Correction: Salimiyekta et al. Random Regression Model for Genetic Evaluation and Early Selection in the Iranian Holstein Population. Animals 2021, 11, 3492.

There was an error in the original publication [...].

Comparison of different response variables in genomic prediction using GBLUP and ssGBLUP methods in Iranian Holstein cattle.

We compared the reliability and bias of genomic evaluation of Holstein bulls for milk, fat, and protein yield with two methods of genomic best linear unbiased prediction (GBLUP) and single-step GBLUP (ssGBLUP). Four response variables of estimated breeding value (EBV), daughter yield deviation (DYD), de-regressed proofs based on Garrick (DRPGR) and VanRaden (DRPVR) were used as dependent variables. The effects of three weighting methods for diagonal elements of the incidence matrix associated with residuals were also explored. The reliability and the absolute deviation from 1 of the regression coefficient of the response variable on genomic prediction (Dev) using GBLUP and ssGBLUP methods were estimated in the validation population. In the ssGBLUP method, the genomic prediction reliability and Dev from un-weighted DRPGR method for milk yield were 0.44 and 0.002, respectively. In the GBLUP method, the corresponding measurements from un-weighted EBV for fat were 0.52 and 0.008, respectively. Moreover, the un-weighted DRPGR performed well in ssGBLUP with fat yield values for reliability and Dev of 0.49 and 0.001, respectively, compared to equivalent protein yield values of 0.38 and 0.056, respectively. In general, the results from ssGBLUP of the un-weighted DRPGR for milk and fat yield and weighted DRPGR for protein yield outperformed other models. The average reliability of genomic predictions for three traits from ssGBLUP was 0.39 which was 0.98% higher than the average reliability from GBLUP. Likewise, the Dev of genomic predictions was lower in ssGBLUP than GBLUP. The average Dev of predictions for three traits from ssGBLUP and GBLUP were 0.110 and 0.144, respectively. In conclusion, genomic prediction using ssGBLUP outperformed GBLUP both in terms of reliability and bias.

Random Regression Model for Genetic Evaluation and Early Selection in the Iranian Holstein Population.

The objective of this study was to use a model to predict breeding values for sires and cows at an early stage of the first lactation of cows and progeny groups in the Iranian Holstein population to enable the early selection of sires. An additional objective was to estimate genetic and phenotypic parameters associated with this model. The accuracy of predicted breeding values was investigated using cross-validation based on sequential genetic evaluations emulating yearly evaluation runs. The data consisted of 2,166,925 test-day records from 456,712 cows calving between 1990 and 2015. (Co)-variance components and breeding values were estimated using a random regression test-day model and the average information (AI) restricted maximum likelihood method (REML). Legendre polynomial functions of order three were chosen to fit the additive genetic and permanent environmental effects, and a homogeneous residual variance was assumed throughout lactation. The lowest heritability of daily milk yield was estimated to be just under 0.14 in early lactation, and the highest heritability of daily milk yield was estimated to be 0.18 in mid-lactation. Cross-validation showed a highly positive correlation of predicted breeding values between consecutive yearly evaluations for both cows and sires. Correlation between predicted breeding values based only on records of early lactation (5-90 days) and records including late lactation (181-305 days) were 0.77-0.87 for cows and 0.81-0.94 for sires. These results show that we can select sires according to their daughters' early lactation information before they finish the first lactation. This can be used to decrease generation interval and to increase genetic gain in the Iranian Holstein population.

Estimation of additive and non-additive genetic variance component for growth traits in Adani goats.

Non-additive genetic effects are important to increase the accuracy of estimating genetic parameters for growth traits. The aim of this study was to estimate genetic parameters and variance components, specially dominance and epistasis genetic effects, for growth traits (birth weight (BW), weaning weight (WW), 3 (W3), 6 (W6), 9 (W9), and 12 (W12) month weight) in Adani goats. Analyses were carried out using Bayesian method via Gibbs sampler animal model by fitting of 18 different models. All fixed effects (sex, type of birth, age of dam, and year) showed significant effects on BW, WW, W3, and W6, whereas the type of birth and age of dam were not significant on W9 and W12. With the best model, direct heritability estimates were 0.347, 0.178, 0.158, 0.359, 0.278, and 0.281 for BW, WW, W3, W6, W9, and W12 traits, respectively. Maternal permanent environmental effect was significant for BW and WW, but maternal genetic effect was significant only for W3. Dominance and epitasis effects were significant almost for all traits and as a proportion of phenotypic variance were ranged from 0.115 to 0.258 and 0.107 to 0.218, respectively. The range of accuracy of breeding values estimated for growth traits with appropriate evaluation models was from 0.521 to 0.652, 0.616 to 0.694, and 0.548 to 0.684 for the all animals, 10% of the best males and 50% of the best females, respectively. When dominance and epistasis effects added to models, the error variance was reduced and the accuracy of estimated breeding values increased. The accuracy of the best model showed a significant difference with the accuracy of other models (p < 0.01). The result of the present study suggests that non-additive genetic effects should be in genetic evaluation models for goat growth traits because of its effect on accuracy of estimated breeding values.

Genetic analysis of growth rate and Kleiber ratio in Zandi sheep.

Genetic parameters for average daily gain from birth to weaning (ADGa), birth to 6 months (ADGb), weaning to 6 months (ADGc), weaning to yearling age (ADGd), and corresponding Kleiber ratios (KRa, KRb, KRc, and KRd) were estimated by using records of 3,533 Zandi lambs, descendent of 163 sires and 1265 dams, born between 1991 and 2005 at the Zandi Sheep Breeding Station at Khojir National Park, Tehran, Iran. A derivative-free algorithm combined with a series of six single-trait linear animal models was used to estimate phenotypic variance and its direct, maternal, and residual components. In addition, bivariate analyses were done to estimate (co)variance components between traits. Estimates of direct heritability (h(2)) were 0.11, 0.15, 0.09, 0.10, 0.10, 0.10, 0.06, and 0.07 for ADGa, ADGb, ADGc, ADGd, KRa, KRb, KRc, and KRd, respectively, thereby indicating the presence of low additive genetic variation for growth rate and Kleiber ratio in this population of Zandi sheep. Maternal genetic component was found to be significant on ADGa and KRa and contributed 3% and 5%, respectively, in total phenotypic variance of ADGa and KRa. A widespread range of genetic correlations among traits studied was observed. Except for negative genetic correlations between ADGa and KRc, ADGa and KRd, and between KRa and KRc, in other cases, genetic correlations were positive and moderate to very high. Phenotypic correlations ranged from -0.49 (ADGa/KRd) to 0.94 (ADGc/KRc). These results indicate that selecting for improved growth rate or Kleiber ratio in Zandi sheep would generate a relatively slow genetic progress.