1 Single Step method : theoretical background

1.1 Simple derivation of GBLUP Models for genomic selection are abundant. However, most of them rely (yet not all; [1] ) in a hierarchical formulation in which SNP markers (or haplotypes) have additive effect on the trait of interest [2]. We will focus here in models including biallelic SNP markers. Thus, n markers will have n effects, a1 ... an. Although markers have 2 alleles, a single effect can be defined for each marker according to the notion of substitution effect [3]. For ease of development, substitution effects are centered around 0. Expressions for the values of different genotypes can be found in Falconer [3], and they are (these will be referred to as “allele coding”):