Heterogeneity of variance and genetic parameters for milk production in cattle, using Bayesian inference

The goal of this study was to verify the effect of heterogeneity of variance (HV) on milk production in up to 305 days of lactation (L305) of daughters of Girolando, Gir and Holstein sires, as well as in the genetic evaluation of these sires and their progenies. in Brazil. The model included contemporary groups (consisting of herd, year and calving season) as a fixed effect, cow age at calving (linear and quadratic effects) and heterozygosity (linear effect) as covariates, in addition to the random effects of direct additive genetic and environmental, permanent and residual. The first analysis consisted of the single-trait animal model, with L305 records (disregarding HV). The second considered classes of standard deviations (SD): two-trait model including low and high classes (considering HV), according to the standardized means of L305 for herd-year of calving. The low SD class was composed of herds with SD equal to or less than zero and the high class with positive SD values. Estimates of (co)variance components and breeding values were obtained separately for each scenario using Bayesian inference via Gibbs sampling. Different heritability was estimated. Higher for the high DP class in the Gir (0.20) and Holstein (0.15) breeds, not occurring the same in the Girolando breed, with a lower value among the classes for the high DP (0.10). High values of genetic correlations were also found between low and high SD classes (0.88; 0.85 and 0.79) for the Girolando, Gir and Holstein breeds, respectively. Like the order correlations (Spearman) which were also high for the three breeds analyzed (equal to or above 0.92). Thus, the presence of HV had a smaller impact for L305 and did not affect the genetic evaluation of sires.

Development of genetic evaluation for milk production traits of Holsteins in Japan

The procedure used for the genetic evaluation of dairy cattle in Japan has developed from a lactation sire–MGS model to a multiple‐lactation random regression test‐day animal model. Genetic evaluation of Holstein bulls in Japan began in 1989 with the use of field‐style progeny testing; dairy herd improvement program data from all over Japan were used, along with a sire and maternal grandsire model. In 1993, an animal model was introduced to estimate breeding values for yield and type traits. A random regression test‐day model was first applied in 2010. In the business of breeding dairy cattle, it is very important to users that estimated breeding values are reliable and stable among subsequent routine evaluations. With experience in the genetic evaluation of dairy cattle in Japan, Japanese researchers have found ways to improve the stability of estimated breeding values. These modifications involve changes in data editing, development of evaluation models, changes to the structures of unknown‐parent groups, awareness of the problems of predicting lactation yield from partial test‐day records, and adjustment for heterogeneity within herd variances. Here, I introduce developments in, and our experiences with, the genetic evaluation of yield traits of Holstein cattle in Japan.

Empirical and deterministic accuracies of across-population genomic prediction

BACKGROUND

Differences in linkage disequilibrium and in allele substitution effects of QTL (quantitative trait loci) may hinder genomic prediction across populations. Our objective was to develop a deterministic formula to estimate the accuracy of across-population genomic prediction, for which reference individuals and selection candidates are from different populations, and to investigate the impact of differences in allele substitution effects across populations and of the number of QTL underlying a trait on the accuracy.

METHODS

A deterministic formula to estimate the accuracy of across-population genomic prediction was derived based on selection index theory. Moreover, accuracies were deterministically predicted using a formula based on population parameters and empirically calculated using simulated phenotypes and a GBLUP (genomic best linear unbiased prediction) model. Phenotypes of 1033 Holstein-Friesian, 105 Groninger White Headed and 147 Meuse-Rhine-Yssel cows were simulated by sampling 3000, 300, 30 or 3 QTL from the available high-density SNP (single nucleotide polymorphism) information of three chromosomes, assuming a correlation of 1.0, 0.8, 0.6, 0.4, or 0.2 between allele substitution effects across breeds. The simulated heritability was set to 0.95 to resemble the heritability of deregressed proofs of bulls.

RESULTS

Accuracies estimated with the deterministic formula based on selection index theory were similar to empirical accuracies for all scenarios, while accuracies predicted with the formula based on population parameters overestimated empirical accuracies by ~25 to 30%. When the between-breed genetic correlation differed from 1, i.e. allele substitution effects differed across breeds, empirical and deterministic accuracies decreased in proportion to the genetic correlation. Using a multi-trait model, it was possible to accurately estimate the genetic correlation between the breeds based on phenotypes and high-density genotypes. The number of QTL underlying the simulated trait did not affect the accuracy.

CONCLUSIONS

The deterministic formula based on selection index theory estimated the accuracy of across-population genomic predictions well. The deterministic formula using population parameters overestimated the across-population genomic accuracy, but may still be useful because of its simplicity. Both formulas could accommodate for genetic correlations between populations lower than 1. The number of QTL underlying a trait did not affect the accuracy of across-population genomic prediction using a GBLUP method.

Genotype by feeding system interaction in the genetic evaluation of Jersey cattle for milk yield

Results of studies in dairy cattle about the magnitude of the genotype-environment interaction (GEI) are variable, depending on the definitions of genotype and environment. Therefore, the objective of this study was to determine the magnitude of the interaction of genotype and feeding system (confinement and grazing) in the Mexican genetic evaluation of Jersey cattle for milk yield. The number of lactations and animals in the pedigree used were 5122 and 18 432. An animal model and the MTDFREML program were used to estimate genetic parameters and predict genetic values of the animals. Bivariate analysis was carried out considering the performance of confined and grazing cows as two different traits. Three indicator variables were used to assess GEI: (i) magnitude of the genetic correlation coefficients, (ii) correlation between predicted breeding values and (iii) frequency of coincidence in the ranking of top sires. The magnitude of GEI depended on the choice of the indicator variable. The estimate of genetic correlation coefficient less than unity (0.76; P < 0.05) suggested the presence of biologically important GEI. The differences in phenotypic averages and variances between confinement and grazing systems seem to be the main causes for the genotype by environment interaction detected. However, the correlation coefficient between breeding values from confined and grazing animals (0.96) and the frequency of coincidence between breeding values of common sires within the top 100 in confinement and grazing (0.86) indicated low-to-moderate re-ranking of animals or top sires. In addition, the high correlations between predicted breeding values of Mexican genetic evaluation and the two environments (0.99 and 0.93 for confinement and grazing) indicated that for the two feeding systems, breeding values from national analyses could be safely used.

Genetic parameters and genotype x environment interaction for feed efficiency traits in steers fed grower and finisher diets

The objective of this study was to examine the genetic parameters and genetic correlations of feed efficiency traits in steers (n = 490) fed grower or finisher diets in 2 feeding periods. A bivariate model was used to estimate phenotypic and genetic parameters using steers that received the grower and finisher diets in successive feeding periods, whereas a repeated animal model was used to estimate the permanent environmental effects. Genetic correlations between the grower-fed and finisher-fed regimens were 0.50 ± 0.48 and 0.78 ± 0.43 for residual feed intake (RFI) and G:F, respectively. The moderate genetic correlation between the 2 feeding regimens may indicate the presence of a genotype × environment interaction for RFI. Permanent environmental effects (expressed in percentage of phenotypic variance) were detected in the grower-fed steers for ADG (38%), DMI (30%), RFI (18%), and G:F (40%) and also in the finisher-fed steers for ADG (28%), DMI (35%), metabolic mid-weight (23%), and RFI (10%). Heritability estimates were 0.08 ± 0.10 and 0.14 ± 0.15 for the grower-fed steers and 0.42 ± 0.16 and 0.40 ± 17 for the finisher-fed steers for RFI and G:F, respectively. The dependency of the RFI on the feeding regimen may have serious implications when selecting animals in the beef industry. Because of the higher cost of grains, feed efficiency in the feedlot might be overemphasized, whereas efficiency in the cow herd and the backgrounding segments may have less emphasis. These results may also favor the retention (for subsequent breeding) of cows whose steers were efficient in the feedlot sector. Therefore, comprehensive feeding trials may be necessary to provide more insight into the mechanisms surrounding genotype × environment interaction in steers.

Genetic and environmental causes of variation in milk production traits of Sahiwal cattle in Pakistan

Data from about 4000 Sahiwal cows from eight large herds in Pakistan were used to study the influence of genetic and environmental factors on some milk production traits. First-lactation mean values were 1363 kg, 1395 kg and 252 days for milk yield up to 305 days after calving, total lactation yield and lactation length, respectively. Second and third lactation yields were proportionately 0·12 and 0·18 higher, respectively, at 305 days. The effect of herd-year at calving was by far the most important source of variation for all traits. Heritabilities estimated in uni- and trivariate analyses, using restricted maximum likelihood (REML) with an expectation maximization algorithm for an animal model, ranged from 0·14 to 0·17 for first-lactation traits. The estimates were generally lower for second lactation and higher for third lactation traits. Genetic correlation between lactations for the same trait were close to unity, whilst the phenotypic were considerably lower. Repeatabilities for milk yield traits were 0·42 and for lactation length 0·31. Genetic and phenotypic correlations between first-lactation 305-day milk yield and lactation length were 0·83 and 0·71, respectively. Genetic trends for all traits were close to zero but a substantial deterioration in performance, caused by negative environmental factors, was observed. Although the heritabilities were low, the prospects for genetic improvement are good, as indicated by a rather large additive genetic variation. A multivariate animal model, including the first three lactations of 305-day milk yield, was recommended for the most accurate prediction of breeding values for milk production.

Heterogeneity of variance and dairy cattle breeding

The effects of heterogeneity among herds in phenotypic variance (σ2p) and in heritability (h2) on the accuracy of evaluation of dairy sires and cows are discussed with reference to estimates from field data. It is argued that heterogeneity of σ2P can be accounted for by using a (Bayesian) regression procedure. While the same procedure could be used to correct for heterogeneity of h2, in most practical situations the sampling errors of the h2 estimates for individual herds are likely to be so large that regressed estimates of h2 will differ little from each other, so constant values can be assumed.

Genetic and environmental factors influencing milk, protein and fat yields of pasture-based dairy cows in Tasmania

The objective of this study was to provide an update on milk production performance, heritability, genetic and phenotypic correlations among production traits that are valuable for management, breeding and selection decisions in pasture-based dairy systems. The study utilised a total of 106 990 lactation records of Holstein–Friesian (FF), Jersey (JJ) and their crossbreds (HF) from 428 Tasmanian dairy herds collected between 2000 and 2005. The data were analysed using the least-squares approach with a general linear model and restricted maximum likelihood approach with a linear animal model. Results indicated highly significant (P < 0.01) effects of breed, herd size, cow’s parity, season and year of calving on milk, protein and fat yields. Average milk and protein yields per cow per lactation were highest in the FF breed (5212 L and 171 kg, respectively) and lowest in the JJ breed (3713 L and 143 kg, respectively). FF cows also produced 13.5 kg more milk fat than JJ and HF cows. Furthermore, milk, fat and protein yields were highest for cows calving during spring and lowest for autumn-calving cows. It was also evident that cows in very large herds (>1110 cows/herd) out-produced those in smaller herds. Heritability was highest for milk yield and lowest for somatic cell count ranging from 0.28 to 0.41. Genetic and phenotypic correlations between milk, fat and protein yields ranged from 0.41 to 0.85, and 0.66 to 0.92, respectively. However, genetic and phenotypic correlations between the log of somatic cell count and the production traits ranged from 0.03 to 0.09 and –0.03 to –0.05. We conclude that breed, herd size, parity, season and year of calving were among the main factors correlated with the productivity of dairy cows in Tasmania and adjustments for these factors would be mandatory for any unbiased comparison of lactation performance within and between pasture-based dairy production systems. The practical application of this information would be valuable to dairy farmers for decisions related to breeding, selection and management of their herds.

Heritability of Morningness‐Eveningness and Self‐Report Sleep Measures in a Family‐Based Sample of 521 Hutterites

Individual variation in the phase and amplitude of human circadian rhythms is well known, but the impact of heritable factors on such variation is less clear. We estimated the narrow-sense heritability for selected circadian and sleep timing, quality, and duration measures among related members of the Hutterites, an endogamous, religious community (n=521 participants). "Morningness-eveningness" (M/E), a stable trait reflecting circadian phase, was evaluated using the Composite Scale (CS). Subjective sleep measures were assessed using the Sleep Timing Questionnaire. Initial analyses reconfirmed the impact of age on M/E. Previously reported correlations between M/E scores and the sleep measures were also noted, demonstrating the construct validity of the questionnaires among the participants. Following corrections for age, gender, and colony of residence, significant narrow-sense heritability was noted for M/E (23%). The heritability for subjective sleep measures (related to timing, duration, and quality) were statistically significant for all but one variable, and varied between 12.4% and 29.4%. Thus, significant heritable influences on human circadian phase and subjective sleep indices can be detected through family-based studies. In view of the impact of circadian malfunction on human health, it may be worthwhile to map genetic factors impacting circadian and sleep variation.

Heterogeneity of variance for milk traits at climitical regions in Holstein dairy cattle in Iran and the best method(s) for data transformation

In this research, heterogeneity of variance components in cattle populations at climatical regions in the first three lactations was studied. The data set included the following: 161328 records of first, 123369 records of second and 81013 records of third lactations, which was collected by Animal Breeding Center of Iran from 1983 to 2004. Records of three lactations were divided in the base of Domarten method. Bartlett test for heterogeneity of variance components was significant among all subgroups. In order to decrease the heterogeneity of variance components, we used several data transformation methods including Logarithmic, Square root and Arc sin transformations. Logarithmic transformation decreased the heterogeneity of variance components in the three lactations and other methods had not effect for removing the heterogeneity in any group. Genetic parameters and heritability were estimated for three lactations by MATVEC program, using animal model. Results showed that the heritability estimates of milk yield were decreased from the first lactation to the third; also the heritability estimates of transformed data were slightly higher than the original data. Comparison between estimated parameters in single trait and two traits analysis, before and after data transformation, showed that there were not significant differences between derived results.

Genotype by Environment Interaction for Production Traits While Accounting for Heteroscedasticity

Grazing (G) provides an alternative management system for dairy production. Heteroscedasticity (HV) of the data may bias estimates of genetic correlations of yield traits between environments, an indicator of genotype-by-environment interaction (GxE). The objective of this study was to investigate the effect of HV on estimates of heritabilities and genetic correlations for mature-equivalent milk, protein, and fat yield, and lactation-average somatic cell scores of daughters, and to determine if HV affects the ability of sire's predicted transmitting ability (PTA) to predict daughter production in G and confinement (C) herds. Data consisted of 72,489 records from 35,674 cows in 366 G herds from 11 states, and 117,629 records from 50,963 cows in 373 C herds from the same 11 states plus 1 geographically contiguous state. Herds were divided into variance quartiles (Q(V)1-Q(V)4) based on milk yield. A transformation was used to reduce HV by standardizing the within-herd standard deviation to the average across-herd standard deviation of a base year for each parity, and was similar to the method used in current USDA-DHIA genetic evaluations. Regression of daughter yield on sire PTA showed that PTA overestimated production of all traits in Q(V)1-Q(V)3 and of milk in Q(V)4 of G herds. For C herds, yields of milk in Q(V)1 and Q(V)2, and of protein and fat in Q(V)1 were overestimated, and protein was underestimated in Q(V)4. Reducing HV had little effect on G herds, but for C herds, regression did not differ from unity for milk and protein in Q(V)1 and Q(V)2. For milk, protein, and fat in G, heritabilities were approximately 0.17, 0.17, and 0.19, respectively. The heritabilities for milk, protein, and fat in C herds were approximately 0.16, 0.17, and 0.21, respectively. Genetic correlations between C and G did not suggest a GxE in 3 upper quartiles, but a possible GxE (correlation = 0.21, estimated standard error = 0.22) for the lowest quartile. Reducing HV did not affect estimates of heritabilities or genetic correlations. Results indicated that modest evidence for existence of GxE did not arise solely from HV.

Ajustamento para heterogeneidade de variâncias para produção de leite e gordura entre rebanhos da raça Pardo-Suíça no Brasil

Para verificar o efeito da inclusão das interações reprodutor x rebanho e reprodutor x rebanho-ano como fator de ajustamento da heterogeneidade de variância, registros de produção de leite e gordura foram estratificados, com base no desvio-padrão fenotípico da produção de leite ajustada, em duas classes: baixo (<1.280kg) e alto (>1.280kg) desvio-padrão. Três modelos foram utilizados, sem e com interação reprodutor x rebanho e reprodutor x rebanho-ano, em análises de característica única, geral e em cada classe de desvio-padrão. Médias e componentes de variâncias foram maiores na classe de alto desvio-padrão. Na classe de baixo desvio-padrão, a herdabilidade não se alterou com a inclusão dos efeitos de interação no modelo, sendo de 0,34 para produção de leite e de 0,32 para produção de gordura. Na classe de alto desvio-padrão, as herdabilidades foram: 0,37, 0,35 e 0,36, e de 0,35, 0,32 e 0,35, para produção de leite e gordura, nos modelos sem, com interação reprodutor x rebanho e com interação reprodutor x rebanho-ano, respectivamente. A inclusão do efeito de interação reprodutor x rebanho nos modelos foi significativa (P<0,01) para produção de gordura, em análise geral e na classe de alto desvio-padrão, pelo teste da razão de verossimilhança.

Adjustments for heterogeneous herd-year variances in a random regression model for genetic evaluations of Polish Black-and-White cattle

The study investigated the existence of heterogeneous variance in first-lactation daily milk yield of Polish Black-and-White cows across herds in different years. Bayesian Information Criterion was used to show that the model with unequal residual variances for different herd-years was more plausible than the model assuming equal variances. A method of adjusting phenotypic records was developed to account for unequal variability in herd-years. Factors used for the data adjustment considered variation of general residuals and residuals for specific herd-years. The size of herd-year was also taken into account. Varied power of corrections was used to analyze the effect of adjustment on estimated breeding values. The method was applied to daily milk records of 817,165 primiparous cows. The effectiveness of the data adjustment was evaluated by the analysis of differences between each bull's breeding value and its parental index. Data correction reduced the average difference and variance of differences between breeding values and parental indices. Accounting for the size of herd-year classes in correction factors improved the efficiency of heterogeneous variance adjustment.

Factors that cause genotype by environment interaction and use of a multiple-trait herd-cluster model for milk yield of Holstein cattle from Brazil and Colombia

Descriptive herd variables (DVHE) were used to explain genotype by environment interactions (G x E) for milk yield (MY) in Brazilian and Colombian production environments and to develop a herd-cluster model to estimate covariance components and genetic parameters for each herd environment group. Data consisted of 180,522 lactation records of 94,558 Holstein cows from 937 Brazilian and 400 Colombian herds. Herds in both countries were jointly grouped in thirds according to 8 DVHE: production level, phenotypic variability, age at first calving, calving interval, percentage of imported semen, lactation length, and herd size. For each DVHE, REML bivariate animal model analyses were used to estimate genetic correlations for MY between upper and lower thirds of the data. Based on estimates of genetic correlations, weights were assigned to each DVHE to group herds in a cluster analysis using the FASTCLUS procedure in SAS. Three clusters were defined, and genetic and residual variance components were heterogeneous among herd clusters. Estimates of heritability in clusters 1 and 3 were 0.28 and 0.29, respectively, but the estimate was larger (0.39) in Cluster 2. The genetic correlations of MY from different clusters ranged from 0.89 to 0.97. The herd-cluster model based on DVHE properly takes into account G x E by grouping similar environments accordingly and seems to be an alternative to simply considering country borders to distinguish between environments.

Estimated Heterogeneity of Phenotypic Variance of Test-Day Yield with a Structural Variance Model

First-lactation test-day milk, fat, and protein yields from New York, Wisconsin, and California herds from 1990 through 2000 were adjusted additively for age and lactation stage. A random regression model with third-order Legendre polynomials for permanent environmental and genetic effects was used. The model included a random effect with the same polynomial regressions for 2 yr of calvings within herd (herd-time effect) to provide herd-specific lactation curves that can change every 2 yr. (Co)variance components were estimated using expectation-maximization REML simultaneously with phenotypic variances that were modeled using a structural variance model. Maximum heritability for test-day milk yield was estimated to be approximately 20% around 200 to 250 d in milk; heritabilities were slightly lower for test-day fat and protein yields. Herd-time effects explained 12 to 20% of phenotypic variance and had the greatest impact at start of lactation. Variances of test-day yields increased with time, subclass size, and milking frequency. Test month had limited influence on variance. Variance increased for cows in herds with low and high milk yields and for early and late lactation stages. Repeatabilities of variances observed for a given class of herd, test-day, and milking frequency were 14 to 17% across nested variance subclasses based on lactation stage.

Genotype by environment interaction for yield and somatic cell score with alternative environmental definitions

Differential genetic expression in high and low opportunity Sicilian Holstein-Friesian and Brown Swiss herd environments was investigated using endogenous and exogenous variables in a set of three definitions. Results of genetic by environmental interaction were compared using alternative environmental definitions: within herd-year standard deviation for mature equivalent milk yield (HYSD), detectable incidence of normal vs. abnormal (peakless) lactation and herds clustered by causal relationships from high and low frequency use of nutrition, milking, health and animal handling practices. Data for genetic analysis consisted of first-lactation standardized yields of milk, fat and protein, and weighted somatic cell score for 8897 daughters of 825 Holstein-Friesian sires and 1143 daughters of 220 Brown Swiss sires. Components of covariance, heritabilities, and genetic correlations were estimated using bivariate and multivariate sire models for average and contrasting environments for each definition. Sire variances for yields were consistently smaller in the low opportunity environments of both breeds. Except for differential incidence of abnormal lactation in Friesian herds, correlated yield response in less privileged environments was 0.41 to 0.81 as much as in high opportunity environments, a substantial loss. Genetic correlations between HYSD environments for yield traits of Friesian were 0.48 to 0.66 but exceeded 0.80 for other definitions. Less correlated response in somatic cell score was also predicted for environments with low use of yield-enhancing practices (0.66 for Friesian and 0.61 for Brown Swiss), which may have resulted from less health care and poorer milking management. Therefore, unfavorable management interactions likely foster unequal gains from selection in contrasting environments defined exogenously or by incidence of peakless lactation. Conversely, greater genetic as well as phenotypic response is expected from additional inputs of nutrition, health care and milking management.

Genetic analysis of Holstein cattle populations in Brazil and the United States

Genetic relationships between Brazilian and US Holstein cattle populations were studied using first-lactation records of 305-d mature equivalent (ME) yields of milk and fat of daughters of 705 sires in Brazil and 701 sires in the United States, 358 of which had progeny in both countries. Components of(co)variance and genetic parameters were estimated from all data and from within herd-year standard deviation for milk (HYSD) data files using bivariate and multivariate sire models and DFREML procedures distinguishing the two countries. Sire (residual) variances from all data for milk yield were 51 to 59% (58 to 101%) as large in Brazil as those obtained from half-sisters in the average US herd. Corresponding proportions of the US variance in fat yield that were found in Brazil were 30 to 41% for the sire component of variance and 48 to 80% for the residual. Heritabilities for milk and fat yields from multivariate analysis of all the data were 0.25 and 0.22 in Brazil, and 0.34 and 0.35 in the United States. Genetic correlations between milk and fat were 0.79 in Brazil and 0.62 in the United States. Genetic correlations between countries were 0.85 for milk, 0.88 for fat, 0.55 for milk in Brazil and fat in the US, and 0.67 for fat in Brazil and milk in the United States. Correlated responses in Brazil from sire selection based on the US information increased with average HYSD in Brazil. Largest daughter yield response was predicted from information from half-sisters in low HYSD US herds (0.75 kg/kg for milk; 0.63 kg/kg for fat), which was 14% to 17% greater than estimates from all US herds because the scaling effects were less severe from heterogeneous variances. Unequal daughter response from unequal genetic (co)variances under restrictive Brazilian conditions is evidence for the interaction of genotype and environment. The smaller and variable yield expectations of daughters of US sires in Brazilian environments suggest the need for specific genetic improvement strategies in Brazilian Holstein herds. A US data file restricting daughter information to low HYSD US environments would be a wise choice for across-country evaluation. Procedures to incorporate such foreign evaluations should be explored to improve the accuracy of genetic evaluations for the Brazilian Holstein population.

Effect of herd environment on the genetic and phenotypic relationships among milk yield, conception rate, and somatic cell score in Holstein cattle

A total of 248,230 primiparous records of Holstein cows calving from 1987 to 1994 (daughters of 588 sires in 3042 herds) was used to evaluate potential genotype by environment interactions among mature equivalent milk yield, lactation mean somatic cell score, and conception rate at first service. Herds were classified into low and high environmental groups using three different criteria: standard deviation of herd mature equivalent milk yield, a combination of herd mature equivalent milk yield mean and standard deviation, and the herd mean of body weight at first calving divided by age at first calving. Genetic parameters were modeled by using multiple-trait linear mixed models and were fitted using the multiple-trait derivative-free software. Heritabilities for mature equivalent milk yield, lactation mean somatic cell score, and conception rate at first service were 0.221, 0.106, and 0.015 in low environment herds and 0.300, 0.093, and 0.009 in high environment herds, respectively. Genetic (and phenotypic) correlations between mature equivalent milk yield and lactation mean somatic cell score, mature equivalent milk yield and conception rate at first service, and lactation mean somatic cell score and conception rate at first service were 0.277, -0.417, and -0.209, (-0.049, -0.180, and -0.040) and 0.173, -0.318, and -0.144, (-0.087, -0.166, and -0.035) in low and high environment herds, respectively. The genetic correlations between pairs of traits were consistently smaller in high environment herds, suggesting that differences in management between the two environment levels lessened the antagonistic genetic association between the traits studied. A long-range plan for low environment herds should focus on improving the level of management, which would greatly reduce the unfavorable correlated changes in lactation mean somatic cell score and conception rate at first service associated with the genetic improvement of mature equivalent milk yield.

Method R estimates of heritability for milk, fat, and protein yields of United States dairy cattle

Heritabilities for milk, fat, and protein yields were estimated from first lactation data used for USDA-Dairy Herd Improvement Association (DHIA) genetic evaluations. Contemporary group assignments and standard deviations within herd-year were determined with the procedure used for national evaluations. Pedigree data were included for animals born since 1970; yield data were included for cows born since 1980. Lactation records were divided into four mutually exclusive data sets based on standard deviations. Ranges for standard deviations were chosen so that data sets were approximately equal in size. Method R was used to estimate heritability with 25 different random samples of half of the data for each data set. Because of the large number of Holstein observations, estimates of heritability for Holsteins were based on random subsets of the complete data file; each subset included approximately 5% of the data. Mean heritability estimates increased with standard deviations, and estimates ranged from 0.18 to 0.51 across breeds. Repeatability estimates for milk yield of Holsteins were approximately 0.50 and did not change with standard deviation. These heritability estimates were higher than those previously used in the USDA-DHIA genetic evaluation. Heritability used in the USDA-DHIA genetic evaluation have been increased based on these results.

An investigation into heterogeneity of variance for milk and fat yields of Holstein cows in Brazilian herd environments

Heterogeneity of variance in Brazilian herd environments was studied using first-lactation 305-day mature equivalent (ME) milk and fat records of Holstein cows. Herds were divided into two categories, according to low or high herd-year phenotypic standard deviation for ME milk (HYSD). There were 330 sires with daughter records in both HYSD categories. Components of (co)variance, heritability, and genetic correlations for milk and fat yields were estimated using a sire model from bivariate analyses with a restricted maximum likelihood (REML) derivative-free algorithm. Sire and residual variances for milk yield in low HYSD herds were 79 and 57% of those obtained in high HYSD herd. For fat yield they were 67 and 60%, respectively. Heritabilities for milk and fat yields in low HYSD herds were larger (0.30 and 0.22) than in high HYSD herds (0.23 and 0.20). Genetic correlation between expression in low and high HYSD herds was 0.997 for milk yield and 0.985 for fat yield. Expected correlated response in low HYSD herds based on sires selected on half-sister information from high HYSD was 0.89 kg/kg for milk and 0.80 kg/kg for fat yield. Genetic evaluations in Brazil need to account for heterogeneity of variances to increase the accuracy of evaluations and the selection efficiency for milk and fat yields of Holstein cows. Selection response will be lower in low variance herds than in high variance herds because of reduced differences in daughter response and among breeding values of sires in low HYSD herds. Genetic investments in sire selection to improve production are more likely to be successful in high HYSD herds than in low HYSD Brazilian herds.

Application of an autoregressive process to estimate genetic parameters and breeding values for daily milk yield in a tropical herd of Lucerna cattle and in United States Holstein herds

The objectives of this study were to estimate from test day records the genetic and environmental (co)variance components, correlations, and breeding values to increase genetic gain in milk yield of Lucerna and US Holstein cattle. The effects of repeated observations (within cow) were explained by first-order autoregressive processes within and across lactations using an animal model. Estimates of variance components and correlation coefficients between test days were obtained using derivative-free REML methodology. The autoregressive structure significantly reduced the model error component by disentangling the short-term environmental effects. The additional information and the more heterogeneous environmental variances between lactations in the multiple-lactation test day model than in the first lactation model provided substantially larger estimates of additive genetic variance (0.62 kg2 for Lucerna; 14.73 kg2 for Holstein), heritability (0.13 for Lucerna; 0.42 for Holstein), and individual genetic merit. Rank correlations of breeding values from multiple lactations and from first lactations ranged from 0.18 to 0.37 for females and from 0.73 to 0.89 for males, respectively. Consequently, more selection errors and less genetic gain would be expected from selection decisions based on an analysis of first lactation only, and greater accuracy would be achieved from multiple lactations. Results indicated that substantial genetic gain was possible for milk yield in the Lucerna herd (34 kg/yr). Estimates of genetic variance for Holsteins were larger than previously reported, which portends more rapid genetic progress in US herds also; under our assumptions, increases would be from 173 to 197 kg/yr.

Variance of interaction effects of sire and herd for yield traits of Holsteins in California, New York, and Pennsylvania with an animal model

An animal model with a REML algorithm was used to estimate variances of additive genetic effects and interaction effects of sire and herd. Milk and fat yields were analyzed for first, second, and third lactations of Holsteins from California, New York, and Pennsylvania. Twenty samples of data were used in the study: 10 from California, 4 from New York, and 6 from Pennsylvania. Mean number of lactations per sample was 36,820 from 18,189 cows in 156 herds. Mean fractions of phenotypic variance of interaction effects of sire and herd for milk and fat yields were .015 and .019 for first lactation and .019 and .021 for all (up to three) lactations rather than the .14 used for national genetic evaluations in the US. Mean heritability estimates for milk and fat yields were .26 and .24 for first lactation and .21 and .21 for all lactations in California and .34 and .35 for first lactations and .28 and .29 for all lactations in New York. Sums of variances of permanent environmental and interaction effects of sire and herd were similar to those used for national genetic evaluations in the US. Analysis of another 10 samples from California and 10 samples from New York showed only slightly different fractions of phenotypic variance for milk yield for interaction effects of sire by herd, sire by herd by year, and sire by herd by year by season: .023, .027, and .037 for California and .023, .017, and .023 for New York, respectively.

Estimates of variability for somatic cell count measurements in the Iowa dairy industry

The SCC collected from 15 instruments in 12 laboratories were used to quantify accuracy, repeatability, and reproducibility in the Iowa dairy industry. For each of three trials, milk was sampled at the morning milking from 30 different Holsteins in the Iowa State University herd. Identified samples and unidentified duplicates were provided for each participating instrument. Mean SCC was 418,000 cells/ml, and mean SCC for duplicates ranged from 9000 to 3,966,000. Accuracy for a set of 30 duplicates was lowest for trial 1 (CV = 16.4%) and highest for trial 2 (CV = 7.6%). Intraclass correlations estimated repeatability and were .99 for all but one instrument. Coefficients of variation for repeatability (weighted mean = 11.4%) were similar to estimates for accuracy (weighted mean = 11.0%), but reproducibility was considerably lower (30.0%). Samples were classified by SCC as very low, < 125,000; low, 125,000 to 249,000; medium, 250,000 to 500,000; and high, > 500,000. Repeatability for high samples was higher than repeatability for very low SCC samples; coefficient of variation for high SCC samples was 6.8% but was > 25.0% for samples with < 500,000 cells. Repeatability was within standards set by the industry, but current procedures for quality control may not adequately address reproducibility.

Relationship between production and days open at different levels of herd production

Five production variables and days open were analyzed using 611,680 records from 348,243 cows in 5694 herds enrolled in the Wisconsin DHI program. Production variables included 305-d milk production and several production measures adjusted for combinations of mature equivalent, fat and protein content, and effects of days open. Herds were divided into four groups by herd production. Heritability estimates for production variables ranged from .27 for mature equivalent milk that was corrected for fat and protein content and adjusted for days open to .34 for mature equivalent milk and for mature equivalent milk that was adjusted for days open. Adjustment of production records for days open had little impact on heritability estimates of production traits. Heritability for days open was approximately .05. Heritability estimates were larger for all measures of production and for days open for the herds with higher mean production. The effects of parity and season were important for both adjusted and unadjusted measures of production. After production variables were adjusted for mature equivalent factors, large differences remained between REML estimates of fixed effects of parity and season. For days open, estimates were larger for later parity cows and were highest for cows calving during spring. For measures of production, estimates were largest between first and second parity cows and between winter and summer calvings. Within herd, days open were longer for cows with higher production. Regressions of days open on production records that were not adjusted for days open were significantly larger for the herds at lower production.

Adjustment for heterogeneous variance in genetic evaluations for conformation of United States Holsteins

A method was developed to account for heterogeneous phenotypic variance for final type (conformation) score within herd-year-month-classifier subclasses for national genetic evaluations of US Holsteins. Phenotypic variances decreased 3.5-fold as within-subclass means increased from 70 to 89 points, and variances increased slightly over time and with increases in subclass size and proportion of registered animals. A model containing known management characteristics was fitted to phenotypic standard deviations within subclass, and resulting solutions were used to estimate the prior variance for each subclass. Prior estimates and phenotypic variance estimates within subclass were combined using Bayesian methods, resulting in posterior estimates that contained more information than either the prior estimates or the within-subclass statistics. Observations were standardized to a common variance using the mean of the posterior density of the phenotypic standard deviation within subclass. Moderate changes in PTA occurred for low reliability bulls, bulls with many progeny in a single herd, and foreign bulls subjected to positive assortative mating. Significant increases occurred in PTA of superior cows in subclasses with high means. Incorporation of a heterogeneous variance adjustment into national genetic evaluations should increase fairness of selection among cows and young bulls and may increase the rate of genetic gain from female selection.

Effect of sampling status and adjustment for heterogeneous variance on bias in bull evaluations

Holstein bulls were assigned to sampling categories (AI stud, AI nonstud, or non-AI) based on bull code, controller number, and age at semen distribution. The AI stud bulls were sampled through traditional progeny-testing programs of 13 AI organizations; AI nonstud bulls had AI semen collection reported by another organization or by multiple organizations. The non-AI bulls had no reported AI semen collection. Actual daughter yield deviations for these three groups of bulls were compared with expected performance (parent average) to provide an indication of whether evaluations were free from bias for daughter yield deviations. Mean difference of daughter yield deviation from parent average was close to 0 kg for animal model evaluations of all 22,930 bulls but was positively biased by 46 kg of milk for AI nonstud bulls. Mean PTA and reliabilities for parents were highest for AI stud bulls and lowest for non-AI bulls. The AI stud bulls varied least and were intermediate for mean management, approximated as mean daughter yield minus bull PTA. Management was highest for AI nonstud bulls, which suggested that adjustment for heterogeneous variance might reduce bias. However, the effect of this adjustment on mean difference of daughter yield deviation from parent average was small.

Method and effect of adjustment for heterogeneous variance of Holstein conformation traits

Type classification records of Canadian Holsteins were investigated for evidence of heterogeneous variance across herds. Data consisted of records for 1,139,104 cows from 20,226 herds with classifications on 26 conformation traits collected from 1982 through 1992 and 338,046 cows from 9600 herds with classifications on 2 additional traits from 1990 through 1992. Phenotypic standard deviations of herd-round-classifier were fitted to a mixed model that included round, classifier, and region as fixed effects, herd size as a covariant, and herd as a random effect. Estimates of the variance components, solutions of fixed effects, and BLUP estimates for herd were obtained by maximum likelihood procedures. Repeatability of within-herd standard deviation across rounds ranged from 1.4 to 10.3% for the 28 traits. Type classification data were subsequently standardized for phenotypic standard deviations of herd-round-classifier that were derived from estimates of the fixed effects and the BLUP estimate of the herd effect. Genetic evaluations for cows and bulls were produced from adjusted and unadjusted data. Correlations between 3754 sire and 1,142,782 cow estimated transmitting abilities obtained from unadjusted and adjusted data were essentially unity. Although some evidence of heterogeneous variance existed across herds for 28 conformation traits, standardization of the classification records had only a minor effect on genetic evaluations.

Estimation of heterogeneous within-herd variance components using empirical Bayes methods: a simulation study

Genetic evaluation using BLUP can accommodate heterogeneous variances if the necessary variance components are known; this may require estimation of variance components within each heterogeneous subclass. Properties of sire and residual variance estimates obtained by an empirical Bayes approach, which combines within-herd and prior estimates, were examined via simulation. Prior estimates were obtained using REML across herds, as if variances were homogeneous. Convergence was improved by incorporation of prior information such that variance component estimates could be obtained in within-herd situations for which a REML algorithm failed to converge. Accuracy of sire variance estimates was greatest when both within-herd and prior information were used, but improvement in accuracy of residual variance estimates associated with incorporation of prior information was minimal. Correlations between sires' standardized true transmitting abilities and PTA that used empirical Bayes variance estimates were larger than those obtained when heterogeneity was ignored. Proportions of sires selected, based on standardized PTA, from environments with differing genetic and residual variances became more uniform as the relative weight placed on within-herd data in variance estimation increased. Thus, useful variance component estimates can be obtained within individual herds by using empirical Bayes methods with across-herd estimates as prior information; this may allow prediction of breeding values that are less influenced by heterogeneous variances.

Genetic parameters for yield traits of Holsteins, including lactose and somatic cell score

First lactation milk, fat, protein, and lactose yields and percentage yields were analyzed using a multiple-trait sire model including herd-year-season, sire group, and age of cow as fixed effects. Somatic cell score was fit both as a fixed effect in the model and as an additional dependent variable in two analyses with almost identical results. Variance components were estimated using REML with an expectation-maximization algorithm including sire relationships. Lactose means ranged from 4.84 to 4.97% across three dairy breeds. Data used to estimate variance components were first lactation Holstein records collected from 1986 to 1988 from 5246 daughters of 392 AI sires. Heritability estimates were .30, .29, .27, and .26 for milk, fat, protein, and lactose yields; .45, .47, and .53 for fat, protein, and lactose percentage yields; and .16 for somatic cell score. Genetic correlations of lactose percentage with milk, fat, protein, fat and protein percentages, and somatic cell score were -.30, -.16, -.21, .10, .29, and -.11, respectively, and phenotypic correlations were -.08, -.02, .01, .11, .29, and -.15.

Power of likelihood ratio tests for heterogeneity of intraclass correlation and variance in balanced half-sib designs

Statistical power of likelihood ratio tests was investigated for detection of heterogeneous variances and intraclass correlation in balanced half-sib designs. Powers of likelihood ratio tests were obtained from simulations. For half-sib designs of sires nested within herds, true intraclass correlations and phenotypic variances, and estimates thereof, were repeatedly sampled, and likelihood ratio tests were conducted. The power for detecting heterogeneity of intraclass correlations was low, but the power for detecting heterogeneous phenotypic variances was nearly always 100%. For balanced cross-classified designs, sires had progeny in all herds, and data were simulated by assuming that heterogeneity of between- and within-sire components was the result of a herd-dependent scale effect. Using this model, the power to detect heterogeneous between-sire components was substantially higher than the corresponding power to detect heterogeneous intraclass correlations in the nested design. It seems unlikely that reliable inference about heterogeneity of genetic variances or heritabilities between individual herds from daily cattle field data can be made.