Key assumptions in our study were that heifers and cows genotyped by breeding companies are elite females and that the cows genotyped for the research project could be considered as representative of the commercial population. Indeed, each breeding company has its own strategy for bull dam selection: some companies genotype a relatively large proportion of the population and select on a broad basis, while others are more selective and only genotype top females based on their total merit index. Different breeding companies may put a different emphasis on different traits, or the sire analysts may focus on a limited number of maternal cow families, which are more likely to be affected by preferential treatment. For the cows genotyped in the research project, even if the sires (constraint set on number of genotyped progeny) were the most used within each breed, this group of cows may not be a perfect random sample of the commercial population. However, the two groups of cows are easily identified when considering the average EBV of the cows, since the elite group presented a superiority of 0.4 to 1 genetic standard deviations for each breed and trait. The lowest difference in EBV between the elite and “randomly selected” groups was observed in the Montbéliarde breed, likely because the objective of the main breeding organization involved in this breed is to genotype a large proportion of candidates from the whole population. Thus, the elite group includes some females that would not strictly fit with a selection criterion mainly based on milk yield EBV for the Montbéliarde breed. It should also be emphasized that elite cows were genotyped before their first calving, thus, it is unlikely that preferential treatment occurred for all elite cows, especially those with a disappointing GEBV.
Milk yield is obviously a more important trait in the breeding goal, which explains why the superiority of the elite group over the “randomly selected” group is greater for this trait. However, the elite group was also genetically superior for SCC. Thus any difference in results between the two traits when comparing the two female groups cannot be explained only by the genetic superiority of the elite group.
The two traits not only differ in nature (a production trait vs a health trait) but also in their heritability, which is 0.3 for milk yield and 0.15 for SCC in our case. This difference in heritability has an impact on the amount of information that a cow’s own performance contributes to its GEBV; own performance will have a larger impact on the cow’s GEBV for milk yield because of this higher heritability.
A main feature of the genomic prediction model is that polygenic effects (based on pedigree) and haplotype effects (based on marker information) are estimated jointly. This is useful to properly estimate both terms, compared with blending procedures  for instance. However, both polygenic and haplotype effects may be affected by biases in the phenotypic data used.
Correlations between GEBV(DYD+YD) and GEBV(DYD) presented a different pattern between milk yield and SCC. Indeed, except for the Montbéliarde breed, these correlations were very similar for the elite and “randomly selected” groups for SCC but for milk yield, the decrease in correlation was lower for the elite group than for the “randomly selected” group (difference of up to 0.04). This provides the first evidence of the existence of a bias induced by including own phenotypes of genotyped cows in genomic evaluation.
Correlations were also higher for SCC than for milk yield. However, as already mentioned, this can be mainly explained by the lower heritability of SCC. Indeed, the information that is added by a cow’s own phenotype (YD) is less for a lowly heritable trait and is, therefore, expected to result in smaller changes in GEBV.
The reference population for the Holstein breed was much larger than that for the two other breeds. This results in more precisely estimated marker effects and more stable genomic evaluations for the Holstein breed. This may be the reason why correlations of GEBV were higher for this breed, regardless of the group and trait considered. This may also explain why the differences observed between the elite and “randomly selected” groups were smaller for this breed.
Differences between GEBV(DYD+YD) and GEBV(DYD) were computed for the two traits for each cow in the two groups. Graphical representations of these differences (Figures 1, 2, 3) clearly showed a different pattern for milk yield for the elite group compared to the “randomly selected” group and for SCC. A large fraction of the elite cows presented a positive difference for milk yield, meaning that including their own record in genomic predictions led to an increase of their GEBV. This phenomenon was not observed for SSC or for the “randomly selected” group, for which differences were almost equally distributed between positive and negative values.
When expressed in genetic standard deviation units, the average differences observed confirmed that the elite group for milk yield presented different characteristics than the “randomly selected” group or for SCC. Admittedly, the mean values were not strictly equal to 0 for the “randomly selected” group or for SCC, and it is difficult to explain why. However, the mean difference was up to 0.3 genetic standard deviations (in the Normande breed) higher for the elite group than for the “randomly selected” group.
The elite group was also genetically superior for SCC but no real difference between GEBV(DYD+YD) and GEBV(DYD) was observed in either the elite or the “randomly selected” groups. This means that the systematic overestimation of GEBV observed when milk yield YD are included is induced by inflated performances of the elite group. This clearly demonstrates the existence of a bias of GEBV for milk yield but not for SCC. Preferential treatment is the most immediate explanation for this bias, although we cannot exclude some genetic underestimation of the elite cows in our models which did not account for the records of the dams.
Our findings were obtained considering a group of cows as a whole. This does not mean that every single individual of this group has inflated performances. In particular, the GEBV decreased for a significant proportion of the elite cows when their own YD were included.
Wiggans et al.  also demonstrated the existence of a bias in genomic evaluations when using unadjusted records for genotyped cows in the reference population. Indeed, for milk yield in Holsteins, the regression coefficient of the progeny test EBV of bulls on their GEBV prior to progeny testing decreased when unadjusted records for genotyped cows were included. The regression coefficient is a measure of how inflated GEBV are compared to EBV and showed a bias equal to 50 kg. The realized reliability, calculated as the squared correlation between GEBV and deregressed proofs for bulls of the validation population, was also lower when records on cows were included. Furthermore, they also observed a bias in genomic predictions equations, as marker effects of the X chromosome presented a specific pattern, suggesting that females behaved systematically differently than males.
Since a bias from including records on genotyped cows has now been demonstrated in genomic evaluations, it is necessary to develop methods to correct it. The first solution is to not use own records of genotyped cows. It is possible to estimate direct genomic breeding values obtained using a reference population consisting of bulls only, or to use GEBV (obtained after blending for instance) in which the polygenic component only includes performance (DYD) of male relatives. However, such a solution is not completely satisfactory. First, the AI industry may want to include own records of genotyped cows even if it does not increase reliabilities of genomic evaluations. Secondly, and more importantly, this solution implies that a large amount of potentially valuable information is not used. With the release of an efficient low density SNP chip  to genotype females at a reduced cost, one can expect that many heifers from commercial herds will be genotyped in the near future, providing a large number of genotyped cows. Obviously, for most of these commercial animals, records are likely to be unbiased and they will build up the reference population of the future.
Another solution is to adjust (i.e. pre-correct) the own phenotype of genotyped cows before their inclusion in genomic evaluation. This is the option retained by Wiggans et al. , who proposed to adjust the mean and variances of the estimated Mendelian sampling term of genotyped cows, such that they are similar to those of bulls. Interesting improvements in several measures related to bias of GEBV and prediction equations were reported. However, whether they are adjusted or not, it is not really possible to distinguish a positive Mendelian sampling from a bias due to preferential treatment for records of cows.
Single-step procedures  are appealing because non-genotyped individuals benefit from marker information of their genotyped relatives. It has also some interesting properties in terms of bias due to pre-selection of young bulls. However, solutions to remove bias induced by preferential treatment (such as blending, or adjustment of Mendelian sampling terms) are still needed.