The impact of genetic relationship information on genomic breeding values in German Holstein cattle

<p>Abstract</p> <p>Background</p> <p>The impact of additive-genetic relationships captured by single nucleotide polymorphisms (SNPs) on the accuracy of genomic breeding values (GEBVs) has been demonstrated, but recent studies on data obtained from Holstein populations have ignored this fact. However, this impact and the accuracy of GEBVs due to linkage disequilibrium (LD), which is fairly persistent over generations, must be known to implement future breeding programs.</p> <p>Materials and methods</p> <p>The data set used to investigate these questions consisted of 3,863 German Holstein bulls genotyped for 54,001 SNPs, their pedigree and daughter yield deviations for milk yield, fat yield, protein yield and somatic cell score. A cross-validation methodology was applied, where the maximum additive-genetic relationship (<it>a</it>_<it>max</it>) between bulls in training and validation was controlled. GEBVs were estimated by a Bayesian model averaging approach (BayesB) and an animal model using the genomic relationship matrix (G-BLUP). The accuracy of GEBVs due to LD was estimated by a regression approach using accuracy of GEBVs and accuracy of pedigree-based BLUP-EBVs.</p> <p>Results</p> <p>Accuracy of GEBVs obtained by both BayesB and G-BLUP decreased with decreasing <it>a</it>_{<it>max </it>}for all traits analyzed. The decay of accuracy tended to be larger for G-BLUP and with smaller training size. Differences between BayesB and G-BLUP became evident for the accuracy due to LD, where BayesB clearly outperformed G-BLUP with increasing training size.</p> <p>Conclusions</p> <p>GEBV accuracy of current selection candidates varies due to different additive-genetic relationships relative to the training data. Accuracy of future candidates can be lower than reported in previous studies because information from close relatives will not be available when selection on GEBVs is applied. A Bayesian model averaging approach exploits LD information considerably better than G-BLUP and thus is the most promising method. Cross-validations should account for family structure in the data to allow for long-lasting genomic based breeding plans in animal and plant breeding.</p

A function accounting for training set size and marker density to model the average accuracy of genomic prediction.

Prediction of genomic breeding values is of major practical relevance in dairy cattle breeding. Deterministic equations have been suggested to predict the accuracy of genomic breeding values in a given design which are based on training set size, reliability of phenotypes, and the number of independent chromosome segments ([Formula: see text]). The aim of our study was to find a general deterministic equation for the average accuracy of genomic breeding values that also accounts for marker density and can be fitted empirically. Two data sets of 5'698 Holstein Friesian bulls genotyped with 50 K SNPs and 1'332 Brown Swiss bulls genotyped with 50 K SNPs and imputed to ∼600 K SNPs were available. Different k-fold (k = 2-10, 15, 20) cross-validation scenarios (50 replicates, random assignment) were performed using a genomic BLUP approach. A maximum likelihood approach was used to estimate the parameters of different prediction equations. The highest likelihood was obtained when using a modified form of the deterministic equation of Daetwyler et al. (2010), augmented by a weighting factor (w) based on the assumption that the maximum achievable accuracy is [Formula: see text]. The proportion of genetic variance captured by the complete SNP sets ([Formula: see text]) was 0.76 to 0.82 for Holstein Friesian and 0.72 to 0.75 for Brown Swiss. When modifying the number of SNPs, w was found to be proportional to the log of the marker density up to a limit which is population and trait specific and was found to be reached with ∼20'000 SNPs in the Brown Swiss population studied

Open Access

The impact of genetic relationship information on genomic breeding values in German Holstein cattl

Predicted and empirical values of when extrapolating the accuracy.

<p>Empirical values of (black dots) of the ten replicates with different k-fold scenarios using 4′000 individuals and of the 20-fold runs of the fifty replicates using 5′698 Holstein-Friesian animals in total. Expected values (grey lines) use the number of derived with a Maximum-Likelihood approach in the original equation of Daetwyler et al. (2010) (D1, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0081046#pone-0081046-g007" target="_blank">Figure 7A</a>) and in the modified equation of Daetwyler et al. (2010) (D2, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0081046#pone-0081046-g007" target="_blank">Figure 7B</a>).</p

Fitted values of the number of independent chromosome segments () and weighting factors (w) with the Maximum-Likelihood approach and the corresponding natural logarithm of the likelihoods when using the Holstein-Friesian data set.

1<p>D1 uses the formula of Daetwyler et al. (2010) to calculate the expected values of accuracy, G1 and G2 are based on Goddard et al. (2011) without and with the proposed correction factor, respectively. D2 is a modified equation of Daetwyler et al. (2010) while G3 is based on Goddard et al. (2011) with the weighting factor not defined like in the original publication but like in D2.</p

Empirical values and expected values of for somatic cell score in Holstein-Friesian data.

<p>Empirical values of and expected values using the number of derived with a Maximum-Likelihood approach for the Holstein-Friesian data set in the original equation of Daetwyler et al. (2010) (D1) as well as in a modified form (D2) and in the equation of Goddard et al. (2011) without (G1) and with (G2) the proposed correction factor, respectively, and with the factor b not further determined (G3). For the empirical values, the mean and the standard deviation over the 50 replicates in each k-fold scenario of the Holstein-Friesian data set are shown.</p

Regression of weighting factor w on the reciprocal of the logarithm of the marker density in Holstein-Friesian.

<p>Regression of the weighting factor w on the reciprocal of the natural logarithm of the marker density for the traits milk yield and somatic cell score in the Holstein-Friesian data set. The marker density was defined as the number of markers used divided by the length of the used parts of the genome in Morgan. The dots mark the values derived with the Maximum likelihood approach using the modified equation of Daetwyler et al. (2010) (D2) to describe the expected value of accuracy and the empirical data sets.</p

Fitted values of the number of independent chromosome segments () and weighting factors (w) with the Maximum-Likelihood approach and the corresponding natural logarithm of the likelihoods for different methods and different SNP sets when using the Holstein-Friesian data set.

1<p>D2 is a modified equation of Daetwyler et al. (2010) while G3 is based on Goddard et al. (2011) with the weighting factor not defined like in the original publication but like in D2.</p

Fitted values of the number of independent chromosome segments () and weighting factors (w) with the Maximum-Likelihood approach and the corresponding natural logarithm of the likelihoods for method D2 and different SNP sets when using the Brown Swiss data set.

<p>Fitted values of the number of independent chromosome segments () and weighting factors (w) with the Maximum-Likelihood approach and the corresponding natural logarithm of the likelihoods for method D2 and different SNP sets when using the Brown Swiss data set.</p