Animal model genetic evaluation of type traits for five dairy cattle breeds

A system to calculate genetic evaluations based on an animal model was developed for final score (single-trait model) and 15 linear type traits (multitrait model) of Ayrshires, Brown Swiss, Guernseys, Jerseys, and Milking Shorthorns. (Co)variance components were estimated from appraisals that were scored during 1988 and later and that included all linear traits. The model for (co)variance components included fixed effects for interactions of herd, appraisal date, and parity; parity and appraisal age; and parity and lactation stage. Random effects were included for permanent environment, animal, and residual. A canonical transformation was used with approximate diagonalization. Data for estimating breeding values included appraisals from 1980. Effects for appraisal age and lactation stage were defined within appraisal year group. The model for calculation of breeding values also included a random effect of interaction between herd and sire. Solutions for appraisal age from a preliminary analysis were smoothed with a quadratic curve to generate additive age adjustments by month for appraisal age, parity, and appraisal year group. Correlations of solutions from this model and from the former USDA sire model for bulls that were born during 1975 or later and that had 20 daughters were highest (generally 0.90) for Guernseys and were lowest (generally <0.80) for Milking Shorthorns. The evaluation system was implemented in February 1998 and was extended to Red and Whites

Use of sequential estimation of regressions and effects on regressions to solve large multitrait test-day models

An alternative algorithm for the solution of random regression models for analysis of test-day yield was developed to allow use of those models with extremely large data sets such as the US database for dairy records. Equations were solved in two iterative steps: 1) estimation or update of regression coefficients based on test-day yields for a given lactation and 2) estimation of fixed and random effects on those coefficients. Solutions were shown to be theoretically equivalent to traditional solutions for this class of random regression models. In addition to the relative simplicity of the proposed method, it allows several other techniques to be applied in the second step: 1) a canonical transformation to simplify computations (uncorrelated regressions) that could make use of recent advances in solution algorithms that allow missing values, 2) a transformation to limit the number of regressions and to create variates with biological meanings such as lactation yield or persistency, 3) more complicated (co)variance structures than those usually considered in random regression models (e.g., additional random effects such as the interaction of herd and sire), and 4) accommodation of data from 305-d records when no test-day records are available. In a test computation with 176,495 test-day yields for milk, fat, and protein from 22,943 first-lactation Holstein cows, a canonical transformation was applied, and the biological variates of 305-d yield and persistency were estimated. After five rounds of iteration with a sequential solution scheme for the two-step algorithm, maximum relative differences from previous genetic solutions were 0.98 for 305-d yield and >0.99 for persistency

Sire Effects in Different Housing Systems

Over 1,000 Holstein herds in New York\u27s Dairy Herd Improvement Cooperative were classified as to housing system. The two housing systems considered were stanchions and free stalls. First-lactation records (21,285) produced in these herds by daughters sired through artificial insemination were analyzed to determine if housing system would affect sire ranking. The study covered records started in 1964 through 1967. The sire component of variance was estimated for each housing system for deviations of these records from their adjusted herdmate averages. The covariance between the means of daughters in each housing system was computed. The genetic correlation between sire effects in the two systems was determined by dividing this covariance by the geometric mean of the sire components of variance for the two housing systems. The estimated correlation was near unity for each year of the study, indicating essentially complete agreement between sire rankings in the two housing systems

Within-herd effects of age at test day and lactation stage on test-day yields

Variance ratios were estimated for random within-herd effects of age at test day and lactation stage, on test-day yield and somatic cell score to determine whether including these effects would improve the accuracy of estimation. Test-day data starting with 1990 calvings for the entire US Jersey population and Holsteins from California, Pennsylvania, Wisconsin, and Texas were analyzed. Test-day yields were adjusted for across-herd effects using solutions from a regional analysis. Estimates of the relative variance ( fraction of total variance) due to within-herd age effects were small, indicating that regional adjustments for age were adequate. The relative variances for within-herd lactation stage were large enough to indicate that accuracy of genetic evaluations could be improved by including herd stage effects in the model for milk, fat, and protein, but not for somatic cell score. Because the within-herd lactation stage effect is assumed to be random, the effect is regressed toward the regional effects for small herds, but in large herds, lactation curves become herd specific. Model comparisons demonstrated the greater explanatory power of the model with a within-herd-stage effect as prediction error standard deviations were greater for the model without this effect. The benefit of the within-herd-stage effects was confirmed in a random regression model by comparing variance components from models with and without random within-herd regressions and through log-likelihood ratio tests

Accounting for heterogeneous variances in multitrait evaluation of Jersey type traits

peer reviewedThe multitrait genetic evaluation system for type traits was modified to estimate adjustments for heterogeneous variance (HV) simultaneously with estimated breeding values (EBV) for final score and 14 linear traits. Each variance within herd, year, and parity was regressed toward a predicted variance, which was determined by fitting a model with fixed effects of the mean final score for herd, size of the contemporary group, appraisal month, and year-season and a random effect for herd-appraisal date. Herd-appraisal date was included as a random effect to regress the observed heterogeneity for a given herd-appraisal date toward the fixed effects. Method R was used to estimate variances for the heterogeneity model in each EBV iteration. To evaluate the effect of the adjustment, parent averages were calculated from evaluations with recent appraisals removed. The adjustment slightly improved correlations within birth year between those parent averages and EBV from current data on bulls for most traits, but did not improve correlations for final score, strength, dairy form, teat length, or foot angle. Annual trends for EBV were lower with HV adjustment than for unadjusted EBV for all traits except final score and rump angle for cows and rump width for bulls, which were essentially unchanged. Standard deviations of Mendelian sampling (evaluation minus mean of parent evaluations) declined less over time for HV-adjusted than for unadjusted evaluations. The slope at year 2000 of Mendelian-sampling standard deviations from HV-adjusted evaluations ranged from 10.0% for udder depth to 42.7% for teat length compared with the slope for unadjusted evaluations. This HV adjustment, which was implemented for USDA evaluations in May 2001 for Jerseys and in 2002 for other breeds, improves the accuracy of evaluations, particularly comparisons over time, by accounting for the change in variation

Estimation of (co)variance components for Jersey type traits using a repeatability model

(Co)variance components for final score and 15 linear type traits of Jersey cows were estimated by multitrait REML using multiple diagonalization and a repeatability model with 34,999 records of 22,354 cows. Multiple diagonalization gave relative off-diagonals (ratio of squared off-diagonals to the product of diagonals) of <0.1%. Heritabilities and repeatabilities, respectively, were estimated as 0.29 and 0.48 for final score, 0.40 and 0.57 for stature, 0.26 and 0.39 for strength, 0.28 and 0.43 for dairy form, 0.13 and 0.25 for foot angle, 0.13 and 0.25 for rear legs (side view), 0.27 and 0.41 for body depth, 0.31 and 0.52 for rump angle, 0.22 and 0.33 for thurl width, 0.22 and 0.36 for fore udder attachment, 0.28 and 0.46 for rear udder height, 0.26 and 0.42 for rear udder width, 0.32 and 0.48 for udder depth, 0.20 and 0.36 for udder cleft, 0.29 and 0.46 for front teat placement, and 0.31 and 0.48 for teat length. Estimates of heritability generally were higher, and estimates of repeatability were lower, than values used previously for USDA genetic evaluations, which were based on data from the 1970s and early 1980s. Final score was highly correlated both genetically and phenotypically with dairy form and rear udder traits. These estimates of heritabilities and (co)variance components are necessary for multitrait genetic evaluation of linear type traits of US Jerseys

Comparison of Genetic Evaluations from Animal Model and Modified Contemporary Comparison

ABSTRACT Comparisons were made between characteristics of Modified Contemporary Comparison and animal model evaluations with data available for January 1989 USDA-DHIA genetic evaluations. The animal model system&apos;s requirement that cows have a valid first lactation record resulted in a decrease in cows and daughters included. New flexible comparison groups were slightly larger for small herds and much smaller for large herds, which resulted in overall smaller and more uniform-sized comparison groups. Determining the optimal method of defining management groups was not undertaken. Correlations between bull evaluations from the two procedures ranged from .92 to .95 across breeds. Increases in reliability over repeatability were substantial for bulls with limited daughter information and small for widely used bulls. Correlations between evaluations for cows born in 1985 were .92 to .96, whereas those for cows born in 1980 (old enough to have daughters affecting animal model evaluations) were lower (.90 to .93), as expected. Reliabilities for cows were .02 to .05 higher than repeatabilities. Cows with more daughters increased more in evaluation and accuracy between the two procedures and were genetically superior. Bulls and cows with more prior information, cows with higher past evaluations, and Holstein bulls with higher past evaluations tended to have larger increases in ITA. Genetic trend estimates were different for the animal model, whic

Evaluation and interpretation of regional and site-specific hydrochemical data bases for water quality assessment

International audienceThe spatial distribution of stream water composition, as determined by the Geochemical Baseline Survey of the Environment (G-BASE) conducted by the British Geological Survey (BGS) can be successfully related under baseflow conditions to bedrock geochemistry. Further consideration of results in conjunction with site-specific monitoring data enables factors controlling both spatial and temporal variability in major element composition to be highlighted and allows the value of the survey to be enhanced. Hence, chemical data (i) from streams located on Lower Silurian (Llandovery) bedrock at 1 km2 resolution collected as part of the G-BASE survey of Wales and the West Midlands and (ii) from catchment monitoring studies located in upland mid-Wales (conducted by Institute of Terrestrial Ecology), have been considered together as an example. Classification of the spatial survey data set in terms of potentially controlling factors was carried out so as to illustrate the level of explanation they could give in terms of observed spatial chemical variability. It was therefore hypothesised that on a geological lithostratigraphic series of limited geochemical contrast, altitude and land-use factors provide better explanation of this variability than others such as lithology at sampling site and stream order. At an individual site, temporal variability was also found to be of considerable significance and, at a monthly time-step, is explicable in terms of factors such as antecedent conditions and seasonality. Data suggest that the degree of this variability may show some relationship with stream order and land-use. Monitoring data from the region also reveal that relationships between stream chemistry and land-use may prove to be strong not only at base flow but also in storm flow conditions. In a wider context, predictions of the sensitivity of stream water to acidification based on classifications of soil and geology are successful on a regional scale. However, the study undertaken here has shown that use of such classification schemes on a catchment scale results in considerable uncertainty associated with prediction. Uncertainties are due to the large degree of variability in stream chemistry encountered both spatially within geological units and temporally at individual sampling sites

Genomic evaluations with many more genotypes

<p>Abstract</p> <p>Background</p> <p>Genomic evaluations in Holstein dairy cattle have quickly become more reliable over the last two years in many countries as more animals have been genotyped for 50,000 markers. Evaluations can also include animals genotyped with more or fewer markers using new tools such as the 777,000 or 2,900 marker chips recently introduced for cattle. Gains from more markers can be predicted using simulation, whereas strategies to use fewer markers have been compared using subsets of actual genotypes. The overall cost of selection is reduced by genotyping most animals at less than the highest density and imputing their missing genotypes using haplotypes. Algorithms to combine different densities need to be efficient because numbers of genotyped animals and markers may continue to grow quickly.</p> <p>Methods</p> <p>Genotypes for 500,000 markers were simulated for the 33,414 Holsteins that had 50,000 marker genotypes in the North American database. Another 86,465 non-genotyped ancestors were included in the pedigree file, and linkage disequilibrium was generated directly in the base population. Mixed density datasets were created by keeping 50,000 (every tenth) of the markers for most animals. Missing genotypes were imputed using a combination of population haplotyping and pedigree haplotyping. Reliabilities of genomic evaluations using linear and nonlinear methods were compared.</p> <p>Results</p> <p>Differing marker sets for a large population were combined with just a few hours of computation. About 95% of paternal alleles were determined correctly, and > 95% of missing genotypes were called correctly. Reliability of breeding values was already high (84.4%) with 50,000 simulated markers. The gain in reliability from increasing the number of markers to 500,000 was only 1.6%, but more than half of that gain resulted from genotyping just 1,406 young bulls at higher density. Linear genomic evaluations had reliabilities 1.5% lower than the nonlinear evaluations with 50,000 markers and 1.6% lower with 500,000 markers.</p> <p>Conclusions</p> <p>Methods to impute genotypes and compute genomic evaluations were affordable with many more markers. Reliabilities for individual animals can be modified to reflect success of imputation. Breeders can improve reliability at lower cost by combining marker densities to increase both the numbers of markers and animals included in genomic evaluation. Larger gains are expected from increasing the number of animals than the number of markers.</p

Second-price auctions with private entry costs

We study asymmetric second-price auctions under incomplete information. The bidders have potentially different, commonly-known, valuations for the object and private information about their entry costs. The seller, however, does not benefit from these entry costs. We calculate the equilibrium strategies of the bidders and analyze the optimal design for the seller in this environment