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Routine genomic evaluations in animal breeding are usually based on either a BLUP with genomic relationship matrix (GBLUP) or single nucleotide polymorphism (SNP) BLUP model. For a multi-step genomic evaluation, these 2 alternative genomic models were proven to give equivalent predictions for genomic reference animals. The model equivalence was verified also for young genotyped animals without phenotypes. Due to incomplete linkage disequilibrium of SNP markers to genes or causal mutations responsible for genetic inheritance of quantitative traits, SNP markers cannot explain all the genetic variance. A residual polygenic effect is normally fitted in the genomic model to account for the incomplete linkage disequilibrium. In this study, we start by showing the proof that the multi-step GBLUP and SNP BLUP models are equivalent for the reference animals, when they have a residual polygenic effect included. Second, the equivalence of both multistep genomic models with a residual polygenic effect was also verified for young genotyped animals without phenotypes. Additionally, we derived formulas to convert genomic estimated breeding values of the GBLUP model to its components, direct genomic values and residual polygenic effect. Third, we made a proof that the equivalence of these 2 genomic models with a residual polygenic effect holds also for single-step genomic evaluation. Both the single-step GBLUP and SNP BLUP models lead to equal prediction for genotyped animals with phenotypes (e.g., reference animals), as well as for (young) genotyped animals without phenotypes. Finally, these 2 single-step genomic models with a residual polygenic effect were proven to be equivalent for estimation of SNP effects, too. [ABSTRACT FROM AUTHOR]

Compared with the currently widely used multi-step genomic models for genomic evaluation, single-step genomic models can provide more accurate genomic evaluation by jointly analyzing phenotypes and genotypes of all animals and can properly correct for the effect of genomic preselection on genetic evaluations. The objectives of this study were to introduce a single-step genomic model, allowing a direct estimation of single nucleotide polymorphism (SNP) effects, and to develop efficient computing algorithms for solving equations of the single-step SNP model. We proposed an alternative to the current single-step genomic model based on the genomic relationship matrix by including an additional step for estimating the effects of SNP markers. Our single-step SNP model allowed flexible modeling of SNP effects in terms of the number and variance of SNP markers. Moreover, our single-step SNP model included a residual polygenic effect with trait-specific variance for reducing inflation in genomic prediction. A kernel calculation of the SNP model involved repeated multiplications of the inverse of the pedigree relationship matrix of genotyped animals with a vector, for which numerical methods such as preconditioned conjugate gradients can be used. For estimating SNP effects, a special updating algorithm was proposed to separate residual polygenic effects from the SNP effects. We extended our single-step SNP model to general multiple-trait cases. By taking advantage of a block-diagonal (co)variance matrix of SNP effects, we showed how to estimate multivariate SNP effects in an efficient way. A general prediction formula was derived for candidates without phenotypes, which can be used for frequent, interim genomic evaluations without running the whole genomic evaluation process. We discussed various issues related to implementation of the single-step SNP model in Holstein populations with an across-country genomic reference population. [ABSTRACT FROM AUTHOR]

In this study, 3 strategies for controlling progeny inbreeding in mating plans were compared. The strategies used information from pedigree inbreeding coefficients, genomic relationships, or shared runs of homozygosity. The strategies were compared for the reduction in genetic gain and progeny inbreeding that would be expected from selected matings, and for the decrease of homozygosity of deleterious recessive alleles. Using real pedigree, genotype [43,115 single nucleotide polymorphism (SNP) markers], and estimated breeding value data from Holstein cattle, mating plans were derived for herds of 300 cows with 20 sires available for mating, replicated 50 times. Each of the 300 individuals allocated as dams were matched to 1 of 20 sires to maximize genetic merit minus the penalty for estimated progeny inbreeding, and given the restriction that the sire could not be mated to more than 10% of the cows. The strategy that used a genomic relationship matrix (GRM) was the most effective in reducing average progeny inbreeding; this strategy also resulted in fewer homozygous SNP out of 1,000 low-frequency SNP compared with the strategy using pedigree information. In the future, large numbers of cattle may be genotyped for low-density SNP panels. A GRM constructed using 3,123 SNP produced results similar to a GRM constructed using the full 43,115 SNP. These results demonstrate that using GRM information, a 1% reduction in progeny inbreeding (valued at around $5 per cow) can be made with very little compromise in the overall breeding objective. These results and the availability of low-cost, low-density genotyping make it attractive to apply mating plans that use genomic information in commercial dairy herds. [ABSTRACT FROM AUTHOR]

The existence of a genotype x environment interaction (G x E) for fertility traits, survival, and milk yield traits was examined by considering performance recorded in different calving systems (seasonal, split, and year round) or regions as different traits. For fertility traits and survival, G x E were also investigated by applying a random regression model using continuous environmental variables, such as level of herd milk production, temperature-humidity index, and herd size as environmental descriptors. The traits considered were calving interval, calving to first service interval (CFS), 25-d nonreturn rate at first service, pregnancy rate, survival, milk yield, fat yield, and protein yield and percentage. Data on Holstein-Friesian cows that calved between 1997 and 2005 were analyzed. The number of cows included in the analyses ranged from approximately 21,000 for pregnancy rate to approximately one-half million for survival. For all traits, heterogeneity in additive and phenotypic variances was observed. For example, for CFS the additive genetic and phenotypic variance in seasonal calving herds was only 9 and 15% of that in year-round calving herds, respectively. Genetic correlations among calving systems for milk yield traits were greater than 0.96. For calving interval, the lowest genetic correlation, of 0.83, was between split and year-round calving herds, but for CFS and pregnancy rate, genetic correlations as low as 0.37 were observed, although these estimates were associated with large standard errors. Genetic correlations between traits recorded in different Australian regions were greater than 0.89. Heritability and phenotypic variance for milk yield traits were the greatest in region 1, which consisted of Queensland, West Australia, South Australia, and New South Wales, and were least in region 3, which included Gippsland and Tasmania, in accordance with mean milk yield levels. Genetic correlations as low as 0.5 for some fertility traits between the 5th and 95th percentile of the distribution of the environmental descriptors, such as herd size and average herd milk production, were also observed. However, these estimates had large standard errors. Regardless of the environmental descriptor used, there was no evidence for the presence of a large G x E that resulted in economically significant reranking of bulls. [ABSTRACT FROM AUTHOR]

We compared the outcome of mating programs based on different evaluation models that included nonadditive genetic effects (dominance and heterozygosity) in addition to additive effects. The additive and dominance marker effects and the values of regression on average heterozygosity were estimated using 632,003 single nucleotide polymorphisms from 7,902 and 7,510 Holstein cows with calving interval and production (milk, fat, and protein yields) records, respectively. Expected progeny values were computed based on the estimated genetic effects and genotype probabilities of hypothetical progeny from matings between the available genotyped cows and the top 50 young genomic bulls. An index combining the traits based on their economic values was developed and used to evaluate the performance of different mating scenarios in terms of dollar profit. We observed that mating programs with nonadditive genetic effects performed better than a model with only additive effects. Mating programs with dominance and heterozygosity effects increased milk, fat, and protein yields by up to 38, 1.57, and 1.21 kg, respectively. The inclusion of dominance and heterozygosity effects decreased calving interval by up to 0.70 d compared with random mating. The average reduction in progeny inbreeding by the inclusion of nonadditive genetic effects in matings compared with random mating was between 0.25 to 1.57 and 0.64 to 1.57 percentage points for calving interval and production traits, respectively. The reduction in inbreeding was accompanied by an average of A$8.42 (Australian dollars) more profit per mating for a model with additive, dominance, and heterozygosity effects compared with random mating. Mate allocations that benefit from nonadditive genetic effects can improve progeny performance only in the generation where it is being implemented, and the gain from specific combining abilities cannot be accumulated over generations. Continuous updating of genomic predictions and mate allocation programs are required to benefit from nonadditive genetic effects in the long term. [ABSTRACT FROM AUTHOR]

A new breeding value that combines the amount of feed saved through improved metabolic efficiency with predicted maintenance requirements is described. The breeding value includes a genomic component for residual feed intake (RFI) combined with maintenance requirements calculated from either a genomic or pedigree estimated breeding value (EBV) for body weight (BW) predicted using conformation traits. Residual feed intake is only available for genotyped Holsteins; however, BW is available for all breeds. The RFI component of the "feed saved" EBV has 2 parts: Australian calf RFI and Australian lactating cow RFI. Genomic breeding values for RFI were estimated from a reference population of 2,036 individuals in a multi-trait analysis including Australian calf RFI (n = 843), Australian lactating cow RFI (n = 234), and UK and Dutch lactating cow RFI (n = 958). In all cases, the RFI pheno-types were deviations from a mean of 0, calculated by correcting dry matter intake for BW, growth, and milk yield (in the case of lactating cows). Single nucleotide polymorphism effects were calculated from the output of genomic BLUP and used to predict breeding values of 4,106 Holstein sires that were genotyped but did not have RFI phenotypes themselves. These bulls already had BW breeding values calculated from type traits, from which maintenance requirements in kilograms of feed per year were inferred. Finally, RFI and the feed required for maintenance (through BW) were used to calculate a feed saved breeding value and expressed as the predicted amount of feed saved per year. Animals that were 1 standard deviation above the mean were predicted to eat 66 kg dry matter less per year at the same level of milk production. In a data set of geno-typed Holstein sires, the mean reliability of the feed saved breeding value was 0.37. For Holsteins that are not genotyped and for breeds other than Holsteins, feed saved is calculated using BW only. From April 2015, feed saved has been included as part of the Australian national selection index, the Balanced Performance Index (BPI). Selection on the BPI is expected to lead to modest gains in feed efficiency. [ABSTRACT FROM AUTHOR]

Selection of animals for breeding ranked on estimated breeding value maximizes genetic gain in the next generation but does not necessarily maximize long-term response. An alternative method, as practiced by plant breeders, is to build a desired genotype by selection on specific loci. Maximal long-term response in animal breeding requires selection on estimated breeding values with constraints on coancestry. In this paper, we compared long-term genetic response using either a genotype building or a genomic estimated breeding value (GEBV) strategy for the Australian Selection Index (ASI), a measure of profit. First, we used real marker effects from the Australian Dairy Herd Improvement Scheme to estimate breeding values for chromosome segments (approximately 25 cM long) for 2,650 Holstein bulls. Second, we selected 16 animals to be founders for a simulated breeding program where, between them, founders contain the best possible combination of 2 segments from 2 animals at each position in the genome. Third, we mated founder animals and their descendants over 30 generations with 2 breeding objectives: (1) to create a population with the "ideal genotype," where the best 2 segments from the founders segregate at each position, or (2) obtain the highest possible response in ASI with coancestry lower than that achieved under breeding objective 1. Results show that genotype building achieved the ideal genotype for breeding objective 1 and obtained a large gain in ASI over the current population (+A$864.99). However, selection on overall GEBV had greater short-term response and almost as much long-term gain (+A$820.42). When coancestry was lowered under breeding objective 2, selection on overall GEBV achieved a higher response in ASI than the genotype building strategy. Selection on overall GEBV seems more flexible in its selection decisions and was therefore better able to precisely control coancestry while maximizing ASI. We conclude that selection on overall GEBV while minimizing average coancestry is the more practical strategy for dairy cattle where selection is for highly polygenic traits, the reproductive rate is relatively low, and there is low tolerance of coancestry. The outcome may be different for traits controlled by few loci of relatively large effects or for different species. In contrast to other simulations, our results indicate that response to selection on overall GEBV may continue for several generations. This is because long-term genetic change in complex traits requires favorable changes to allele frequencies for many loci located throughout the genome. [ABSTRACT FROM AUTHOR]

Achieving accurate genomic estimated breeding values for dairy cattle requires a very large reference population of genotyped and phenotyped individuals. Assembling such reference populations has been achieved for breeds such as Holstein, but is challenging for breeds with fewer individuals. An alternative is to use a multi-breed reference population, such that smaller breeds gain some advantage in accuracy of genomic estimated breeding values (GEBV) from information from larger breeds. However, this requires that marker-quantitative trait loci associations persist across breeds. Here, we assessed the gain in accuracy of GEBV in Jersey cattle as a result of using a combined Holstein and Jersey reference population, with either 39,745 or 624,213 single nucleotide polymorphism (SNP) markers. The surrogate used for accuracy was the correlation of GEBV with daughter trait deviations in a validation population. Two methods were used to predict breeding values, either a genomic BLUP (GBLUP_mod), or a new method, BayesR, which used a mixture of normal distributions as the prior for SNP effects, including one distribution that set SNP effects to zero. The GBLUP_mod method scaled both the genomic relationship matrix and the additive relationship matrix to a base at the time the breeds diverged, and regressed the genomic relationship matrix to account for sampling errors in estimating relationship coefficients due to a finite number of markers, before combining the 2 matrices. Although these modifications did result in less biased breeding values for Jerseys compared with an unmodified genomic relationship matrix, BayesR gave the highest accuracies of GEBV for the 3 traits investigated (milk yield, fat yield, and protein yield), with an average increase in accuracy compared with GBLUP_mod across the 3 traits of 0.05 for both Jerseys and Holsteins. The advantage was limited for either Jerseys or Holsteins in using 624,213 SNP rather than 39,745 SNP (0.01 for Holsteins and 0.03 for Jerseys, averaged across traits). Even this limited and nonsignificant advantage was only observed when BayesR was used. An alternative panel, which extracted the SNP in the transcribed part of the bovine genome from the 624,213 SNP panel (to give 58,532 SNP), performed better, with an increase in accuracy of 0.03 for Jerseys across traits. This panel captures much of the increased genomic content of the 624,213 SNP panel, with the advantage of a greatly reduced number of SNP effects to estimate. Taken together, using this panel, a combined breed reference and using BayesR rather than GBLUP_mod increased the accuracy of GEBV in Jerseys from 0.43 to 0.52, averaged across the 3 traits. [ABSTRACT FROM AUTHOR]

Single nucleotide polymorphism (SNP) associations with milk production traits found to be significant in different screening experiments, including SNP in genes hypothesized to be in gene pathways affecting milk production, were tested in a validation population to confirm their association. In total, 423 SNP were genotyped across 411 Holstein bulls, and their association with 6 milk production traits--Australian Selection Index (indicating the profitability of an animal's milk production), protein, fat, and milk yields, and protein and fat composition--were tested using single SNP regressions. Seventy-two SNP were significantly associated with one or more of the traits; their effects were in the same direction as in the screening experiment and therefore their association was considered validated. An over-representation of SNP (43 of the 423) on chromosome 20 was observed, including a SNP in the growth hormone receptor gene previously published as having an association with protein composition and protein and milk yields. The association with protein composition was confirmed in this experiment, but not the association with protein and milk yields. A multiple SNP regression analysis for all SNP on chromosome 20 was performed for all 6 traits, which revealed that this mutation was not significantly associated with any of the milk production traits and that at least 2 other quantitative trait loci were present on chromosome 20. [ABSTRACT FROM AUTHOR]

Multiple-trait genome-wide association study (GWAS) analyses were compared with single-trait GWAS for power to discover and subsequently validate genetic markers (single nucleotide polymorphisms; SNP) associated with dairy traits. The SNP associations were discovered in 1 Holstein population and validated in both a Holstein population consisting of bulls younger than those in the discovery population and a Jersey population. The multivariate methods used were a principal component analysis and a series of bivariate analyses. The statistical power of detecting associations using multiple-trait GWAS was as good as or better than that of the best single-trait GWAS. Additional SNP associations were found with the multivariate methods that had not been discovered in the singletrait analyses; this was achieved without an increase in the false discovery rate. From the multivariate analysis, 4 common pleiotropic patterns were identified among the putative quantitative trait loci (QTL) affecting the Australian selection index. These patterns could be interpreted as a primary effect of the putative QTL on 1 or more milk components and secondary effects on other components. The multivariate analysis did not appear to increase the precision with which putative QTL were mapped. [ABSTRACT FROM AUTHOR]

Genome-wide association studies (GWAS) were used to discover genomic regions explaining variation in dairy production and fertility traits. Associations were detected with either single nucleotide polymorphism (SNP) markers or haplotypes of SNP alleles. An across-breed validation strategy was used to narrow the genomic interval containing causative mutations. There were 39,048 SNP tested in a discovery population of 780 Holstein sires and validated in 386 Holsteins and 364 Jersey sires. Previously identified mutations affecting milk production traits were confirmed. In addition, several novel regions were identified, including a putative quantitative trait loci for fertility on chromosome 18 that was detected only using haplotypes greater than 3 SNP long. It was found that the precision of quantitative trait loci mapping increased with haplotype length as did the number of validated haplotypes discovered, especially across breed. Promising candidate genes have been identified in several of the validated regions. [ABSTRACT FROM AUTHOR]

Good performance in extended lactations of dairy cattle may have a beneficial effect on food costs, health, and fertility. Because data for extended lactation performance is scarce, lactation persistency has been suggested as a suitable selection criterion. Persistency phenotypes were calculated in several ways: P1 was yield relative to an approximate peak, P2 was the slope after peak production, and P3 was a measure derived to be phenotypically uncorrelated to yield and calculated as a function of linear regressions on test-day deviations of days in milk. Phenotypes P1, P2, and P3 were calculated for sires as solutions estimated from a random regression model fitted to milk yield. Because total milk yield, calculated as the sum of daily sire solutions, was correlated to P1 and P2 (r = 0.30 and 0.35 for P1 and P2, respectively), P1 and P2 were also adjusted for milk yield (P1adj and P2adj, respectively). To find genomic regions associated with the persistency phenotypes, we used a discovery population of 743 Holstein bulls proven before 2005 and 2 validation data sets of 357 Holstein bulls proven after 2005 and 294 Jersey sires. Two strategies were used to search for genomic regions associated with persistency: 1) persistency solutions were regressed on each single nucleotide polymorphism (SNP) in turn and 2) a genomic selection method (BayesA) was used where all SNP were fitted simultaneously. False discovery rates in the validation data were high (>66% in Holsteins and >77% in Jerseys). However, there were 2 genomic regions on chromosome 6 that validated in both breeds, including a cluster of 6 SNP at around 13.5 to 23.7 Mbp and another cluster of 5 SNP (70.4 to 75.6 Mbp). A third cluster validated in both breeds on chromosome 26 (0.33 to 1.46 Mbp). Validating SNP effects across 2 breeds is unlikely to happen by chance even when false discovery rates within each breed are high. However, marker-assisted selection on these selected SNP may not be the best way to improve this trait because the average variation explained by validated SNP was only 1 to 2%. Genomic selection could be a better alternative. Correlations between genomic breeding values predicted using all SNP simultaneously and estimated breeding values based on progeny test were twice as high as the equivalent correlations between estimated breeding values and parent average. Persistency is a good candidate for genomic selection because the trait is expressed late in lactation. [ABSTRACT FROM AUTHOR]

Dairy farming is carried out under a wide range of production environments, including large variations in the level of feeding. Although reranking of dairy sires based on the level of feeding of their daughters has been reported, detecting the genetic mutations that cause this genotype by environment interaction has not been previously attempted. In our experiment to find genetic markers for such mutations, we selected 388 Holstein bulls from the Australian dairy bull population and genotyped them for 9,919 single nucleotide polymorphism (SNP) markers. Production data, consisting of first-lactation test-day records for milk yield, fat yield, protein yield, protein percentage, and fat percentage, from the daughters of the genotyped bulls were used to estimate the effect of each SNP, which was modeled as a regression on herd mean test-day yield, where herd mean test-day yield is a descriptor of the environment. Data were analyzed with 4 models; in 2 models, daughter records were analyzed directly, with and without taking sire relationships into account. With the other 2 models, sire reaction norms for each trait were calculated and marker effects on the sire reaction norms were estimated with and without taking sire relationships into account. The results showed that using daughter records directly and accounting for sire relationships was necessary to obtain high power and to limit the number of false positives. With this approach, SNP with significant effects were found for all traits. Log transformation of the data did not affect the power of gene detection. The significant markers were categorized according to their joint effects on production and environmental sensitivity. Potential gene candidates and application of the markers is discussed. About one-third of the significant markers affect intercept and slope in opposite directions, and some of these facilitate marker-assisted selection for robustness. [ABSTRACT FROM AUTHOR]

A new technology called genomic selection is revolutionizing dairy cattle breeding. Genomic selection refers to selection decisions based on genomic breeding values (GEBV). The GEBV are calculated as the sum of the effects of dense genetic markers, or haplotypes of these markers, across the entire genome, thereby potentially capturing all the quantitative trait loci (QTL) that contribute to variation in a trait. The QTL effects, inferred from either haplotypes or individual single nucleotide polymorphism markers, are first estimated in a large reference population with phenotypic information. In subsequent generations, only marker information is required to calculate GEBV. The reliability of GEBV predicted in this way has already been evaluated in experiments in the United States, New Zealand, Australia, and the Netherlands. These experiments used reference populations of between 650 and 4,500 progeny-tested Holstein-Friesian bulls, genotyped for approximately 50,000 genome-wide markers. Reliabilities of GEBV for young bulls without progeny test results in the reference population were between 20 and 67%. The reliability achieved depended on the heritability of the trait evaluated, the number of bulls in the reference population, the statistical method used to estimate the single nucleotide polymorphism effects in the reference population, and the method used to calculate the reliability. A common finding in 3 countries (United States, New Zealand, and Australia) was that a straightforward BLUP method for estimating the marker effects gave reliabilities of GEBV almost as high as more complex methods. The BLUP method is attractive because the only prior information required is the additive genetic variance of the trait. All countries included a polygenic effect (parent average breeding value) in their GEBV calculation. This inclusion is recommended to capture any genetic variance not associated with the markers, and to put some selection pressure on low-frequency QTL that may not be captured by the markers. The reliabilities of GEBV achieved were significantly greater than the reliability of parental average breeding values, the current criteria for selection of bull calves to enter progeny test teams. The increase in reliability is sufficiently high that at least 2 dairy breeding companies are already marketing bull teams for commercial use based on their GEBV only, at 2 yr of age. This strategy should at least double the rate of genetic gain in the dairy industry. Many challenges with genomic selection and its implementation remain, including increasing the accuracy of GEBV, integrating genomic information into national and international genetic evaluations, and managing long-term genetic gain. [ABSTRACT FROM AUTHOR]

A 5 yr whole-system study, beginning in June 1994, compared the productivity of high [HGM; Australian Breeding Value (ABV) of 49.1 kg of fat plus protein] and low [LGM; ABV of 2.3 kg of fat plus protein] genetic merit cows. Cows from both groups were fed at 3 levels of concentrate (C): 0.34 (low C), 0.84 (medium C), and 1.71 (high C) t of DM/cow per lactation. Thus, there were 6 treatments (farmlets) composed of 18 cows each. The 30 blocks of pasture on each farmlet were matched between farmlets for pasture growth before the study (and soil characteristics and aspect). Cows were culled, and pasture and feed use were managed so as not to bias any one treatment. Genetic merit, level of feeding, and their interaction were significant effects for protein content, protein/cow, and milk and protein/ha. For fat and milk yield/cow, genetic merit and level of feeding were significant, whereas there was no significant effect of genetic merit on fat content. The difference of 46.8 kg of fat plus protein yield between the ABV of HGM and LGM cows and the actual difference in production between the 2 groups was not significantly different except for low C (27 kg) cows. This was due to a 3-fold lower protein yield difference (6 kg/cow) compared with an ABV difference for protein yield of 17.9 kg/cow. The dramatic effect of treatment on protein is in line with differences in the mean protein content (2.89% for the HGM - low C cows compared with a mean of 3.02% for the remaining groups) and mean body condition score [4.3 for HGM - low C cows compared with 4.8 for the mean of the remaining groups (scale 1 to 8)], both indicators reflecting a higher negative energy balance in the HGM - low C cows. When individual cow production was plotted against ABV for production of milk or protein yield all relationships were quadratic, but the slope was relatively flat (low response to ABV) for the low C cows, steeper for the medium C cows and steepest (but not linear) for the high C cows. The relationship between ABV for fat yield and actual fat yield was linear for all levels of concentrate. The mean milk yield/ha from pasture for the 6 farmlets over the 5 yr was 11,868 L, 11,417 L, or 7,761 L for the HGM cows fed at low C, medium C, or high C, respectively, and 10,579 L, 9,800 L, or 5,812 L for LGM cows, fed at low C, medium C, or high C, respectively. The response to concentrates fed was very high for the HGM - medium C cows at 0.115 kg fat plus protein or 1.75 L milk/kg of concentrate fed, with comparable figures of 0.083 kg and 1.0 L, 0.86 kg and 1.47 L and 0.066 and 0.92 L/kg of concentrate fed for the HGM - high C, LGM - medium C, and LGM - high C, respectively. The results show a significant genetic merit by environment (level of feeding) interaction for reproduction and most production parameters when considered in terms of the individual cow and the whole farm system. [ABSTRACT FROM AUTHOR]

The objective of this study was to apply reaction norm models to milk recording data to investigate genetic variation in and environmental sensitivity of susceptibility to milk fat depression (MFD). Data comprised 556,276 test-day records of 80,493 heifers in 1043 herds. Breeding values and genetic variances for fat percentage and fat yield were estimated by applying random regression models to average herd-test-day fat percentage. Genetic and permanent environmental correlations between fat yield expressed in different environments ranged, respectively, from 0.83 to 1.00 and from 0.29 to 1.00. Genetic and permanent environmental correlations between fat percentage expressed in different environments ranged, respectively, from 0.87 to 1.00 and from -0.05 to 0.99. Two traits were defined for MFD. The first trait reflected variation of milk fat percentage of animals within lactation after correction for year-season, herd-test-day, age-at-calving, and stage-of-lactation. This trait had an estimated heritability of about 5% and a genetic correlation between the fifth and 95th percentile of the data of 0.50. The second trait reflected the deviation of an animal's fat percentage on a test-day from its expected fat percentage based on fat percentage on the first test-day. This trait had an estimated heritability of about 4% and a genetic correlation between the fifth and 95th percentile of the data of 0.43. The correlation between estimated breeding values of sires for the 2 MFD traits was -0.3. Our results suggest that genetic variation in susceptibility to MFD is present and that selection for reduced susceptibility to MFD is possible. [ABSTRACT FROM AUTHOR]

In Australia, dairy farming is carried out in environments that vary in many ways, including level of feeding and climate variables such as temperature and humidity. The aim of this study was to assess the magnitude of genotype x environment interactions (GxE) on milk production traits (milk yield, protein yield, and fat yield) for a range of environmental descriptors. The environment on individual test days was described by herd size (HS), average herd protein yield (AHTDP), herd test-day coefficient of variation for protein yield (HTDCV), and temperature humidity index (THI). A sire random regression model was used to model the response of a sire's daughters to variation in the environment and to calculate the genetic correlation between the same traits measured in two widely different environments. Using test-day records, rather than average lactation yields, allowed exploitation of within-cow variation as well as between-cow variation at different levels of AHTDP, and led to more accurate estimates of sire breeding values for "response to environment." The greatest GxE observed was due to variation in AHTDP, with a genetic correlation of 0.78 between protein yield when AHTDP = 0.54 kg and protein yield when AHTDP = 1.1 kg (the 5th and 95th percentile of the distribution of AHTDP). The GxE was also observed for THI, with a genetic correlation of 0.90 between protein yield at the 5th and 95th percentile of THI. The use of response to environment estimated breeding values to improve the accuracy of international sire evaluations is discussed. [ABSTRACT FROM AUTHOR]

A correction to the article "Invited review: Genomic Selection in Dairy Cattle: Progress and Challenges," that was published in the 2009 issue is presented.

The welfare of calves is important to both farmers and consumers. Practices that increase the proportion of calves born alive and enable them to thrive through to weaning contribute to improved sustainability. Stillbirths (SB) are calvings where the calf dies at birth or within 24 h after birth. Preweaning mortality (PWM) refers to calves that die after the first day of life but before weaning based on termination data. Both SB and PWM are binary traits characterized by low heritability. Data collection for these traits is incomplete, compared with traits such as milk yield in cows. Despite these challenges, genetic variation can be measured and used to produce breeding tools, such as EBVs, to reduce calf mortality over time. The aim of this study was to compare the performance of various linear models to predict SB and PWM traits in Holstein and Jersey cattle and evaluate their applicability for industry-wide use in the Australian dairy industry. Calving records from around 2.25 million Holstein and Jersey dams were obtained from DataGene's Central Data Repository from the year 2000 onward, to calculate genetic parameters. About 7% of calves were recorded as SB in the period from 2000 to 2021 (n = 1.48 million calvings). The prevalence of PWM was much lower than SB during the same period at 2% (n = 0.89 million calves). Genetic parameters were estimated for SB direct, SB maternal, and PWM using bivariate linear models with calving ease (CE) as the second trait in the model. The heritability of these calf traits was low and varied between 1% and 5% depending on the breed, trait, and model. In Holstein cattle, heritabilities were 2% for PWM and SB direct and 1% for SB maternal, whereas in Jersey cattle heritabilities were 5% for PWM, 2% for SB direct, and 1% for SB maternal. The genetic trends for both SB direct and SB maternal in Holstein cattle indicate improvement in both traits, whereas there was no apparent increase or decrease in PWM in the past 2 decades. The coefficient of genetic variation for SB direct and PWM was between 11.7% and 23.0% in Holstein and Jersey cattle, demonstrating considerable genetic variation in calf survival traits as a first step to using genetic selection to increase the proportion of calves born alive and calves weaned. A focus on improved calf and calving recording practices is expected to increase the reliability of genetic predictions., (The Authors. Published by Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

Fertility in dairy cattle has declined as an unintended consequence of single-trait selection for high milk yield. The unfavorable genetic correlation between milk yield and fertility is now well documented; however, the underlying physiological mechanisms are still uncertain. To understand the relationship between these traits, we developed a method that clusters variants with similar patterns of effects and, after the integration of gene expression data, identifies the genes through which they are likely to act. Biological processes that are enriched in the genes of each cluster were then identified. We identified several clusters with unique patterns of effects. One of the clusters included variants associated with increased milk yield and decreased fertility, where the "archetypal" variant (i.e., the one with the largest effect) was associated with the GC gene, whereas others were associated with TRIM32, LRRK2, and U6-associated snRNA. These genes have been linked to transcription and alternative splicing, suggesting that these processes are likely contributors to the unfavorable relationship between the 2 traits. Another cluster, with archetypal variant near DGAT1 and including variants associated with CDH2, BTRC, SFRP2, ZFHX3, and SLITRK5, appeared to affect milk yield but have little effect on fertility. These genes have been linked to insulin, adipose tissue, and energy metabolism. A third cluster with archetypal variant near ZNF613 and including variants associated with ROBO1, EFNA5, PALLD, GPC6, and PTPRT were associated with fertility but not milk yield. These genes have been linked to GnRH neuronal migration, embryonic development, or ovarian function. The use of archetypal clustering to group variants with similar patterns of effects may assist in identifying the biological processes underlying correlated traits. The method is hypothesis generating and requires experimental confirmation. However, we have uncovered several novel mechanisms potentially affecting milk production and fertility such as GnRH neuronal migration. We anticipate our method to be a starting point for experimental research into novel pathways, which have been previously unexplored within the context of dairy production., (The Authors. Published by Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

The longevity of dairy cattle has economic, animal welfare, and health implications and is influenced by the frequency of mortality on the farm and sale for slaughter. In this study cows removed from the herd due to death or slaughter during the lactation were coded 1 and cows that were not terminated were coded 0. Genetic parameters for mortality rates (MR) and slaughter rates (SR) were estimated for Holstein (H) and Jersey (J) breeds by applying both linear (LM) and threshold (TM) sire models using about 1.2 million H and 286,000 J cows. Estimated breeding values (EBV) for MR and SR were predicted using animal models to assess the opportunity for selection and genetic trends. Cow termination data, recorded between 1990 and 2020 on a voluntary basis by Australian dairy farmers, were analyzed. Cow MR has increased from below 1% in the 1990s to 4.1% and 3.6% in recent years in H and J cows, respectively. Most dead cows (∼36%) left the herd before 120 d of lactation, while cows that were slaughtered left the herd toward the end of the lactation. Using the LM, heritability (h 2 ) estimates for MR were lower (1%) than those for SR (2%-3.5%). When h 2 were estimated using a TM, the estimates for both traits varied between 4% and 20%, suggesting that the difference in incidence level is one of the reasons for the difference in the h 2 values between MR and SR. Early test-day milk yield (MY) and 305-d MY (305-d MY) have unfavorable genetic correlations (0.32-0.41) with MR in both breeds. The genetic correlations of calving interval with MR were stronger (0.54-0.68) than with SR (0.28-0.45) suggesting that poor fertility can serve as an early indicator of poor cow health that may lead to increased risk of death. High early test-day somatic cell count is genetically associated with increased likelihood of slaughter (0.24-0.46), but not with increased likelihood of death. In H, 305-d protein yield (PY) had the strongest genetic correlation (-0.34 to -0.40) with SR whereas in J, both 305-d PY and fat yield showed high genetic (-0.64 to -0.70) and moderate environmental (-0.35 to -0.37) correlations with SR. The genetic correlation of removal from the herd due to death and slaughter was negative (-0.3) in J and zero in H. Strong selection for improved fertility and survival and less selection emphasis for MY, has led to an improvement in the genetic trend for cow MR in H and the trend in J has stabilized. Although genetic evaluations for cow MR are feasible, the reliabilities of the EBV are low and the level of cow MR in Australia are relatively low compared with similar countries. Therefore, genetic evaluation for survival based on mortality and slaughter data could be sufficient in the current selection circumstances where breeding objectives are broadly defined. Nevertheless, all Australian farmers should be encouraged to continue recording mortality and slaughter data for monitoring of the trends and for future development of genetic evaluations., (© 2023, The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

We conducted a retrospective cohort study to validate the efficacy of the Australian multitrait fertility estimated breeding value (EBV). We did this by determining its associations with phenotypic measures of reproductive performance (i.e., submission rate, first service conception rate, and early calving). Our secondary aim was to report the associations between these reproductive outcomes and management and climate-related factors hypothesized to affect fertility. Our study population included 38 pasture-based dairy herds from the northern Victorian irrigation region in Australia. We collected records for 86,974 cows with 219,156 lactations and 438,578 mating events from the date on which managers started herd recording until December 2016, comprising both fertility-related data such as insemination records, calving dates, and pregnancy test results, and systems-related data such as production, herd size, and calving pattern. We also collected hourly data from 2004 to 2017 from the closest available weather station to account for climate-related factors (i.e., temperature humidity index; THI). Multilevel Cox proportional hazard models were used to analyze time-to-event outcomes (days to first service, days to cow calving following the planned herd calving start date), and multilevel logistic regression models for binomial outcomes (conception to first service) in the Holstein-Friesian and Jersey breeds. A 1-unit increase in daughter fertility EBV was associated with a 5.4 and 8.2% increase in the daily hazard of calving in the Holstein-Friesian and Jersey breeds respectively. These are relative increases (i.e., a Holstein-Friesian herd with a 60% 6-wk in-calf rate would see an improvement to 63.2% with a 1-unit increase in herd fertility EBV). Similar results were obtained for submission and conception rate. Associations between 120-d milk yield and reproductive outcome were complicated by interactions with 120-d protein percentage and calving age, depending on the breed and outcome. In general, we found that the reproductive performance of high milk-yielding animals deteriorated faster with age than low milk-yielding animals, and high protein percentage exacerbated the differences between low and high milk-yielding animals. Climate-related factors were also associated with fertility, with a 1-unit increase in maximum THI decreasing first service conception rate by 1.2% for Holstein-Friesians but having no statistically significant association in the Jersey breed. However, THI had a negative association in both breeds on the daily hazard of calving. Our study validates the efficacy of the daughter fertility EBV for improving herd reproductive performance and identifies significant associations between 120-d milk and protein yields and THI on the fertility of Australian dairy cows., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

Methane is a greenhouse gas of high interest to the dairy industry, with 57% of Australia's dairy emissions attributed to enteric methane. Enteric methane emissions also constitute a loss of approximately 6.5% of ingested energy. Genetic selection offers a unique mitigation strategy to decrease the methane emissions of dairy cattle, while simultaneously improving their energy efficiency. Breeding objectives should focus on improving the overall sustainability of dairy cattle by reducing methane emissions without negatively affecting important economic traits. Common definitions for methane production, methane yield, and methane intensity are widely accepted, but there is not yet consensus for the most appropriate method to calculate residual methane production, as the different methods have not been compared. In this study, we examined 9 definitions of residual methane production. Records of individual cow methane, dry matter intake (DMI), and energy corrected milk (ECM) were obtained from 379 animals and measured over a 5-d period from 12 batches across 5 yr using the SF 6 tracer method and an electronic feed recording system, respectively. The 9 methods of calculating residual methane involved genetic and phenotypic regression of methane production on a combination of DMI and ECM corrected for days in milk, parity, and experimental batch using phenotypes or direct genomic values. As direct genomic values (DGV) for DMI are not routinely evaluated in Australia at this time, DGV for FeedSaved, which is derived from DGV for residual feed intake and estimated breeding value for bodyweight, were used. Heritability estimates were calculated using univariate models, and correlations were estimated using bivariate models corrected for the fixed effects of year-batch, days in milk, and lactation number, and fitted using a genomic relationship matrix. Residual methane production candidate traits had low to moderate heritability (0.10 ± 0.09 to 0.21 ± 0.10), with residual methane production corrected for ECM being the highest. All definitions of residual methane were highly correlated phenotypically (>0.87) and genetically (>0.79) with one another and moderately to highly with other methane candidate traits (>0.59), with high standard errors. The results suggest that direct selection for a residual methane production trait would result in indirect, favorable improvement in all other methane traits. The high standard errors highlight the importance of expanding data sets by measuring more animals for their methane emissions and DMI, or through exploration of proxy traits and combining data via international collaboration., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

The objectives of this study were (1) to evaluate the computational feasibility of the multitrait test-day single-step SNP-BLUP (ssSNP-BLUP) model using phenotypic records of genotyped and nongenotyped animals, and (2) to compare accuracies (coefficient of determination; R 2 ) and bias of genomic estimated breeding values (GEBV) and de-regressed proofs as response variables in 3 Australian dairy cattle breeds (i.e., Holstein, Jersey, and Red breeds). Additive genomic random regression coefficients for milk, fat, protein yield and somatic cell score were predicted in the first, second, and third lactation. The predicted coefficients were used to derive 305-d GEBV and were compared with the traditional parent averages obtained from a BLUP model without genomic information. Cow fertility traits were evaluated from the 5-trait repeatability model (i.e., calving interval, days from calving to first service, pregnancy diagnosis, first service nonreturn rate, and lactation length). The de-regressed proofs were only for calving interval. Our results showed that ssSNP-BLUP using multitrait test-day model increased reliability and reduced bias of breeding values of young animals when compared with parent average from traditional BLUP in Australian Holsten, Jersey, and Red breeds. The use of a custom selection of approximately 46,000 SNP (custom XT SNP list) increased the reliability of GEBV compared with the results obtained using the commercial Illumina 50K chip (Illumina, San Diego, CA). The use of the second preconditioner substantially improved the convergence rate of the preconditioned conjugate gradient method, but further work is needed to improve the efficiency of the computation of the Kronecker matrix product by vector. Application of ssSNP-BLUP to multitrait random regression models is computationally feasible., (Copyright © 2020 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

The aim of this study was to investigate the feasibility of using mid-infrared (MIR) spectroscopy analysis of milk samples to increase the power and precision of genome-wide association studies (GWAS) for milk composition and to better distinguish linked quantitative trait loci (QTL). To achieve this goal, we analyzed phenotypic data of milk composition traits, related MIR spectra, and genotypic data comprising 626,777 SNP on 5,202 Holstein, Jersey, and crossbred cows. We performed a conventional GWAS on protein, lactose, fat, and fatty acid concentrations in milk, a GWAS on individual MIR wavenumbers, and a partial least squares regression (PLS), which is equivalent to a multi-trait GWAS, exploiting MIR data simultaneously to predict SNP genotypes. The PLS detected most of the QTL identified using single-trait GWAS, usually with a higher significance value, as well as previously undetected QTL for milk composition. Each QTL tends to have a different pattern of effects across the MIR spectrum and this explains the increased power. Because SNP tracking different QTL tend to have different patterns of effect, it was possible to distinguish closely linked QTL. Overall, the results of this study suggest that using MIR data through either GWAS or PLS analysis applied to genomic data can provide a powerful tool to distinguish milk composition QTL., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Genomic prediction is widely used to select candidates for breeding. Size and composition of the reference population are important factors influencing prediction accuracy. In Holstein dairy cattle, large reference populations are used, but this is difficult to achieve in numerically small breeds and for traits that are not routinely recorded. The prediction accuracy is usually estimated using cross-validation, requiring the full data set. It would be useful to have a method to predict the benefit of multibreed reference populations that does not require the availability of the full data set. Our objective was to study the effect of the size and breed composition of the reference population on the accuracy of genomic prediction using genomic BLUP and Bayes R. We also examined the effect of trait heritability and validation breed on prediction accuracy. Using these empirical results, we investigated the use of a formula to predict the effect of the size and composition of the reference population on the accuracy of genomic prediction. Phenotypes were simulated in a data set containing real genotypes of imputed sequence variants for 22,752 dairy bulls and cows, including Holstein, Jersey, Red Holstein, and Australian Red cattle. Different reference populations were constructed, varying in size and composition, to study within-breed, multibreed, and across-breed prediction. Phenotypes were simulated varying in heritability, number of chromosomes, and number of quantitative trait loci. Genomic prediction was carried out using genomic BLUP and Bayes R. We used either the genomic relationship matrix (GRM) to estimate the number of independent chromosomal segments and subsequently to predict accuracy, or the accuracies obtained from single-breed reference populations to predict the accuracies of larger or multibreed reference populations. Using the GRM overestimated the accuracy; this overestimation was likely due to close relationships among some of the reference animals. Consequently, the GRM could not be used to predict the accuracy of genomic prediction reliably. However, a method using the prediction accuracies obtained by cross-validation using a small, single-breed reference population predicted the accuracy using a multibreed reference population well and slightly overestimated the accuracy for a larger reference population of the same breed, but gave a reasonably close estimate of the accuracy for a multibreed reference population. This method could be useful for making decisions regarding the size and composition of the reference population., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Cost-effective high-density (HD) genotypes of livestock species can be obtained by genotyping a proportion of the population using a HD panel and the remainder using a cheaper low-density panel, and then imputing the missing genotypes that are not directly assayed in the low-density panel. The efficacy of genotype imputation can largely be affected by the structure and history of the specific target population and it should be checked before incorporating imputation in routine genotyping practices. Here, we investigated the efficacy of imputation in crossbred dairy cattle populations of East Africa using 4 different commercial single nucleotide polymorphisms (SNP) panels, 3 reference populations, and 3 imputation algorithms. We found that Minimac and a reference population, which included a mixture of crossbred and ancestral purebred animals, provided the highest imputation accuracy compared with other scenarios of imputation. The accuracies of imputation, measured as the correlation between real and imputed genotypes averaged across SNP, were around 0.76 and 0.94 for 7K and 40K SNP, respectively, when imputed up to a 770K panel. We also presented a method to maximize the imputation accuracy of low-density panels, which relies on the pairwise (co)variances between SNP and the minor allele frequency of SNP. The performance of the developed method was tested in a 5-fold cross-validation process where various densities of SNP were selected using the (co)variance method and also by alternative SNP selection methods and then imputed up to the HD panel. The (co)variance method provided the highest imputation accuracies at almost all marker densities, with accuracies being up to 0.19 higher than the random selection of SNP. The accuracies of imputation from 7K and 40K panels selected using the (co)variance method were around 0.80 and 0.94, respectively. The presented method also achieved higher accuracy of genomic prediction at lower densities of selected SNP. The squared correlation between genomic breeding values estimated using imputed genotypes and those from the real 770K HD panel was 0.95 when the accuracy of imputation was 0.64. The presented method for SNP selection is straightforward in its application and can ensure high accuracies in genotype imputation of crossbred dairy populations in East Africa., (The Authors. Published by FASS Inc. and Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

Genomic prediction is applicable to individuals of different breeds. Empirical results to date, however, show limited benefits in using information on multiple breeds in the context of genomic prediction. We investigated a multitask Bayesian model, presented previously by others, implemented in a Bayesian stochastic search variable selection (BSSVS) model. This model allowed for evidence of quantitative trait loci (QTL) to be accumulated across breeds or for both QTL that segregate across breeds and breed-specific QTL. In both cases, single nucleotide polymorphism effects were estimated with information from a single breed. Other models considered were a single-trait and multitrait genomic residual maximum likelihood (GREML) model, with breeds considered as different traits, and a single-trait BSSVS model. All single-trait models were applied to each of the 2 breeds separately and to the pooled data of both breeds. The data used included a training data set of 6,278 Holstein and 722 Jersey bulls, as well as 374 Jersey validation bulls. All animals had genotypes for 474,773 single nucleotide polymorphisms after editing and phenotypes for milk, fat, and protein yields. Using the same training data, BSSVS consistently outperformed GREML. The multitask BSSVS, however, did not outperform single-trait BSSVS, which used pooled Holstein and Jersey data for training. Thus, the rigorous assumption that the traits are the same in both breeds yielded a slightly better prediction than a model that had to estimate the correlation between the breeds from the data. Adding the Holstein data significantly increased the accuracy of the single-trait GREML and BSSVS in predicting the Jerseys for milk and protein, in line with estimated correlations between the breeds of 0.66 and 0.47 for milk and protein yields, whereas only the BSSVS model significantly improved the accuracy for fat yield with an estimated correlation between breeds of only 0.05. The relatively high genetic correlations for milk and protein yields, and the superiority of the pooling strategy, is likely the result of the observed admixture between both breeds in our data. The Bayesian model was able to detect several QTL in Holsteins, which likely enabled it to outperform GREML. The inability of the multitask Bayesian models to outperform a simple pooling strategy may be explained by the fact that the pooling strategy assumes equal effects in both breeds; furthermore, this assumption may be valid for moderate- to large-sized QTL, which are important for multibreed genomic prediction., (Copyright © 2018 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

A deterministic model to calculate rates of genetic gain and inbreeding was used to compare a range of breeding scheme designs under genomic selection (GS) for a population of 140,000 cows. For most schemes it was assumed that the reliability of genomic breeding values (GEBV) was 0.6 across 4 pathways of selection. In addition, the effect of varying reliability on the ranking of schemes was also investigated. The schemes considered included intense selection in male pathways and genotyping of 1,000 young bulls (GS-Y). This scheme was extended to include selection in females and to include a "worldwide" scheme similar to GS-Y, but 6 times as large and assuming genotypes were freely exchanged between 6 countries. An additional worldwide scheme was modeled where GEBV were available through international genetic evaluations without exchange of genotypes. Finally, a closed nucleus herd that used juvenile in vitro embryo transfer in heifers was modeled so that the generation interval in female pathways was reduced to 1 or 2 yr. When the breeding schemes were compared using a GEBV reliability of 0.6, the rates of genetic gain were between 59 and 130% greater than the rate of genetic gain achieved in progeny testing. This was mainly through reducing the generation interval and increasing selection intensity. Genomic selection of females resulted in a 50% higher rate of genetic gain compared with restricting GS to young bulls only. The annual rates of inbreeding were, in general, 60% lower than with progeny testing, because more sires of bulls and sires of cows were selected, thus increasing the effective population size. The exception was in nucleus breeding schemes that had very short generation intervals, resulting in higher rates of both gain and inbreeding. It is likely that breeding companies will move rapidly to alter their breeding schemes to make use of genomic selection because benefits to the breeding companies and to the industry are considerable., (Copyright © 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Genetic parameters for daily somatic cell counts (SCC) of the first three parities were estimated for Australian Dairy Cattle. Most of the data analyses were carried out with a sire random regression model. The estimates were compared with those from conventional ten-trait analyses and animal models. In the first-parity estimates of heritabilities (h2) were low (0.04 to 0.05) at the beginning of the lactation and higher (0.11 to 0.13) at the end. The average h2 estimated from random regression sire model, random regression animal model and conventional multitrait sire model were 0.09, 0.09, and 0.08, respectively, in the first lactation. The average h2 were 0.09 and 0.11 in the second and third parities, respectively. Genetic correlations between daily log(e) SCC within parity were high for adjacent tests (nearly 1) and low (as low as 0.30) between the beginning and the end of the lactation. Generally, the genetic correlations between parities depend on how far apart they are and on whether they are on the same day in any two parities. Across parities, on average, genetic correlations between parities 1 and 3 were the lowest and those between 1 and 2 intermediate, while those between 2 and 3 were the highest. The estimated environmental correlations were lower than the genetic correlations, but the trends were generally similar. Differences in genetic parameter estimates due to model were small, except for some genetic correlations. The high residual error variances, the low h2, and the inconsistency in genetic correlations that were observed particularly at the beginning of the first lactation suggest that log(e) SCC early in the first lactation may be related to a spike in SCC as result of infection and (or) onset of lactation while SCC later in lactation represents a sustained response to infection. Accounting for the variation in heritabilities and correlations should improve the accuracy of genetic evaluations for SCC based on test day records.

In the analysis of test day records for dairy cattle, covariance functions allow a continuous change of variances and covariances of test day yields on different lactation days. The equivalence between covariance functions as an infinite dimensional extension of multivariate models and random regression models is shown in this paper. A canonical transformation procedure is proposed for random regression models in large-scale genetic evaluations. Two methods were used to estimate covariance function coefficients for first parity test day yields of Holsteins: 1) a two-step procedure fitting covariance functions to matrices with estimated genetic and residual covariances between predetermined periods of lactation and 2) REML directly from data with a random regression model. The first method gave more reliable estimates, particularly for the periphery of the trajectory. The goodness of fit of a random regression model based on covariables describing the shape of the lactation curve was nearly the same as random regression on Legendre polynomials. In the latter model, two and three regression coefficients were sufficient to fit the covariance structure for additive genetic and permanent environment, respectively. The eigenfunction pattern revealed the possibility of selection for persistency. Covariance functions can be usefully implemented in large-scale test day models by means of random regressions.

The breeding objective is usually to increase the profit of the firm, industry, or society that is investing in a breeding program. This objective should include long-term genetic gain and nonadditive genetic changes such as inbreeding depression and possibly a weighting against the variability of outcome. The breeding objective is described by a profit function that takes genetic values as input and produces profit as outcome. This profit function may be a bioeconomic model of the farm. The traits in the profit function should relate as directly as possible to all sources of income and costs. The profit function can include variables controlled by management decisions if these interact with genetic merit. The differences between genotypes should be evaluated when management variables are optimized for each genotype. In the long term, mean profit is expected to be close to zero, and all costs are assumed to be variable costs. Under these conditions, the relative economic weights are the same, regardless of how the farm is constrained how the unit for which profit is calculated, whether the perspective is that of individual producers, an industry, or consumers. However, if price signals are not passed along the chain from consumers to seed-stock breeders, the economic weights become distorted. The use to which breeding objectives are put, the perspective from which they are calculated, the rescaling and biological versus economic objectives, and the special problems associated with the inclusion of length of herdlife in the objective are discussed.

Multiple-trait BLUP evaluations of test day records require a large number of genetic parameters. This study estimated covariances with a reduced model that included covariance functions in two dimensions (stage of lactation and herd production level) and all three yield traits. Records came from all six states in Australia, were evenly distributed across the herd production levels, but decreased with increasing lactation stage from 9693 records for the 1st mo of lactation to 4199 records for the 10th mo. Using the variance component estimation package and a bivariate animal model, 1176 genetic (co)variances and 312 environmental (co)variances were estimated for 48 traits (1, 4, 7, and 10 mo of lactation; herd production levels of < 20, 20 to 22, 22 to 24, > 24 kg of milk/d; and milk, fat, and protein yields). The genetic (co)variances could be predicted by a multiplicative model that included 1) a term dependent on which yields (milk, fat, or protein) were involved in the covariance, 2) the covariance functions for month of lactation and herd production level, and 3) a covariance function for the interaction between these. This model required only 27 parameters instead of the 1176 (co)variances. For the environmental (co)variances, a model was fitted that contained several additional covariance functions. This model reduced the number of parameters from 312 to 71. For the same trait at the same production level, genetic correlations between test days ranged from 0.59 to 1, and environmental correlations ranged from 0.17 to 0.48. Genetic correlations between milk and fat, milk and protein, and fat and protein were 0.38, 0.83, 0.59, respectively, and correlations between the herd production levels ranged from 0.79 to 0.97. Failure to consider herd production level in a test day model evaluation might result, for instance, in overweighting of early lactation information from high production herds compared with information coming from bulls tested across all production levels.

A multitrait analysis of test day yields is proposed that includes 60 traits [3 yield traits (milk, fat, and protein), 2 parity groups (first and later) per yield trait, and 10 stages of lactation per parity]. To reduce the computations needed for the 60 traits, test day effects are estimated within the herd before analysis across herds, the rank of t he genetic (co)variance matrix is reduced, a canonical transformation is used with missing values replace by their expectations, and a repeatability model is applied to allow inclusion of parities after second. Historical 305-d records are included through their correlations with test day effects. Possible benefits from this model include 1) more accurate estimation of environmental effects from including the influence of particular days of recording, 2) optimal use of information from all test days (especially for lactations with long intervals from calving to first test or between tests), 3) improved accuracy of evaluations for component yields through contributions from information for milk yield, and 4) greater stability of bull evaluations from accounting for genetic differences among daughters in the shape of lactation curve and maturity rate.

Genetic parameters, such as heritabilities and genetic correlations were estimated for milk yield, survival, workability, and type traits for Australian Holstein-Friesian and Jersey cattle. All analyses were performed using multivariate REML with a sire model. Heritabilities for lactation yield traits were moderate, ranging from .20 to .28, and heritabilities for mean test day deviations were approximately .40 higher. Heritabilities for survival (probability of surviving to the next lactation) were low, ranging from .02 to .08. Genetic correlations between survival scores were high, ranging from .37 to .98, in particular between adjacent survival scores (on average .91 and .97 for Holstein-Friesians and Jerseys). Heritabilities for stayabilities were larger, ranging from .03 to .22. On average, genetic correlations between stayabilities were very high, ranging from .66 to .99. For milking speed, temperament, and likeability, heritability estimates ranged from .18 (for likeability in Holstein-Friesians) to .29 (for milking speed in Jerseys). Undesirable scores for milking speed and temperament had negative genetic correlations with stayabilities (correlations approximately -.20). Heritabilities for type traits were all moderate (.11 to .42), and genetic correlations among type traits and between type traits and production traits were large. Phenotypic correlations between type traits and stayabilities were low. Generally, genetic correlations between type traits and stayabilities were low although the standard errors of those estimates were large.

The replacement of other black and white cattle strains by the North American Holstein breed, which itself is dominated by a small number of elite sires, has reduced the genetic diversity of the global population. Intense selection on a global basis leads to rapid genetic improvement but reduces effective population size. The optimal global effective population size was chosen to maximize the net present value of all future benefits from the breeding program. Two separate discount rates were used to reflect concerns about the long-term costs of small effective population size. This led to a higher optimal number of bull-sires than in past analyses. The optimum was sensitive to the magnitude of inbreeding depression and to the discount rates, but not to the variance caused by new mutations and the size of the world population. The genetic correlation between the breeding objectives of different AI studs controls the extent to which they all select the same sires of sons and, hence, affects the global effective population size. The prediction is made that different countries will select partially different sires, but genetically isolated strains will not reemerge. A better global breeding program is likely when selection of sires takes account of inbreeding depression and small genotype by environment interactions.