Correction to: Genomic evaluation for a three-way crossbreeding system considering breed-of-origin of alleles

Correction to: Genet Sel Evol (2017) 49:75 https://doi.org/10.1186/s12711-017-0350-1

After publication of our article [1], we found a typo in the formula to build the genomic relationship matrix using allele frequencies across all genotyped pigs (matrix) and the genomic relationship matrix using breed-specific allele frequencies (matrix), and we noted that the description to this formula is not very clear. In this paper, we describe the corrected formula and provide a clarification.

In the paragraph Genomic relationship matrix using allele frequencies across all genotyped pigs (G _A matrix), page 4, second column, line 21, a “2” is missing in the formula, i.e., it incorrectly says that D is diagonal with $D_{jj} = \frac{1}{{p_{j} \left( {1 - p_{j} } \right)}}$.

Instead, D is diagonal with $D_{jj} = \frac{1}{{2p_{j} \left( {1 - p_{j} } \right)}}$.

Similarly, in the paragraph Genomic relationship matrix using breed-specific allele frequencies (G _B matrix), page 4, second column, line 33, a “2” is missing in the formula, i.e., it incorrectly says that D ^B is diagonal with $D_{jj}^{B} = \frac{1}{{p\left( {1 - p_{Bj} } \right)}}$.

Instead, D ^B is diagonal with $D_{jj}^{B} = \frac{1}{{2p_{Bj} \left( {1 - p_{Bj} } \right)}}$.

In the same paragraph, page 4, second column, line 29, p _B is confusingly defined as: “The vector of the frequencies of the counted allele (p _Bj ). p _Bj was obtained by summing the contribution of each pure breed j and the weighted contribution of the CB. The weight was 0.5 for S, and 0.25 for LR and LW.”

For clarification, p _B is the vector of the frequencies of the counted allele at locus j (p _Bj ). For PB, p _Bj was specific for each breed B (i.e., S, LR, and LW). For CB, p _Bj was the weighted contribution of each breed. The weights considered for the CB were 0.5 for S, 0.25 for LR and 0.25 for LW.

The original article was corrected.