Estimates of genetic parameters for 320-day pelvic measurements of males and females and calving ease of 2-year-old females.

Records from 12 breed groups collected from 1983 to 1991, included in the Germ Plasm Utilization project at the U.S. Meat Animal Research Center, were analyzed separately by breed group and combined to estimate heritabilities and genetic correlations for 320-d male and female pelvic width, height, and area, and for 320-d male pelvic and female 2-yr-old calving ease. Calving ease was analyzed as a trait of the dam using 1) actual and 2) binary scale calving ease scores with a covariate of calf birth weight. A bivariate animal model and derivative-free REML incorporating sparse matrix techniques were used. When breed groups were analyzed separately, heritability estimates of male and female 320-d pelvic traits varied by breed group and sex. Average genetic correlations between male and female 320-d pelvic width, pelvic height, and pelvic area were large and positive. When breed groups were combined (n = 26,071), heritability estimates for 320-d pelvic traits were moderate in size. Genetic correlations of .68, .48, and .61, between male and female 320-d pelvic width, height, and area, respectively, suggest male and female pelvic traits are largely under the same genetic control but are correlated traits rather than the same trait. Heritability estimates for actual calving ease in 2-yr-olds ranged from .00 to .49 in separate breed group analyses, and from .00 to .37 for binary measures. When breed groups were combined, heritability was .11 for actual calving ease and was .09 on the binary scale.(ABSTRACT TRUNCATED AT 250 WORDS)

Correlations for genetic expression for growth of calves of Hereford and Angus dams using a multivariate animal model.

The purpose of this study was to estimate the correlation between the expression of genes from sires in purebred and crossbred progeny (rPC) and in Hereford and Angus F1 calves (rHA). Performance traits were weights at birth, 200 d, and 365 d. Progeny from Hereford, Polled Hereford, and Angus bulls mated to Hereford or Angus cows were used to estimate rPC. Progeny from Charolais, Shorthorn, Simmental, Limousin, Maine-Anjou, Chianina, Gelbvieh, Tarentaise, and Salers bulls mated to Hereford or Angus cows were used to estimate rHA. Performances in purebreds (P) and crosses (C) or in Hereford (H) and Angus (A) F1 calves were treated as separate traits. A multivariate animal model with birth year-cow age-sex subclasses, random correlated direct and maternal additive genetic effects, and maternal permanent environmental effects was used. Separate analyses were done by breed of sire. A derivative-free algorithm was used to obtain REML estimates of (co)variance components. Weighted averages across breeds of estimates of heritability for P, C, H, and A were, respectively, .61, .51, .47, and .40 for birth weight, .41, .46, .37, and .34 for weaning weight, and .50, .49, .42, and .46 for yearling weight. Estimates of rPC ranged from .88 to .97, .55 to .94, and .68 to .86 for weights at birth, 200 d, and 365 d, respectively. Estimates of rHA ranged from .43 to .99, .56 to .95, and .50 to .98 for weights at birth, 200 d, and 365 d, respectively. Weighted averages of estimates of rPC and rHA across sire breeds were, respectively, .93 and .85 for birth weight, .77 and .73 for weaning weight, and .76 and .86 for yearling weight. These results indicate that ranking of sires producing purebreds or crosses, or crossbred calves from different breeds of dams, is approximately the same for birth and yearling weights, but some reranking might occur for weaning weight.

Sequential transformation for multiple traits for estimation of (co)variance components with a derivative-free algorithm for restricted maximum likelihood.

Transformation of multiple-trait records that undergo sequential selection can be used with derivative-free algorithms to maximize the restricted likelihood in estimation of covariance matrices as with derivative methods. Data transformation with appropriate parts of the Choleski decomposition of the current estimate of the residual covariance matrix results in mixed-model equations that are easily modified from round to round for calculation of the logarithm of the likelihood. The residual sum of squares is the same for transformed and untransformed analyses. Most importantly, the logarithm of the determinant of the untransformed coefficient matrix is an easily determined function of the Choleski decomposition of the residual covariance matrix and the determinant of the transformed coefficient matrix. Thus, the logarithm of the likelihood for any combination of covariance matrices can be determined from the transformed equations. Advantages of transformation are 1) the multiple-trait mixed-model equations are easy to set up, 2) the least squares part of the equations does not change from round to round, 3) right-hand sides change from round to round by constant multipliers, and 4) less memory is required. An example showed only a slight advantage of the transformation compared with no transformation in terms of solution time for each round (1 to 5%).

Estimates of variances due to direct and maternal effects for growth traits of Romanov sheep.

Records of growth traits of 2,086 Romanov lambs were used to estimate variance components for an animal model and genetic correlations between growth traits. Traits analyzed were birth weight (BWT), weaning weight (WW), 90-d weight (W90), and daily gain for the periods birth to weaning (DG1) and weaning to 90 d (DG2). Weaning was at approximately 40 d. Variance components were estimated using restricted maximum likelihood with an animal model including fixed effects for year x season, sex, rearing type, and litter size and random effects for the direct genetic effect of the animal (with relative variance h2), the maternal genetic effect (with relative variance m2), the permanent environmental effect (with relative variance c2), and random residual effect. Genetic correlations were estimated for a model with the same fixed effects and only additive genetic effects. Estimates of the variances of random effects, h2, m2, and c2, respectively, as a proportion of phenotypic variance were .04, .22, .10 (BWT); .34, .25, .0 (WW); .09, .01, .07 (W90); .26, .17, .02 (DG1); and .15, .01, .03 (DG2). Estimates of genetic correlations were .12 (BWT with WW); .24 (BWT with W90); .48 (WW with W90); .69 (DG1 with DG2); -.01 (BWT with DG1); .05 (BWT with DG2); .59 (WW with DG1); .47 (WW with DG2); .67 (W90 with DG1); and .98 (W90 with DG2). Results suggest that selection should be effective for WW, DG1, and DG2 but less effective for BWT and W90. An important maternal effect was observed for BWT, WW, and DG1. The estimates of genetic correlations showed no genetic antagonisms among the traits.

Estimated breeding values for meat characteristics of crossbred cattle with an animal model.

Longissimus muscle area, shear force measure, and sensory panel scores for flavor, juiciness, and tenderness, and marbling score were obtained from 682 steer carcasses, resulting from crosses among five Bos taurus and Bos indicus breeds. The single-trait model used included birth year and as covariates breed fractions, weaning age, and days on feed. The numerator relationship matrix was for 1,350 animals (682 steers, 74 pure breed and 52 F1-cross sires and 542 dams). The coefficient matrix was inverted to examine standard errors of prediction. Estimated breeding value is the sum of the estimate of genetic deviation and the weighted (fractions) sum of estimates of breed effects. Heritabilities used in estimating breeding values were .62, .06, .05, .11, .05, and .43 for longissimus muscle area, shear force, flavor, juiciness, tenderness, and marbling score. Sires within a breed or crossbred group tended to rank similarly due to large differences among breed effects (e.g., the six Sahiwal sires ranked in the highest six places for shear force). These results illustrate that for traits with large breed differences, selection of the proper breed should be done before selection within that breed.

Derivative-free restricted maximum likelihood estimation in animal models with a sparse matrix solver.

Estimation of (co)variance components by derivative-free REML requires repeated evaluation of the log-likelihood function of the data. Gaussian elimination of the augmented mixed model coefficient matrix is often used to evaluate the likelihood function, but it can be costly for animal models with large coefficient matrices. This study investigated the use of a direct sparse matrix solver to obtain the log-likelihood function. The sparse matrix package SPARSPAK was used to reorder the mixed model equations once and then repeatedly to solve the equations by Cholesky factorization to generate the terms required to calculate the likelihood. The animal model used for comparison contained 19 fixed levels, 470 maternal permanent environmental effects, and 1586 direct and 1586 maternal genetic effects, resulting in a coefficient matrix of order 3661 with .3% nonzero elements after including numerator relationships. Compared with estimation via Gaussian elimination of the unordered system, utilization of SPARSPAK required 605 and 240 times less central processing unit time on mainframes and personal computers, respectively. The SPARSPAK package also required less memory and provided solutions for all effects in the model.

Estimates of genetic parameters for direct and maternal effects on embryonic survival in swine.

Survival of 16,838 potential embryos was determined by counting corpora lutea and fetuses at 50 d of gestation for 1,081 litters by 225 sires. These data, coded as 1 or 0 depending on whether an ovulation was represented by a fetus, were used to estimate direct and maternal additive genetic variances and their covariance for embryonic survival. Data were from first-parity gilts of a Large White-Landrace composite population subdivided into two lines, one selected for an index of ovulation rate and embryonic survival for seven generations and a contemporary control line. Variance components were obtained by ANOVA and expectations of covariances among relatives and by derivative-free restricted maximum likelihood (DFREML) in an animal model. As a trait of the embryo, heritability of direct effects obtained with ANOVA was 3.8%, heritability of maternal effects was 1.5%, and the genetic correlation between them was -.51. After adjustment of embryonic survival for ovulation rate, lower estimates of each parameter were obtained with ANOVA. Heritability of embryonic survival as a trait of the dam was 9 to 10%. Estimates of heritability of both direct and maternal effects obtained with DFREML were less than 1% and the genetic correlation between them was -.64. When survival of embryos from only those dams with 15 or more ovulations was analyzed, heritability of maternal effects was 4.4%. Estimates of common environmental effects on embryonic survival ranged from 5 to 7%.

Association of sire dystocia transmitting ability with progeny linear type traits in Holsteins.

Data on 13 traits of 11,260 progeny of 775 sires in the Carnation Genetics linear type appraisal program were analyzed to determine the association between sire dystocia transmitting ability and progeny linear type traits. Mean linear type scores ranged from 25.0 to 29.8 on a scale of 1 to 50. Parity, stage of lactation, and interactions of evaluator by parity and evaluator by stage were sources of variation for most traits. First quartile (easy) and fourth quartile (most difficult) sires grouped by dystocia transmitting ability differed in daughter linear type scores for stature, dairy character, rump angle, center ligament, udder depth, teat length, teat placement, and rump width. Differential use of easy calving bulls on heifers might result in progeny with lower type scores for stature, dairy character, rump angle, legs, and rump width. Average type scores differed by less than 1 unit for all traits, indicating little correlated response in linear type traits through use of bulls whose progeny are born with least difficulty.

Genetic trend for milk yield from doe evaluations in the northeast United States.

Milk production records of 306 Alpine, 72 LaMancha, 170 Nubian, 84 Saanen, and 235 Toggenburg does born in the Northeast from 1972 through 1979 were used to estimate trends of additive genetic value. Estimated transmitting abilities were doubled and averaged for all does born in each year to obtain yearly estimates of genetic value. Genetic trends from regression of yearly mean genetic value on year of birth for Alpine, LaMancha, Nubian, Saanen, and Toggenburg averaged 11.4, -7.9, 1.9, 14.6, and 11.7 kg per year. Genetic trends were less than theoretically possible, indicating that more effective selection schemes are needed, although because of the limited number of does, the trends may not represent actual trends.