Estimation of genetic parameters and breeding values for feed intake and energy balance using pedigree relationships or single-step genomic evaluation in Holstein Friesian cows

At the beginning of lactation, high-performing dairy cows often experience a severe energy deficit, which in turn is associated with metabolic stress. Increasing feed intake (FI) or reducing the energy deficit during this period could improve the metabolic stability and thus the health of the animals. Genomic selection for the first time enables the inclusion of this hard-to-measure trait in breeding programs. The objective of the current study was the estimation of genetic parameters and genomic breeding values for FI and energy balance (EB). For this purpose, 1,374 Holstein Friesian (HF) dairy cows from 8 German research farms were phenotyped with standardized FI data protocols. After data editing, phenotypic data of HF comprised a total of 40,012 average weekly FI records with a mean of 21.8 ± 4.3 kg/d. For EB 33,376 average weekly records were available with a mean of 3.20 ± 29.4 MJ of NE_L/d. With the Illumina Bovine SNP50 BeadChip (Illumina Inc., San Diego, CA) 1,128 of phenotyped cows were genotyped. Thirty-five female candidates of the HF population were genotyped but not phenotyped. Pedigree information contained sires and dams 4 generations back. The random regression animal model included the fixed effects of herd test week (alternatively, herd group test week), parity, and stage of lactation, modeled by the function according to Ali and Schaeffer (1987). For both the random permanent environmental effect across lactations and the random additive genetic effect, third-order Legendre polynomials were chosen. Additionally, a random permanent environmental cow effect within lactation was included. Analyses for heritabilities, genetic correlations between different lactation stages, and breeding values were estimated using, respectively, pedigree relationships and single-step genomic evaluation, carried out with the DMU software package (Madsen et al., 2013). This allowed for comparison of conventional reliabilities with genomic-assisted reliabilities based on real data, to evaluate the gain of genotyping. Heritability estimates ranged between 0.12 and 0.50 for FI, and 0.15 and 0.48 for EB, and increased toward the end of lactation. Genetic correlations were weak between early and late lactation, with a value of 0.05 for FI and negative with a value of -0.05 for EB. Reliabilities for genomic values of cows for FI and EB ranged between 0.33 and 0.61, and 0.27 and 0.47, respectively. For the genotyped cows without phenotypes, the inclusion of genomic relationship leads to an increase of the average reliability of the breeding value for FI by nearly 9% and for EB by 4%. The results show the possibility of combining pedigree, genotypes, and phenotypes for increasing FI or EB to reduce health and reproductive problems, especially at the beginning of lactation. Nevertheless, the reference population needs to be extended to reach higher breeding value reliabilities.

Intake, efficiency, and feeding behavior characteristics of Holstein-Friesian cows of divergent Economic Breeding Index evaluated under contrasting pasture-based feeding treatments

The objective of the current study was to explore differences in dry matter intake, intake capacity, production efficiency, energy balance, and grazing behavior, of 2 divergent genetic groups (GG) of lactating Holstein-Friesian, selected using the Irish Economic Breeding Index (EBI). The GG were evaluated across 3 spring calving pasture-based feeding treatments (FT) over 3 yr. The 2 divergent GG were (1) high EBI, representative of the top 5% nationally (elite), and (2) EBI representative of the national average (NA). In each year 90 elite and 45 NA cows were randomly allocated to 1 of 3 FT: control, lower grass allowance, and high concentrate. Although FT did affect animal performance, there were few notable incidences of GG × FT interaction. The elite cows expressed lower daily milk yield (-1 kg) compared with NA. Elite cows did, however, express higher daily concentrations of milk fat (+3.7 g/kg) and protein (+2.1 g/kg) compared with NA. Daily yield of milk solids and net energy of lactation (NE_L) was similar for both GG. Body weight (BW) was greater for NA (+13 kg) compared with elite, whereas mean body condition score was greater (+0.14) for elite compared with NA. Intake did not differ significantly between GG. Intake capacity, expressed as total dry matter intake/100 kg of BW, was greater with elite compared with NA. Production efficiency expressed as yield of milk solids per 100 kg of BW was greater with elite compared with NA, although milk solids/total dry matter intake did not differ between GG. Expressed as NE_L as a proportion of net energy intake minus net energy of maintenance (NE_L/NE_I - NE_M) and NE_I/milk solids kg, indicated a slight reduction in the utilization of ingested energy for milk production with elite compared with NA. This is, however, suggested as favorable as it manifested as a more positive energy balance with elite compared with NA and so is likely to enhance robustness, increase longevity, and increase overall lifetime efficiency. Noteworthy was a consistent numerical trend toward more intense grazing activity with elite compared with NA cows, exhibited in the numerically greater grazing time (+19 min) and total number of bites per day (+2,591).

Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently

Background

The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) method, such as single-step genomic BLUP (ssGBLUP), simultaneously analyses phenotypic, pedigree, and genomic information of genotyped and non-genotyped animals. In contrast to ssGBLUP, SNP effects are fitted explicitly as random effects in the ssSNPBLUP model. Similarly, principal components associated with the genomic information can be fitted explicitly as random effects in a single-step principal component BLUP (ssPCBLUP) model to remove noise in genomic information. Single-step genomic BLUP is solved efficiently by using the preconditioned conjugate gradient (PCG) method. Unfortunately, convergence issues have been reported when solving ssSNPBLUP by using PCG. Poor convergence may be linked with poor spectral condition numbers of the preconditioned coefficient matrices of ssSNPBLUP. These condition numbers, and thus convergence, could be improved through the deflated PCG (DPCG) method, which is a two-level PCG method for ill-conditioned linear systems. Therefore, the first aim of this study was to compare the properties of the preconditioned coefficient matrices of ssGBLUP and ssSNPBLUP, and to document convergence patterns that are obtained with the PCG method. The second aim was to implement and test the efficiency of a DPCG method for solving ssSNPBLUP and ssPCBLUP.

Results

For two dairy cattle datasets, the smallest eigenvalues obtained for ssSNPBLUP (ssPCBLUP) and ssGBLUP, both solved with the PCG method, were similar. However, the largest eigenvalues obtained for ssSNPBLUP and ssPCBLUP were larger than those for ssGBLUP, which resulted in larger condition numbers and in slow convergence for both systems solved by the PCG method. Different implementations of the DPCG method led to smaller condition numbers, and faster convergence for ssSNPBLUP and for ssPCBLUP, by deflating the largest unfavourable eigenvalues.

Conclusions

Poor convergence of ssSNPBLUP and ssPCBLUP when solved by the PCG method are related to larger eigenvalues and larger condition numbers in comparison to ssGBLUP. These convergence issues were solved with a DPCG method that annihilates the effect of the largest unfavourable eigenvalues of the preconditioned coefficient matrix of ssSNPBLUP and of ssPCBLUP on the convergence of the PCG method. It resulted in a convergence pattern, at least, similar to that of ssGBLUP.

Electronic supplementary material

The online version of this article (10.1186/s12711-018-0429-3) contains supplementary material, which is available to authorized users.