Estimate Co Variance Components Research Articles

Non-negative least-squares variance and covariance component estimation using the positive-valued function for errors-in-variables models

Abstract Although (co)variance component estimation has been widely applied in the errors-in-variables (EIV) model, the occurrence of negative variance components is still a major issue in the estimated variance components. This problem may be due to the following unfavorable factors: 1) unreasonable selection of initial variance values; 2) low redundancy in the EIV functional model; 3) improper design in the EIV stochastic model, and 4) other data quality problems. Many attempts have been made to prevent the appearance of negative variance components. In this contribution, a novel and efficient non-negative least-squares variance component estimation using the PVF (PVF-NLS-VCE) is introduced, which can simultaneously estimate the unknown (co)variance components in the EIV stochastic model and the parameters in the EIV functional model. Its principle is to implicitly impose a non-negative constraint by replacing the variance component with the positive-valued function (PVF) whose range is the set of positive real numbers. Two numerical examples using real and simulated data are presented. The numerical results of linear regression are identical to those obtained based on least-squares variance component estimation (LS-VCE) with positive initial values of variance components. The numerical results of two-dimensional affine transformation are shown to prevent negative variance components and precede those obtained by LS-VCE with a negative initial value of variance component. Both numerical examples verify the effectiveness of the PVF-NLS-VCE method whether the initial values of variance components are positive or negative. The proposed PVF-NLS-VCE is a simple, convenient and flexible method to achieve the non-negative estimates of variance components, which can reduce sensitivity to initial value selection and automatically guarantee a non-negative definite covariance matrix.

Genetic correlation between feed efficiency and carcass traits in Nellore cattle in Brazil

The aim was to estimate the genetic correlations between residual feed intake (RFI) and dry matter intake (DMI) with carcass finish (CF), rib eye area (REA), and marbling (MAR) of Nellore cattle. Data from 7,808 animals were considered. In addition, data from 2,261 females included in the complete database were also considered. Estimates of variance and covariance components, as well as heritabilities and genetic correlations were obtained by means of two-character analysis under animal model. Heritability estimates were found to be moderate for the RFI (0.22) and DMI (0.29) traits. It was observed that genetic correlation was close to zero for all traits, except between RFI and REA (-0.11). However, considering the female population, there was an increase in the estimated genetic correlation between RFI and DMI, although still a favorable genetic association of low magnitude (-0.30). There was also an increase in the genetic association of REA with RFI (-0.21). It can be concluded that the direct selection for RFI and DMI will not influence the CF, MAR, or REA of Nellore cattle. However, this selection may generate some favorable responses in MAR and REA in Nellore females.

Unmodeled-error-corrected stochastic assessment for a standalone GNSS receiver regardless of the number of tracked frequencies

Appropriate stochastic modeling is crucial to Global Navigation Satellite System (GNSS) applications. However, traditional methods based on the zero baseline and ultra-short baseline cannot accurately estimate the stochastic characteristics of GNSS measurements of a complete receiving system, i.e., receiver, antenna, low-noise amplifier, and cable. We propose the unmodeled-error-corrected stochastic assessment methods that can be used for a standalone receiver regardless of the number of tracked frequencies. First, the raw observation equations considering the unmodeled errors are deduced based on the geometry-free or geometry-based model. Second, some parameters are chosen as the datum for rank deficiency elimination. Third, the multi-epoch parameterization is used to correct the unmodeled errors in the reparametrized observation model. Finally, the covariance component estimation can be applied to determine the variance components. Three different and representative measurement campaigns were conducted, including the low-cost board, integrated receiver, and smart phone. The results show that the proposed method based on a standalone receiver can assess the stochastic characteristics of GNSS measurements. Since the stochastic characteristics of different low-cost receivers share different patterns, and the noise from the internal antenna cannot be easily ignored, the proposed method is essential.

Optimization of undifferenced and uncombined PPP stochastic model based on covariance component estimation

Optimization of undifferenced and uncombined PPP stochastic model based on covariance component estimation

Model definition for genetic evaluation of purebred and crossbred lambs including heterosis.

Crossbreeding is a common practice among commercial sheep producers to improve animal performance. However, genetic evaluation of U.S. sheep is performed within breed type (terminal sire, semi-prolific, and western range). While incorporating crossbred records may improve assessment of purebreds, it requires accounting for heterotic and breed effects in the evaluation. The objectives of this study were to: 1) describe the development of a paternal composite (PC) line, 2) determine the effect of direct and maternal heterosis on growth traits of crossbred lambs, 3) estimate (co)variance components for direct and maternal additive, and uncorrelated maternal environmental, effects, and 4) provide an interpretation of the estimates of random effects of genetic groups, and to use those solutions to compare the genetic merit of founding breed subpopulations. Data included purebred and crossbred records on birth weight (BN; n = 14,536), pre-weaning weight measured at 39 or 84 d (WN; n = 9,362) depending on year, weaning weight measured at 123 d (WW; n = 9,297), and post-weaning weight measured at 252 d (PW; n = 1,614). Mean (SD) body weights were 5.3 (1.1), 16.8 (3.9) and 28.0 (7.6), 39.1 (7.2), and 54.2 (8.7) kg for BN, WN (at the two ages), WW, and PW, respectively. In designed experiments, the Siremax, Suffolk, Texel, Polypay, Columbia, Rambouillet, and Targhee breeds were compared within the same environment. Estimates of heterotic effects and covariance components were obtained using a multiple trait animal model. Genetic effects based on founders' breeds were significant and included in the model. Percent estimates of direct heterosis were 2.89 ± 0.61, 2.60 ± 0.65, 4.24 ± 0.56, and 6.09 ± 0.86, and estimates of maternal heterosis were 1.92 ± 0.87, 4.64 ± 0.80, 3.95 ± 0.66, and 4.04 ± 0.91, for BN, WN, WW, and PW, respectively. Correspondingly, direct heritability estimates were 0.17 ± 0.02, 0.13 ± 0.02, 0.17 ± 0.02, and 0.46 ± 0.04 for BN, WN, WW, and PW. Additive maternal effects accounted for trivial variation in PW. For BN, WN, and WW, respectively, maternal heritability estimates were 0.16 ± 0.02, 0.10 ± 0.02, and 0.07 ± 0.01. Uncorrelated maternal environmental effects accounted for little variation in any trait. Direct and maternal heterosis had considerable impact on growth traits, emphasizing the value of crossbreeding and the need to account for heterosis, in addition to breed effects, if crossbred lamb information is included in genetic evaluation.

Genetic parameters of milk and lactation curve traits of dairy cattle from research farms in Thailand.

ObjectiveThis study was aimed to estimate the genetic parameters, including genetic and phenotypic correlations, of milk yield, lactation curve traits and milk composition of Thai dairy cattle from three government research farms.MethodsThe data of 25,789 test-day milk yield and milk composition records of 1,468 cattle from lactation 1 to 3 of Holstein Friesian (HF) and crossbred HF dairy cattle calved between 1990 and 2015 from three government research farms in Thailand were analysed. 305-day milk yield was estimated by the Wood model and a test interval method. The Wood model was used for estimating cumulative 305-day milk yield, peak milk yield, days to peak milk yield and persistency. Genetic parameters were estimated using linear mixed models with herd, breed group, year and season of calving as fixed effects, and animals linked to a pedigree as random effects, together with a residual error. Univariate models were used to estimate variance components, heritability, estimated breeding values (EBVs) and repeatability of each trait, while pairwise bivariate models were used to estimate covariance components and correlations between traits in the same lactation and in the same trait across lactations.ResultsThe heritability of 305-day milk yield, peak milk yield and protein percentage have moderate to high estimates ranging from 0.19 to 0.45 while days to peak milk yield, persistency and fat percentage have low heritability ranging from 0.08 to 0.14 in lactation 1 cows. Further, heritability of most traits considered was higher in lactation 1 compared with lactations 2 and 3. For cows in lactation 1, high genetic correlations were found between 305-day milk yield and peak milk yield (0.86±0.07) and days to peak milk yield and persistency (0.99±0.02) while estimates of genetic correlations between the remaining traits were imprecise due to the high standard errors. The genetic correlations within the traits across lactation were high. There was no consistent trend of EBVs for most traits in the first lactation over the study period.ConclusionBoth the Wood model and test interval method can be used for milk yield estimates in these herds. However, the Wood model has advantages over the test interval method as it can be fitted using fewer test-day records and the estimated model parameters can be used to derive estimates of other lactation curve parameters. Milk yield, peak milk yield and protein percentage can be improved by a selection and mating program while days to peak milk yield, persistency and fat percentage can be improved by including into a selection index.

Genetic effects of heat stress on milk fatty acids in Brazilian Holstein cattle

The present study aimed to estimate covariance components of milk fatty acids (FA) and to compare the genomic estimated breeding values under general and heat-stress effects. Data consisted of 38,762 test-day records from 6,344 Holstein cows obtained from May 2012 through January 2018 on 4 dairy herds from Brazil. Single-trait repeatability test-day models with random regressions as a function of temperature-humidity index values were used for genetic analyses. The models included contemporary groups, parity order (1-6), and days in milk classes as fixed effects, and general and thermotolerance additive genetic and permanent environmental as random effects. Notably, differences in heritability estimates between environments (general and heat stress) increased (0.03 to 0.06) for unsaturated FA traits, such as unsaturated, monounsaturated, and polyunsaturated, at higher heat-stress levels. In contrast, heritability estimated between environments for saturated FA traits, including saturated FA, palmitic acid (C16:0), and stearic acid (C18:0) did not observe significant differences between environments. In addition, our study revealed negative genetic correlations between general and heat-stress additive genetic effects (antagonistic effect) for the saturated FA, C16:0, C18:0, and C18:1, which ranged from -0.007 to -0.32. Spearman's ranking correlation between genomic estimated breeding values ranged from -0.27 to 0.99. Results indicated a moderate to strong interaction of genotype by the environment for most FA traits comparing a heat-stress environment with thermoneutral conditions. Our findings point out novel opportunities to explore the use of FA milk profile and heat-stress models.

Estimation of co-variance components and genetic parameters of fertility and production traits in crossbred cattle of Kerala

Estimation of co-variance components and genetic parameters of fertility and production traits will help to find out the relative importance of genetic and environmental components of each trait and to develop a genetic evaluation system for overall improvement in performances of crossbred cattle of Kerala. In the present study, major fertility trait considered was daughters pregnancy rate (DPR), measures the percentage of non-pregnant animals that become pregnant during each oestrous cycle. Data pertaining to 1180 crossbred cattle sired by 208 Frieswal bulls, spread over a period of 16 years from 2003 to 2019, maintained at different farms of Kerala Veterinary and Animal Sciences University and field centres of ICAR- Filed Progeny Testing Scheme were analysed in the study. Estimates of covariance components and genetic parameters were obtained using restricted maximum likelihood (REML) approach using average information (AI) algorithm. It was observed that DPR had low heritability (0.092 ± 0.03), compared to 305 days milk yield (MY) (0.170 ± 0.094) and fat percent (FP) (0.173 ± 0.072). Phenotypic (rp), genetic (rg) and residual (re) correlation indicated unfavourable association of fertility with production traits. The estimates of variance and (co)variance components were computed by multivariate animal model. The results indicated that DPR was having lower direct additive (σ2a) 0.046 and environmental variance (σ2c) 0.063 compared to other traits. Highest additive genetic variance (σ2a) 27035.8 was obtained for MY. The study estimates the magnitude of correlations and covariances of fertility and production traits. Since DPR had lower additive genetic variance and negative association with milk production traits in cattle, it would be included as an indirect measure in the evaluation and breeding programs of crossbred cattle of Kerala.

PSXI-9 Heterotic and breed effects in crossbred lambs

Abstract Given its benefits on animal performance, crossbreeding is common commercially. Genetic evaluation of sheep in the U.S. is performed within breed type (terminal, maternal wool, range, hair). While incorporating crossbred records may improve assessment of purebreds, it requires accounting for heterotic and breed effects in the evaluation. The objectives were to i) determine the generalized effects of direct and maternal heterosis on growth traits of crossbred lambs, and ii) estimate covariance components for direct and maternal additive, and uncorrelated maternal environmental, effects among those traits. Data included body weights (BW) at birth (BN; n = 14395), pre-weaning (WN; n = 9298), weaning (WW; n = 9230), and post-weaning (PW; n = 1593). Mean (SD) BW were 5.3 (1.1), 22.2 (8.7), 39.1 (7.2), and 54.2 (8.7) kg for BN, WN, WW, and PW, respectively. Estimates of heterotic effects and covariance components were obtained using a multiple trait animal model. Genetic effects based on founders’ breeds were included, being significant. Estimates of direct heterosis were 3.04 ± 0.61, 2.62 ± 0.64, 3.99 ± 0.54, and 5.97 ± 0.86%, and estimates of maternal heterosis were 1.86 ± 0.87, 4.42 ± 0.79, 3.69 ± 0.66, and 3.77 ± 0.90%, for BN, WN, WW, and PW, respectively. Direct heritability estimates were 0.17 ± 0.02, 0.13 ± 0.02, 0.18 ± 0.02, and 0.47 ± 0.04 for BN, WN, WW, and PW, respectively. Additive maternal effects defined trivial variation in PW. For BN, WN, and WW, respectively, maternal heritability estimates were 0.17 ± 0.02, 0.10 ± 0.02, and 0.07 ± 0.02. Uncorrelated maternal effects defined little variation in any trait. Direct and maternal heterosis had considerable impact on growth traits, emphasizing the value of crossbreeding and the need to account for heterosis, in addition to breed effects, if crossbred lamb information is included in genetic evaluation.

Estimation of co-variance components, genetic parameters, and genetic trends of reproductive traits in community-based breeding program of Bonga sheep in Ethiopia.

ObjectiveThe objectives of the study were to evaluate reproductive performance and selection response through genetic trend of community-based breeding programs (CBBPs) of Bonga sheep.MethodsReproduction traits data were collected between 2012 and 2018 from Bonga sheep CBBPs. Phenotypic performance was analyzed using the general linear model procedures of Statistical Analysis System. Genetic parameters were estimated by univariate animal model for age at first lambing (AFL) and repeatability models for lambing interval (LI), litter size (LS), and annual reproductive rate (ARR) traits using restricted maximum likelihood method of WOMBAT. For correlations bivariate animal model was used. Best model was chosen based on likelihood ratio test. The genetic trends were estimated by the weighted regression of the average breeding value of the animals on the year of birth/lambing.ResultsThe overall least squares mean±standard error of AFL, LI, LS, and ARR were 375± 12.5, 284±9.9, 1.45±0.010, and 2.31±0.050, respectively. Direct heritability estimates for AFL, LI, LS, and ARR were 0.07±0.190, 0.06±0.120, 0.18±0.070, and 0.25±0.203, respectively. The low heritability for both AFL and LI showed that these traits respond little to selection programs but rather highly depend on animal management options. The annual genetic gains were −0.0281 days, −0.016 days, −0.0002 lambs and 0.0003 lambs for AFL, LI, LS, and ARR, respectively.ConclusionImplications of the result to future improvement programs were improving management of animals, conservation of prolific flocks and out scaling the CBBP to get better results.

Analysis of Genetic Parameters for Reproductive Traits in Crossbred Dairy Cattle Maintained at Holetta Agricultural Research Center.

This study was aimed to generate information on variance components and the resulting genetic parameters (heritability, repeatability, genetic and phenotypic correlations and genetic trends) of some economic traits of Borena and its crosses with Holstein Friesian dairy cattle maintained at Holetta agricultural research center dairy farm. Traits studied were age at first service (AFS), age at first calving (AFC), calving interval (CI), days open (DO) and number of service per conception (NSC). Overall, 11331 dairy cattle reproductive performance records were used for the study. WOMBAT, which is a software package for quantitative genetic analysis of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters were employed and obtained. Heritability values of reproductive traits were from very low (0.071, 0.082 and 0.012) for CI, DO and NSC to moderate (0.3 and 0.22) for AFC and AFS traits. Repeatability estimate for CI, DO and NSC were low (0.17, 0.17 and 0.129). Strong and positive genetic correlation (0.98) was appeared between AFS and AFC traits. Negative genetic correlations were observed between AFS and DO (-0.001), AFC and DO (-0.05), AFS and NSC (-0.022), AFC and NSC (-0.29) and CI and NSC (-0.31). AFS were negative phenotypic correlation with CI, DO and NSC. Similarly, AFC was negative phenotypic correlation with CI and DO. Low phenotypic correlation was observed between AFC and NSC, CI and DO, CI and NSC and, DO and NSC. Strong and positive phenotypic correlation was appeared between AFS and AFC. The regression coefficient of mean breeding value for NSC, CI, DO, AFC and AFS on year of birth were -0.0066x+13.25 times/year, -1.19x+2387.4 days/year, -1.23x+2445.6 days/year, 0.2x-410 months/year and 0.48x-980 months/year, respectively.

Estimates of covariance components and genetic parameters for growth, average daily gain and Kleiber ratio in Harnali sheep.

The aim of the present study was to estimate the (co)variance components and genetic parameters for various growth traits (weight at birth (BWT) and 3 (WT3), 6 (WT6), 9 (WT9), and 12 (WT12) months of age), average daily gain (ADG1, 0-3; ADG2, 3-6; and ADG3, 6-12months of age), and Kleiber's ratio (KR1:ADG1/WT30.75 and KR2:ADG2/WT60.75) by using records of 526 lambs of 41 sires and 186 dams in Harnali Sheep maintained at Department of Animal Genetics and Breeding, Lala Lajpat Rai University of Veterinary and Animal Sciences, Hisar (Haryana), India for the period of year 2014-2019. Restricted maximum likelihood procedure (REML) was employed for estimation of covariance components and genetic parameters by considering direct effects with or without maternal effects. The estimates of direct heritability for BWT, WT3, WT6, WT9, WT12, ADG1, ADG2, ADG3, KR1, and KR2 were 0.10, 0.45, 0.32, 0.36, 0.23, 0.43, 0.02, 0.001, 0.38, and 0.02, respectively. It was observed that maternal effects had significant influence on BWT trait only, and corresponding estimate of maternal heritability was 0.16. This indicated the importance of maternal ability in Harnali sheep for initial growth performance. Moderate estimate of direct additive heritability of weaning weight (WT3) and moderate genetic correlations of it with other traits indicated that the current practice of selection at 6months may be replaced by early selection at WT3 in order to improve the growth performance in Harnali sheep.

Variance-covariance component estimation for structured errors-in-variables models with cross-covariances

In this contribution, an iterative algorithm for variance-covariance component estimation based on the structured errors-in-variables (EIV) model is proposed. We introduce the variable projection principle and derive alternative formulae for the structured EIV model by applying Lagrange multipliers, which take the form of a least-squares solution and are easy to implement. Then, least-squares variance component estimation (LS-VCE) is applied to estimate different (co)variance components in a structured EIV model. The proposed algorithm includes the estimation of covariance components, which is not considered in other recently proposed approaches. Finally, the estimability of the (co)variance components of the EIV stochastic model is discussed in detail. The efficacy of the proposed algorithm is demonstrated through two applications: multiple linear regression and auto-regression, on simulated datasets or on a real dataset with some assumptions.

Estimation of genetic parameters for chosen udder traits of different dairy ewes

Morphology of udder in ewes in one experimental herd was examined on the basis of linear evaluation (7 traits; 9 points scale; 1145 data for each trait) and exact measurements of udder (6 parameters; 1055 measurements at each trait) were taken. Estimation of covariance components and genetic parameters were done using REML and BLUP-AM (VCE 4.0 package) for 7 traits (linear evaluation) or 6 traits (udder measurements) . Heritability coefficients for individual traits of linear evaluation varied from 0.090–0.294. Heritability coefficient (h2) for teat position was 0.242, 0.275 for teat size , and 0.294 for cistern depth, which is related to teat position. The highest value of genetic correlation (rg=0.980) was found between cistern depth and teat position. Negative genetic correlation was detected between teat position and teat size (–0.381), and teat position and udder cleft (–0.404). Heritability coefficients and genetic correlations of exact measurements of udder were comparable with traits of linear evaluation. For the parameter, udder length and rear udder depth, the detected band-measures were h2 = 0.219 or 0.223. Highest h2 was found for cistern depth (0.480), teat length (0.358) and teat angle (0.290) similar to linear evaluation.

Genetic evaluation of growth in Barki sheep using random regression models.

The objective of the current study was to estimate covariance components of growth at different ages from birth to yearling in Barki lambs. A total of 16,496 records for body weights at birth (W0), 3 (W3), 6 (W6), 9 (W9), and 12 (12) months of age for Barki lambs were available. Two statistical approaches were used; multi-trait (MT) and random regression (RR) animal models assuming two random effects only, additive genetic effect (σ2a) and permanent environmental effect (σ2pe) of the animal. Regarding the RR model, Legendre polynomials (LP) of different orders for the random parts were compared in order to evaluate the most appropriate model. Bayesian information and Akaike information criteria suggested that the optimal RR model included the third order for fixed effect of lamb age and σ2pe, and fourth order of LP for σ2a (LP343). Estimates of direct heritability (h2a) from LP343 showed an ascending pattern, as it was 0.06 ± 0.03 for birth weight and reached to the peak at 9months (0.42 ± 0.02). Thereafter, it declined again at the end of trajectory (12 months of age; 0.27 ± 0.03). The MT model showed a fluctuated pattern and lower estimates of h2a (0.19 ± 0.03, 0.11 ± 0.02, 0.12 ± 0.02, 0.11 ± 0.03, and 0.16 ± 0.04 for W0, W3, W6, W9, and W12, respectively). Considerably, similar ascending patterns of the ratio of σ2pe to phenotypic variance were reported from both RR (from 3 to 50%) and MT models (from 5 to 20%). Of interest, the RR model showed higher predicting ability of the breeding values compared with the MT model, which is an indicator for the suitability of RR models for analyzing the consecutive growth traits in sheep. Results suggested that the Barki sheep has a potential for genetic selection based on weight at different ages with selection likely to be more efficient at 9 months of age.

Estimation of co-variance components, genetic parameters and genetic trends of VIAscan carcass traits of New Zealand Romney lambs

The aim of this study was to estimate co-variance components, genetic parameters and direct genetic trends of carcass traits of New Zealand Romney lambs assessed by VIAscan technology. Data for VIAscan carcass traits of 3389 lambs that included hot carcass weight (VHW); subcutaneous fat depth near the 12th rib (VGR) and meat yield (expressed as a percentage of VHW in the shoulder (SHY%), loin (LNY%), hind leg (LGY%) and whole carcass (TY%) were analyzed by employing different animal models for univariate and multivariate analysis using restricted maximum likelihood (REML) procedures with ignoring or including maternal effects. Year of birth, parity of ewe and type of birth were included in the model as fixed factors, as well as the linear covariate of age of lamb at drafting was fitted into the model. Based on the most appropriate model, estimates of direct heritability (h2a) ranged from moderate to high for VHW (0.29 ± 0.02), VGR (0.56 ± 0.09), SHY% (0.34 ± 0.07), LNY% (0.37 ± 0.06), LGY% (0.38 ± 0.08) and TY% (0.31 ± 0.02), however, the estimates of maternal heritability (h2m) ranged from low to moderate for VHW (0.10 ± 0.03), VGR (0.38 ± 0.08), SHY% (0.18 ± 0.02), LNY% (0.15 ± 0.04), LGY% (0.19 ± 0.02) and TY% (0.17 ± 0.02). VHW was positively genetically correlated with all VIAscan carcass traits (0.151 to 0.563) except LGY% (−0.145). VGR was positively genetically correlated with both VHW (0.563) and LNY% (0.003), and negatively genetically correlated with the rest of carcass traits (−0.008 to −0.472). The genetic correlation of TY% was negative with VGR (−0.229) and positive with the other carcass traits (0.151 to 0.878). SHY%, LNY% and LGY% were moderately positively genetically correlated with each other with a range (0.538–0.601). Estimating the direct genetic trends of VIAscan carcass traits during the period of study indicated that a high genetic progress was achieved in the desired direction for VHW, LNY%, LGY% and TY%, and in the undesired direction for VGR. The moderate to high heritability estimates for VIAscan carcass traits indicated that these traits could respond to direct selection. Such information is important in designing breeding strategies for improving carcass traits in New Zealand Romney lambs.

The use of new technologies in horse selection

Received: 2018-09-12 | Accepted: 2018-11-27 | Available online: 2018-12-31 https://doi.org/10.15414/afz.2018.21.04.186-189 Most successful selection strategies are not in use in horse selection. This study describes the use of current strategies of selection in horse and tries to answers why well known, scientifically proven selection strategies are still not implemented. In the era of genomic selection (GS) in animal breeding, decision making in horse selection, even classical values (BV), are not fully taken advantage of. Breeding organizations (BO) which implement BVs as selection criteria in their programs show great success in genetic gain. However, a horse's achievements and the popularity of its relatives still plays an important role in selection level. Genomic based selection tools in horse have limitations in quantitative traits since it is difficult to establish reference population. Mendelian traits have been studied for several years, especially those related to horse health and functional longevity (long sport or race careers), yet there are still only a small number of validated mendelian traits offered for horses. The important benefit of GS is the prevention of related mating based on genomic data, in addition to pedigree data. The specialty in horse is the use of cloning. From the point of view of genetic variability, cloning is useful in enabling geldings or non-genetically infertile animals to carry genes to next generations. In sport and race BOs, stallions from foreign BOs are frequently used. In such cases a need for comparable BVs exists. These factors were the motivation behind the establishment of Interstallion 20 years ago. Due to difficulties in BO collaboration, Interstallion has not been as successful as planned. On the whole, it is expected that the sector of horse selection will need to change considerably in the future. 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Available at: http://www.wbfsh.org/GB/Rankings/Breeder%20and%20Studbook%20rankings.aspx [Accessed 12 September 2018].

Genetic trends and trade-offs between growth and reproductive traits in a Nellore herd.

The knowledge of genetic trends and trade-offs between growth and reproductive traits might be useful to understand the evolution of these traits in livestock and natural populations of animals. We estimated the genetic trends and trade-offs between pre-weaning growth and calving intervals of Nellore animals from a commercial farm. Two-trait animal models were used to estimate covariance components and breeding values (EBV) for direct and maternal genetic effects of pre-weaning growth and direct genetic effects of calving intervals. Regression analyses were performed to examine the relationship between direct and maternal EBV of pre-weaning growth and direct EBV of calving intervals (dependent variables) and the coefficient of generation of each animal (independent variable). We also performed regression analyses to examine the relationship between direct EBV of calving intervals (dependent variables) and direct and maternal EBV of pre-weaning growth (independent variables). The genetic trends for direct and maternal genetic effect for pre-weaning growth were significant and presented genetic evolution in the studied Nellore herd. The genetic trends for the reproductive traits were also significant but indicated genetic changes in an unfavorable way. The genetic correlations between direct effects of pre-weaning growth and calving intervals traits and the genetic correlations between maternal effects of pre-weaning growth traits and direct effects of calving interval traits were not different from zero. The presence of trade-offs between the direct effects of growth and reproductive traits were confirmed through regression from direct EBV of calving intervals over EBV of pre-weaning growth traits. In addition, regression analyses showed that selection to increase pre-weaning growth also increased calving intervals. Our results showed that pre-weaning growth and calving intervals are increasing over generations and that trade-offs occurred between those traits in the studied Nellore herd.

Effects of Genotype by Environment Interaction on Genetic Gain and Genetic Parameter Estimates in Red Tilapia (Oreochromis spp.).

The extent to which genetic gain achieved from selection programs under strictly controlled environments in the nucleus that can be expressed in commercial production systems is not well-documented in aquaculture species. The main aim of this paper was to assess the effects of genotype by environment interaction on genetic response and genetic parameters for four body traits (harvest weight, standard length, body depth, body width) and survival in Red tilapia (Oreochromis spp.). The growth and survival data were recorded on 19,916 individual fish from a pedigreed population undergoing three generations of selection for increased harvest weight in earthen ponds from 2010 to 2012 at the Aquaculture Extension Center, Department of Fisheries, Jitra in Kedah, Malaysia. The pedigree comprised a total of 224 sires and 262 dams, tracing back to the base population in 2009. A multivariate animal model was used to measure genetic response and estimate variance and covariance components. When the homologous body traits in freshwater pond and cage were treated as genetically distinct traits, the genetic correlations between the two environments were high (0.85–0.90) for harvest weight and square root of harvest weight but the estimates were of lower magnitudes for length, width and depth (0.63–0.79). The heritabilities estimated for the five traits studied differed between pond (0.02 to 0.22) and cage (0.07 to 0.68). The common full-sib effects were large, ranging from 0.23 to 0.59 in pond and 0.11 to 0.31 in cage across all traits. The direct and correlated responses for four body traits were generally greater in pond than in cage environments (0.011–1.561 vs. −0.033–0.567 genetic standard deviation units, respectively). Selection for increased harvest body weight resulted in positive genetic changes in survival rate in both pond and cage culture. In conclusion, the reduced selection response and the magnitude of the genetic parameter estimates in the production environment (i.e., cage) relative to those achieved in the nucleus (pond) were a result of the genotype by environment interaction and this effect should be taken into consideration in the future breeding program for Red tilapia.

MODELOS DE REGRESSÃO ALEATÓRIA ATRAVÉS DO PESO CORPORAL EM CURVAS DE CRESCIMENTO DE AVES

In modern genetic evaluations, random regression models have been used as a custom tool in order to analyze longitudinal traits such as the ones involved in animal growth. Such traits as body weight have an easy mensuration and an excellent response to selection, which is a suitable and important feature for animal breeding programs. The purpose of this review is to discuss about different random regression models that are involved in farm bird growth. The random regression models are recommended as an alternative to genetic evaluation of traits that are regularly measured during the animal life. These models allow the prediction of regression coefficients that represent the behavior of the additive genetic value for each animal in the specific evaluated trait in relation to time (age). Thus, interminable values for the independent variable are considered 340 Colloquium Agrariae, vol. 13, n. Especial, Jan–Jun, 2017, p. 321-347 ISSN: 1809-8215. DOI: 10.5747/ca.2017.v13.nesp.000238 within a defined interval, through deviations of each animal in relation to an estimated and fixed curve. The covariance component estimates assigned to random regression coefficients allow the covariance estimation between any values of the independent variable for a modeled random effect, which is accomplished by the covariance function. Therefore, random regression models improve the use of the weight information, when covariance structures between the studied ages are taken into account during the evaluation. They also allow the description of the estimated variance components that are involved in growth, besides granting presumptions for others in the curve inside the interval estimation.