Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle.

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polynomial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high.     

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.     

Estimation of correlation between maternal permanent environmental effects of related dams in beef cattle

Weaning weights from Gelbvieh (GV; n = 82,138) and Limousin (LM; n = 88,639) calves were used to estimate genetic and environmental variance components with models that included different values for the correlation (lambda) between permanent environmental effects of dams and their daughters. Each analysis included fixed discrete effects of contemporary group, sex of calf, age of dam at calving, and month of calving, a fixed continuous effect of age of calf, random direct and maternal additive genetic effects, permanent environmental effects due to dams, and residual effects. The REML procedure was employed with a "grid search," in which the likelihood was computed for a series of values for lambda. For both breeds, models that included a nonzero value for lambda fitted the data significantly better than the model that did not include lambda. The maximum restricted likelihood was obtained for lambda of approximately -0.2 for both breeds. Estimates of residual and direct genetic variances were similar for all values of lambda, including zero; however, estimates of maternal genetic variance and maternal heritability increased slightly, and maternal permanent environmental variance and the proportion of the maternal variance to the total (phenotypic) variance decreased slightly, when the correlated structure for permanent environmental effects was assumed. As the value of lambda became more negative, absolute values of the direct-maternal genetic covariance and direct-maternal correlation estimates were decreased. Pearson and rank correlations for direct genetic, maternal genetic, and maternal environmental effects estimated with and without lambda were very high (>0.99). These results indicated that the linear relationship between maternal permanent environmental effects of dams and their daughters for weaning weight is negative but low in both breeds. Considering this relationship in the operational model did not significantly affect estimated breeding values, and thus, it may not be important in genetic evaluations.     

Effects of sire misidentification on estimates of genetic parameters for birth and weaning weights in Hereford cattle

Birth weights (4,155) and weaning weights (3,884) of Line 1 Herefords collected at the Fort Keogh Livestock and Range Research Laboratory in Miles City, MT, between the years of 1935 to 1989 were available. To study the effect of misidentification on estimates of genetic parameters, the sire identification of calf was randomly replaced by the identification of another sire based on the fraction of progeny each sire contributed to a yearly calf crop. Misidentification rates ranged from 5 to 50% with increments of 5%. For each rate of misidentification, 100 replicates were obtained and analyzed with single-trait and two-trait analyses with a restricted maximum likelihood (REML) algorithm. Two different models were used. Both models contained year x sex combinations and ages of dam as fixed effects, calendar birth date as a fixed covariate, and random animal and maternal genetic effects and maternal permanent environment effects. Model 2 also included sire x year combinations as random effects. As the rate of misidentification increased, estimates of the direct-maternal genetic correlation increased for both traits, with both models, for all analyses. With singletrait analyses, estimates of the fraction of variance that were due to sire x year interaction effects increased slightly for birth weight (near zero) and decreased slightly (0.015 to 0.004) for weaning weight as misidentification increased. With two-trait analyses, estimates of fraction of variance that were due to sire x year effects gradually decreased for weaning weight as misidentification increased. With the two-trait analyses, and with both models, as the level of sire misidentification increased, estimates of the genetic correlation between direct effects gradually increased, and estimates of the correlation between maternal effects gradually decreased. Estimates of the direct-maternal genetic correlation were more positive with Model 2 than with Model 1 for all levels of misidentification. Results of this study indicate that misidentification of sires would severely bias estimates of genetic parameters and would reduce genetic gain from selection.     

Direct and maternal (co)variance components and heritability estimates for body weights in Chokla sheep

Estimates of (co)variance components were obtained for weights at birth, weaning and 6, 9 and 12 months of age in Chokla sheep maintained at the Central Sheep and Wool Research Institute, Avikanagar, Rajasthan, India, over a period of 21 years (1980–2000). Records of 2030 lambs descended from 150 rams and 616 ewes were used in the study. Analyses were carried out by restricted maximum likelihood (REML) fitting an animal model and ignoring or including maternal genetic or permanent environmental effects. Six different animal models were fitted for all traits. The best model was chosen after testing the improvement of the log-likelihood values. Direct heritability estimates were inflated substantially for all traits when maternal effects were ignored. Heritability estimates for weight at birth, weaning and 6, 9 and 12 months of age were 0.20, 0.18, 0.16, 0.22 and 0.23, respectively in the best models. Additive maternal and maternal permanent environmental effects were both significant at birth, accounting for 9% and 12% of phenotypic variance, respectively, but the source of maternal effects (additive versus permanent environmental) at later ages could not be clearly identified. The estimated repeatabilities across years of ewe effects on lamb body weights were 0.26, 0.14, 0.12, 0.13, and 0.15 at birth, weaning, 6, 9 and 12 months of age, respectively. These results indicate that modest rates of genetic progress are possible for all weights.     

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.     

Genetic parameters for nuclear and nonnuclear inheritance in three synthetic lines of beef cattle differing in mature size.

Genetic parameters for nuclear and cytoplasmic genetic effects were estimated from preweaning growth data collected on three synthetic lines of beef cattle differing in mature size. Lines of small-, medium-, and large-framed calves were represented in each of two research herds (Rhodes and McNay). Variance components were estimated separately by herd and size line for birth weight and 205-d weight (WW) by REML with an animal mode using an average of 847 and 427 calf records from Rhodes and McNay, respectively. Model 1 included effects of fixed year, sex of calf, age of dam, and random additive direct (a), additive maternal genetic (m), covariance (a,m), permanent environment affecting the dam, and residual error. Model 2 differed from Model 1 by including random cytoplasmic lineage effects and by ignoring permanent environmental effects. Model 1--direct (maternal) heritability estimates for birth weight at Rhodes were .62(.03) for small, .67(.06) for medium, and .30(.11) for large lines. Genetic correlations between direct and maternal effects for birth weight were .67, -.16, and .48 for the respective size groups. For WW at Rhodes, direct (maternal) heritability estimates were .30(.29), .30(.14), and .10(.16) for small, medium, and large lines, respectively, with genetic correlations of -.34 (small), -.12 (medium), and .17 (large). Heritability estimates at McNay were similar to those at Rhodes, except that maternal genetic heritabilities for WW were smaller (.10, small; .01, medium; .00, large). Model 2--estimates for nuclear genetic effects were consistent with the estimates from Model 1. Cytoplasmic variance accounted for 0 to 5% of the total random variance in birth weight. For WW, cytoplasmic variance was negligible at Rhodes and accounted for 4% of the total random variance in the large line at McNay, averaging less than the permanent environment. Results failed to indicate that cytoplasmic variance was important for preweaning performance.     

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.     

Age of dam and sex of calf adjustments and genetic parameters for gestation length in Charolais cattle

To estimate adjustment factors and genetic parameters for gestation length (GES), AI and calving date records (n = 40,356) were extracted from the Canadian Charolais Association field database. The average time from AI to calving date was 285.2 d (SD = 4.49 d) and ranged from 274 to 296 d. Fixed effects were sex of calf, age of dam (2, 3, 4, 5 to 10, > or = 11 yr), and gestation contemporary group (year of birth x herd of origin). Variance components were estimated using REML and 4 animal models (n = 84,332) containing from 0 to 3 random maternal effects. Model 1 (M1) contained only direct genetic effects. Model 2 (M2) was G1 plus maternal genetic effects with the direct x maternal genetic covariance constrained to zero, and model 3 (M3) was G2 without the covariance constraint. Model 4 (M4) extended G3 to include a random maternal permanent environmental effect. Direct heritability estimates were high and similar among all models (0.61 to 0.64), and maternal heritability estimates were low, ranging from 0.01 (M2) to 0.09 (M3). Likelihood ratio tests and parameter estimates suggested that M4 was the most appropriate (P < 0.05) model. With M4, phenotypic variance (18.35 d2) was partitioned into direct and maternal genetic, and maternal permanent environmental components (hd2 = 0.64 +/- 0.04, hm2 = 0.07 +/- 0.01, r(d,m) = -0.37 +/- 0.06, and c2 = 0.03 +/- 0.01, respectively). Linear contrasts were used to estimate that bull calves gestated 1.26 d longer (P < 0.02) than heifers, and adjustments to a mature equivalent (5 to 10 yr old) age of dam were 1.49 (P < 0.01), 0.56 (P < 0.01), 0.33 (P < 0.01), and -0.24 (P < 0.14) d for GES records of calves born to 2-, 3-, 4-, and > or = 11-yr-old cows, respectively. Bivariate animal models were used to estimate genetic parameters for GES with birth and adjusted 205-d weaning weights, and postweaning gain. Direct GES was positively correlated with direct birth weight (BWT; 0.34 +/- 0.04) but negatively correlated with maternal BWT (-0.20 +/- 0.07). Maternal GES had a low, negative genetic correlation with direct BWT (-0.15 +/- 0.05) but a high and positive genetic correlation with maternal BWT (0.62 +/- 0.07). Generally, GES had near-zero genetic correlations with direct and maternal weaning weights. Results suggest that important genetic associations exist for GES with BWT, but genetic correlations with weaning weight and postweaning gain were less important.     

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.     

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 for growth traits for a composite terminal sire breed of sheep.

Records of 9,055 lambs from a composite population originating from crossing Columbia rams to Hampshire x Suffolk ewes at the U.S. Meat Animal Research Center were used to estimate genetic parameters among growth traits. Traits analyzed were weights at birth (BWT), weaning (7 wk, WWT), 19 mo (W19), and 31 mo (W31) and postweaning ADG from 9 to 18 or 19 wk of age. The ADG was also divided into daily gain of males (DGM) and daily gain of females (DGF). These two traits were analyzed with W19 and with W31 in three-trait analyses. (Co)variance components were estimated with REML for an animal model that included fixed effects of sex, age of dam, type of birth or rearing, and contemporary group. Random effects were direct and maternal genetic of animal and dam with genetic covariance, maternal permanent environmental, and random residual. Estimates of direct heritability were .09, .09, .35, .44, .19, .16, and .23 for BWT, WWT, W19, W31, ADG, DGM, and DGF, respectively. Estimates of maternal permanent environmental variance as a proportion of phenotypic variance were .09, .12, .03, .03, .03, .06, and .02, respectively. Estimates of maternal heritability were .17 and .09 for BWT and WWT and .01 to .03 for other traits. Estimates of genetic correlations were large among W19, W31, and ADG (.69 to .97), small between BWT and W31 or ADG, and moderate for other pairs of traits (.32 to .45). The estimate of genetic correlation between DGM and DGF was .94, and the correlation between maternal permanent environmental effects for these traits was .56. For the three-trait analyses, the genetic correlations of DGM and DGF with W19 were .69 and .82 and with W31 were .67 and .67, respectively. Results show that models for genetic evaluation for BWT and WWT should include maternal genetic effects. Estimates of genetic correlations show that selection for ADG in either sex can be from records of either sex (DGM or DGF) and that selection for daily gain will result in increases in mature weight but that BWT is not correlated with weight at 31 mo.     

Estimation of direct, maternal, and grandmaternal genetic effects for weaning weight in several breeds of beef cattle.

Weaning weights from nine parental breeds and three composites were analyzed to estimate variance due to grandmaternal genetic effects and to compare estimates for variance due to maternal genetic effects from two different models. Number of observations ranged from 794 to 3,465 per population. Number of animals in the pedigree file ranged from 1,244 to 4,326 per population. Two single-trait animal models were used to obtain estimates of covariance components by REML using an average information method. Model 1 included random direct and maternal genetic, permanent maternal environmental, and residual environmental effects as well as fixed sex x year and age of dam effects. Model 2 in addition included random grandmaternal genetic and permanent grandmaternal environmental effects to account for maternal effects of a cow on her daughter's maternal ability. Non-zero estimates of proportion of variance due to grandmaternal effects were obtained for 7 of the 12 populations and ranged from .03 to .06. Direct heritability estimates in these populations were similar with both models. Existence of variance due to grandmaternal effects did not affect the estimates of maternal heritability (m2) or the correlation between direct and maternal genetic effects (r(am)) for Angus and Gelbvieh. For the other five populations, magnitude of estimates increased for both m2 and r(am) when estimates of variance due to grandmaternal effects were not zero. Estimates of the correlation between maternal and grandmaternal genetic effects were large and negative. These results suggest that grand-maternal effects exist in some populations, that when such effects are ignored in analyses maternal heritability may be underestimated, and that the correlation between direct and maternal genetic effects may be biased downward if grandmaternal effects are not included in the model for weaning weight of beef cattle.     

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.     

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.     

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.     

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.     

Estimation of maternal variance components considering cow-calf contacts under extensive pastoral systems

Traditional methods of variance component estimation for traits under maternal influence consist of partitioning the variance into direct additive genetic, maternal additive genetic, permanent maternal environmental, and error variance components. This partitioning is based on the assumption that each calf is nurtured and fed exclusively by its own dam. However, under extensive pastoral systems, voluntary cross-suckling may occur and could be quantified by using contact loggers recording cow-calf affiliations. A simulation study was conducted to test several variance models for partitioning maternal variation by including information on cow-calf contacts. The results indicated that weighting maternal genetic and permanent maternal environmental effects by the relative time calves spent with particular cows, including their own mothers, is feasible and significantly increased the log-likelihood of the models. However, the interpretation of the variance components in terms of traditional direct and maternal heritability is no longer straightforward. The need for further research and implications for the industry are discussed.     

Genetic analysis on body weight at different ages in broiler chicken raised in commercial environment

A multivariate model was developed and used to estimate genetic parameters of body weight (BW) at 1–6 weeks of age of broilers raised in a commercial environment. The development of model was based on the predictive ability of breeding values evaluated from a cross-validation procedure that relied on half-sib correlation. The multivariate model accounted for heterogeneous variances between sexes through standardization applied to male and female BWs differently. It was found that the direct additive genetic, permanent environmental maternal and residual variances for BW increased drastically as broilers aged. The drastic increase in variances over weeks of age was mainly due to scaling effects. The ratio of the permanent environmental maternal variance to phenotypic variance decreased gradually with increasing age. Heritability of BW traits ranged from 0.28 to 0.33 at different weeks of age. The direct genetic effects on consecutive weekly BWs had high genetic correlations (0.85–0.99), but the genetic correlations between early and late BWs were low (0.32–0.57). The difference in variance components between sexes increased with increasing age. In conclusion, the permanent environmental maternal effect on broiler chicken BW decreased with increasing age from weeks 1 to 6. Potential bias of the model that considered identical variances for sexes could be reduced when heterogeneous variances between sexes are accounted for in the model.     

Association of a genetic marker with blood serum insulin-like growth factor-I concentration and growth traits in Angus cattle

The objective of this research was to evaluate a biallelic genetic marker identified in the first promoter region of the bovine IGF-I gene. The point mutation was identified as a T-to-C transition by sequencing the polymorphic fragments. A PCR-RFLP procedure was developed for determining the marker genotypes. Marker genotypes were determined for 760 Angus calves from divergent lines that were created by selection for high or low serum IGF-I concentration (allele A: 63.9%, B: 36.1%). Data were analyzed using the multiple-trait derivative-free restricted maximum likelihood computer programs with animal models. The full animal model included fixed effects of marker genotype, birth year, season of birth, sex, age of dam, and selection line; random effects of animal, maternal genetic, and maternal permanent environmental effects; and a covariate for age of calf. Traits analyzed included blood serum IGF-I concentrations on d 28, 42, and 56 of the postweaning test, mean IGF-I concentration, birth weight, weaning weight, on-test weight, off-test weight, off-test hip height, postweaning gain, and weight gain during the 20-d period immediately after weaning. Results from the analysis across selection lines showed a significant association of the BB genotype with higher weight gain during the first 20 d after weaning and a slight dominance effect of the marker on postweaning gain. Analysis within the low IGF-I line also showed a significant association of the BB genotype with higher weight gain during the first 20 d after weaning and with on-test weight, although analysis within the high IGF-I line did not show any significant association. The associated effects of the marker need to be verified in other cattle populations.