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.     

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

We quantified the potential increase in accuracy of expected breeding value for weights of Nelore cattle, from birth to mature age, using multi-trait and random regression models on Legendre polynomials and B-spline functions. A total of 87,712 weight records from 8144 females were used, recorded every three months from birth to mature age from the Nelore Brazil Program. For random regression analyses, all female weight records from birth to eight years of age (data set I) were considered. From this general data set, a subset was created (data set II), which included only nine weight records: at birth, weaning, 365 and 550 days of age, and 2, 3, 4, 5, and 6 years of age. Data set II was analyzed using random regression and multi-trait models. The model of analysis included the contemporary group as fixed effects and age of dam as a linear and quadratic covariable. In the random regression analyses, average growth trends were modeled using a cubic regression on orthogonal polynomials of age. Residual variances were modeled by a step function with five classes. Legendre polynomials of fourth and sixth order were utilized to model the direct genetic and animal permanent environmental effects, respectively, while third-order Legendre polynomials were considered for maternal genetic and maternal permanent environmental effects. Quadratic polynomials were applied to model all random effects in random regression models on B-spline functions. Direct genetic and animal permanent environmental effects were modeled using three segments or five coefficients, and genetic maternal and maternal permanent environmental effects were modeled with one segment or three coefficients in the random regression models on B-spline functions. For both data sets (I and II), animals ranked differently according to expected breeding value obtained by random regression or multi-trait models. With random regression models, the highest gains in accuracy were obtained at ages with a low number of weight records. The results indicate that random regression models provide more accurate expected breeding values than the traditionally finite multi-trait models. Thus, higher genetic responses are expected for beef cattle growth traits by replacing a multi-trait model with random regression models for genetic evaluation. B-spline functions could be applied as an alternative to Legendre polynomials to model covariance functions for weights from birth to mature age.     

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.     

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.     

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 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.     

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.     

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.     

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.     

Random regression analyses using B-splines to model growth of Australian Angus cattle

Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses. Basic theory of splines in mixed model analyses is reviewed, and estimates from analyses of weights of Australian Angus cattle from birth to 820 days of age are presented. 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 with age were modelled through B-splines of age at recording. A total of thirteen analyses, considering different combinations of linear, quadratic and cubic B-splines and up to six knots, were carried out. Results showed good agreement for all ages with many records, but fluctuated where data were sparse. On the whole, analyses using B-splines appeared more robust against "end-of-range" problems and yielded more consistent and accurate estimates of the first eigenfunctions than previous, polynomial analyses. A model fitting quadratic B-splines, with knots at 0, 200, 400, 600 and 821 days and a total of 91 covariance components, appeared to be a good compromise between detailedness of the model, number of parameters to be estimated, plausibility of results, and fit, measured as residual mean square error.     

Exploration of cytoplasmic inheritance as a contributor to maternal effects in Welsh Mountain sheep

Cytoplasmic effects were investigated using a dataset comprising three breeding groups of Welsh Mountain sheep. The influences of cytoplasmic effects were investigated by comparing animal models with and without a random term representing cytoplasmic effects. The models were applied to the eight-week weight, scan weight (mean 152 days) and ultrasonically scanned muscle and fat depth. The animal model included the random effects of animals and the maternal additive genetic, maternal permanent environmental and maternal common environmental effects. In total there were 24 569, 10 509, 8389, 8369 records for the eight-week weight, scan weight, muscle depth and fat depth respectively. Four subsets were further analysed containing maternal lines with at least five, ten, fifteen and twenty animals/line. There was no evidence of cytoplasmic effects on eight-week weight and muscle depth. Cytoplasmic effects contributed 1–2% of phenotypic variance for scan-weight and fat depth, but the effect was generally non-significant (P > 0.05). As the number of animals per maternal line increased, the magnitude of cytoplasmic effects also increased for these traits. Direct heritability estimates for the eight-week weight, scan weight, muscle depth and fat depth using the full dataset were 0.18, 0.25, 0.24, and 0.21 respectively.     

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.     

Multiple trait model combining random regressions for daily feed intake with single measured performance traits of growing pigs

A random regression model for daily feed intake and a conventional multiple trait animal model for the four traits average daily gain on test (ADG), feed conversion ratio (FCR), carcass lean content and meat quality index were combined to analyse data from 1 449 castrated male Large White pigs performance tested in two French central testing stations in 1997. Group housed pigs fed ad libitum with electronic feed dispensers were tested from 35 to 100 kg live body weight. A quadratic polynomial in days on test was used as a regression function for weekly means of daily feed intake and to escribe its residual variance. The same fixed (batch) and random (additive genetic, pen and individual permanent environmental) effects were used for regression coefficients of feed intake and single measured traits. Variance components were estimated by means of a Bayesian analysis using Gibbs sampling. Four Gibbs chains were run for 550 000 rounds each, from which 50 000 rounds were discarded from the burn-in period. Estimates of posterior means of covariance matrices were calculated from the remaining two million samples. Low heritabilities of linear and quadratic regression coefficients and their unfavourable genetic correlations with other performance traits reveal that altering the shape of the feed intake curve by direct or indirect selection is difficult.     

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.     

Body condition score of Nellore beef cows: a heritable measure to improve the selection of reproductive and maternal traits

Despite the economic importance of beef cattle production in Brazil, female reproductive performance, which is strongly associated with production efficiency, is not included in the selection index of most breeding programmes due to low heritability and difficulty in measure. The body condition score (BCS) could be used as an indicator of these traits. However, so far little is known about the feasibility of using BCS as a selection tool for reproductive performance in beef cattle. In this study, we investigated the sources of variation in the BCS of Nellore beef cows, quantified its association with reproductive and maternal traits and estimated its heritability. BCS was analysed using a logistic model that included the following effects: contemporary group at weaning, cow weight and hip height, calving order, reconception together with the weight and scores of conformation and early finishing assigned to calves at weaning. In the genetic analysis, variance components of BCS were estimated through Bayesian inference by fitting an animal model that also included the aforementioned effects. The results showed that BCS was significantly associated with all of the reproductive and maternal variables analysed. The estimated posterior mean of heritability of BCS was 0.24 (highest posterior density interval at 95%: 0.093 to 0.385), indicating an involvement of additive gene action in its determination. The present findings show that BCS can be used as a selection criterion for Nellore females.     

Genetic parameters for milk, fat and protein yields in Murrah buffaloes (Bubalus bubalis Artiodactyla, Bovidae)

The objective of the present study was to estimate genetic parameters for test-day milk, fat and protein yields and 305-day-yields in Murrah buffaloes. 4,757 complete lactations of Murrah buffaloes were analyzed. Co-variance components were estimated by the restricted maximum likelihood method. The models included additive direct genetic and permanent environmental effects as random effects, and the fixed effects of contemporary group, milking number and age of the cow at calving as linear and quadratic covariables. Contemporary groups were defined by herd-year-month of test for test-day yields and by herd-year-season of calving for 305-day yields. The heritability estimates obtained by two-trait analysis ranged from 0.15 to 0.24 for milk, 0.16 to 0.23 for protein and 0.13 to 0.22 for fat, yields. Genetic and phenotypic correlations were all positive. The observed population additive genetic variation indicated that selection might be an effective tool in changing population means in milk, fat and protein yields.     

Generating data in models including direct and maternal dominance effects

Algorithms are presented to simulate multiple generations of animal data by a model including direct additive genetic, maternal additive genetic, direct dominance, maternal dominance and permanent environmental effects. Dominance effects were computed as parental subclasses. Testing involved five single trait models that included direct contemporary group and direct additive effects, and different combinations of maternal, permanent environmental, and dominance effects. Simulated populations included 5 generations of animals and 20 contemporary groups per generation. The base population contained 200 sires and 600 dams. Variance components were estimated by Average-Information Restricted Maximum Likelihood (AIREML). No significant bias was observed. The simulation algorithms can be used in research involving dominance models, such as evaluation of mating systems exploiting special combining abilities of prospective parents.     

(Co)variance components, genetic parameters and annual trends for calf weights in a Brahman herd kept on floodable savanna

(Co)variance components and genetic parameters were estimated for body weights of an elite Brahman herd under a designed, supervised management and genetic program, including strategic artificial insemination (AI). Restricted maximum likelihood methods were used with a univariate animal model for birth weight (BW) and a bivariate model for weaning weight (205-day weight, 205W) and 18-month weight (548-day weight, 548W). Models included random animal direct and maternal genetic effects, maternal permanent environmental effect (c2), and sex-year-month of birth-age of dam and genetic group (identified and unidentified paternity), as fixed effects. Analysis A1 included all calves and analysis A2 included only those with identified sires. Of the 8,066 calves born, 36% were progeny of AI, 11% from single sire and 53% from multi-sire herds. They were born from 1985 to 1998, from 2559 dams and 146 sires (78 identified). Estimates of direct, maternal and total heritabilities from A1 for BW, 205W and 548W were: 0.23, 0.07 and 0.30; 0.08, 0.14 and 0.16; 0.16, 0.04 and 0.28, respectively. Corresponding estimates of direct maternal genetic correlations were 0.22, 0.07 and 0.86, and c2 estimates were 0.04, 0.14 and 0.04, respectively. Estimates of direct and maternal genetic, and permanent environmental correlations between 205W and 548W were: 0.66, 0.70 and 1.00. Variances and genetic parameters from A1 and A2 were, in general, very similar. Estimates of phenotypic, and direct and maternal genetic trends per year from A1 were: 0.393, 0.004 and 0.003 kg (BW), 3.367, 0.142 and 0.115 kg (205W), 1.813, 0.263 and 0.095 kg (548W). Estimates of direct and maternal genetic trends from A2 were: 0.033 and -0.002 kg (BW); 0.186 and 0.276 kg (205W); 0.471 and 0.136 kg (548W). The modern selection methods that have been used recently should be continued, with emphasis on the improvement of cow efficiency for sustainable beef production on floodable savanna combined with improved pasture.     

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。