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Using spline functions (segmented polynomials) in regression models requires the knowledge of the location of the knots. Knots are the points at which independent linear segments are connected. Optimal positions of knots for linear splines of different orders were determined in this study for different scenarios, using existing estimates of covariance functions and an optimization algorithm. The traits considered were test-day milk, fat and protein yields, and somatic cell score (SCS) in the first three lactations of Canadian Holsteins. Two ranges of days in milk (from 5 to 305 and from 5 to 365) were taken into account. In addition, four different populations of Holstein cows, from Australia, Canada, Italy and New Zealand, were examined with respect to first lactation (305 days) milk only. The estimates of genetic and permanent environmental covariance functions were based on single- and multiple-trait test-day models, with Legendre polynomials of order 4 as random regressions. A differential evolution algorithm was applied to find the best location of knots for splines of orders 4 to 7 and the criterion for optimization was the goodness-of-fit of the spline covariance function. Results indicated that the optimal position of knots for linear splines differed between genetic and permanent environmental effects, as well as between traits and lactations. Different populations also exhibited different patterns of optimal knot locations. With linear splines, different positions of knots should therefore be used for different effects and traits in random regression test-day models when analysing milk production traits. [ABSTRACT FROM AUTHOR]

Heat stress was evaluated as a factor in differences between regional evaluations for milk yield in the United States. The national data set (NA) consisted of 56 million first-parity, test-day milk yields on 6 million Holsteins. The Northeastern subset (NE) included 12.5 million records on 1.3 million first-calved heifers from 8 states, and the Southeastern subset (SE) included 3.5 million records on 0.4 million heifers from 11 states. Climatic data were available from 202 public weather stations. Each herd was assigned to the nearest weather station. Average daily temperature-humidity index (meanTHI) 3 d before test date was used as an indicator of heat stress. Two test-day repeatability models were implemented. Effects included in both models were herd-test date, age at calving class, frequency of milking, days in milk x season class, additive genetic (regular breeding value) and permanent environmental effects. Additionally, the second model included random regressions on degrees of heat stress (t = max[0, meanTHI - 72]) for additive genetic (breeding value for heat tolerance) and permanent environmental effects. Both models were fitted with the national and regional data sets. Correlations involved estimated breeding values (EBV) from SE and NE for sires with ≥100 and ≥300 daughters in each region. When heat stress was ignored (first model) the correlations of regular EBV between SE and NE for sires with ≥100 (≥300) daughters were 0.85 (0.87). When heat stress was considered (second model), the correlation increased by up to 0.01. The correlations of heat stress EBV between NE and SE for sires with ≥100 (≥300, ≥700) daughters were 0.58 (0.72, 0.81). Evaluations for heat tolerance were similar in cooler and hotter regions for high-reliability sires. Heat stress as modeled explains only a small amount of regional differences, partly because test-day records depict only snapshots of heat stress. [ABSTRACT FROM AUTHOR]

A simulation study examined issues important for genetic evaluation of growth in beef cattle by random regression models with cubic Legendre polynomials (RRML) and linear splines with three knots (RRMS) compared with multiple-trait models (MTM). Parameters for RRML were obtained by conversion from covariance functions. Parameters for MTM and RRMS were extracted from RRML at 1, 205, and 365 d; parameters for RRMS were the same as MTM for all effects except the permanent environment and the residual. Four data sets were generated assuming RRML included records at 1, 205, and 365 d; at 1, 160 to 250, and 320 to 410 d; at 1, 100, 205, 300, and 365 d; and at 1, 55 to 145, 160 to 250, 275 to 325, and 320 to 410 d. Accuracies were computed as correlations between the true (simulated) and predicted breeding values. With the first data set, excel- lent agreement in accuracy was obtained for all models. With the second data set, the accuracy of MTM dropped by up to 1.5% compared with the first data set, but accuracy was unchanged for both RRML and RRMS. With the third (fourth) data set, accuracies of RRML were up to 2.4% (2.5%) higher than with the first (second) data set. Small differences in accuracy between RRML and RRMS were found with the third and fourth data sets, which were traced to inflated correlations especially between 1 and 205 d in RRMS; inflation could be decreased by adding one extra knot at 100 d to RRMS. Diagonalization of random coefficients was crucial for RRML but not for RRMS, resulting in approximately six (two) times faster convergence with RRML (RRMS). Reduction of dimensionality in RRML associated with small eigenvalues caused a less accurate evaluation for birth weight. Genetic evaluation of growth by RRM requires careful implementation. The RRMS is simpler to implement than the RRML. [ABSTRACT FROM AUTHOR]

The purpose of this study was to quantify the effect of heat stress on genotype by environment interaction among different regions of the United States. The national data consisted of 55.5 million first parity test-day (TD) milk yield records on 5.8 million Holstein cows. Subsets of the national data were from the Northeast (NE) with 12.5 million TD records on 1.3 million cows, and from the Southeast (SE) with 3.5 million TD records on 0.36 million cows. Meteorological data from 202 public weather stations were matched with herds based on distance. Daily mean temperature-humidity index (THI) was calculated from temperature and relative humidity records three days prior to TD. The first model that lacked the effect of heat stress included fixed effects of herd-test date, age at calving class, frequency of milking, and DIM x season class, and random genetic additive (regular breeding value) and permanent environmental effects. The second model that accounted for heat stress included two additional random regressions on degrees of heat stress (t=max[0,THI-72]), one for additive genetic (heat breeding value) and one for permanent environmental effect. Breeding values (BV) were computed by BLUP90IOD. Correlations involved sires with at least 300 daughters in regions being compared. When heat stress was ignored, the correlations of regular BV between NE and SE were 0.86. When the heat stress was considered, the correlation increased by 0.01. The correlation between heat BV for NE x SE was 0.72. Heat stress effect as applied explains only a fraction of differences in sire ranking between SE and the NE. The real impact of heat stress may be higher because THI as used accounts only for a fraction of variability due to heat and low correlations are in part due to limited accuracies. [ABSTRACT FROM AUTHOR]

Abstract Background Effectiveness of genomic selection and fine mapping is determined by the level of linkage disequilibrium (LD) across the genome. Knowledge of the range of genome-wide LD, defined as a non-random association of alleles at different loci, can provide an insight into the optimal density and location of single-nucleotide polymorphisms (SNPs) for genome-wide association studies and can be a keystone for interpretation of results from QTL mapping. Results Linkage disequilibrium was measured by |D'| and r2 between 38,590 SNPs (spaced across 29 bovine autosomes and the X chromosome) using genotypes of 887 Holstein bulls. The average level of |D'| and r2 for markers 40-60 kb apart was 0.72 and 0.20, respectively in Holstein cattle. However, a high degree of heterogeneity of LD was observed across the genome. The sample size and minor allele frequency had an effect on |D'| estimates, however, r2 was not noticeably affected by these two factors. Syntenic LD was shown to be useful for verifying the physical location of SNPs. No differences in the extent of LD and decline of LD with distance were found between the intragenic and intergenic regions. Conclusions A minimal sample size of 444 and 55 animals is required for an accurate estimation of LD by |D'| and r2, respectively. The use of only maternally inherited haplotypes is recommended for analyses of LD in populations consisting of large paternal half-sib families. Large heterogeneity in the pattern and the extent of LD in Holstein cattle was observed on both autosomes and the X chromosome. The extent of LD was higher on the X chromosome compared to the autosomes.

Preadjustment of phenotypic records is an alternative to accounting for the effect of pregnancy within the genetic evaluation model. Variance components used in the Canadian Test-Day Model may need to be re-estimated after preadjusting for pregnancy. The objective of this study was to assess the effect of preadjusting test-day yields on variance components and estimated breeding values using a random regression test-day model in a random sample of Ayrshire cows. A random sample of 981 Canadian Ayrshire cows from 18 complete herds (average of 54.5 cows/herd) was analyzed. Two data sets were created using the same animals, one with unadjusted milk, fat, and protein yields, and one data set with test-day records adjusted for pregnancy effects. Pregnancy effect estimates from a previous study were used for additive preadjustment of records. Variance components were estimated using both data sets. Results were very similar between the 2 data sets for all estimated genetic parameters (heritabilities, genetic, and permanent environmental correlations). The relative squared differences were very small: 0.05% for heritabilities, 0.20% for genetic correlations, and 0.18% for permanent environmental correlations. Furthermore, paired Student's t-tests showed that the differences between the genetic parameters of data sets adjusted and unadjusted for pregnancy effect were not significantly different from 0. Results from this study show that preadjusting data for pregnancy did not yield changes in covariance component estimates, thus suggesting that preadjusting test-day records could be a feasible solution to account for pregnancy in the Canadian Test-Day Model without changing the current model. Estimated breeding values (EBV) were calculated for both data sets to observe the impact of preadjusting for pregnancy. Overall, the largest changes in EBV seen when preadjusting for pregnancy (compared with unadjusted records) occurred for nonpregnant elite cows, whose EBV declined. Preadjusting for pregnancy before genetic evaluations improves the estimation of breeding values by adding the negative impact of pregnancy back onto pregnant cow test-day records, causing an increase in their production EBV. [ABSTRACT FROM AUTHOR]