Thus, to benefit from the advantage of using sequence data compared to BovineHD genotype data for genomic prediction, it is necessary to aim for a large training set with a small average relationship between the animals, and possibly to pre-select SNPs based on functional information.
In a simulation study using dairy cattle data, it was concluded that using a training set with animals that have a low average relationship is beneficial for genomic prediction [ 7].
Vector u is a (m × 1) vector of SNP effects assumed normally distributed u i ~ N 0, ), e is a vector of random deviates where is the error variance, v i is the polygenic breeding value of the i th animal, with variance A, where A is the average relationship matrix.
Genetic merit is an aggregate breeding value, while average relationship is derived from a matrix of genetic relationships.
Average (genomic) EBV reliabilities increased with heritability and with a decrease in the average relationship within the reference population.
OCS was carried out by maximising the genetic merit of the new cohort while applying a penalty to the average relationship of the current generation, which included the new cohort.
Key animals were identified iteratively with p m = A m − 1 ∗ c m [ 5], where A is the numerator relationship matrix of m selected animals with pedigree information lasting back to 1920, c is a vector representing the average relationship of the selected animals to the entire population and p is a vector with the proportion of genetic diversity captured by m animals.
Animals for the reference population were selected based on p m = A m − 1 c m [ 20], where Am is a subset of the numerator relationship matrix, c is a vector representing the average relationship of m selected animals with the entire population and p is a vector of the proportion of the gene pool captured by the m animals.
Specifically, m animals were selected with, where p is a vector that contains the percentage of gene pool diversity captured by m animals, is a subset of the inverse numerator relationship matrix for m animals and c is a vector representing the average relationship of the m animals selected to the entire genotyped population.
The deep reference population was an attempt to reduce the average relationship between reference animals compared to the shallow reference population.
