Cubic-spline interpolation to estimate effects of inbreeding on milk yield in first lactation Holstein cows.

Milk yield records (305d, 2X, actual milk yield) of 123,639 registered first lactation Holstein cows were used to compare linear regression (y = ß(0) + ß(1)X + e), quadratic regression, (y = ß(0) + ß(1)X + ß(2)X(2) + e) cubic regression (y = ß(0) + ß(1)X + ß(2)X(2) + ß(3)X(3) +e) and fixed factor models, with cubic-spline interpolation models, for estimating the effects of inbreeding on milk yield. Ten animal models, all with herd-year-season of calving as fixed effect, were compared using the Akaike corrected-Information Criterion (AICc). The cubic-spline interpolation model with seven knots had the lowest AICc, whereas for all those labeled as "traditional", AICc was higher than the best model. Results from fitting inbreeding using a cubic-spline with seven knots were compared to results from fitting inbreeding as a linear covariate or as a fixed factor with seven levels. Estimates of inbreeding effects were not significantly different between the cubic-spline model and the fixed factor model, but were significantly different from the linear regression model. Milk yield decreased significantly at inbreeding levels greater than 9%. Variance component estimates were similar for the three models. Ranking of the top 100 sires with daughter records remained unaffected by the model used.

Cubic-spline interpolation to estimate effects of inbreeding on milk yield in first lactation Holstein cows

Milk yield records (305d, 2X, actual milk yield) of 123,639 registered first lactation Holstein cows were used to compare linear regression (y = β0 + β1X + e) ,quadratic regression, (y = β0 + β1X + β2X2 + e) cubic regression (y = β0 + β1X + β2X2 + β3X3 + e) and fixed factor models, with cubic-spline interpolation models, for estimating the effects of inbreeding on milk yield. Ten animal models, all with herd-year-season of calving as fixed effect, were compared using the Akaike corrected-Information Criterion (AICc). The cubic-spline interpolation model with seven knots had the lowest AICc, whereas for all those labeled as "traditional", AICc was higher than the best model. Results from fitting inbreeding using a cubic-spline with seven knots were compared to results from fitting inbreeding as a linear covariate or as a fixed factor with seven levels. Estimates of inbreeding effects were not significantly different between the cubic-spline model and the fixed factor model, but were significantly different from the linear regression model. Milk yield decreased significantly at inbreeding levels greater than 9 percent. Variance component estimates were similar for the three models. Ranking of the top 100 sires with daughter records remained unaffected by the model used.

Age-of-dam adjustment factors for birth and weaning weight records of beef cattle: a review.

Age-of-dam adjustment factors are used to preadjust birth and weaning weight data for national beef cattle genetic evaluations. Adjustments are used in order to make the means of the different age-of-dam subclasses similar so that a fair comparison of animals can be performed. A review was made of various research studies that have estimated age-of-dam adjustment factors for birth weight and weaning weight of beef cattle. In general, birth weight age-of-dam adjustment factors are the same across the sexes, but weaning weight age-of-dam adjustment factors differ across the sexes, with heifer calves receiving smaller adjustments than their male counterparts. Additionally, adjustment factors vary greatly across breeds. Preadjustment of records is difficult to do because a perfect estimate of adjustments is not possible. A more appropriate method for adjusting for age-of-dam is to simultaneously adjust during national genetic evaluations.

A large-sample QTL study in mice: I. Growth.

By use of long-term selection lines for high and low growth, a large-sample (n = approximately 1,000 F2) experiment was conducted in mice to further understand the genetic architecture of complex polygenic traits. In combination with previous work, we conclude that QTL analysis has reinforced classic polygenic paradigms put in place prior to molecular analysis. Composite interval mapping revealed large numbers of QTL for growth traits with an exponential distribution of magnitudes of effects and validated theoretical expectations regarding gene action. Of particular significance, large effects were detected on Chromosome (Chr) 2. Regions on Chrs 1, 3, 6, 10, 11, and 17 also harbor loci with significant contributions to phenotypic variation for growth. Despite the large sample size, average confidence intervals of approximately 20 cM exhibit the poor resolution for initial estimates of QTL location. Analysis with genome-wide and chromosomal polygenic models revealed that, under certain assumptions, large fractions of the genome may contribute little to phenotypic variation for growth. Only a few epistatic interactions among detected QTL, little statistical support for gender-specific QTL, and significant age effects on genetic architecture were other primary observations from this study.

A large-sample QTL study in mice: II. Body composition.

Using lines of mice having undergone long-term selection for high and low growth, a large-sample (n = approximately 1,000 F2) experiment was conducted to gain further understanding of the genetic architecture of complex polygenic traits. Composite interval mapping on data from male F2 mice (n = 552) detected 50 QTL on 15 chromosomes impacting weights of various organ and adipose subcomponents of growth, including heart, liver, kidney, spleen, testis, and subcutaneous and epididymal fat depots. Nearly all aggregate growth QTL could be interpreted in terms of the organ and fat subcomponents measured. More than 25% of QTL detected map to MMU2, accentuating the relevance of this chromosome to growth and fatness in the context of this cross. Regions of MMU7, 15, and 17 also emerged as important obesity "hot-spots." Average degrees of directional dominance are close to additivity, matching expectations for body composition traits. A strong QTL congruency is evident among heart, liver, kidney, and spleen weights. Liver and testis are organs whose genetic architectures are, respectively, most and least aligned with that for aggregate body weight. In this study, growth and body weight are interpreted in terms of organ subcomponents underlying the macro aggregate traits, and anchored on the corresponding genomic locations.

A large-sample QTL study in mice: III. Reproduction.

Using lines of mice having undergone long-term selection for high and low growth, a large-sample (n approximately to 1000 F2) experiment was conducted to gain further understanding of the genetic architecture of complex polygenic traits. Composite interval mapping on data from 10-week-old F2 females (n = 439) detected 15 quantitative trait loci (QTLs) on 5 chromosomes that influence reproduction traits characterized at day 16 of gestation. These QTL are broadly categorized into two groups: those where effects on the number of live fetuses (LF) were accompanied by parallel effects on the number of dead fetuses (DF), and those free of such undesirable effects. QTL for ovulation rate (OR) did not overlap with QTL for litter size, potentially indicating the importance of uterine capacity. Large dominance effects were identified for most QTL detected, and overdominance was also present. The QTL of largest effects were detected in regions of Chromosome 2, where large QTL effects for growth and fatness have also been found and where corroborating evidence from other studies exists. Considerable overlap between locations of QTL for reproductive traits and for growth traits corresponds well with the positive correlations usually observed among these sets of phenotypes. Some support for the relevance of QTL x genetic background interactions in reproduction was detected. Traits with low heritability demand considerably larger sample sizes to achieve effective power of QTL detection. This is unfortunate as traits with low heritability are among those that could most benefit from QTL-complemented breeding and selection strategies in food animal production.

Sparse inverse of covariance matrix of QTL effects with incomplete marker data.

Gametic models for fitting breeding values at QTL as random effects in outbred populations have become popular because they require few assumptions about the number and distribution of QTL alleles segregating. The covariance matrix of the gametic effects has an inverse that is sparse and can be constructed rapidly by a simple algorithm, provided that all individuals have marker data, but not otherwise. An equivalent model, in which the joint distribution of QTL breeding values and marker genotypes is considered, was shown to generate a covariance matrix with a sparse inverse that can be constructed rapidly with a simple algorithm. This result makes more feasible including QTL as random effects in analyses of large pedigrees for QTL detection and marker assisted selection. Such analyses often use algorithms that rely upon sparseness of the mixed model equations and require the inverse of the covariance matrix, but not the covariance matrix itself. With the proposed model, each individual has two random effects for each possible unordered marker genotype for that individual. Therefore, individuals with marker data have two random effects, just as with the gametic model. To keep the notation and the derivation simple, the method is derived under the assumptions of a single linked marker and that the pedigree does not contain loops. The algorithm could be applied, as an approximate method, to pedigrees that contain loops.

Indices de máximo beneficio económico para la selección de sementales Holstein en México / Maximum profit for Holstein sire selection in Mexico

Se desarrollaron índices para maximizar el beneficio económico en la selección de sementales Holstein para inseminación artifical. Las ponderaciones se obtuvieron a partir de un modelo del beneficio económico con selcción continua, a partir de parámetros biológicos y económicos del proceso de selección en hatos productores de leche en méxico. El índice de beneficio para 10 años de horizonte de inversión fue IB10 = 2.14 X precio por kg de leche X PTAL MEX - 19.92 X precio por dosis de semen. PTAL MEX es la capacidad predicha transmisible (predicted transmiting obility) para la producción de leche en Mexico. El índice de beneficio para 20 años de horizonte de inversión fue IB20 = 5.80 X precio por kg de leche PTAL Mex - 32.12 precio por dosis de semen. El valor económico de un kg de PTAL Mex para un horizonte de 10 años fue 0.107 X precio por kg de leche, el valor para 20 años fue 0.181 X precio por kg de leche. Se discuten aspectos relativos a la aplicación del índice con toros en México y otros países