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1.
Rules for forming the mixed-model equations for the reduced animal model with all relationships and including maternal effects have been set out by Quaas and Pollak. They also have shown how to simplify the mixed-model equations when genetic group effects are included in the model with what has become known as the Q-P transformation. Westell has given rules for calculating the coefficients for the Q-P transformed equations that are associated with the inverse of the numerator relationship matrix and genetic group effects. Those rules can be extended to include maternal effects and genetic groups for maternal as well as direct effects. As with the rules of Quaas and Pollak for the equations for the reduced animal model, a similar set of rules can be obtained for the genetic groups model after the Q-P transformation. The rules are derived easily by examining the algebraic results of absorbing the direct and maternal breeding value equations for non-parents into the parent breeding value, group and fixed effects equations. These rules involve Westell's rules and the inverse elements of the genetic (co)variance matrix for direct and maternal additive genetic effects. The rules make calculation of breeding values for parents for models including direct and maternal genetic group effects nearly as easy as for models without genetic group effects. Back solution for direct and maternal breeding values of non-parents similarly is as simple as when genetic group effects are not in the model.  相似文献   

2.
Effects of foster dams can be included in genetic evaluations using animal models with maternal effects in several ways. The alternatives discussed involve minor changes in computing strategies from strategies used with reduced animal models that predict breeding values for direct and maternal effects. The easiest alternative is to assign foster dams to groups by breed and time period and add equations for fixed effects of breed-period. Random and, assumed, independent effects of foster dams can be nested in breed-period groups. If foster dams do not repeat, then those effects can be absorbed into equations for other fixed effects, additive direct breeding value and breed-period effects by slightly modifying least squares contributions to coefficients of those equations. A third alternative for foster dams of the same breed is to add breeding values for foster dams for direct and maternal effects to solution vectors for breeding values. Equations are similar to those without foster dams, except that least squares contributions to coefficient matrix and right-hand sides are to equations for maternal breeding values and nongenetic maternal effects of foster dams rather than biological dams. Relationships and covariance between direct and maternal effects contribute mixed-model coefficients to direct and maternal breeding value equations of biological dams. This alternative basically requires only larger solution vectors for direct and maternal breeding values to accommodate foster dams that might not be included. The fourth alternative includes a vector of maternal breeding values for foster dams of each breed of foster dams and would require using rules of Westell to calculate coefficients due to relationships and fixed maternal genetic groups within each breed of foster dam. These alternatives do not require much additional computational effort compared with full or reduced animal model equations when the transformation to predict breeding values is used with Westell's rules to calculate coefficients due to relationships and genetic group effects due to prior genetic selection.  相似文献   

3.
Variance and covariance components were estimated for weaning weight from Senepol field data for use in the reduced animal model for a maternally influenced trait. The 4,634 weaning records were used to evaluate 113 sires and 1,406 dams on the island of St. Croix. Estimates of direct additive genetic variance (sigma 2A), maternal additive genetic variance (sigma 2M), covariance between direct and maternal additive genetic effects (sigma AM), permanent maternal environmental variance (sigma 2PE), and residual variance (sigma 2 epsilon) were calculated by equating variances estimated from a sire-dam model and a sire-maternal grandsire model, with and without the inverse of the numerator relationship matrix (A-1), to their expectations. Estimates were sigma 2A, 139.05 and 138.14 kg2; sigma 2M, 307.04 and 288.90 kg2; sigma AM, -117.57 and -103.76 kg2; sigma 2PE, -258.35 and -243.40 kg2; and sigma 2 epsilon, 588.18 and 577.72 kg2 with and without A-1, respectively. Heritability estimates for direct additive (h2A) were .211 and .210 with and without A-1, respectively. Heritability estimates for maternal additive (h2M) were .47 and .44 with and without A-1, respectively. Correlations between direct and maternal (IAM) effects were -.57 and -.52 with and without A-1, respectively.  相似文献   

4.
Reliabilities for a multiple-trait maternal model were obtained by combining reliabilities obtained from single-trait models. Single-trait reliabilities were obtained using an approximation that supported models with additive and permanent environmental effects. For the direct effect, the maternal and permanent environmental variances were assigned to the residual. For the maternal effect, variance of the direct effect was assigned to the residual. Data included 10,550 birth weight, 11,819 weaning weight, and 3,617 postweaning gain records of Senepol cattle. Reliabilities were obtained by generalized inversion and by using single-trait and multiple-trait approximation methods. Some reliabilities obtained by inversion were negative because inbreeding was ignored in calculating the inverse of the relationship matrix. The multiple-trait approximation method reduced the bias of approximation when compared with the single-trait method. The correlations between reliabilities obtained by inversion and by multiple-trait procedures for the direct effect were 0.85 for birth weight, 0.94 for weaning weight, and 0.96 for postweaning gain. Correlations for maternal effects for birth weight and weaning weight were 0.96 to 0.98 for both approximations. Further improvements can be achieved by refining the single-trait procedures.  相似文献   

5.
First parity calving difficulty scores from Italian Piemontese cattle were analysed using a threshold mixed effects model. The model included the fixed effects of age of dam and sex of calf and their interaction and the random effects of sire, maternal grandsire, and herd‐year‐season. Covariances between sire and maternal grandsire effects were modelled using a numerator relationship matrix based on male ancestors. Field data consisted of 23 953 records collected between 1989 and 1998 from 4741 herd‐year‐seasons. Variance and covariance components were estimated using two alternative approximate marginal maximum likelihood (MML) methods, one based on expectation‐maximization (EM) and the other based on Laplacian integration. Inferences were compared to those based on three separate runs or sequences of Markov Chain Monte Carlo (MCMC) sampling in order to assess the validity of approximate MML estimates derived from data with similar size and design structure. Point estimates of direct heritability were 0.24, 0.25 and 0.26 for EM, Laplacian and MCMC (posterior mean), respectively, whereas corresponding maternal heritability estimates were 0.10, 0.11 and 0.12, respectively. The covariance between additive direct and maternal effects was found to be not different from zero based on MCMC‐derived confidence sets. The conventional joint modal estimates of sire effects and associated standard errors based on MML estimates of variance and covariance components differed little from the respective posterior means and standard deviations derived from MCMC. Therefore, there may be little need to pursue computation‐intensive MCMC methods for inference on genetic parameters and genetic merits using conventional threshold sire and maternal grandsire models for large datasets on calving ease.  相似文献   

6.
Although epistatic effects are well defined and, in principle, can be exploited in quantitative-genetic selection theory, they often are ignored or even treated as nuisance parameters in practical applications. Traditionally, epistasis is considered as an interaction between genes at unspecified loci. Inspired by the observation that functional genes are often organised in physical clusters, we developed a model to combine additive effects and additive × additive interactions in linked gene clusters of defined length. Malécot's kinship concept is extended to identity by descent probabilities for chromosome segments of a given length in Morgan units, called epistatic kinship. Using the analogy of Malécot's kinship and Wright's relationship and inbreeding coefficients, epistatic relationship coefficients and epistatic inbreeding coefficients are defined. Simple rules are given to set up the epistatic numerator relationship matrix and its inverse directly from a pedigree list. The well-known single locus parameters and algorithms to set up the additive numerator relationship matrix and its inverse are a special case of the suggested methodology for a chromosome segment length of null Morgan. A proof of concept of the suggested method is given with a small simulation study. Assuming additive, linked epistatic and residual variance components, 100 replicated data sets for 1000 individuals are generated. From these data, residual maximum likelihood estimates of the variance components and of the chromosome segment size are obtained. Potential applications of the methodology are discussed. Given that a substantial variance component is attributed to this effect, the expected genetic gain can be increased on the short term if selection is on additive and epistatic effects, the latter comprising additive × additive interaction effect of loci in linkage disequilibrium. This extra benefit, however, will diminish through crossing over in subsequent generations. Despite some practical problems yet to be solved, the suggested model and algorithms open new perspectives to use a higher proportion of genetic variability in selection and breeding.  相似文献   

7.
(Co)variance components, direct and maternal breed additive, dominance, and epistatic loss effects on preweaning weight gain of beef cattle were estimated. Data were from 478,466 animals in Ontario, Canada, from 1986 to 1999, including records of both purebred and crossbred animals from Angus, Blonde d'Aquitaine, Charolais, Gelbvieh, Hereford, Limousin, Maine-Anjou, Salers, Shorthorn, and Simmental breeds. The genetic model included fixed direct and maternal breed additive, dominance, and epistatic loss effects, fixed environmental effects of age of the calf, contemporary group, and age of the dam x sex of the calf, random additive direct and maternal genetic effects, and random maternal permanent environment effects. Estimates of direct and maternal additive genetic, maternal permanent environmental and residual variances, expressed as proportions of the phenotypic variance, were 0.32, 0.20, 0.12, and 0.52, respectively. Correlation between direct and maternal additive genetic effects was -0.63. Breed ranking was similar to previous studies, but estimates showed large SE. The favorable effects of direct and maternal dominance (P < 0.05) on preweaning gain were equivalent to 1.3 and 2.3% of the phenotypic mean of purebred calves, respectively. The same features for direct and maternal epistatic loss effects were -2.2% (P < 0.05) and -0.1% (P > 0.05). The large SE of breed effects were likely due to multicollinearity among predictor variables and deficiencies in the dataset to separate direct and maternal effects and may result in a less reliable ranking of the animals for across breed comparisons. Further research to identify the causes of the instability of estimates of breed additive, dominance, and epistatic loss genetic effects, and application of alternative statistical methods is recommended.  相似文献   

8.
Several studies have noted high negative correlations between maternal genetic and direct additive effects and their influence on additive and maternal heritability of early growth traits in sheep. Multigeneration data from the Suffolk Sire Reference Scheme (SSRS) were used to investigate the effect of data structure on estimates of direct and maternal (co)variances for lamb 8-wk weight. In all analyses the additive, maternal genetic, maternal environmental, and residual effects were fitted along with the covariance between direct and maternal additive effects. The contributions of particular genetic relationships to the estimates were studied by analyzing subsets of the SSRS data. A further eight subsets were formed having 10% or 50% of the dams with their own records and having one or two, three or four, five or six, and more than six offspring per dam. Analysis of data having only 10% of the dams with their own record and one or two offspring records yielded a high negative correlation (-0.99) between direct and maternal genetic effects. However, the seven other data sets with more records per dam or a higher proportion of dams with their own records produced values of -0.35 to -0.51. Data structure and the number of dams and granddams with records are important determinants of estimated direct and maternal effects in early growth traits.  相似文献   

9.
Mixed-model equations for the reduced animal model with maternal effects and different genetic grouping of unknown parents for additive direct and maternal effects are derived. The matrices that relate the expected value and the variance of the breeding values of non-parents to the parents, as well as the different contributions of parental and non-parental breeding values, to the resulting mixed-model equations are presented. Mis-specification of additive maternal variance and the additive covariance between direct and maternal effects, arising from missing information on the dams of known individuals with records, is discussed. To avoid an incorrect specification of the variance-covariance matrix of the records without having to invert a nondiagonal variance of the residual terms, the breeding values of the unknown dams of individuals with records are included in the equations. Breeding values of non-parents are back-solved after the solutions for genetic groups and breeding values of parents are computed as simply as in cases in which maternal effects are absent. A numerical example is included to illustrate the derivations.  相似文献   

10.
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.  相似文献   

11.
Calving ease scores from Holstein dairy cattle in the Walloon Region of Belgium were analysed using univariate linear and threshold animal models. Variance components and derived genetic parameters were estimated from a data set including 33 155 calving records. Included in the models were season, herd and sex of calf × age of dam classes × group of calvings interaction as fixed effects, herd × year of calving, maternal permanent environment and animal direct and maternal additive genetic as random effects. Models were fitted with the genetic correlation between direct and maternal additive genetic effects either estimated or constrained to zero. Direct heritability for calving ease was approximately 8% with linear models and approximately 12% with threshold models. Maternal heritabilities were approximately 2 and 4%, respectively. Genetic correlation between direct and maternal additive effects was found to be not significantly different from zero. Models were compared in terms of goodness of fit and predictive ability. Criteria of comparison such as mean squared error, correlation between observed and predicted calving ease scores as well as between estimated breeding values were estimated from 85 118 calving records. The results provided few differences between linear and threshold models even though correlations between estimated breeding values from subsets of data for sires with progeny from linear model were 17 and 23% greater for direct and maternal genetic effects, respectively, than from threshold model. For the purpose of genetic evaluation for calving ease in Walloon Holstein dairy cattle, the linear animal model without covariance between direct and maternal additive effects was found to be the best choice.  相似文献   

12.
The objective of this study was to examine the feasibility of using random regression-spline (RR-spline) models for fitting growth traits in a multibreed beef cattle population. To meet the objective, the results from the RR-spline model were compared with the widely used multitrait (MT) model when both were fit to a data set (1.8 million records and 1.1 million animals) provided by the American Gelbvieh Association. The effect of prior information on the EBV of sires was also investigated. In both RR-spline and MT models, the following effects were considered: individual direct and maternal additive genetic effects, contemporary group, age of the animal at measurement, direct and maternal heterosis, and direct and maternal additive genetic mean effect of the breed. Additionally, the RR-spline model included an individual direct permanent environmental effect. When both MT and RR-spline models were applied to a data set containing records for weaning weight (WWT) and yearling weight (YWT) within specified age ranges, the rankings of bulls' direct EBV (as measured via Pearson correlations) provided by both models were comparable, with slightly greater differences in the reranking of bulls observed for YWT evaluations (>or=0.99 for BWT and WWT and >or=0.98 for YWT); also, some bulls dropped from the top 100 list when these lists were compared across methods. For maternal effects, the estimated correlations were slightly smaller, particularly for YWT; again, some drops from the top 100 animals were observed. As in regular MT multibreed genetic evaluations, the heterosis effects and the additive genetic effects of the breed could not be estimated from field data, because there were not enough contemporary groups with the proper composition of purebred and crossbred animals; thus, prior information based on literature values had to be included. The inclusion of prior information had a negligible effect in the overall ranking for bulls with greater than 20 birth weight progeny records; however, the effect of prior information for breeds or groups poorly represented in the data was important. The Pearson correlations for direct and maternal WWT and YWT ranged from 0.95 to 0.98 when comparing evaluations of data sets for which the out-of-range age records were removed or retained. Random regression allows for avoiding the discarding of records that are outside the usual age ranges of measurement; thus, greater accuracies are achieved, and greater genetic progress could be expected.  相似文献   

13.
Variances and covariances for birth weight, gain from birth to weaning (ADG), and 205-d weight were obtained from a sire-dam model and a sire-maternal grandsire model for a herd of Angus and a herd of Hereford cattle. Estimates of direct additive genetic variance (sigma 2A), maternal additive genetic variance (sigma 2M), covariance between direct and maternal additive genetic effects (sigma AM), permanent environmental variance (sigma 2PE), and residual variance (sigma 2e) were obtained both with and without the inverse of the numerator relationship matrix (A-1) included. Estimates of heritability for direct genetic effects (h2A), maternal genetic effects (h2M), and the correlation between direct and maternal effects (rAM) for birth weight were .37, .18, and -.01 in Angus and .53, .23, and -.19 in Herefords, respectively, for the analyses without A-1. For the analyses with A-1, estimates of h2A, h2M, and rAM were .42, .22, and -.12 for Angus and .58, .22, and -.13 for Herefords, respectively. Estimates of h2A, h2M, and rAM for ADG were .43, .15, and -.44 in Angus and .52, .38, and -.03 in Herefords, respectively, without A-1. With A-1, estimates of h2A, h2M, and rAM were .57, .15, and -.32 for Angus and .58, .39, and -.05 for Herefords, respectively. Estimates of h2A, h2M, and rAM for 205-d weight were .49, .15, and -.46 for Angus and .58, .43, and -.06 for Herefords, respectively, without A-1. With A-1, estimates of h2A, h2M, and rAM were .63, .16, and -.36 for Angus and .66, .43, and -.08 for Herefords, respectively. Estimates of h2A were higher with A-1 than without A-1, but estimates of h2M were similar. Using variances and covariances obtained from analyses including A-1 generally gave higher estimates of direct breeding values than using variances and covariances obtained from analyses not including A-1. Both Pearson product-moment and Spearman rank correlations were high (.99) between estimates of breeding values from the two analyses, although some changes in rank did occur.  相似文献   

14.
The present study was conducted on 1,002 reproductive records of 430 Jersey crossbred cattle, descended from 57 sires and 198 dams, maintained at the Eastern Regional Station of ICAR-National Dairy Research Institute, Kalyani, Nadia, West Bengal, India to investigate the influence of direct genetic, maternal genetic and maternal permanent environmental effect on three most important reproductive traits viz., number of service per conception (NSPC), days open (DO) and calving interval (CI) of Jersey crossbred cattle. Six single-trait animal models (including or excluding maternal genetic or permanent environmental effects) were fitted to analyse these traits, and the best model was chosen after testing the significant increase in the log-likelihood values when additional parameters were added in the model. Direct heritability estimates for NSPC, DO and CI from the best model were 0.10, 0.14 and 0.20, respectively. The maternal permanent environmental (c2) effects on reproductive traits accounted for almost negligible fraction of the total phenotypic variance in this study. The maternal genetic effects (m2) also contributed very little (0%–3%) to the total phenotypic variance except for CI where it was important and accounted for 20% of phenotypic variance. A significantly large negative genetic correlation was observed between direct and maternal genetic effects for all traits, suggesting the presence of antagonistic relationship between dam's direct additive component and daughter's additive genetic component. Results suggest that both direct and maternal effects were important only for CI but not for other traits. Therefore, both direct additive effects and maternal genetic effect need to be considered for improving this trait by selection.  相似文献   

15.
Genomic imprinting should be considered in animal breeding systems to avoid lead in bias in genetic parameter estimation. The objective of this study was to clarify the effects of pedigree information on imprinting variances for carcass traits and fatty acid composition in Japanese Black cattle. Carcass records [carcass weight, rib eye area, rib thickness (RT), subcutaneous fat thickness and beef marbling score (BMS)] and fatty acid composition were obtained for 11,855 Japanese Black feedlot cattle. To estimate and compare the imprinting variances for the traits, two imprinting models with different pedigree information [the sire–dam gametic relationship matrix (Model 1) and the sire–maternal grandsire (MGS) numerator relationship matrix (Model 2)] were fitted. The ratio of the imprinting variance to the total additive genetic variance for RT (6.33%) and BMS (19.00%) was significant in Model 1, but only that for BMS (21.09%) was significant in Model 2. This study revealed that fitting the sire–MGS model could be useful in estimating imprinting variance under certain conditions, such as when restricted pedigree information is available. Furthermore, the present result suggested that the maternal gametic effects on BMS should be included in breeding programmes for Japanese Black cattle to avoid selection bias caused by imprinting effects.  相似文献   

16.
Parameters for direct and maternal dominance were estimated in models that included non-additive genetic effects. The analyses used weaning weight records adjusted for age of dam from populations of Canadian Hereford (n = 467,814), American Gelbvieh (n = 501,552), and American Charolais (n = 314,552). Method R estimates of direct additive genetic, maternal additive genetic, permanent maternal environment, direct dominance, and maternal dominance variances as a proportion of the total variance were 23, 12, 13, 19, and 14% in Hereford; 27, 7, 10, 18, and 2% in Gelbvieh; and 34, 15, 15, 23, and 2% in Charolais. The correlations between direct and maternal additive genetic effects were -0.30, -0.23, and -0.47 in Hereford, Gelbvieh, and Charolais, respectively. The correlations between direct and maternal dominance were -0.38, -0.02, and -0.04 in Hereford, Gelbvieh, and Charolais, respectively. Estimates of inbreeding depression were -0.20, -0.18, and -0.13 kg per 1% of inbreeding for Hereford, Gelbvieh, and Charolais, respectively. Estimates of the maternal inbreeding depression were -0.01, -0.02, and -0.02 kg, respectively. The high ratio of direct dominance to additive genetic variances provided some evidence that direct dominance effects should be considered in beef cattle evaluation. However, maternal dominance effects seemed to be important only for Hereford cattle.  相似文献   

17.
Animals bred in pastoral systems are often part of multiple-sire groups, introducing uncertainty into pedigrees. Genetic evaluation of sires and dams in such instances is complicated by the uncertainty of parenthood. This article defines a simple and rapid algorithm to compute the inverse of a numerator relationship matrix under uncertain parenthood. The algorithm can accommodate inbreeding and uncertainty of parenthood on both paternal and maternal sides of the pedigree.  相似文献   

18.
Maternal effects are an important source of variation in early growth and body traits in sheep but are often excluded from genetic analyses. Maternal additive genetic, maternal environmental, and cytoplasmic effects were investigated in a large Suffolk breeding scheme using a range of models involving different combinations of these effects with the direct additive genetic effect. Weights at 8 wk of age and at scanning (mean age 146 d) and ultrasonically measured muscle and fat depth were analyzed using an animal model on 55,683 (8-wk weight) and 28,947 (scanning traits) lamb records. Simple additive models always overestimated the heritability of all traits when compared to more complex models. The successive inclusion of maternal environmental, maternal genetic, and the covariance between direct and maternal additive effects in the model significantly improved the fit for almost all models and all traits, as indicated by a likelihood ratio test. Under the full model, the heritability of both weight traits was low (0.14 and 0.20 for 8-wk and scanning weight, respectively). The maternal additive and maternal environmental effects, as a proportion of the phenotypic variance, were similar (0.10 and 0.08 for 8-wk weight and 0.07 and 0.06 for scanning weight). The two scanning traits had higher heritabilities (0.29 and 0.27 for muscle depth and fat depth, respectively) with low levels of maternal genetic and maternal environmental variance. No evidence was found of a cytoplasmic effect on any of the traits studied under the full model. Breeding schemes for early growth and body traits in sheep should account for maternal effects in their genetic evaluations in order to improve their accuracy. The exact model to use will depend on the trait and individual circumstances of the scheme.  相似文献   

19.
Estimates of (co)variance and genetic parameters of birth, weaning (205 days) and yearling (365 days) weight were obtained using single-trait animal models. The data were analysed by restricted maximum likelihood, fitting an animal model that included direct and maternal genetic and permanent environmental effects. The data included records collected between 1976 and 2001. The pedigree information extended as far back as early 1960s. The heritabilities for direct effects of birth, weaning and yearling weights were 0.36, 0.29 and 0.25, respectively. Heritability estimates for maternal effects were 0.13, 0.16 and 0.15 for birth, weaning and yearling weights, respectively. The correlations between direct and maternal additive genetic effects were negative for all traits analysed. The results indicate that both direct and maternal effects should be included in a selection programme for all the traits analysed.  相似文献   

20.
绵羊生长性状母本效应方差组分、遗传参数估计的研究   总被引:5,自引:0,他引:5  
本文利用公畜母畜模型和公畜外祖父模型估计了初生重、断奶重的直接加性遗传方差、母本遗传方差和遗传参数,得出初生重的直接加性遗传效应、母本遗传效应和总的加性遗传效应的遗传力分别为:0.164、0.101、0.103;断奶重相应的各遗传力为:0.076、0.108、0.081。初生重和断奶重二性状加性遗传效应和母本遗传效应间的遗传相关为:-0.57和-0.36。  相似文献   

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