Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. 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 appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.     

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.     

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.     

Genetic parameters of body weight in sheep estimated via random regression and multi-trait animal models

Variance components for five consecutive measurements of body weight in Polish sheep were estimated using random regression and multi-trait animal models. The data included between 7856 and 31694 body weight records at 5 age classes from birth to 150 days of age. The random additive genetic, maternal environmental and individual permanent environmental effects were fitted. All variance components were increasing over time (not at equal rates), which reflects increasing phenotypic mean and variance with age. Direct heritability tended to increase with age, whereas the effect of dam was reduced for older ages, and the proportion of permanent environmental component was relatively stable. Generally, similar tendencies were registered for estimates obtained via multi-trait animal model. The results confirm that there is a scope for genetic improvement in growth pattern in Polish sheep.     

Polynomials to model the growth of young bulls in performance tests

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.     

Estimates of direct and maternal covariance functions for growth of Australian beef calves from birth to weaning

Records for birth and subsequent, monthly weights until weaning on beef calves of two breeds in a selection experiment were analysed fitting random regression models. Independent variables were orthogonal (Legendre) polynomials of age at weighing in days. Orders of polynomial fit up to 6 were considered. Analyses were carried out fitting sets of random regression coefficients due to animals'' direct and maternal, additive genetic and permanent environmental effects, with changes in variances due to temporary environmental effects modelled through a variance function, estimating up to 67 parameters. Results identified similar patterns of variation for both breeds, with maternal effects considerably more important in purebred Polled Herefords than a four-breed synthetic, the so-called Wokalups. Conversely, repeatabilities were higher for the latter. For both breeds, heritabilities decreased after birth, being lowest when maternal effects were most important around 100 days of age. Estimates at birth and weaning were consistent with previous, univariate results.     

Genetic parameters for stayability to consecutive calvings in Zebu cattle

Longer-lived cows tend to be more profitable and the stayability trait is a selection criterion correlated to longevity. An alternative to the traditional approach to evaluate stayability is its definition based on consecutive calvings, whose main advantage is the more accurate evaluation of young bulls. However, no study using this alternative approach has been conducted for Zebu breeds. Therefore, the objective of this study was to compare linear random regression models to fit stayability to consecutive calvings of Guzerá, Nelore and Tabapuã cows and to estimate genetic parameters for this trait in the respective breeds. Data up to the eighth calving were used. The models included the fixed effects of age at first calving and year-season of birth of the cow and the random effects of contemporary group, additive genetic, permanent environmental and residual. Random regressions were modeled by orthogonal Legendre polynomials of order 1 to 4 (2 to 5 coefficients) for contemporary group, additive genetic and permanent environmental effects. Using Deviance Information Criterion as the selection criterion, the model with 4 regression coefficients for each effect was the most adequate for the Nelore and Tabapuã breeds and the model with 5 coefficients is recommended for the Guzerá breed. For Guzerá, heritabilities ranged from 0.05 to 0.08, showing a quadratic trend with a peak between the fourth and sixth calving. For the Nelore and Tabapuã breeds, the estimates ranged from 0.03 to 0.07 and from 0.03 to 0.08, respectively, and increased with increasing calving number. The additive genetic correlations exhibited a similar trend among breeds and were higher for stayability between closer calvings. Even between more distant calvings (second v. eighth), stayability showed a moderate to high genetic correlation, which was 0.77, 0.57 and 0.79 for the Guzerá, Nelore and Tabapuã breeds, respectively. For Guzerá, when the models with 4 or 5 regression coefficients were compared, the rank correlations between predicted breeding values for the intercept were always higher than 0.99, indicating the possibility of practical application of the least parameterized model. In conclusion, the model with 4 random regression coefficients is recommended for the genetic evaluation of stayability to consecutive calvings in Zebu cattle.     

Estimation of genetic parameters for monthly egg production in laying hens based on random regression models

Heritability and genetic correlations of monthly egg production under random regression models were estimated. Three layer lines (A22, A88, K66) in six consecutive generations were analysed. A22 (13, 770 recorded hens) and A88 (13, 950 recorded hens) are maternal lines of Rhode Island White birds selected on egg production and shell colour; K66 (9, 351 recorded birds) is a paternal line of Rhode Island Red birds selected on egg weight. Eight models with different orders of Legendre polynomials were applied. Adequacy of the models was checked by the Akaike Information Criterion. According to the most adequate model including second order Legendre polynomials for fixed effects and third order for additive genetic and permanent environmental effects, relatively high heritabilities were estimated in the first (h²=0.3) and final (h² above 0.3) periods of production with a substantial decrease in heritability during the egg production peak. Methodology based on random regression animal models can be recommended for genetic evaluation of laying hens.     

Milk yield persistency in Brazilian Gyr cattle based on a random regression model

With the objective of evaluating measures of milk yield persistency, 27,000 test-day milk yield records from 3362 first lactations of Brazilian Gyr cows that calved between 1990 and 2007 were analyzed with a random regression model. Random, additive genetic and permanent environmental effects were modeled using Legendre polynomials of order 4 and 5, respectively. Residual variance was modeled using five classes. The average lactation curve was modeled using a fourth-order Legendre polynomial. Heritability estimates for measures of persistency ranged from 0.10 to 0.25. Genetic correlations between measures of persistency and 305-day milk yield (Y305) ranged from -0.52 to 0.03. At high selection intensities for persistency measures and Y305, few animals were selected in common. As the selection intensity for the two traits decreased, a higher percentage of animals were selected in common. The average predicted breeding values for Y305 according to year of birth of the cows had a substantial annual genetic gain. In contrast, no improvement in the average persistency breeding value was observed. We conclude that selection for total milk yield during lactation does not identify bulls or cows that are genetically superior in terms of milk yield persistency. A measure of persistency represented by the sum of deviations of estimated breeding value for days 31 to 280 in relation to estimated breeding value for day 30 should be preferred in genetic evaluations of this trait in the Gyr breed, since this measure showed a medium heritability and a genetic correlation with 305-day milk yield close to zero. In addition, this measure is more adequate at the time of peak lactation, which occurs between days 25 and 30 after calving in this breed.     

Genetic analysis of body weights of individually fed beef bulls in South Africa using random regression models

The aim of this study was to estimate genetic parameters for body weights of individually fed beef bulls measured at centralized testing stations in South Africa using random regression models. Weekly body weights of Bonsmara bulls (N = 2919) tested between 1999 and 2003 were available for the analyses. The model included a fixed regression of the body weights on fourth-order orthogonal Legendre polynomials of the actual days on test (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, and 84) for starting age and contemporary group effects. Random regressions on fourth-order orthogonal Legendre polynomials of the actual days on test were included for additive genetic effects and additional uncorrelated random effects of the weaning-herd-year and the permanent environment of the animal. Residual effects were assumed to be independently distributed with heterogeneous variance for each test day. Variance ratios for additive genetic, permanent environment and weaning-herd-year for weekly body weights at different test days ranged from 0.26 to 0.29, 0.37 to 0.44 and 0.26 to 0.34, respectively. The weaning-herd-year was found to have a significant effect on the variation of body weights of bulls despite a 28-day adjustment period. Genetic correlations amongst body weights at different test days were high, ranging from 0.89 to 1.00. Heritability estimates were comparable to literature using multivariate models. Therefore, random regression model could be applied in the genetic evaluation of body weight of individually fed beef bulls in South Africa.     

Genetic parameter estimates and response to selection for weight and testicular traits in Nelore cattle

We estimated genetic parameters for various phases of body and testicular growth until 550 days of age in Nelore cattle, using Bayesian inference, including correlation values and error estimates. Weight and scrotal records of 54,182 Nelore animals originating from 18 farms participating in the Brazilian Nelore Breeding Program (PMGRN) were included. The following traits were measured: weight at standard ages of 120 (W120), 210 (W210), 365 (W365), 450 (W450), and 550 (W550) days; weight gain between 120/210 (WG1), 210/365 (WG2), 365/450 (WG3), 450/550 (WG4), 120/365 (WG5), 120/450 (WG6), 120/550 (WG7), 210/450 (WG8), 210/550 (WG9), and 365/550 (WG10) days of age; scrotal circumference at 365 (SC365), 450 (SC450) and 550 (SC550) days of age, and testicular growth between 365/450 (TG1), 450/550 (TG2) and 365/550 (TG3) days of age. The model included contemporary group (current farm, year and two-month period of birth, sex, and management group) and age of dam at calving, divided into classes as fixed effects. The model also included random effects for direct additive, maternal additive and maternal permanent environmental, and residual effects. The direct heritability estimates ranged from 0.23 to 0.39, 0.13 to 0.39 and 0.32 to 0.56 for weights at standard ages, weight gains and testicular measures, respectively. The genetic correlations between weights (0.69 to 0.94) and scrotal circumferences (0.91 to 0.97) measured at standard ages were higher than those between weight gain and testicular growth (0.18 to 0.97 and 0.36 to 0.77, respectively). The weights at standard ages responded more effectively to selection, and also gave strong correlations with the other traits.     

Genetic modelling of test day records in dairy sheep using orthogonal Legendre polynomials

Test day milk yields of three lactations in Sfakia sheep were analyzed fitting a random regression (RR) model, regressing on orthogonal polynomials of the stage of the lactation period, i.e. days in milk. Univariate (UV) and multivariate (MV) analyses were also performed for four stages of the lactation period, represented by average days in milk, i.e. 15, 45, 70 and 105 days, to compare estimates obtained from RR models with estimates from UV and MV analyses. The total number of test day records were 790, 1314 and 1041 obtained from 214, 342 and 303 ewes in the first, second and third lactation, respectively. Error variances and covariances between regression coefficients were estimated by restricted maximum likelihood. Models were compared using likelihood ratio tests (LRTs). Log likelihoods were not significantly reduced when the rank of the orthogonal Legendre polynomials (LPs) of lactation stage was reduced from 4 to 2 and homogenous variances for lactation stages within lactations were considered. Mean weighted heritability estimates with RR models were 0.19, 0.09 and 0.08 for first, second and third lactation, respectively. The respective estimates obtained from UV analyses were 0.14, 0.12 and 0.08, respectively. Mean permanent environmental variance, as a proportion of the total, was high at all stages and lactations ranging from 0.54 to 0.71. Within lactations, genetic and permanent environmental correlations between lactation stages were in the range from 0.36 to 0.99 and 0.76 to 0.99, respectively. Genetic parameters for additive genetic and permanent environmental effects obtained from RR models were different from those obtained from UV and MV analyses.     

母体遗传效应对青海细毛羊生产性能遗传参数估计的影响

为了研究母体遗传效应对青海细毛羊生长性状、产毛性状的影响,文章采用平均信息最大约束似然法应用不同混合动物模型估计青海细毛羊生产性状的遗传参数,并采用似然比检验对不同模型进行比较分析。各模型中均包括固定效应、个体直接加性遗传效应、残差效应;随机效应为:个体永久环境效应、母体遗传效应、母体永久环境效应。不同模型对随机效应作了不同考虑:模型1不考虑个体永久环境效应、母体遗传效应、母体永久环境效应;模型2考虑母体永久环境效应;模型3考虑母体遗传效应;模型4考虑母体遗传效应和母体永久环境效应;模型5考虑个体永久环境效应和母体遗传效应;模型6考虑个体永久环境效应、母体遗传效应、母体永久环境效应。各模型估计的初生重遗传力为:0.1896~0.3781;断奶重遗传力为:0.2537~0.2890;周岁重遗传力范围:0.2244~0.3225;成年羊体重遗传力范围:0.2205~0.3983;产毛量遗传力为:0.1218~0.1490;羊毛细度遗传力为:0.0983~0.4802;羊毛长度遗传力为:0.1170~0.1311。与模型1相比,模型3对于初生重、断奶重差异显著(P<0.01),对于周岁重、成年羊体重各模型与模型1的似然比检验差异不显著(P>0.05);与模型6相比,模型4、5对于羊毛细度差异显著(P<0.01),模型4对羊毛长度差异显著(P<0.05),对于产毛量各模型与模型6似然比检验差异不显著(P>0.05)。生长性状中初生重、断奶重受母体遗传效应影响显著,周岁重、成年羊体重受母体遗传效应影响不显著;产毛性状中羊毛细度、长度受母体遗传效应影响显著,产毛量受母体遗传效应影响较弱。     

母体遗传效应对青海细毛羊生产性能遗传参数估计的影响

为了研究母体遗传效应对青海细毛羊生长性状、产毛性状的影响, 文章采用平均信息最大约束似然法应用不同混合动物模型估计青海细毛羊生产性状的遗传参数, 并采用似然比检验对不同模型进行比较分析。各模型中均包括固定效应、个体直接加性遗传效应、残差效应; 随机效应为：个体永久环境效应、母体遗传效应、母体永久环境效应。不同模型对随机效应作了不同考虑：模型1不考虑个体永久环境效应、母体遗传效应、母体永久环境效应; 模型2考虑母体永久环境效应; 模型3考虑母体遗传效应; 模型4考虑母体遗传效应和母体永久环境效应; 模型5考虑个体永久环境效应和母体遗传效应; 模型6考虑个体永久环境效应、母体遗传效应、母体永久环境效应。各模型估计的初生重遗传力为：0.1896~0.3781; 断奶重遗传力为：0.2537~0.2890; 周岁重遗传力范围：0.2244~0.3225; 成年羊体重遗传力范围：0.2205~0.3983; 产毛量遗传力为：0.1218~0.1490; 羊毛细度遗传力为：0.0983~0.4802; 羊毛长度遗传力为：0.1170~0.1311。与模型1相比, 模型3对于初生重、断奶重差异显著(P<0.01), 对于周岁重、成年羊体重各模型与模型1的似然比检验差异不显著(P>0.05); 与模型6相比, 模型4、5对于羊毛细度差异显著(P<0.01), 模型4对羊毛长度差异显著(P<0.05), 对于产毛量各模型与模型6似然比检验差异不显著(P>0.05)。生长性状中初生重、断奶重受母体遗传效应影响显著, 周岁重、成年羊体重受母体遗传效应影响不显著; 产毛性状中羊毛细度、长度受母体遗传效应影响显著, 产毛量受母体遗传效应影响较弱。     

Estimating genetic covariance functions assuming a parametric correlation structure for environmental effects

A random regression model for the analysis of "repeated" records in animal breeding is described which combines a random regression approach for additive genetic and other random effects with the assumption of a parametric correlation structure for within animal covariances. Both stationary and non-stationary correlation models involving a small number of parameters are considered. Heterogeneity in within animal variances is modelled through polynomial variance functions. Estimation of parameters describing the dispersion structure of such model by restricted maximum likelihood via an "average information" algorithm is outlined. An application to mature weight records of beef cow is given, and results are contrasted to those from analyses fitting sets of random regression coefficients for permanent environmental effects.     

(Co)Variance components and genetic parameter estimates for growth traits in Moghani sheep

Genetic parameters were estimated for birth weight (BW), weaning weight (WW), yearling weight (YW), average daily gain from birth to weaning (ADG1) and average daily gain from weaning to yearling (ADG2) in Moghani sheep. Maximum number of data was 4237 at birth, but only 1389 records at yearling were investigated. The data was collected from 1995 to 2007 at the Breeding Station of Moghani sheep in Jafarabad, Moghan, Iran. (Co)Variance components and genetic parameters were estimated with different models which including direct effects, with and without maternal additive genetic effects as well as maternal permanent environmental effects using restricted maximum likelihood (REML) method. The most appropriate model for each trait was determined based on likelihood ratio tests and Akaike's Information Criterion (AIC). Maternal effects were important only for pre-weaning traits. Direct heritability estimates for BW, ADG1, WW, ADG2 and YW were 0.07, 0.08, 0.09, 0.09 and 0.17, respectively. Fractions of variance due to maternal permanent environmental effects on phenotypic variance were 0.08 for ADG1. Maternal heritability estimates for BW and WW were 0.18 and 0.06, respectively. Multivariate analysis was performed using the most appropriate models obtained in univariate analysis. Direct genetic correlations among studied traits were positive and ranged from 0.37 for BW–ADG2 to 0.85 for ADG1–YW. Maternal genetic correlation estimate between BW and WW was 0.33. Phenotypic and environmental correlation estimates were generally lower than those of genetic correlation. Low direct heritability estimates imply that mass selection for these traits results in slow genetic gain.     

Genetic parameter estimates for pre-weaning performance and reproduction traits in Markhoz goats

Genetic parameters for growth, mortality and reproductive performances of Markhoz goats were estimated from data collected during 1993–2010 at Markhoz goat Performance Testing Station in Sanandaj, Iran. For kid performance traits 3763 records were available for birth weight (BW), 2931 for weaning weight (WW), average daily gain (ADG) and Kleiber ratio (KR) (approximated as ADW/WW^0.75) and 3032 for pre-weaning mortality (PWM). For doe reproductive performance traits there were 2920 records available for litter size at birth (LSB), litter size at weaning (LSW), total litter weight at birth (TLWB) and litter mean weight per kid born (LMWKB), and 2182 for total litter weight at weaned (TLWW) and litter mean weight per kid weaned (LMWKW). Genetic parameters were estimated with univariate and bivariate models using restricted maximum likelihood (REML) procedures. Random effects were explored by fitting additive direct genetic effects, maternal additive genetic effects, maternal permanent environmental effects, the covariance between direct and maternal genetic effects, and common litter effects in different models for pre-weaning traits of kids. Also, in addition to an animal model, sire and threshold models, using a logit link function, were used for analyses of PWM. Models for LSB, LSW, TLWB, TLWW, LMWKB, and LMWKW included direct additive genetic effects, permanent environmental effects due to the animal as well as service sire effects. Estimated direct heritabilities were moderate for pre-weaning traits (0.22 for BW, 0.16 for WW, 0.21 for ADG, and 0.27 for KR and 0.29 for PWM), and low for reproduction traits (0.01 for LSB, 0.01 for LSW, 0.02 for TLWB, 0.03 for TLWW, 0.07 for LMWKB, and 0.06 for LMWKW). The estimates for the maternal additive genetic variance ratios were lower than direct heritability for BW (0.07) and KR (0.04). The estimate for the maternal permanent environmental variance ratios (c²) varied from 0.01 for KR to 0.07 for WW and ADG. The magnitude of common litter variance ratios (l²) was more substantial for BW (0.46) than the PWM (0.19) and KR (0.16). The estimate for the permanent environmental variance due to the animal (c²) ranged from 0.03 for LMWKB to 0.07 for TLWB and LMWKW, whereas service sire effects (s²) ranged from 0.02 to 0.04. The correlation between direct and maternal genetic effects were negative and high for BW (?0.51) and KR (?0.62). The genetic correlations between pre-weaning growth traits were positive and moderate to strong, as were genetic correlations between reproductive traits. Between BW and PWM the correlation was ?0.35. Phenotypic and environmental correlations for all traits were generally lower than genetic correlations.     

Estimates of (co)variance components due to direct and maternal effects for body weights in Jamunapari goats

Estimates of (co)variance components were obtained for weights at birth, weaning and at 6, 9 and 12 months of age in Jamunapari goats maintained at the Central Institute for Research on Goats, Makhdoom, Mathura, India, over a period of 23 years (1982 to 2004). Records of 4301 kids descended from 204 sires and 1233 does 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 weights at birth, weaning and at 6, 9 and 12 months of age were 0.12, 0.18, 0.13, 0.17 and 0.21, respectively. Maternal heritability of body weight declined from 0.19 at birth to 0.08 at weaning and was near zero and not significant thereafter. Estimates of the fraction of variance due to maternal permanent environmental effects were 0.09, 0.13 and 0.10 for body weights at weaning, 6 months and 9 months of age, respectively. Results suggest that maternal additive effects were important only in the early stages of growth, whereas a permanent environmental maternal effect existed from weaning to 9 months of age. These results indicate that modest rates of genetic progress appear possible for all weights.     

National evaluation for calving ease,gestation length and birth weight by linear and threshold model methodologies

Data included 393,097 calving ease, 129,520 gestation length, and 412,484 birth weight records on 412,484 Gelbvieh cattle. Additionally, pedigrees were available on 72,123 animals. Included in the models were effects of sex and age of dam, treated as fixed, as well as direct, maternal genetic and permanent environmental effects and effects of contemporary group (herd-year-season), treated as random. In all analyses, birth weight and gestation length were treated as continuous traits. Calving ease (CE) was treated either as a continuous trait in a mixed linear model (LM), or as a categorical trait in linear-threshold models (LTM). Solutions in TM obtained by empirical Bayes (TMEB) and Monte Carlo (TMMC) methodologies were compared with those by LM. Due to the computational cost, only 10,000 samples were obtained for TMMC. For calving ease, correlations between LM and TMEB were 0.86 and 0.78 for direct and maternal genetic effects, respectively. The same correlations but between TMEB and TMMC were 1.00 and 0.98, respectively. The correlations between LM and TMMC were 0.85 and 0.75, respectively. The correlations for the linear traits were above.97 between LM and TMEB but as low as 0.91 between LM and TMMC, suggesting insufficient convergence of TMMC. Computing time required was about 2 hrs, 5 hrs, and 6 days for LM, TMEB and TMMC, respectively, and memory requirements were 169, 171, and 445 megabytes, respectively. Bayesian implementation of threshold model is simple, can be extended to multiple categorical traits, and allows easy calculation of accuracies; however, computing time is prohibitively long for large models.     

Estimation of genetic parameters and variance components for growth traits in Romosinuano cattle in the Colombian humid tropics

(Co)variance components and genetic parameters were estimated for body weights of a Romosinuano herd located in Sinú Valley, Cordoba, Colombia. Restricted maximum likelihood methods were used with a univariate animal model for birth weight, weaning weight (270 days), 16-month weight (480 days), weaning daily gain, and post-weaning daily gain. Models included random animal direct and maternal genetic effects, maternal permanent environmental effect (c2), and sex-year-month of birth and age of dam, as fixed effects. Estimates of direct effect for birth weight, weaning weight, 480-day weight, weaning daily gain, and post-weaning daily gain were: 0.25 +/- 0.0001, 0.34 +/- 0.063, 0.33 +/- 0.066, 0.32 +/- 0.062, and 0.17 +/- 0.052, respectively. Estimates of direct maternal genetic effects were low and ranged from 0.06 +/- 0.003 for birth weight to 0.20 +/- 0.054 for weaning daily gain. The genetic correlations between direct and maternal genetic effects were negative and low for 480-day weight (-0.05 +/- 0.219) and showed values of -0.37 +/- 0.007, -0.34 +/- 0.133, -0.33 +/- 0.135, and -0.38 +/- 0.232 for birth, weaning weight, weaning, and post-weaning daily gain, respectively. Permanent environmental maternal effects were not significant; the highest values were found for weaning weight, and weaning daily gain (0.086 +/- 0.031 and 0.078 +/- 0.031, respectively). We conclude that direct and maternal effects should be included in a selection program for all of these traits, and also that selection of weaning weights would be the most productive way to improve performance in Romosinuano cattle.