extensions, options and details are described: compatibility of genomic and pedigree 28 relationships, Bayesian regressions, multiple trait models, computational aspects, etc. Many 29 details scattered through a series of papers are put together into this paper. 30