Use of genomic recursions and algorithm for proven and young animals for single‐step genomic BLUP analyses – a simulation study

The purpose of this study was to examine accuracy of genomic selection via single‐step genomic BLUP (ssGBLUP) when the direct inverse of the genomic relationship matrix ( G ) is replaced by an approximation of G ^?1 based on recursions for young genotyped animals conditioned on a subset of proven animals, termed algorithm for proven and young animals (APY). With the efficient implementation, this algorithm has a cubic cost with proven animals and linear with young animals. Ten duplicate data sets mimicking a dairy cattle population were simulated. In a first scenario, genomic information for 20k genotyped bulls, divided in 7k proven and 13k young bulls, was generated for each replicate. In a second scenario, 5k genotyped cows with phenotypes were included in the analysis as young animals. Accuracies (average for the 10 replicates) in regular EBV were 0.72 and 0.34 for proven and young animals, respectively. When genomic information was included, they increased to 0.75 and 0.50. No differences between genomic EBV (GEBV) obtained with the regular G ^?1 and the approximated G ^?1 via the recursive method were observed. In the second scenario, accuracies in GEBV (0.76, 0.51 and 0.59 for proven bulls, young males and young females, respectively) were also higher than those in EBV (0.72, 0.35 and 0.49). Again, no differences between GEBV with regular G ^?1 and with recursions were observed. With the recursive algorithm, the number of iterations to achieve convergence was reduced from 227 to 206 in the first scenario and from 232 to 209 in the second scenario. Cows can be treated as young animals in APY without reducing the accuracy. The proposed algorithm can be implemented to reduce computing costs and to overcome current limitations on the number of genotyped animals in the ssGBLUP method.     

Is single-step genomic REML with the algorithm for proven and young more computationally efficient when less generations of data are present?

Efficient computing techniques allow the estimation of variance components for virtually any traditional dataset. When genomic information is available, variance components can be estimated using genomic REML (GREML). If only a portion of the animals have genotypes, single-step GREML (ssGREML) is the method of choice. The genomic relationship matrix (G) used in both cases is dense, limiting computations depending on the number of genotyped animals. The algorithm for proven and young (APY) can be used to create a sparse inverse of G (GAPY~-1) with close to linear memory and computing requirements. In ssGREML, the inverse of the realized relationship matrix (H⁻¹) also includes the inverse of the pedigree relationship matrix, which can be dense with a long pedigree, but sparser with short. The main purpose of this study was to investigate whether costs of ssGREML can be reduced using APY with truncated pedigree and phenotypes. We also investigated the impact of truncation on variance components estimation when different numbers of core animals are used in APY. Simulations included 150K animals from 10 generations, with selection. Phenotypes (h² = 0.3) were available for all animals in generations 1–9. A total of 30K animals in generations 8 and 9, and 15K validation animals in generation 10 were genotyped for 52,890 SNP. Average information REML and ssGREML with G⁻¹ and GAPY~-1 using 1K, 5K, 9K, and 14K core animals were compared. Variance components are impacted when the core group in APY represents the number of eigenvalues explaining a small fraction of the total variation in G. The most time-consuming operation was the inversion of G, with more than 50% of the total time. Next, numerical factorization consumed nearly 30% of the total computing time. On average, a 7% decrease in the computing time for ordering was observed by removing each generation of data. APY can be successfully applied to create the inverse of the genomic relationship matrix used in ssGREML for estimating variance components. To ensure reliable variance component estimation, it is important to use a core size that corresponds to the number of largest eigenvalues explaining around 98% of total variation in G. When APY is used, pedigrees can be truncated to increase the sparsity of H and slightly reduce computing time for ordering and symbolic factorization, with no impact on the estimates.     

Utility of on- and off-farm weather records for studies in genetics of heat tolerance

Utility of weather information from on-farm and weather stations was evaluated for the application in studies on the genetics of heat stress. Daily milk yield of 31 primiparous Holstein cows was collected at Tifton, GA, from April 28 to July 19, 1993. Weather information was recorded on-farm and was available from weather stations in Georgia. Analyses used daily average of temperature–humidity index (THI). Effects of threshold of heat stress and the rate of decline in milk after the threshold were estimated. With on-farm weather data, threshold was at THI = 22 and rate of decline was − 1.12 kg of milk per unit of THI measured 2 days before milking. At the Tifton weather station, 3 km away from the farm, the threshold was THI = 20 and the rate was the same. With data from Macon, Columbus, Atlanta, and Athens stations, the threshold was at 20, 21, 20, and 20, respectively, and the rate of decline with a 2 day lag was − 0.88, − 1.02, − 0.90, and − 0.97 kg of milk per unit of THI. Subsequent analysis included 2260 test day records from the same farm from 1993 to 2003 and weather data from Tifton station. The highest rate of decline on milk yield of − 0.22 kg per unit of THI occurred at the threshold of 20 and no lag. For data restricted to 1999–2003, the threshold increased to 22 and the rate to − 0.46 kg per THI unit. Public stations provide satisfactory information for national genetic evaluation for heat stress. Critical parts in such an evaluation are modeling of test days and accounting for changes among farms and weather stations over time.     

Threshold-linear estimation of genetic parameters for farrowing mortality, litter size, and test performance of Large White sows

Up to 109,447 records of 49,656 Large White sows were used to evaluate the genetic relationship between number of pigs born dead (BD) and number born alive (BA) in first and later parities. Performance data (n = 30,832) for ultrasound backfat (BF) at the end of the test and days to reach 113.5 kg (AD) were used to estimate their relationships with BD and BA at first parity in a four-trait threshold-linear analysis (TL). Effects were year-farm, contemporary group (CG: farm-farrowing year-farrowing month) and animal additive genetic. At first parity, estimates of heritability were 0.09, 0.09, 0.37, and 0.31 for BA, BD, AD, and BF, respectively. The estimate of genetic correlation between BD and litter size was -0.04 (BD-BA). Corresponding values with test traits were both -0.14 (BD-AD, BD-BF). Estimates of genetic correlation between BA and performance traits were 0.08 (BA-AD) and 0.05 (BA-BF). The two test traits were moderately negatively correlated (-0.22). For later parities, a six-trait (BD, BA in three parities) TL model was implemented. The estimates of additive genetic variances and heritability increased with parity for BD and BA. Estimates of heritabilities were: 0.09, 0.10, and 0.11 for BD, and 0.09, 0.12, and 0.12 for BA in parities one to three, respectively. Estimates of genetic correlations between different parities were high (0.91 to 0.96) for BD, and slightly lower (0.74 to 0.95) for BA. Genetic correlations between BD and BA were low and positive (0.02 to 0.17) for BA in Parities 1 and 2, but negative (-0.04 to -0.10) for BA in Parity 3. Selection for increased litter size should have little effect on farrowing piglet mortality. Intense selection for faster growth and increased leanness should increase farrowing piglet mortality of first-parity sows. A repeatability model with a simple correction for the heterogeneity of variances over parities could be implemented to select against farrowing mortality. The genetic components of perinatal piglet mortality are independent of the ones for litter size in the first parity, and they show an undesirable, but not strong, genetic association in second parity.     

A practical longitudinal model for evaluating growth in Gelbvieh cattle

Genetic evaluation of growth in Gelbvieh beef cattle was examined by multiple-trait (MTM) and random regression (RRM) analysis. The data set comprised 541,108 animals with 1,120,086 records. Approximately 15% of the animals in the data set had at least one record measured outside of the accepted MTM age ranges for weaning weight (Wwt) and yearling weight (Ywt). Fourteen percent of Wwt records and 19% of Ywt records were measured outside the accepted ranges for MTM analysis, and thus were excluded from MTM evaluations. Two RRM evaluations were performed using cubic Legendre polynomials (RRML) and linear splines (RRMS) with three knots at 1, 205, and 365 d of age. Data Set 1 (d1) utilized all available records, whereas Data Set 2 (d2) included only records measured within MTM ranges (1 d, 160 to 250 d, and 320 to 410 d). The RRML models did not reach convergence until diagonalization was imposed. After diagonalization, it was found that all longitudinal models required fewer iterations to converge than the MTM. Correlations between the MTM, RRML-d2, and RRMS-d2 evaluations were >or=0.99 for all three traits, indicating that these models were equivalent when predicting breeding values from data within the MTM age ranges. Correlations between MTM, RRML-d1, and RRMS-d1 were >0.99 for Bwt and >0.95 for Wwt and Ywt. The lower correlations for Wwt and Ywt indicate that the added information does affect breeding value prediction. The RRM has the capability to incorporate records measured at all ages into genetic evaluations at a computing cost similar to the MTM.     

Central injection of exogenous IL-1β in the control activities of hypothalamic-pituitary-gonadal axis in anestrous ewes

This study was performed to determine the effect of intracerebroventricular (icv) injection of interleukin (IL)-1β on the gene expression, translation and release of gonadotropin-releasing hormone (GnRH) and the GnRH receptor (GnRHR) gene expression in the hypothalamus of anestrous ewes. In the anterior pituitary gland (AP), the expression of genes encoding: GnRHR, β subunits of luteinizing hormone (LH) and folliculotropic hormone (FSH) was determined as well as the effect of IL-1β on pituitary gonadotropins release. The relative mRNA level was determined by real-time PCR, GnRH concentration in the cerebrospinal fluid (CSF) was assayed by ELISA and the plasma concentration of LH and FSH were determined by radioimmunoassay. Our results showed that icv injection of IL-1β (10 or 50 μg/animal) decreased the GnRH mRNA level in the pre-optic area (POA) (35% and 40% respectively; p ≤ 0.01) and median eminence (ME) (75% and 70% respectively; p ≤ 0.01) and GnRHR gene expression in ME (55% and 50% respectively; p ≤ 0.01). A significant decrease in GnRHR mRNA level in the AP in the group treated with the 50 μg (60%; p ≤ 0.01) but not with the 10 μg dose was observed. The centrally administrated IL-1β lowered also GnRH concentration in the CSF (60%; p ≤ 0.01) and reduced the intensity of GnRH translation in the POA (p ≤ 0.01). It was not found any effect of icv IL-1β injection upon the release of LH and FSH. However, the central injection of IL-1β strongly decreased the LHβ mRNA level (41% and 50%; p ≤ 0.01; respectively) and FSHβ mRNA in the case of the 50 μg dose (49%; p ≤ 0.01) in the pituitary of anestrous ewes. These results demonstrate that the central IL-1β is an important modulator of the GnRH biosynthesis and release during immune/inflammatory challenge.     

Evaluation of a multi-line broiler chicken population using a single-step genomic evaluation procedure

Effects on prediction of analysing a multi-line chicken population as one line were evaluated. Body weight records were provided by Cobb-Vantress for two lines of broiler chickens. Phenotypic records for 183 695 and 164 149 broilers and genotypic records for 3195 and 3001 broilers were available for each line. Lines were combined to create a multi-line population and analysed using a single-step procedure combining the additive relationship matrix and the genomic relationship matrix (G). G was scaled using allele frequencies from each line, the multi-line population, or 0.5. When allele frequencies were calculated from each line, distributions of diagonal elements were bimodal. When allele frequencies were calculated from the multi-line population, the distribution of diagonal elements had one peak. When allele frequency 0.5 was used, the distribution was bimodal. Genomic estimated breeding values (GEBVs) were predicted using each allele frequency. GEBVs differed with allele frequency but had ≥ 0.99 correlations with GEBVs predicted with correct allele frequencies. Means of each line and differences in mean between the lines differed based on allele frequencies. Assumed allele frequencies have little impact on ranking within line but larger impact on ranking across lines. G may be used to evaluate multiple populations simultaneously but must be adjusted to obtain properly scaled estimates when population structure is unknown.     

Investigating the persistence of accuracy of genomic predictions over time in broilers

Accuracy of genomic predictions is an important component of the selection response. The objectives of this research were: 1) to investigate trends for prediction accuracies over time in a broiler population of accumulated phenotypes, genotypes, and pedigrees and 2) to test if data from distant generations are useful to maintain prediction accuracies in selection candidates. The data contained 820K phenotypes for a growth trait (GT), 200K for two feed efficiency traits (FE1 and FE2), and 42K for a carcass yield trait (CY). The pedigree included 1,252,619 birds hatched over 7 years, of which 154,318 from the last 4 years were genotyped. Training populations were constructed adding 1 year of data sequentially, persistency of accuracy over time was evaluated using predictions from birds hatched in the three generations following or in the years after the training populations. In the first generation, before genotypes became available for the training populations (first 3 years of data), accuracies remained almost stable with successive additions of phenotypes and pedigree to the accumulated dataset. The inclusion of 1 year of genotypes in addition to 4 years of phenotypes and pedigree in the training population led to increases in accuracy of 54% for GT, 76% for FE1, 110% for CY, and 38% for FE2; on average, 74% of the increase was due to genomics. Prediction accuracies declined faster without than with genomic information in the training populations. When genotypes were unavailable, the average decline in prediction accuracy across traits was 41% from the first to the second generation of validation, and 51% from the second to the third generation of validation. When genotypes were available, the average decline across traits was 14% from the first to the second generation of validation, and 3% from the second to the third generation of validation. Prediction accuracies in the last three generations were the same when the training population included 5 or 2 years of data, and a decrease of ~7% was observed when the training population included only 1 year of data. Training sets including genomic information provided an increase in accuracy and persistence of genomic predictions compared with training sets without genomic data. The two most recent years of pedigree, phenotypic, and genomic data were sufficient to maintain prediction accuracies in selection candidates. Similar conclusions were obtained using validation populations per year.     

Genetic components of heat stress in finishing pigs: development of a heat load function

The objective of this study was to quantify the effect of heat stress during the life of a pig on its final weight, as a first step toward a genetic evaluation for heat tolerance. Data included carcass weights of 23,556 crossbred pigs [Duroc x (Landrace x Large White)] raised on 2 farms in North Carolina and slaughtered from May 2005 through December 2006. Weather data were available from a nearby weather station. Lifetime of a pig was assumed to be partitioned into 2 periods. During an initial period, the effect of heat stress was assumed to be negligible or compensated for later. During the second period ending in slaughtering, the ADG was assumed to be affected linearly by heat load. Weekly heat load was calculated as degrees of average temperature-humidity index in excess of a threshold (18 degrees C). The total heat load (H) was the sum of weekly heat loads during the second period. During the months of January to May H was 0; H reached a peak in September. The final BW during the peak of heat stress decreased about 6 kg compared with BW during months of non-heat stress. Weekly and monthly averages of carcass weight generally moved similarly to H. However, there were large fluctuations unrelated to H; the fluctuations were different on the 2 farms. The model included the effects of farm-year of slaughter, sex, age at slaughter, and H, where age at slaughter and H were linear regressions. In analyses, the threshold was varied from 16 to 20 degrees C, and the second period was varied from 8 to 16 wk. The greatest R(2) (10.4%) was at the threshold of temperature-humidity index = 18 degrees C for a period of 10 wk. Varying the threshold and the length of time reduced R(2) less than 1%. Least squares means of year-month and year-week of carcass weight were calculated using a model with the fixed effects farm-year-month or farm-year-week of slaughter, sex, and age at slaughter (linear covariate), and the random effect of birth litter. Changes in BW of finisher pigs due to heat stress can be quantified by H during the last 10 wk of the life of the pig.