Estimation of direct and maternal genetic and permanent environmental effects for weights from birth to 356 days of age in a herd of Japanese Black cattle using random regression

A total of 11,815 weight records from 23,94 Japanese Black calves was used to estimate direct, maternal, direct permanent environmental, and maternal permanent environmental effects on growth from birth to 356 d of age. The data were collected from a herd of Japanese Black cattle in Shiroshi city, Miyagi prefecture, Japan. A random regression model, including parity of dam and year-season of calving-sex of calf as fixed effects and animal, dam, animal permanent environmental, and maternal permanent environmental as random effects, was fitted to the data using Legendre polynomials for age of calf. Direct heritability estimates increased from 0.38 at birth to 0.65 at 120 d of age, decreased to 0.38 at 300 d, and then increased again up to 0.47 at 356 d. The ratio of animal permanent environmental variance to phenotypic variance decreased from 0.41 at birth to 0.12 at 90 d, and then increased gradually up to 0.40 at 270 d and oscillated around this value up to the end of the test period. Maternal genetic heritabilities increased from 0.04 at birth to 0.09 at 120 d and then decreased to 0.06 thereafter, whereas the variance ratios due to maternal permanent environment were fairly constant across the age trajectory, fluctuating around the value of 0.03. Direct genetic, phenotypic, maternal genetic, animal permanent environmental, and maternal permanent environmental correlations between different ages were all positive, and they generally decreased as the interval between ages increased. These correlations were lower between weights from nonadjacent ages than those between weights from adjacent ages. Results suggest that selection on preweaning weights would have a positive effect on weights at later ages.     

Random regression models on Legendre polynomials to estimate genetic parameters for weights from birth to adult age in Canchim cattle*

The objective of this work was to estimate covariance functions for direct and maternal genetic effects, animal and maternal permanent environmental effects, and subsequently, to derive relevant genetic parameters for growth traits in Canchim cattle. Data comprised 49 011 weight records on 2435 females from birth to adult age. The model of analysis included fixed effects of contemporary groups (year and month of birth and at weighing) and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were allowed to vary and were modelled by a step function with 1, 4 or 11 classes based on animal’s age. The model fitting four classes of residual variances was the best. A total of 12 random regression models from second to seventh order were used to model direct and maternal genetic effects, animal and maternal permanent environmental effects. The model with direct and maternal genetic effects, animal and maternal permanent environmental effects fitted by quadric, cubic, quintic and linear Legendre polynomials, respectively, was the most adequate to describe the covariance structure of the data. Estimates of direct and maternal heritability obtained by multi‐trait (seven traits) and random regression models were very similar. Selection for higher weight at any age, especially after weaning, will produce an increase in mature cow weight. The possibility to modify the growth curve in Canchim cattle to obtain animals with rapid growth at early ages and moderate to low mature cow weight is limited.     

Genetic parameters estimated with multitrait and linear spline-random regression models using Gelbvieh early growth data

Estimates of direct and maternal genetic parameters in beef cattle were obtained with a random regression model with a linear spline function (SFM) and were compared with those obtained by a multitrait model (MTM). Weight data of 18,900 Gelbvieh calves were used, of which 100, 75, and 17% had birth (BWT), weaning (WWT), and yearling (YWT) weights, respectively. The MTM analysis was conducted with a three-trait maternal animal model. The MTM included an overall linear partial fixed regression on age at recording for WWT and YWT, and direct-maternal genetic and maternal permanent environmental effects. The SFM included the same effects as MTM, plus a direct permanent environmental effect and heterogeneous residual variance. Three knots, or breakpoints, were set to 1, 205, and 365 d. (Co)variance components in both models were estimated with a Bayesian implementation via Gibbs sampling using flat priors. Because BWT had no variability of age at recording, there was good agreement between corresponding components of variance estimated from both models. For WWT and YWT, with the exception of the sum of direct permanent environmental and residual variances, there was a general tendency for SFM estimates of variances to be lower than MTM estimates. Direct and maternal heritability estimates with SFM tended to be lower than those estimated with MTM. For example, the direct heritability for YWT was 0.59 with MTM, and 0.48 with SFM. Estimated genetic correlations for direct and maternal effects with SFM were less negative than those with MTM. For example, the direct-maternal correlation for WWT was -0.43 with MTM and -0.33 with SFM. Estimates with SFM may be superior to MTM due to better modeling of age in both fixed and random effects.     

Analyses of growth curves of nellore cattle by multiple-trait and random regression models

The purpose of this study was to compare estimates of genetic parameters for sequential growth of beef cattle using two models and two data sets. Growth curves of Nellore cattle were analyzed using body weights measured at ages 1 (birth weight) to 733 d. Two data samples were created, one with 71,867 records sampled from all herds (MISS), and the other with 74,601 records sampled from herds with no missing traits (NMISS). Records preadjusted to a fixed age were analyzed by a multiple-trait model (MTM), which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were by REML, with five traits at a time. The random regression model (RRM) included the effects of age of animal, contemporary group, age of dam class, additive direct, additive maternal, permanent environment, and maternal permanent environment. All effects were modeled as cubic Legendre polynomials. These analyses were also by REML. Shapes of estimates of variances by MTM were mostly similar for both data sets for all except late ages, where estimates for MISS were less regular, and for birth weight with MISS. Genetic correlations among ages for the direct and maternal effects were less smooth with MISS. Genetic correlations between direct and maternal effects were more negative for NMISS, where few sires were maternal grandsires. Parameter estimates with RRM were similar to MTM cept that estimates of variances showed more artifacts for MISS; the estimates of additive direct-maternal correlations were more negative with both data sets and approached -1.0 for some ages with NMISS. When parameters of a growth model obtained by used for genetic evaluation, these parameters should be examined for consistency with parameters from MTM and prior information, and adjustments may be required to eliminate artifacts.     

Estimates of genetic covariance functions for growth of Angus cattle

Estimates of covariance functions and genetic parameters were obtained for growth of Angus cattle from birth to 820 days of age. Data comprised 84 533 records on 20 731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights were modelled through random regression on orthogonal polynomials of age at recording. A total of 11 combinations of quadratic, cubic, quartic and quintic polynomials to model direct and maternal genetic effects and permanent environmental effects were considered. Results showed good agreement for all models at ages with many records, but differed at the highest ages and at very early ages with few weights available. Cubic polynomials appeared to be most problematic. The order of polynomial fit for permanent environmental effects of the animal dominated estimates of phenotypic variances and mean squares for residual errors. A model fitting a quartic polynomial for these effects and quadratic polynomials for the other random effects, appeared to be the best compromise between detailedness of the model which could be supported by the data, plausibility of results, and fit, measured as mean square error.     

Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle

Genetic parameters for a random regression model of growth in Gelbvieh beef cattle were constructed using existing estimates. Information for variances along ages was provided by parameters used for routine Gelbvieh multiple-trait evaluation, and information on correlations among different ages was provided by random regression model estimates from literature studies involving Nellore cattle. Both sources of information were combined into multiple-trait estimates; corrected for continuity, smoothness, and general agreement with literature estimates; and extrapolated to 730 d. Covariance functions using standardized Legendre polynomials were fit for the following effects: additive genetic (direct and maternal), and animal and maternal permanent environment. Residual variances at different ages were fitted using linear splines with three knots. Fit was by least squares. The order of polynomials was varied from third to sixth. Increasing the fit beyond cubic provided small improvements in R2 and increased the number of small eigenvalues of covariance matrices, especially for the additive effect. Parameters for a random regression model in beef cattle can be constructed with negligible artifacts from literature estimates. Formulas can easily be modified for other types of polynomials and splines.     

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions.     

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age.     

Random regression models to estimate genetic parameters for weights in Murrah buffaloes

This article reports genetic analysis of the weight at different ages of Murrah water buffaloes, using random regression models (RRM). Models ranging from third to sixth order polynomial were used to describe direct genetic and animal permanent environmental effects. Contemporary group was included as a fixed effect, and a cubic polynomial was used to model the mean curve of the population. The residual was modeled considering a log‐linear function. Two models were selected for study of genetic parameters. The first model included third and sixth order polynomials for direct genetic and animal permanent environmental effects (M36). The second model included sixth order polynomials for all random effects (M66). The estimates of heritability varied from 0.16 + 0.04 (44 days) to 0.38 + 0.04 (568 days) for model M36 and from 0.16 + 0.05 (33 days) to 0.42 + 0.05 (600 days) for model M66. Regarding estimates of the correlation for all effects, the magnitude tended to decline with the increase of the time span between measurements. These results indicate that the species has potential for genetic selection based on weight at different ages, since we found favorable genetic variability within the herd, with selection likely to be more efficient at ages near 600 days.     

Genetic parameters for various random regression models to describe total sperm cells per ejaculate over the reproductive lifetime of boars

The objective of this study was to model the variances and covariances of total sperm cells per ejaculate (TSC) over the reproductive lifetime of AI boars. Data from boars (n = 834) selected for AI were provided by Smithfield Premium Genetics. The total numbers of records and animals were 19,629 and 1,736, respectively. Parameters were estimated for TSC by age of boar classification with a random regression model using the Simplex method and DxMRR procedures. The model included breed, collector, and year-season as fixed effects. Random effects were additive genetic, permanent environmental effect of boar, and residual. Observations were removed when the number of data at a given age of boar classification was < 10 records. Preliminary evaluations showed the best fit with fifth-order polynomials, indicating that the best model would have fifth-order fixed regression and fifth-order random regressions for animal and permanent environmental effects. Random regression models were fitted to evaluate all combinations of first- through seventh-order polynomial covariance functions. Goodness of fit for the models was tested using Akaike's Information Criterion and the Schwarz Criterion. The maximum log likelihood value was observed for sixth-, fifth-, and seventh-order polynomials for fixed, additive genetic, and permanent environmental effects, respectively. However, the best fit as determined by Akaike's Information Criterion and the Schwarz Criterion was by fitting sixth-, fourth-, and seventh-order polynomials; and fourth-, second-, and seventh-order polynomials for fixed, additive genetic, and permanent environmental effects, respectively. Heritability estimates for TSC ranged from 0.27 to 0.48 across age of boar classifications. In addition, heritability for TSC tended to increase with age of boar classification.     

Genetic evaluation of growth of Kenya Boran cattle using random regression models

Data consisting of 18 884 weight records collected from 1273 Boran cattle from birth to 24 months of age were used to estimate covariance functions and genetic parameters for growth of Boran cattle using random regression (RR) models under a situation of small herd size and inconsistent recording. The RR model fitted quadratic Legendre polynomials of age at recording for additive genetic and permanent environmental effects. Genetic variance increased from birth, reaching an asymptotic value at 455 days and was maximum at 525 days of age after which it gradually dropped. Permanent environmental variance increased throughout the trajectory. Estimates of temporary environmental variance were heterogeneous across ages. Direct heritability and permanent environmental variance as a proportion of phenotypic variance fluctuated greatly during the early ages but later stabilized at intermediate to later ages; the estimates ranged from 0.11 to 0.33 and from 0.18 to 0.83, respectively. Genetic correlation estimates were positive, ranging from 0.10 to unity. The estimates declined with increasing in lag between the age points. Phenotypic correlation pattern was erratic between early ages, negatively low (-0.02) between the extreme data points and moderate to highly positive (>0.50) between intermediate and later points, with prominent spikes along the diagonal. It is concluded that RR models have potential for modelling growth of Boran cattle, notwithstanding conditions of small herd sizes and inconsistent recording.     

Genetic and environmental parameters for traits derived from the Brody growth curve and their relationships with weaning weight in Angus cattle

Direct and maternal genetic and environmental variances and covariances were estimated for weaning weight and growth and maturing traits derived from the Brody growth curve. Data consisted of field records of weight measurements of 3,044 Angus cows and 29,943 weaning weight records of both sexes. Growth traits included weights and growth rates at 365 and 550 d, respectively. Maturing traits included the age of animals when they reached 65% of mature weight, relative growth rates, and degrees of maturity at 365 and 550 d. Variance and covariance components were estimated by REML from a set of two-trait animal models including weaning weight paired with a growth or maturing trait. Weaning and cow contemporary groups were defined as fixed effects. Random effects for weaning weight included direct genetic, maternal genetic, and permanent environmental effects. For growth and maturing traits, a random direct genetic effect was included in the model. Direct heritability estimates for growth traits ranged from .46 to .52 and for maturing traits from .31 to .34. Direct genetic correlations between weaning weight and weights and growth rates at 365 and 550 d ranged from .56 to .70. Correlations of maternal weaning genetic effects with direct genetic effects on weights at 365 and 550 d were positive, but those with growth rates were negative. Between weaning weight and degrees of maturity at both 365 and 550 d, direct genetic correlation estimates were .55 and maternal genetic correlations estimates were -.05, respectively. Direct genetic correlations of weaning weight with relative growth rates and age at 65% of mature weight ranged from .04 to .06, and maternal-direct genetic correlation estimates ranged from -.50 to -.56, respectively. These estimates indicate that higher genetic capacity for milk production was related to higher body mass and degrees of maturity between 365 and 550 d of age but was negatively related to absolute and relative growth rates in that life stage.     

绵羊生长性状母本效应方差组分、遗传参数估计的研究

本文利用公畜母畜模型和公畜外祖父模型估计了初生重、断奶重的直接加性遗传方差、母本遗传方差和遗传参数,得出初生重的直接加性遗传效应、母本遗传效应和总的加性遗传效应的遗传力分别为:0.164、0.101、0.103;断奶重相应的各遗传力为:0.076、0.108、0.081。初生重和断奶重二性状加性遗传效应和母本遗传效应间的遗传相关为:-0.57和-0.36。     

Genetic evaluation of growth in nellore cattle by multiple-trait and random regression models

The objective of this study was to identify issues in genetic evaluation of beef cattle for growth by a random regression model (RRM). Genetic evaluation data included 2,946,847 records of up to nine sequential weights of 812,393 Nellore cattle measured at ages ranging from birth to 733 d. Models considered were a five-trait multiple-trait model (MTM) and a cubic RRM. The MTM included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Both additive effects were assumed correlated. The RRM included the same effects as MTM, with the addition of permanent and random error effects. The purpose of the random error effect, which was in addition to a residual effect with constant variance, was to model heterogeneous residual variances. All effects in RRM were modeled as cubic Legendre polynomials. Expected progeny differences (EPD) were obtained iteratively using a preconditioned conjugate gradient algorithm. Numerically accurate solutions with RRM were not obtained until the random regressions were orthogonalized. Computing requirements of RRM were reduced by more than 50%, without affecting the accuracy by removing regressions corresponding to very low eigen-values and by replacing the random error effects with weights. Afterward, the correlations between EPD from RRM and from MTM for EPD on selected weights were between 0.84 and 0.89. For sires with at least 50 progeny, these correlations increased to 0.92 to 0.97. Low correlations were caused by differences in parameters. The RRM applied to growth i s prone to numerical problems. Estimates of EPD with RRM may be more accurate than those with MTM only if accurate parameters are applied.     

Comparison of models to estimate genetic effects of weaning weight of Angus cattle

Weaning weights from nine sets of Angus field data from three regions of the United States were analyzed. Six animal models were used to compare two approaches to account for an environmental dam-offspring covariance and to investigate the effects of sire x herd-year interaction on the genetic parameters. Model 1 included random direct and maternal genetic, maternal permanent environmental, and residual effects. Age at weaning was a covariate. Other fixed effects were age of dam and a herd-year-management-sex combination. Possible influence of a dam's phenotype on her daughter's maternal ability was modeled by including a regression on maternal phenotype (fm) (Model 3) or by fitting grandmaternal genetic and grandmaternal permanent environmental effects (Model 5). Models 2, 4, and 6 were based on Models 1, 3, and 5, respectively, and additionally included sire x herd-year (SH) interaction effects. With Model 3, estimates of fm ranged from -.003 to .014, and (co)variance estimates were similar to those from Model 1. With Model 5, grandmaternal heritability estimates ranged from .02 to .07. Estimates of maternal heritability and direct-maternal correlation (r(am)) increased compared with Model 1. With models including SH, estimates of the fraction of phenotypic variance due to SH interaction effects were from .02 to .10. Estimates of direct and maternal heritability were smaller and estimates of r(am) were greater than with models without SH interaction effects. Likelihood values showed that SH interaction effects were more important than fm and grandmaternal effects. The comparisons of models suggest that r(am) may be biased downward if SH interaction and(or) grandmaternal effects are not included in models for weaning weight.     

Variance components and breeding values for growth traits from different statistical models.

Estimates of genetic parameters resulting from various analytical models for birth weight (BWT, n = 4,155), 205-d weight (WWT, n = 3,884), and 365-d weight (YWT, n = 3,476) were compared. Data consisted of records for Line 1 Hereford cattle selected for postweaning growth from 1934 to 1989 at ARS-USDA, Miles City, MT. Twelve models were compared. Model 1 included fixed effects of year, sex, age of dam; covariates for birth day and inbreeding coefficients of animal and of dam; and random animal genetic and residual effects. Model 2 was the same as Model 1 but ignored inbreeding coefficients. Model 3 was the same as Model 1 and included random maternal genetic effects with covariance between direct and maternal genetic effects, and maternal permanent environmental effects. Model 4 was the same as Model 3 but ignored inbreeding. Model 5 was the same as Model 1 but with a random sire effect instead of animal genetic effect. Model 6 was the same as Model 5 but ignored inbreeding. Model 7 was a sire model that considered relationships among males. Model 8 was a sire model, assuming sires to be unrelated, but with dam effects as uncorrelated random effects to account for maternal effects. Model 9 was a sire and dam model but with relationships to account for direct and maternal genetic effects; dams also were included as uncorrelated random effects to account for maternal permanent environmental effects. Model 10 was a sire model with maternal grandsire and dam effects all as uncorrelated random effects. Model 11 was a sire and maternal grandsire model, with dams as uncorrelated random effects but with sires and maternal grandsires assumed to be related using male relationships. Model 12 was the same as Model 11 but with all pedigree relationships from the full animal model for sires and maternal grandsires. Rankings on predictions of breeding values were the same regardless of whether inbreeding coefficients for animal and dam were included in the models. Heritability estimates were similar regardless of whether inbreeding effects were in the model. Models 3 and 9 best fit the data for estimation of variances and covariances for direct, maternal genetic, and permanent environmental effects. Other models resulted in changes in ranking for predicted breeding values and for estimates of direct and maternal heritability. Heritability estimates of direct effects were smallest with sire and sire-maternal grandsire models.     

Estimates of direct and maternal genetic effects for weights from birth to 600 days of age in Nelore cattle

Estimates of direct and maternal variance and heritability for weights at each week (up to 280 days of age) and month of age (up to 600 days of age) in Zebu cattle are presented. More than one million records on 200 000 animals, weighed every 90 days from birth to 2 years of age, were available. Data were split according to week (data sets 1) or month (data sets 2) of age at recording, creating 54 and 21 data sets, respectively. The model of analysis included contemporary groups as fixed effects, and age of dam (linear and quadratic) and age of calf (linear) effects as covariables. Random effects fitted were additive direct and maternal genetic effects, and maternal permanent environmental effect. Direct heritability estimates decreased from 0.28 at birth, to 0.12–0.13 at about 150 days of age, stayed more or less constant at 0.14–0.16 until 270 days of age and increased with age after that, up to 0.25–0.26. Maternal heritability estimates increased from birth (0.01) to a peak of 0.14 for data sets 1 and 0.07–0.08 for data sets 2 at about 180–210 days of age, before decreasing slowly to 0.07 and 0.05, respectively, at 300 days, and then rapidly diminished after 300 days of age. Permanent environmental effects were 1.5 to four times higher than genetic maternal effects and showed a similar trend.     

Covariance functions and random regression models for cow weight in beef cattle

Data from the first four cycles of the Germplasm Evaluation program at the U.S. Meat Animal Research Center were used to evaluate weights of Angus, Hereford, and F1 cows produced by crosses of 22 sire and 2 dam (Angus and Hereford) breeds. Four weights per year were available for cows from 2 through 8 yr of age (AY) with age in months (AM). Weights (n = 61,798) were analyzed with REML using covariance function-random regression models (CF-RRM), with regression on orthogonal (Legendre) polynomials of AM. Models included fixed regression on AM and effects of cow line, age in years, season of measurement, and their interactions; year of birth; and pregnancy-lactation codes. Random parts of the models fitted RRM coefficients for additive (a) and permanent environmental (c) effects. Estimates of CF were used to estimate covariances among all ages. Temporary environmental effects were modeled to account for heterogeneity of variance by AY. Quadratic fixed regression was sufficient to model population trajectory and was fitted in all analyses. Other models varied order of fit and rank of coefficients for a and c. A parsimonious model included linear and quartic regression coefficients for a and c, respectively. A reduced cubic order sufficed for c. Estimates of all variances increased with age. Estimates for older ages disagreed with estimates using traditional bivariate models. Plots of covariances for c were smooth for intermediate, but erratic for extreme ages. Heritability estimates ranged from 0.38 (36 mo) to 0.78 (94 mo), with fluctuations especially for extreme ages. Estimates of genetic correlations were high for most pairs of ages, with the lowest estimate (0.70) between extreme ages (19 and 103 mo). Results suggest that although cow weights do not fit a repeatability model with constant variances as well as CF-RRM, a repeatability model might be an acceptable approximation for prediction of additive genetic effects.     

Random regression model of growth during the first three months of age in Spanish Merino sheep

A total of 88,727 individual BW records of Spanish Merino lambs, obtained from 30,214 animals between 2 and 92 d of age, were analyzed using a random regression model (RRM). These animals were progeny of 546 rams and 15,586 ewes raised in 30 flocks, between 1992 and 2002, with a total of 45,941 animals in the pedigree. The contemporary groups (animals of the same flock, year, and season, with 452 levels), the lambing number (11 levels), the combination sex of lambs with type of litter (4 levels), and a fixed regression coefficient of age on BW were included as fixed effects. A total of 7 RRM were compared, and the best fit was obtained for a model of order 3 for the direct and maternal genetic effects and for the individual permanent environmental effect. For the maternal permanent environmental effect the best model had an order 2. The residual variance was assumed to be heterogeneous with 10 age classes; the covariance between both genetic effects was included. According to the results of the selected RRM, the heritability for both genetic effects (h(a)2 and h(m)2) increased with age, with estimates of 0.123 to 0.186 for h(a)2 and of 0.059 to 0.108 for h(m)2. The correlations between direct and genetic maternal effects were -0.619 to -0.387 during the first 45 d of age and decreased as age increased, until reaching values from -0.366 to -0.275 between 45 to 75 d of age. Important changes in ranking of the animals were found based on the breeding value estimation with the current method and with the random regression procedure. The use of RRM to analyze the genetic trajectory of growth in this population of Merino sheep is highly recommended.     

Genetic analysis of longitudinal measurements of performance traits in selection lines for residual feed intake in Yorkshire swine

A 5-generation selection experiment in Yorkshire pigs for feed efficiency consists of a line selected for low residual feed intake (LRFI) and a random control line (CTRL). The objectives of this study were to use random regression models to estimate genetic parameters for daily feed intake (DFI), BW, backfat (BF), and loin muscle area (LMA) along the growth trajectory and to evaluate the effect of LRFI selection on genetic curves for DFI and BW. An additional objective was to compare random regression models using polynomials (RRP) and spline functions (RRS). Data from approximately 3 to 8 mo of age on 586 boars and 495 gilts across 5 generations were used. The average number of measurements was 85, 14, 5, and 5 for DFI, BW, BF, and LMA. The RRP models for these 4 traits were fitted with pen × on-test group as a fixed effect, second-order Legendre polynomials of age as fixed curves for each generation, and random curves for additive genetic and permanent environmental effects. Different residual variances were used for the first and second halves of the test period. The RRS models were fitted with the same fixed effects and residual variance structure as the RRP models and included genetic and permanent environmental random effects for both splines and linear Legendre polynomials of age. The RRP model was used for further analysis because the RRS model had erratic estimates of phenotypic variance and heritability, despite having a smaller Bayesian information criterion than the RRP model. From 91 to 210 d of age, estimates of heritability from the RRP model ranged from 0.10 to 0.37 for boars and 0.14 to 0.26 for gilts for DFI, from 0.39 to 0.58 for boars and 0.55 to 0.61 for gilts for BW, from 0.48 to 0.61 for boars and 0.61 to 0.79 for gilts for BF, and from 0.46 to 0.55 for boars and 0.63 to 0.81 for gilts for LMA. In generation 5, LRFI pigs had lower average genetic curves than CTRL pigs for DFI and BW, especially toward the end of the test period; estimated line differences (CTRL-LRFI) for DFI were 0.04 kg/d for boars and 0.12 kg/d for gilts at 105 d and 0.20 kg/d for boars and 0.24 kg/d for gilts at 195 d. Line differences for BW were 0.17 kg for boars and 0.69 kg for gilts at 105 d and 3.49 kg for boars and 8.96 kg for gilts at 195 d. In conclusion, selection for LRFI has resulted in a lower feed intake curve and a lower BW curve toward maturity.