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From this total genomic value, an additive breeding value can be extracted by performing linear approximations as shown in eq. (8) of Gianola et al. [ 4].

An individual's total breeding value can be partitioned into a family component,, which summarizes all its heritable effects on family members (including the direct effect on itself) and is considered the family breeding value here, and a non-family component,, the non-family breeding value.

Formally, a breeding value can be partitioned into two components: (1) the parent average (that is, one individual receives 50% of its genome from each of its two parents) and (2) Mendelian sampling, which is the random sampling of the genome of each parent.

In a random sample of the population, the accuracy of genomic EBV, r g g ˆ 0, being the correlation between the genomic EBV and the true breeding value, can be calculated using (9) r g g ˆ 0 = λ r 2 λ r 2 + 1, where λ = n P / n G n P being the number of individuals in the reference population with both phenotypic records and genotypes [ 6].

Calculation of unbiased accuracy of within breed [ 8] and across breed [ 12] estimated breeding values can be improved by reducing the computational time required of calculation or reducing the sampling error for a given computational time.

Simulations and results on real data suggest that breeding values can be predicted with high accuracy using genetic markers alone.

Consequently, we expect that more accurate estimated breeding values can be obtained when using individual instead of pooled data.

In addition, breeding values can be estimated for each genotype, quantifying the potential of the individual as a parent in the breeding program.

As first proposed by Meuwissen et al. (2001), breeding values can be predicted as the sum of all marker effects by regressing phenotypic values on all available markers.

In this study, we investigated whether direct, indirect and total genetic variances, and breeding values can be estimated from pooled data (pooled by group).

The prior density of breeding values can be expressed as: where A sd is the additive relationship matrix for sires and dams.