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Genotyping costs are among the major constraints for large-scale implementation of genomic selection in many breeds. However, the commercial availability of low density SNP panels (LDP), such as the Illumina Bovine3K Genotyping BeadChip or the Illumina BovineLD BeadChip, which contains around 7K markers , has offered new opportunities to increase the number of animals involved in selection programs. Genotypes obtained from an LDP must be imputed to the 50K platform by using suitable algorithms. Genotype imputation can also be useful when combining data sets that were generated using different SNP chips .
A method that uses the Partial Least Squares Regression (PLSR) technique to impute SNP genotypes was proposed recently . It was tested on a simulated genome consisting of 6000 SNPs equally distributed on six chromosomes and a data set of 5865 individuals (TP = 4665 and PP = 1200). The PLSR method yielded accuracies in marker imputation ranging from 0.99 to 0.86 when 10% or 90% genotypes were imputed, respectively. In the latter case, the accuracy of direct genomic values (DGV) dropped from 0.77 to 0.74. Furthermore, Dimauro et al.  highlighted that, with a fixed percentage (50%) of SNPs to be predicted, imputation accuracies slowly decreased from 98% with TP = 5000, to 87% with TP = 1000 and to 69% with TP = 600. PLSR requires only genotype data, and other data, such as pedigree relationships, is not needed. Therefore, this approach could be useful when the population structure is not known.
To study the performance in a multi-breed sample, 749 Brown Swiss and 470 Simmental bulls were also available. For the multi-breed data set, data from the three breeds were edited together to obtain the same SNPs in all data sets. At the end of the editing procedure, 30 055 markers were retained.
In our experimental data, PLSR was first applied to the Holstein breed. Animals were ranked by age and divided in TP = 1993 (the older bulls) and PP = 100 (the younger) and both 3K and 7K scenarios were investigated. The Beagle software was applied to the same data. No pedigree information was used for either PLSR or Beagle.
PLSR was further used to impute SNP genotypes both in single and multi-breed scenarios based on Holstein, Simmental and Brown Swiss data sets. No MAF threshold was applied in the editing procedure. To investigate whether differences in imputation accuracies between PLSR and the Beagle algorithms could arise with edits based on MAF, the impact of several MAF thresholds (no limit, 0.01, 0.05, 0.10) was evaluated. However, no differences in imputation accuracies were observed between the PLSR and Beagle results.
Mean R values obtained with PLSR in the single-breed scenario were 89,6% and 94,2% for the 3K and 7K LDP, respectively. It is worth mentioning that, in the present study, the ratio between the number of animals (n = 2179 Holstein bulls) involved in the study and the mean number of markers (m = 1497) on each chromosome, Rn/m, was 1.45. Dimauro et al. , tested the PLSR imputation method on a simulated data set with m = 1000 markers on a chromosome and n = 5865 individuals. The resulting Rn/m was 5.9. In ordinary statistics and, even more, in multivariate statistics, the availability of a larger number of observations guarantees more accurate results. Thus, Dimauro et al.  applied the PLSR method in a more optimal dataset, obtaining an imputation accuracy of 0.86. Even if the latter study and the present research are difficult to compare, the large difference between Rn/m ratios suggests that PLSR also works properly with actual data. This is an important result because, if a particular technique gives good results when applied to simulated data, it is not obvious that similar performances are obtained with actual data.
PLSR is an ordinary statistical technique included in the most popular commercial and free software packages that are currently used to perform genomic data analyses, such as SAS® and R. The PLSR approach could thus be easily implemented in software for genomic evaluations previously developed. Moreover, with PLSR, the computing time needed to impute SNP genotypes was, on average, around 10 times lower than with Beagle. For example, with the 7K LDP, PLSR took around 1 h to impute SNP genotypes for the first chromosome, whereas Beagle needed around 8 h. This aspect should not be underrated when an algorithm is chosen to perform imputation. In particular, PLSR could probably be used to impute SNP genotypes from the 50K chip to the denser Illumina 777K platform in a reasonable amount of time. 2b1af7f3a8