Allometric comparison of Georgia dairy heifers on farms and at youth shows.

Studies were conducted to determine the relationship between allometric measures of growth of Holstein dairy heifers and placing in the show ring, and to compare differences in growth between Holstein heifers that are shown and not shown. In the first study, 494 Holstein show heifers were evaluated at the 2012 and 2013 Georgia Junior National Livestock Shows. Measurements were obtained for weight, head length, withers height, hip height, thurl width, and tail length. Heifer mass index (HMI), average daily gain (ADG), and age were calculated. In total, 72.5% of Holstein show heifers were underweight. Average ADG was 0.63 kg/d, which is below the industry recommendation of 0.7 to 0.8 kg/d. Variables were ranked and converted to percentages to account for differences in class size. Withers height, head length, and HMI were most indicative of show placing. In the second study, we compared differences between growth patterns of show heifers and non-show heifers. An additional 293 non-show Holstein heifers were evaluated on 3 Georgia dairy farms during the same period as the show. In total, 43.3% of non-show heifers were underweight. Average ADG for non-show heifers was 0.71 kg/d, which is within the industry recommendation of 0.7 to 0.8 kg/d. Show heifers weighed less for their age than non-show heifers and tended to be taller at the withers than non-show heifers. The HMI scores were similar for younger show and non-show heifers, but older show heifers had lower HMI scores than non-show heifers of the same age. Show heifers had HMI scores that were lower than values calculated from standard growth data. As show heifers matured, ADG decreased, whereas as non-show heifers matured, ADG increased. Youth, leaders, and parents need to be aware of the importance of growing replacement heifers correctly so that heifers calve at 22 to 24 mo of age at an acceptable size and scale and become profitable members of the milking herd.

Estimation of regional genetic parameters for mortality and 305-d milk yield of US Holsteins in the first 3 parities.

Several research reports have indicated increasing dairy cow mortality in recent years. The objectives of this research were to characterize the phenotypic differences in mortality in the first 3 parities across 3 regions of the United States to estimate the heritability of mortality of Holstein cows across regions and parities, and to estimate genetic and environmental correlations between milk yield and mortality across parities and regions. Dairy Herd Information (DHI) milk yield and mortality data were obtained from 3 different US regions: the Southeast (SE), Southwest (SW), and Northeast (NE). A total of 3,522,824 records for the first 3 parities were used: 732,009 (SE), 656,768 (SW), and 2,134,047 (NE) from 1999 to 2008. Cows that received a termination code of 6--"Cow died on the dairy; downer cows that were euthanized should be included here"--were given a mortality score of 2 (dead), whereas all other codes were assigned a mortality score of 1 (alive). Average annual mortalities in the first 3 parities across regions ranged from 2.2 to 7.2%, with mortality frequency increasing with increasing parity across all regions and with the SE having the highest mortality frequency. For genetic analysis, a 2-trait (305-d milk yield and mortality) linear-threshold animal model that fitted fixed effects of herd-year (for 305-d milk yield), cow age, days in milk (in month classes), month-of-termination, and random effects of herd-year (for mortality), animal, and residual was implemented. The model was used to estimate variance components separately for each region and parity. Heritability estimates for mortality were similar for all regions and parities, ranging from 0.04 to 0.07. Genetic correlations between mortality and 305-d milk yield across the first 3 parities were 0.14, 0.20, and 0.29 in SE; -0.01, 0.01, and 0.31 in SW; and 0.28, 0.33, and 0.19 in NE. We detected an adverse genetic relationship between milk production and mortality; however, the moderate magnitudes of the genetic correlations suggest that indices that include both milk yield and mortality could be effective in identifying sires that would provide opportunities for minimizing death loss even when selecting for increased milk yield.

The relationship between weight, age, and average daily gain to show performance of Georgia 4-H and Future Farmers of America (FFA) commercial dairy heifers.

Three studies were conducted to determine the relationship between dairy heifer growth and placing in the show ring. In the first study, 1,744 commercial dairy heifers (all breeds and crossbred animals) were evaluated to determine effects of growth on placing within Georgia Commercial Dairy Heifer Shows from 2007 to 2010. Birth weights were determined using breed birth weight averages, with crossbreeds being the average of 2 parent breeds. Average daily gains (ADG) were calculated and heifers were given rankings based on placing in show and for age and weight. Data was analyzed using the Spearman correlation calculations in the SAS software (SAS Institute Inc., Cary, NC). Age and ADG were inversely correlated (r=-0.89). Mean ADG for all heifers was determined to be 0.65 kg, below National Research Council recommendations of 0.7 to 0.8 kg. No strong relationship (r=-0.07) was observed between ADG and placing. Heavier heifers within a class showed a small positive relationship (r=0.10) with placing. For study 2, 238 heifers shown at the 2010 Georgia Junior National Livestock Show (Perry, GA) were measured and evaluated for ADG, placing, body weight, age, withers height, hip height, hip width, and jaw width. Height at withers had a moderate relationship (r=0.42) with placing, followed by hip height (r=0.32). A positive relationship (r=0.65) was observed between withers height and hip height. The correlation between weight and placing was determined (r=0.11). Age and ADG had a strong inverse relationship (r=-0.87). Study 3 evaluated 1,489 Holstein heifers shown from 2007 to 2010. Data was analyzed using the Penn State Growth Monitor Spreadsheet Curves. In total, 63.75% did not meet Penn State recommendations for body weight gain. Performance and physical features associated with age indicates that commercial dairy heifers are underfed. The effects of heat stress and high feed costs also play a role. This has economic implications because these animals will likely require more time before they enter the milk herd. The Commercial Dairy Heifer Program is vital for youth development in Georgia. However, those involved need to be encouraged to improve nutritional management practices.

Ant colony optimization as a method for strategic genotype sampling.

A simulation study was carried out to develop an alternative method of selecting animals to be genotyped. Simulated pedigrees included 5000 animals, each assigned genotypes for a bi-allelic single nucleotide polymorphism (SNP) based on assumed allelic frequencies of 0.7/0.3 and 0.5/0.5. In addition to simulated pedigrees, two beef cattle pedigrees, one from field data and the other from a research population, were used to test selected methods using simulated genotypes. The proposed method of ant colony optimization (ACO) was evaluated based on the number of alleles correctly assigned to ungenotyped animals (AK(P)), the probability of assigning true alleles (AK(G)) and the probability of correctly assigning genotypes (APTG). The proposed animal selection method of ant colony optimization was compared to selection using the diagonal elements of the inverse of the relationship matrix (A(-1)). Comparisons of these two methods showed that ACO yielded an increase in AK(P) ranging from 4.98% to 5.16% and an increase in APTG from 1.6% to 1.8% using simulated pedigrees. Gains in field data and research pedigrees were slightly lower. These results suggest that ACO can provide a better genotyping strategy, when compared to A(-1), with different pedigree sizes and structures.

Trends for conception rate of Holsteins over time in the southeastern United States.

The purpose of this study was to estimate trends in conception rate (CR) of Holsteins in the southeastern United States over time across month by milk production level and month by days in milk (DIM) subclasses. Data were obtained from Dairy Records Management Systems (Raleigh, NC) and included service records from 10 states (Virginia, Kentucky, North Carolina, South Carolina, Tennessee, Georgia, Florida, Alabama, Mississippi, and Louisiana). After eliminating records with lactation >1 and uncertain and extreme records (records without calving or birth date, with days to service after calving <21 or >250, or without next calving date), the final data set included 827,802 artificial insemination service records for 424,513 cows born from 1985 to 2000, and in 2,953 herds. Effects included in the model were year of birth (1985 to 1989, 1990 to 1994, 1995 to 2000), DIM class, milk production level (high, medium, low based on SD), service month, the covariate of cow age at calving, and 2- and 3-way interactions. Over time, an increase was observed for milk production and an overall decline in CR occurred. Examination of month by milk production subclass least squares means showed that in cool months (November to April) the deterioration of CR over time was small for low and medium milk production cows and virtually none for high-producing cows. However, in other months (May to June), there was a large decline over time in CR for cows in all milk production level subclasses. The trends in CR by DIM subclasses were examined for the months of February, May, June, and August. There was a general increase in CR with increasing DIM for all months within all birth-year groups. The months of February and August were somewhat similar for CR up to 175 DIM for the different birth-year groups. Much larger differences over time were observed for the months of May and June, and it appeared that for these 2 mo, cows in recent periods did not return to the same level of performance as cows in earlier periods. It may be that there has been a decline over time in the ability of cows to handle the onset of heat stress or the switch to pasture-based management systems.

Environmental effects on conception rates of Holsteins in New York and Georgia.

The purpose of this study was to investigate the compounded impact on conception rates (CR) of the effects of milk production, service month, and days in milk (DIM) by using recent artificial insemination records of Holsteins in New York (NY) and Georgia (GA). Dairy Herd Improvement records were obtained from Dairy Records Management Systems in Raleigh, North Carolina. After removing records with lactations >1 and uncertain and extreme records (records without a calving or birth date, with days to service after calving of <21 or >250, and without the next calving date), the final data set comprised 298,015 service records for 160,879 cows and 23,366 service records for 12,184 cows in NY and GA, respectively, from 2000 to 2003. The analytical model included DIM class, milk-production level, service month, the covariate of cow's age at calving, and all 2-way interactions. The 2 states were analyzed separately. In general across the 2 states, CR declined as milk production increased, and CR declined during the hottest months. Conception rate was similar in NY and GA, at approximately 55% from December to April. In NY, CR declined by approximately 10% in May and June and mostly recovered by July. In GA, the CR started declining in May, bottomed at 31% in September, and did not recover until December. The difference in CR between high- and low-producing cows was 7% in NY and 6% in GA. That difference was the strongest from June to July in GA (15%) and was more uniform in NY. The increase in CR with increasing DIM varied across service season. The CR was nearly flat from 50 to 125 DIM in NY for all seasons, except for a large increasing trend in spring. In GA, there was also an increasing trend in fall. Conception rates were similar in NY and GA between December and May, and were strongly influenced by heat stress in GA from June to November. A decline in CR for reasons other than heat stress was present in both states in late spring. High production resulted in a faster decline of the CR in GA under heat stress. Models analyzing service records should include the DIM x season x region interaction.

Genetic evaluations for growth heat tolerance in Angus cattle.

The objectives were to assess the impact of heat stress and to develop a model for genetic evaluation of growth heat tolerance in Angus cattle. The American Angus Association provided weaning weight (WW) and yearling weight (YW) data, and records from the Upper South region were used because of the hot climatic conditions. Heat stress was characterized by a weaning (yearling) heat load function defined as the mean temperature-humidity index (THI) units greater than 75 (70) for 30 (150) d prior to the weigh date. Therefore, a weaning (yearling) heat load of 5 units corresponded to 80 (75) for the corresponding period prior to the weigh date. For all analyses, 82,669 WW and 69,040 YW were used with 3 ancestral generations in the pedigree. Univariate models were a proxy for the Angus growth evaluation, and reaction norms using 2 B-splines for heat load were fit separately for weaning and yearling heat loads. For both models, random effects included direct genetic, maternal genetic, maternal permanent environment (WW only), and residual. Fixed effects included a linear age covariate, age-of-dam class (WW only), and contemporary group for both models and fixed regressions on the B-splines in the reaction norm. Direct genetic correlations for WW were strong for modest heat load differences but decreased to less than 0.50 for large differences. Reranking of proven sires occurred for only WW direct effects for the reaction norms with extreme heat load differences. Conversely, YW results indicated little effect of heat stress on genetic merit. Therefore, weaning heat tolerance was a better candidate for developing selection tools. Maternal heritabilities were consistent across heat loads, and maternal genetic correlations were greater than 0.90 for nearly all heat load combinations. No evidence existed for a genotype × environment interaction for the maternal component of growth. Overall, some evidence exists for phenotypic plasticity for the direct genetic effects of WW, but traditional national cattle evaluations are likely adequately ranking sires for nonextreme environmental conditions.

Regional and seasonal analyses of weights in growing Angus cattle.

This study evaluated the impact of region and season on growth in Angus seed stock. To assess geographic differences, the United States was partitioned into 9 regions based on similar climate and topography related to cow-calf production. Seasonal effects were associated with the month that animals were weighed. The American Angus Association provided growth data, and records were assigned to regions based on the owner's zip code. Most Angus cattle were in the Cornbelt, Lower Plains, Rocky Mountain, Upper Plains, and Upper South regions, with proportionally fewer Angus in Texas compared with the national cow herd. Most calves were born in the spring, especially February and March. Weaning weights (WW; = 49,886) and yearling weights (YW; = 45,168) were modeled with fixed effects of age-of-dam class (WW only), weigh month, region, month-region interaction, and linear covariate of age. Random effects included contemporary group nested within month-region combination and residual. The significant month-region interaction ( < 0.0001) was expected because of the diverse production environments across the country and cyclical fluctuations in forage availability. Additionally, significant seasonal contrasts existed for several regions. Fall-born calves were heavier ( < 0.01) than spring-born calves in the hot and humid Lower South region coinciding with fall being the primary calving season. The North and Upper Plains regions had heavier, spring-born calves ( < 0.01), more than 90% spring calving, and colder climates. Interestingly, no seasonal WW or YW differences existed between spring- and fall-born calves in the upper South region despite challenging environmental conditions. Angus seed stock producers have used calving seasons to adapt to the specific environmental conditions in their regions and to optimize growth in young animals.

Correlations between purebred and crossbred body weight traits in Limousin and Limousin-Angus populations.

The purpose of this study was to estimate correlations between purebred and F1 crossbred performance to verify the appropriateness of current models used in multibreed selection. Records on birth weight (WB) and weaning weight (WW) from purebred Limousins (LIM) and Limousin × Angus progeny (F1) were used to estimate genetic parameters using a multiple-trait (purebred and F1 weights were different traits) approach. For WB, there were 148,647 records for LIM and 17,981 for F1, and for WW, there were 81,585 records for LIM and 21,778 for F1. The fixed effect in models for LIM and F1 animals was contemporary group. Random effects for LIM animals were direct genetic, maternal genetic, and maternal permanent environment effects. Random effects for F1 were sire and dam. The pedigree for Angus dams used for crossing was unavailable and therefore these dams were assumed unrelated. The direct h2 estimates (SE) for purebred animals were 0.41 (0.05) and 0.24 (0.02) for WB and WW, respectively. For F1, the same estimates were 0.22 (0.09) and 0.32 (0.05). Genetic correlations estimates between purebreds and crossbreds were 0.84 (0.07) and 0.64 (0.18) for WB and WW, respectively. The genetic correlation for WW estimated in this study suggests that F1 and purebred information for this trait should not be treated, genetically, as the same trait due to different genetic effects molding it. However, the genetic correlation for WB was much higher, indicating that this trait in purebreds and F1 is essentially the same trait.

Genetic evaluation using single-step genomic best linear unbiased predictor in American Angus.

Predictive ability of genomic EBV when using single-step genomic BLUP (ssGBLUP) in Angus cattle was investigated. Over 6 million records were available on birth weight (BiW) and weaning weight (WW), almost 3.4 million on postweaning gain (PWG), and over 1.3 million on calving ease (CE). Genomic information was available on, at most, 51,883 animals, which included high and low EBV accuracy animals. Traditional EBV was computed by BLUP and genomic EBV by ssGBLUP and indirect prediction based on SNP effects was derived from ssGBLUP; SNP effects were calculated based on the following reference populations: ref_2k (contains top bulls and top cows that had an EBV accuracy for BiW ≥0.85), ref_8k (contains all parents that were genotyped), and ref_33k (contains all genotyped animals born up to 2012). Indirect prediction was obtained as direct genomic value (DGV) or as an index of DGV and parent average (PA). Additionally, runs with ssGBLUP used the inverse of the genomic relationship matrix calculated by an algorithm for proven and young animals (APY) that uses recursions on a small subset of reference animals. An extra reference subset included 3,872 genotyped parents of genotyped animals (ref_4k). Cross-validation was used to assess predictive ability on a validation population of 18,721 animals born in 2013. Computations for growth traits used multiple-trait linear model and, for CE, a bivariate CE-BiW threshold-linear model. With BLUP, predictivities were 0.29, 0.34, 0.23, and 0.12 for BiW, WW, PWG, and CE, respectively. With ssGBLUP and ref_2k, predictivities were 0.34, 0.35, 0.27, and 0.13 for BiW, WW, PWG, and CE, respectively, and with ssGBLUP and ref_33k, predictivities were 0.39, 0.38, 0.29, and 0.13 for BiW, WW, PWG, and CE, respectively. Low predictivity for CE was due to low incidence rate of difficult calving. Indirect predictions with ref_33k were as accurate as with full ssGBLUP. Using the APY and recursions on ref_4k gave 88% gains of full ssGBLUP and using the APY and recursions on ref_8k gave 97% gains of full ssGBLUP. Genomic evaluation in beef cattle with ssGBLUP is feasible while keeping the models (maternal, multiple trait, and threshold) already used in regular BLUP. Gains in predictivity are dependent on the composition of the reference population. Indirect predictions via SNP effects derived from ssGBLUP allow for accurate genomic predictions on young animals, with no advantage of including PA in the index if the reference population is large. With the APY conditioning on about 10,000 reference animals, ssGBLUP is potentially applicable to a large number of genotyped animals without compromising predictive ability.

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.

Problems and possibilities into the next decade involving beef cattle breeding research in the southern region: purebred field data banks.

Beef cattle field records can provide data to generate important research information. The challenge in using field data for animal breeding studies involves proper editing to remove erroneous records and formulating proper models to account for fixed effects and to estimate or predict effects of interest free of bias and(or) with minimum estimation error. Use of field data for testing hypotheses is limited due to the lack of control and knowledge of the conditions under which the data were collected. Therefore, designed studies and field data should be used together to answer important questions. Some of the possible projects that can use field records are the estimation of genetic and environmental relationships among economically important traits, defining environments over which genotype x environment interactions and heterogenous heritabilities are most likely to occur, and pinpointing important fixed effects that must be accounted or adjusted for in genetic prediction models. The goal of research involving field data has been and will continue to be to provide information to improve genetic prediction models and procedures and to provide producers with genetic values with which to make informed selection decisions with a high degree of confidence.

Investigation of genotype x country interactions for growth traits in beef cattle.

The importance of genotype x country interactions for weaning and birth weight and postweaning gain between Argentina (AR), Canada (CA), Uruguay (UY), and the United States (US) for populations of Hereford cattle was investigated. Three sample data sets of computationally manageable sizes were formed for each trait and pairwise combination of countries to investigate possible interactions. Parameters were estimated for each sample data set via an accelerated EM-REML algorithm and multiple-trait animal models that considered either weaning or birth weight as a different trait in each country. Direct and maternal (in parentheses) weaning weight genetic correlation estimates for AR-CA, AR-UY, AR-US, CA-UY, CA-US, and UY-US were 0.82 (0.80), 0.81 (0.72), 0.81 (0.79), 0.83 (0.78), 0.85 (0.82), and 0.86 (0.81), respectively. Direct and maternal (in parentheses) birth weight genetic correlation estimates were 0.92 (0.62), 0.97, (0.85), and 0.99 (0.97) for AR-CA, AR-US, and CA-US, respectively. Birth weight was not analyzed for UY due to small amounts of data. Postweaning gain in CA and US was 160-d gain, and in AR and UY 345-d gain was used. Across-country direct genetic correlations for postweaning gain were estimated for each pairwise country data set using a model that considered weaning weight as the same trait across each country, whereas postweaning gain was treated as a different trait in each country. Direct genetic correlation estimates for postweaning gain for AR-CA, AR-UY, AR-US, CA-UY, CA-US, and US-UY were 0.64, 0.80, 0.51, 0.84, 0.92, and 0.83, respectively. The overall results indicate that weaning and birth weights of Hereford calves can be analyzed as the same trait in all countries with a common set of heritabilities and genetic correlations, after adjustment for heterogenous phenotypic variances across countries. Postweaning gain in CA and US can be considered as the same trait and analyzed using a single set of parameters. Postweaning gain in AR and UY should be considered as a separate trait from postweaning gain in CA and US, and postweaning gain in AR and UY can be considered as the same trait and analyzed using a common heritability, after adjustment for phenotypic variance differences between the two countries.

Two methods for parameter estimation using multiple-trait models and beef cattle field data.

Two methods are presented for estimating variances and covariances from beef cattle field data using multiple-trait sire models. Both methods require that the first trait have no missing records and that the contemporary groups for the second trait be subsets of the contemporary groups for the first trait; however, the second trait may have missing records. One method uses pseudo expectations involving quadratics composed of the solutions and the right-hand sides of the mixed model equations. The other method is an extension of Henderson's Simple Method to the multiple trait case. Neither of these methods requires any inversions of large matrices in the computation of the parameters; therefore, both methods can handle very large sets of data. Four simulated data sets were generated to evaluate the methods. In general, both methods estimated genetic correlations and heritabilities that were close to the Restricted Maximum Likelihood estimates and the true data set values, even when selection within contemporary groups was practiced. The estimates of residual correlations by both methods, however, were biased by selection. These two methods can be useful in estimating variances and covariances from multiple-trait models in large populations that have undergone a minimal amount of selection within contemporary groups.

Simulation study of teat score in first-parity Gelbvieh cows: parameter estimation.

Teat scores from 9,598 first-parity Gelbvieh cows were used to investigate the adequacy of grouping approaches to decrease score misclassifications or inconsistencies as well as to simplify the data collection process. The procedure was tested using simulated data and then validated using teat score records of Gelbvieh cattle. First-parity cows were considered to be 4 yr of age or younger at first calving, did not have multiple records within 280 d, and were at least 50% Gelbvieh. Producers scored cows within 24 h of parturition. Teat score, a subjective measure of teat size, ranged from 0 (very large) to 50 (very small). A linear mixed model that included herd-year, month of calving, and age at calving as systematic effects; regression on the percentage of Gelbvieh; and additive breeding values (BV) and residual as random effects was used to generate the data. Simulated data were analyzed using one of three scoring methods: all values (S50), 10 classes (S10), and five classes (S5). The 10 classes were formed by subdividing every five scores into a single class starting at score zero. Similarly, the five classes were formed by combining every 10 scores into one class. The average Pearson correlations, based on five replicates, between the true and estimated BV (systematic effects) were 0.36 (0.85), 0.35 (0.89), and 0.32 (0.87) using S50, S10, and S5, respectively. Average correlations between estimated BV (systematic effects) were 0.97 (0.95), 0.89 (0.92), and 0.92 (0.97) based on S50 and S10, S50 and S5, and S10 and S5, respectively. Field data were used to validate the simulation procedure. The field data were categorized into 10 classes (F10) and five classes (F5) as described for the simulated data. Pearson correlations between estimated BV (systematic effects) were 0.99 (0.93), 0.93 (0.88), and 0.93 (0.96), based on F50 with F10, F50 with F5, and F10 with F5, respectively. The extremely high correlations between predicted BV based on S50, S10, S5, F50, F10, with F5 suggest that a simplified score classification method could be adopted without compromising the expected genetic progress for the trait under consideration. Furthermore, the difference in corresponding Pearson correlations across the field and simulated data might suggest the presence of some inconsistencies or misclassifications of the actual scoring system.

Comparison of methods for handling censored records in beef fertility data: simulation study.

A simulation study was conducted to compare methods for handling censored records for days to calving in beef cattle data. Days to calving was defined as the time, in days, between when a bull is turned out in the pasture and the subsequent parturition. Simulated data were generated to have data structure and genetic relationships similar to an available field data set. Records were simulated for 33,176 daughters of 4,238 sires. Data were simulated using a mixed linear model that included the fixed effects of contemporary group and sex of calf, linear and quadratic covariates for age at mating, and random effects of animal and residual error. Two methods for handling censored records were evaluated, and two censoring rates of 12 and 20% were applied to assess the influence of higher censoring rates on inferences. Censored records were assigned penalty values on a within-contemporary group basis under the first method (DCPEN). Under the second method (DCSIM), censored records were drawn from their respective predictive distributions. A Bayesian approach via Gibbs sampling was used to estimate variance components and predict breeding values. Posterior means (PM) and standard deviations (SD) of additive genetic variance for DCPEN at 12 and 20% censoring were 23.2 (3.7) and 21.0 (3.6), respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 23.7(3.3) and 21.9 (3.4), respectively. In all cases, the true value of the genetic variance was within the high posterior density (HPD) interval (95%). The PM (SD) of residual variance for DCPEN at 12 and 20% censoring were 415.7 (4.7) and 440.0 (4.8) respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 371.0 (4.3) and 365.4 (4.4), respectively. The true value of the residual variance was within the HPD (95%) for DCSIM, but it was outside this interval for DCPEN at both censoring rates, indicating a systematic bias for this parameter. Bayes Factor and Deviance Information Criteria were used for model comparisons, and both criteria indicated the superiority of the DCSIM method. However, little difference was observed between the two methods for correlations between true breeding values and posterior means of animal effects for sires, indicating that no major reranking of sires would be expected. This finding suggests that either censored data handling technique can be successfully used in a genetic evaluation for days to calving.

Comparison of methods for handling censored records in beef fertility data: field data.

The purpose of this study was to compare methods for handling censored days to calving records in beef cattle data, and verify results of an earlier simulation study. Data were records from natural service matings of 33,176 first-calf females in Australian Angus herds. Three methods for handling censored records were evaluated. Censored records (records on noncalving females) were assigned penalty values on a within-contemporary group basis under the first method (DCPEN). Under the second method (DCSIM), censored records were drawn from their respective predictive truncated normal distributions, whereas censored records were deleted under the third method (DCMISS). Data were analyzed using a mixed linear model that included the fixed effects of contemporary group and sex of calf, linear and quadratic covariates for age at mating, and random effects of animal and residual error. A Bayesian approach via Gibbs sampling was used to estimate variance components and predict breeding values. Posterior means (PM) (SD) of additive genetic variance for DCPEN, DCSIM, and DCMISS were 22.6d2 (4.2d2), 26.1d2 (3.6d2), and 13.5d2 (2.9d2), respectively. The PM (SD) of residual variance for DCPEN, DCSIM, and DCMISS were 431.4d2 (5.0d2), 371.4d2 (4.5d2), and 262.2d2 (3.4d2), respectively. The PM (SD) of heritability for DCPEN, DCSIM, and DCMISS were 0.05 (0.01), 0.07 (0.01), and 0.05 (0.01), respectively. Simulating trait records for noncalving females resulted in similar heritability to the penalty method but lower residual variance. Pearson correlations between posterior means of animal effects for sires with more than 20 daughters with records were 0.99 between DCPEN and DCSIM, 0.77 between DCPEN and DCMISS, and 0.81 between DCSIM and DCMISS. Of the 424 sires ranked in the top 10% and bottom 10% of sires in DCPEN, 91% and 89%, respectively, were also ranked in the top 10% and bottom 10% in DCSIM. Little difference was observed between DCPEN and DCSIM for correlations between posterior means of animal effects for sires, indicating that no major reranking of sires would be expected. This finding suggests little difference between these two censored data handling techniques for use in genetic evaluation of days to calving.

Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: I. Variance component estimation.

Birth weight and calving difficulty were analyzed with Bayesian methodology using univariate linear models, a bivariate linear model, a threshold model for calving difficulty, and a joint threshold-linear model using a probit approach. Field data included 26,006 records of Gelbvieh cattle. Simulated populations were generated using parameters estimated from the field data. The Gibbs sampler was used to obtain estimates of the marginal posterior mean and standard deviation of the (co)variance components, heritabilities, and correlations. In the univariate analyses, the posterior mean of direct heritability for calving difficulty was .23 with the threshold model and .18 with the linear model. Maternal heritabilities were .10 and .08, respectively. In the bivariate analysis, posterior means of direct heritability for calving difficulty were .21 and .18 for the bivariate linear-threshold and linear-linear model, respectively. Maternal heritabilities were .09 and .06, respectively. Direct heritability for birth weight was .25 for the univariate model and .26 for bivariate models. Maternal heritability was .05 for the linear-threshold model and the univariate model and .06 for the bivariate linear model. Genetic correlation between direct genetic effects in both traits was .81 for the linear-threshold model and .79 for the bivariate linear. Residual correlation was .35 for the bivariate linear model and .50 for the bivariate linear-threshold. A simulation study confirmed that the posterior mean of the marginal distribution was suitable as a point estimate for univariate threshold and bivariate linear-threshold models.

Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: II. Comparison of models.

Several models were evaluated in terms of predictive ability for calving difficulty. Data included birth weight and calving difficulty scores provided by the American Gelbvieh Association from 26,006 calves born to first-parity cows and five simulated populations of 6,200 animals each. Included in the model were fixed age of dam x sex interaction effects, random herd-year-season effects, and random animal direct and maternal effects. Bivariate linear-threshold and linear-linear models for birth weight/calving ease and univariate threshold and linear models for calving ease were applied to the data sets. For each data set and model, one-half of calving ease records were randomly discarded. Predictive ability of the different models was defined with the mean square error (MSE) for the difference between a deleted calving ease score and its prediction obtained from the remaining data. In terms of correlation between simulated and predicted breeding values, the threshold models had a 1% advantage for direct genetic effects and 3% for maternal genetic effects. In simulation, the average MSE was .29 for linear-threshold, .32 for linear-linear, .37 for threshold, and .39 for linear model. For the field data set, the MSE was .31, .33, .39, and .40, respectively. Although the bivariate models for calving ease/birth weight were more accurate than univariate models, the threshold models showed a greater advantage under the bivariate model. For the purpose of genetic evaluation for calving difficulty in beef cattle, the use of the linear-threshold model seems justified. In dairy cattle, the evaluation for calving ease can benefit from recording birth weight.

Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle.

Genetic parameters for a random regression model of growth in Gelbvieh beef cattle were constructed using existing estimates. Information for variances along ages was provided by parameters used for routine Gelbvieh multiple-trait evaluation, and information on correlations among different ages was provided by random regression model estimates from literature studies involving Nellore cattle. Both sources of information were combined into multiple-trait estimates; corrected for continuity, smoothness, and general agreement with literature estimates; and extrapolated to 730 d. Covariance functions using standardized Legendre polynomials were fit for the following effects: additive genetic (direct and maternal), and animal and maternal permanent environment. Residual variances at different ages were fitted using linear splines with three knots. Fit was by least squares. The order of polynomials was varied from third to sixth. Increasing the fit beyond cubic provided small improvements in R2 and increased the number of small eigenvalues of covariance matrices, especially for the additive effect. Parameters for a random regression model in beef cattle can be constructed with negligible artifacts from literature estimates. Formulas can easily be modified for other types of polynomials and splines.