In genomic selection, the model estimates the substitution effect of each SNP, which is the difference between the average effect of its two alleles. GEBV is then obtained as the sum of the substitution effects over all SNPs.
Is it really the same thing as the breeding value, which is the sum of the average effect of all the alleles?
I think it depends on your model and assumptions. GEBV is normally computed based on additive genetics affects, it is also easily to model in BLUP, BAYES...methods and additive genetic effects capture very high proportion of breeding values. But you can also include the non-additive genetics effects (dominant and epistasis) in the GEBV and it is may useful in some cases. The paper try to model all of it in pigs : http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045293
There is a clear answer in Vitezica et al 2013 genetics. They explained that when the matrice of molecular data (ie the Z matrix) is computed according to Van Raden (ie taking into account allele frequencies), then the product "Z * SNP effects estimated by GS" gives the breeding value of each individual.
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