Genetic evaluation of mastitis in dairy cattle using linear models, threshold models, and survival analysis: a simulation study

The objective was to study, by simulation, whether survival analysis results in a more precise genetic evaluation for mastitis in dairy cattle than cross-sectional linear models and threshold models by using observation periods for mastitis of 2 lengths (the first 150 d of lactation, and the full lactation, respectively). True breeding values for mastitis liability on the underlying scale were simulated for daughters of 400 sires (average daughter group size, 60 or 150), and the possible event of a mastitis case within lactation for each cow was created. For the linear models and the threshold models, mastitis was defined as a binary trait within either the first 150 d of lactation or the full lactation. For the survival analysis, mastitis was defined as the number of days from calving to either the first case of mastitis (uncensored record) or to the day of censoring (i.e., day of culling, lactation d 150 or day of next calving; censored record). Cows could be culled early in lactation (within 10 d after calving) for calving-related reasons or later on because of infertility. The correlation between sire true breeding values for mastitis liability and sire predicted breeding values was greater when using the full lactation data (0.76) than when using data from the first 150 d (0.70) with an average of 150 daughters per sire. The corresponding results were 0.60 and 0.53, respectively, with an average of 60 daughters per sire. Under these simulated conditions, the method used had no effect on accuracy. The higher accuracy of sire breeding values can be translated into a greater genetic gain, unless counteracted by a longer generation interval.     

Comparison of methods for genetic evaluation of sires for survival of their daughters in the first three lactations.

Several approaches for analysis of survival in the first three lactations were compared using data from approximately 700,000 Canadian Holsteins. Two approaches (linear model and threshold model) were used to analyze a binary measure of survival. Other approaches were survival analyses to evaluate two measures of the number of days that cows were in milk during their first three lactations. One measure restricted days per lactation to < or = 305; the other was based on the actual number of days in milk without an upper limit on days per lactation. Variance components and breeding values (EBV) were estimated. Sire models were used almost exclusively, but one set of EBV was obtained using a linear animal model. Effects in the models were herd-year of calving, age at first calving, interaction of several factors related to herd, and production. Thus, all EBV were for functional herd life. Heritabilities were approximately 0.04, 0.07, and 0.10 from linear, threshold, and survival analyses, respectively. Correlations among sire EBV from all analyses using sire models were high, particularly for linear and threshold models (0.98). In contrast, correlations of EBV from sire models with EBV from the linear animal model were less than 0.90, regardless of the approach taken. In Canada, the current linear animal model remains in use for sire evaluation of herd life, but research with survival analyses will continue.     

Comparison between a Weibull proportional hazards model and a linear model for predicting the genetic merit of US Jersey sires for daughter longevity

Predicted transmitting abilities (PTA) of US Jersey sires for daughter longevity were calculated using a Weibull proportional hazards sire model and compared with predictions from a conventional linear animal model. Culling data from 268,008 Jersey cows with first calving from 1981 to 2000 were used. The proportional hazards model included time-dependent effects of herd-year-season contemporary group and parity by stage of lactation interaction, as well as time-independent effects of sire and age at first calving. Sire variances and parameters of the Weibull distribution were estimated, providing heritability estimates of 4.7% on the log scale and 18.0% on the original scale. The PTA of each sire was expressed as the expected risk of culling relative to daughters of an average sire. Risk ratios (RR) ranged from 0.7 to 1.3, indicating that the risk of culling for daughters of the best sires was 30% lower than for daughters of average sires and nearly 50% lower than than for daughters of the poorest sires. Sire PTA from the proportional hazards model were compared with PTA from a linear model similar to that used for routine national genetic evaluation of length of productive life (PL) using cross-validation in independent samples of herds. Models were compared using logistic regression of daughters' stayability to second, third, fourth, or fifth lactation on their sires' PTA values, with alternative approaches for weighting the contribution of each sire. Models were also compared using logistic regression of daughters' stayability to 36, 48, 60, 72, and 84 mo of life. The proportional hazards model generally yielded more accurate predictions according to these criteria, but differences in predictive ability between methods were smaller when using a Kullback-Leibler distance than with other approaches. Results of this study suggest that survival analysis methodology may provide more accurate predictions of genetic merit for longevity than conventional linear models.     

Estimating genetic values for milk production in the tropics

Variance components and predicted sire values were estimated using 305-d projected and unprojected milk records of varying lengths. Original data consisted of 15,512 lactation records of daughters of 138 Jamaica Hope sires that calved between 1969 and 1981 in 38 commercial dairy herds in Jamaica. Classification of records had little effect on components of variance. Herd-year-season variance decreased from 36% using all lactations to 28% with first lactations only. Sire variance was consistently about 10%. Cow component of variance accounted for 17% of the total variation using all lactations and 36% using all lactations of cows with recorded first lactations. Heritabilities for milk by Henderson's method 1 were five to six times larger than estimated from method 3 due to sire by herd confounding. Predicted sire values were between +400 kg and -400 kg. Rankings of sires with at least 5 progeny were considerably influenced by record classification, especially for sires with highest predicted values. There was less influence on rankings when at least 10 progeny per sire were used while the range in predicted sire values was larger using first lactation records only.     

Implementation of a routine genetic evaluation for longevity based on survival analysis techniques in dairy cattle populations in Switzerland

Genetic evaluation of sires for functional longevity of their daughters based on survival analysis has been implemented in the populations of Braunvieh, Simmental, and Holstein cattle in Switzerland. A Weibull mixed sire-maternal grandsire survival model was used to estimate breeding values of sires with data on cows that calved since April 1, 1980. Data on Braunvieh and Simmental cows included about 1.1 million records, data on Holstein cows comprised about 220,000 records. Data contained approximately 20 to 24% right-censored records and 6 to 9% left-truncated records. Besides the random sire and maternal grandsire effects, the model included effects of herd-year-season, age at first calving, parity, stage of lactation, alpine pasturing (Braunvieh and Simmental), and relative milk yield and relative fat and protein percentage within herd to account for culling for production. Heritability of functional longevity, estimated on a subset of data including approximately 150,000 animals, were 0.181, 0.198, and 0.184 for Braunvieh, Simmental, and Holstein, respectively. Breeding values were estimated for all sires with at least six daughters or three granddaughters in the data. Breeding values of sires are expressed in months of functional productive life and published in sire catalogs along with breeding values for production traits.     

Durability of Traits: Nonlinear Association between Initial and Subsequent Measures

Subjective linearized scores were recorded for milking speed, fore udder smoothness, shoulder looseness, and udder depth on 7357 and 3730 Holstein cows during first and second lactations. Random sire effects in threshold models were estimated for each trait and lactation. There were 95 sires that had estimated effects for all the traits in both lactations. For each trait, sire effects for first and second lactations were used as independent and dependent variables, respectively, in quadratic regression. Sire effects corresponding to milking speed in second lactation had linear relationship to sire effects corresponding to milking speed in first lactation. Similar relationships for udder smoothness, shoulder looseness, and udder depth appeared nonlinear. The quadratic terms associated with prediction equations for shoulder looseness and udder depth were significant. Nonlinear associations between genetic evaluations in first and second lactations may have resulted from aging.     

Prediction of longevity breeding values for US Holstein sires using survival analysis methodology

Breeding values of Holstein sires for daughter longevity in each of 9 geographical regions of the United States were predicted using a Weibull proportional hazards model. Longevity (also commonly referred to as herd life or length of productive life) was defined as the number of days from first calving until culling or censoring. Records from 2,322,389 Holstein cows with first calving from 1990 to 2000 were used. In addition to the sire's additive genetic merit, our failure time model included time-dependent effects of herd-year-season of calving, parity-stage of lactation, and within-herd-year quintiles for mature equivalent fat plus protein yield, as well as the time-independent effect of age at first calving. Sire variances and parameters of the Weibull distribution were estimated separately for each region. The relative risk of culling for daughters of each individual sire was expressed relative to that of daughters of an average sire (within a specific region). Predicted breeding values for functional longevity, expressed as relative risk ratios, ranged from 0.7 to 1.3. Sizable differences were observed between geographical regions in sire rankings, as well as estimated sire variances and gamma parameters (of the distribution of herd-year-season effects), suggesting that a single national ranking may not be appropriate for every region. Two random samples of herds were selected from the full national data set; these contained 375,086 records and 256,751 records, respectively. Predicted transmitting abilities (PTA) of sires for daughter longevity were calculated using the Weibull proportional hazards (sire) model described previously but without the correction for milk production. These were compared with predictions from a linear (animal) model, as currently used for routine genetic evaluation of length of productive life in the United States. Logistic regression of daughters' stayability to 36, 48, 60, 72, or 84 mo of life (among animals that had opportunity to stay that long) on sires' PTA indicated that the proportional hazards model yielded more accurate predictions of daughter longevity than the linear animal model, even though the latter relied on denser pedigree information.     

Heritability of clinical mastitis incidence and relationships with sire transmitting abilities for somatic cell score, udder type traits, productive life, and protein yield

The objective of this study was to determine the relationships among daughter clinical mastitis during first and second lactations and sire transmitting abilities for somatic cell score, udder type traits, productive life, and protein yield. Data on clinical mastitis during first lactation were available for 1795 daughters (in six Pennsylvania herds, one Minnesota herd, and one Nebraska herd) of 283 Holstein sires. Data on clinical mastitis during second lactation were available for 1055 of these daughters. A total of 479 cows had 864 clinical episodes during first lactation, and 230 cows had 384 clinical episodes during second lactation. Clinical mastitis incidence and the total number of clinical episodes during each lactation were regressed on herd-season of calving (a classification variable), age at first calving, lactation length, and sire transmitting abilities taken one at a time. Linear effects, nonlinear effects, and odds ratios were estimated for sire transmitting abilities. Separate analyses were conducted on dependent variables that considered clinical mastitis from: all organisms, coagulase-negative staphylococci, coliform species, streptococci other than Streptococcus agalactiae, and the most common environmental organisms (coliform species and streptococci other than Streptococcus agalactiae). Heritability of clinical mastitis ranged from 0.01 to 0.42. Daughters of sires that transmit the lowest somatic cell score had the lowest incidence of clinical mastitis and the fewest clinical episodes during first and second lactations. Daughters of sires that transmit longer productive life, shallower udders, deeper udder cleft, and strongly attached fore udders had either fewer clinical episodes or lower clinical mastitis incidence during first and second lactations. The incidence of clinical mastitis and the number of clinical episodes per lactation may be reduced by selection for lower somatic cell score, longer productive life, shallower udders, deeper udder cleft, or strongly attached fore udders.     

Short communication: use of culling information in genetic evaluation of fertility and mastitis in Norwegian red cows

Breeding values for clinical mastitis, interval from calving to first insemination, and 56-d nonreturn rate for heifers and primiparous cows, were predicted using multivariate linear-threshold sire models, with or without including information on culling during the first lactation. Breeding values for 3,064 sires were predicted using 3 data sets with an average of 273, 135, and 68 first-crop daughters per sire, respectively. For each data set, accuracies of selection for health and fertility traits were evaluated through the predictive ability of predicted sire breeding values with respect to phenotypic performance of second-crop daughters. The predictive ability of estimated breeding values for clinical mastitis and interval from calving to first insemination did not improve when including information on early culling, irrespective of the size of first-crop daughter groups. For 56-d nonreturn rates (heifer and primiparous cow), sire evaluations based on reduced size of daughter groups tended to predict performance of the future daughters slightly better when including data on early culling. Hence, for breeding programs with direct selection for health and fertility traits there is little to gain by including early culling as additional information.     

Heritability,reliability of genetic evaluations and response to selection in proportional hazard models

The purposes of this study were 1) to investigate the heritability, reliability, and selection response for survival traits following a Weibull frailty proportional hazard model; and 2) to examine the relationship between genetic parameters from a Weibull model, a discrete proportional hazard model, and a binary data analysis using a linear model. Both analytical methods and Monte Carlo simulations were used to achieve these aims. Data were simulated using the Weibull frailty model with two different shapes of the Weibull distribution. Breeding values of 100 unrelated sires with 50 to 100 progeny (with different levels of censoring) were generated from a normal distribution and two different sire variances. For analysis of longevity data on the discrete scale, simulated data were transformed to a discrete scale using arbitrary ends of discrete intervals of 400, 800, or 1200 d. For binary data analysis, an individual's longevity was either 0 (when longevity was less than the end of interval) or 1 (when longevity was equal or greater than the end of interval). Three different statistical models were investigated in this study: a Weibull model, a discrete-time model (a proportional hazard model assuming that the survival data are measured on a discrete scale with few classes), and a linear model based upon binary data. An alternative derivation using basic expressions of reliabilities in sire models suggests a simple equation for the heritability on the original scale (effective heritability) that is not dependent on the Weibull parameters. The predictions of reliabilities using the proposed formulae in this study are in very good agreement with reliabilities observed from simulations. In general, the estimates of reliability from either the discrete model or the binary data analysis were close to estimates from the Weibull model for a given number of uncensored records in this simplified case of a balanced design. Although selection response from the binary data analysis depends on the end of interval point, there is a relatively good agreement between selection responses in the Weibull model and the binary data analysis. In general, when the underlying survival data is from a Weibull distribution, it appears that the method of analyzing data does not greatly affect the results in terms of sire ranking or response to selection, at least for the simplified context considered in this study.     

Body trait profiles in Holstein-Friesians modeled using random regression

Legendre polynomial and cubic spline functions were used in random regression models to model the change in body traits over the course of the first lactation for daughters of 954 sires. Both functions estimated similar genetic variances for d 50 to 250 across lactation for the majority of traits. The heritability of the traits was similar to other studies using univariate models as well as random regression models. There was little difference between the 2 functions in their predictive power for each of the body type traits, as measured by the absolute difference between the predicted and actual type traits and the proportion of the total phenotypic variance explained by the model. Overall, the Legendre polynomial appeared to model these traits slightly better. Plots of the fixed curves and daily sire solutions obtained from the random regression models showed that there were differences in how the traits and sires changed across lactation. The daily sire solutions were then used to predict differences in liveweight of sires’ daughters across first lactation and showed that the daughters of some sires grew faster during first lactation than others. The spatial differences in the body traits that are displayed by this study could be an important indicator of the physical and biological changes that cows are undergoing in their first lactation. Information from these sire profiles could be harnessed to indicate production and functional traits later in life.     

Genetic parameters for hoof health traits estimated with linear and threshold models using alternative cohorts

A national genetic evaluation program for hoof health could be achieved by using hoof lesion data collected directly by hoof trimmers. However, not all cows in the herds during the trimming period are always presented to the hoof trimmer. This preselection process may not be completely random, leading to erroneous estimations of the prevalence of hoof lesions in the herd and inaccuracies in the genetic evaluation. The main objective of this study was to estimate genetic parameters for individual hoof lesions in Canadian Holsteins by using an alternative cohort to consider all cows in the herd during the period of the hoof trimming sessions, including those that were not examined by the trimmer over the entire lactation. A second objective was to compare the estimated heritabilities and breeding values for resistance to hoof lesions obtained with threshold and linear models. Data were recorded by 23 hoof trimmers serving 521 herds located in Alberta, British Columbia, and Ontario. A total of 73,559 hoof-trimming records from 53,654 cows were collected between 2009 and 2012. Hoof lesions included in the analysis were digital dermatitis, interdigital dermatitis, interdigital hyperplasia, sole hemorrhage, sole ulcer, toe ulcer, and white line disease. All variables were analyzed as binary traits, as the presence or the absence of the lesions, using a threshold and a linear animal model. Two different cohorts were created: Cohort 1, which included only cows presented to hoof trimmers, and Cohort 2, which included all cows present in the herd at the time of hoof trimmer visit. Using a threshold model, heritabilities on the observed scale ranged from 0.01 to 0.08 for Cohort 1 and from 0.01 to 0.06 for Cohort 2. Heritabilities estimated with the linear model ranged from 0.01 to 0.07 for Cohort 1 and from 0.01 to 0.05 for Cohort 2. Despite a low heritability, the distribution of the sire breeding values showed large and exploitable variation among sires. Higher breeding values for hoof lesion resistance corresponded to sires with a higher prevalence of healthy daughters. The rank correlations between estimated breeding values ranged from 0.96 to 0.99 when predicted using either one of the 2 cohorts and from 0.94 to 0.99 when predicted using either a threshold or a linear model.     

Heifer fertility and its relationship with cow fertility and production traits in Holstein dairy cattle

Breeding receipts from three AI units were merged with Ontario Dairy Herd Improvement Corporation and Record of Performance production records. Data comprised 53,705 heifer, 41,253 lactation 1, 14,688 lactation 2, and 3054 lactation 3 records by daughters of 2150 sires represented in 15,877 herd-year-seasons of birth. Three measures of heifer fertility, three measures of cow fertility, and three measures of production were investigated. Measures of heifer fertility were ages at first and last breeding and number of inseminations per conception. Cow fertility traits were days from calving to first breeding, days open, and number of inseminations per conception. Production traits were breed class average milk, breed class average fat, and fat percentage. Relationships among these nine traits for the first three lactations were estimated using a maximum likelihood multiple-trait procedure. The linear mixed model for each trait included fixed effects of herd-year-season of birth and genetic groups of sire and the random effect of sire. Transformations of the data for nonnormality had no influence on the estimates of genetic and phenotypic parameters. The heritability of .12 for age at first insemination, which was higher than other heifer fertility traits, indicated that selection would result in genetic response. Genetic and phenotypic correlations between heifer fertility and cow fertility and production traits in all three lactations were not different from zero. There was no genetic antagonism between fertility and subsequent production traits.     

Genetic evaluations of dairy bulls for daughter energy balance profiles using linear type scores and body condition score analyzed using random regression

The difference in body lipid between the start and end of lactation represents the body energy lost (or gained) in support of maintaining lactation including the nonproduction components of lactation. This source of energy is ignored in current genetic evaluations for production for dairy sires. The depletion and accretion of body tissue creates a pattern of body energy content over time that is, in part, under genetic control. Using random regression and field data, we modeled changes in body condition score (BCS) and liveweight, predicted from linear type traits, on first parity cows to produce daily breeding values of their sires for energy balance. These curves show that sires differ in the way their daughters lose and regain body energy throughout lactation. For all sires, the overall mean maximum daughter body energy loss was 1499 MJ (SD = 144 MJ) and occurred at d 99 (SD = 12.8 d) of lactation and the mean total daughter body energy loss at d 305 of lactation was 779 MJ (SD = 224 MJ). In this study, the profiles of body energy loss indicate that daughters of most sires lost body energy before d 150 and then recovered body energy, whereas the daughters of a few sires continued to lose body energy through to the end of lactation. Some sires with high merit for production may have daughters with body tissue mobilization profiles associated with poorer health and fertility leading to higher costs. A method of accounting for this cost could be to correct yield for body tissue mobilization. Deducting kilograms of milk from the breeding value for milk for each sire, equivalent in energy content to the body energy lost, resulted in a correlation of 0.98 between the ranking of sires for milk kilograms before and after adjustment. However, some sires changed rank bylarge amounts, the largest being +355 positions. Breeding values for energy balance can be calculated from single observations of BCS and linear type traits on daughters of a sire; data that can routinely be collected in national conformation assessment schemes.     

Genetic analysis of subclinical mastitis in early lactation of heifers using both linear and threshold models

Subclinical mastitis (SCM) causes economic losses for dairy producers by reducing milk production and leading to higher incidence of clinical mastitis and premature culling. The prevalence of SCM in first-lactation heifers is highest during early lactation. The objective of this study was to estimate genetic parameters for SCM in early lactation in first-parity Holsteins. Somatic cell count test-day records were collected monthly in 91 Canadian herds participating in the National Cohort of Dairy Farms of the Canadian Bovine Mastitis Research Network. Only the first test-day record available between 5 and 30 d in milk was considered for analysis. The final data set contained 8,518 records from first lactation Holstein heifers. Six alternative traits were defined as indicators of SCM, using various cutoff values of SCC, ranging from 150,000 to 400,000 cells/mL. Both linear and threshold animal models were used. Overall prevalence of SCM using the 6 traits ranged from 13 to 24%. Heritability estimates (standard error) from linear and threshold models ranged from 0.037 to 0.057 (0.015 to 0.018) and from 0.040 to 0.051 (0.017 to 0.020), respectively. We found strong genetic correlations (standard error) among alternative SCC traits, ranging from 0.90 to 0.99 (0.013 to 0.069), indicating that these 6 traits were genetically similar. Despite low heritability, based on estimated breeding values (EBV) predicted from both models, we noted exploitable genetic variation among sires. Higher EBV of SCM resistance corresponded to sires with a higher percentage of daughters without SCM. Based on a linear model (all 6 traits), percentage of daughters with SCM ranged from 5 to 13% and from 19 to 33% for the top 10% and worst 10% of 69 sires with minimum 20 daughters in at least 5 herds, respectively. Spearman's rank correlations among EBV of sires predicted from linear (from 0.75 to 0.95) and threshold (from 0.74 to 0.95) models were moderate to high, respectively. Very high rank correlations (0.98 to 0.99) between EBV predicted for the same trait from linear and threshold model indicated that reranking of sires based on model used was minimal. In conclusion, despite low heritability, we found utilizable genetic variation in early lactation of heifers. Hence, genetic selection to improve genetic resistance to SCM in early lactation of heifers was deemed possible.     

Profitability in Daughters of High Versus Average Holstein Sires Selected for Milk Yield of Daughters

Data from 778 cows with 2,461 lactations through three generations of selection at the Iowa State University research herd were used to study differences between daughters of sires selected for high and breed-average Predicted Difference Milk. A profitability function, income minus expense, was calculated for each cow. A fixed, linear model was used to describe lifetime profitability. Daughters of high Predicted Difference Milk sires had 49% higher semen costs, 1% higher reproductive health costs, less than 1% fewer breedings, and less than 1% more reproductive examinations. They had 9% more respiratory costs, 6% more digestive costs, and 8% more skin and skeletal costs. Daughters of high Predicted Difference Milk sires produced 16% more milk, had 26% more mammary costs, and 42% more discarded milk costs. Disregarding breeding costs, they had 21% higher total health costs. Including breeding costs, total health costs were 32% higher. With 9% increased feed costs, they netted 18% more lifetime profit and 18% more profit per day of life. Use of a mixed model, which adjusted for fixed effects and included cows as random variables, showed daughters of high Predicted Difference Milk sires to have 12.5% more milk and 15.5% more profit per lactation. Number of breedings and reproductive examinations increased in later lactations and also in later generations as milk production increased in the daughters of high Predicted Difference Milk sires.     

Genetic analysis of herd life in Quebec Holsteins using Weibull models

Survival analysis methodologies were used to study herd life in Canadian Holstein cows. Herd life was defined as true herd life or the length of time between first calving and censoring. True herd life adjusted for 305-d milk production was defined as functional herd life. Lifetime record (censored or completed) were from 331,147 Holstein cows registered in the Programme d'Analyse des Troupeaux Laitiers du Québec (PATLQ) that calved for the first time between March 1, 1981 and March 31, 1995. The Weibull (proportional hazards) model used to analyze true herd life and functional herd life contained a Weibull baseline hazard function and the time-dependent effects of year of first calving, lactation number by stage of lactation, annual change in herd size and herd-year (random), and the time-independent effects of the milk recording option (supervised or not) and age at first calving. The model for functional herd life included also the time-dependent effect of herd-year-parity class of 305-d milk production. Genetic differences between sires with regard to the hazard function of their daughters was clearly demonstrated. The hazard rate followed a different pattern in later lactations, particularly in the first 240 d in milk. Older age at first calving was found to be associated with higher risks of culling. Changes in herd size had a small impact on the hazard function of animals. The hazard decreased as production of the cow increased. Heritability in the log scale was 0.09 for true herd life and 0.08 for functional herd life, but when heritability was expressed on the original scale, the estimates for the two traits were 0.19 and 0.15, respectively. The difference in the median survival between a bull with an estimated transmitting ability of 0.6 and another bull with an estimated transmitting ability of 1.3 was 690 d or 1.7 lactations. Rank correlations between the official estimated transmitting abilities for true herd life and functional herd life and those obtained in this study were 0.62 and 0.66, respectively.     

Comparison of international dairy sire evaluations from meta-analysis of national estimated breeding values and direct analysis of individual animal performance records

Our objective was to assess the predictive ability of different methodologies for international genetic evaluation of milk yield and to determine the magnitude of differences in the resulting sire estimated breeding values (EBV). Data included first lactation records of 16,057,335 Holstein-sired cows from 237,049 herds in 14 countries. Meta-analysis of national sire EBV using the multiple-trait across country evaluation (MACE) procedure, single-trait analysis of individual animal performance records, multiple-trait analysis of individual animal performance records, and borderless herd cluster model were compared by assessing predictive ability. Comparisons were based on root mean square error of sire EBV from a subset of records from cows calving between 1990 and 1995 and corresponding pedigree indices for sires that received their first genetic evaluations in 1996 or 1997. The number of bulls first evaluated in 1996 or 1997 that were in common between the top 25, 100, and 250 for pedigree index and the top 25, 100, and 250 for EBV were also determined for each method. Average root mean square error of prediction was 10.3 kg2 for the borderless single-trait model, 6.6 kg2 for the borderless herd cluster model, and 6.7 kg2 for both the borderless multiple-trait model and meta-analysis of national sire EBV using MACE. The mean numbers of common bulls among the top 25, 100, and 250, respectively, when selected on pedigree index and subsequent EBV were 11, 48, and 154 for the borderless single-trait model; 16, 66, and 176 for the borderless multiple-trait model; 16, 66, and 178 for the borderless herd cluster model; and 15, 66, and 178 for meta-analysis of national sire EBV using MACE. Rank correlations between sire EBV from different models ranged from 0.77 for the single-trait borderless model and the meta-analysis using MACE to 0.92 for the borderless multiple-trait and the borderless herd cluster models.     

Genetic analysis of longitudinal trajectory of clinical mastitis in first-lactation Norwegian cattle

Clinical mastitis records for 36,178 first-lactation daughters of 245 Norwegian Cattle (NRF) sires were analyzed with a Bayesian longitudinal threshold model. For each cow, the period going from 30 d before calving to 300 d after calving was divided into 11 intervals of 30 d length each. Absence or presence of clinical mastitis within each interval was scored as "0" or "1", respectively. A Bayesian threshold model consisting of a set of explanatory variables plus Legendre polynomials on time of order four was used to describe the trajectory of liability to clinical mastitis. Heritability ranged between 0.07 and 0.13 before calving, from 0.04 to 0.15 during the first 270 d after calving, and increased sharply thereafter, as a consequence of the form of the polynomial. Genetic correlations between adjacent days were close to 1, and decreased when days were further apart. Most genetic correlations were moderate to high. A measure of probability of future daughters contracting clinical mastitis during lactation was computed for each sire. A typical curve had a peak near calving followed by a decrease thereafter. The best sires had a low peak around calving and a low expected probability of mastitis among daughters throughout lactation. Expected fraction of days without mastitis was derived from the probability curves and used for ranking of sires. Rank correlations with genetic evaluations of sires obtained from cross-sectional models were high. However, sire selection was affected markedly, especially at high selection intensity. An advantage of the longitudinal model for clinical mastitis is its ability to take multiple treatments and time aspects into account.     

Genetic analysis of California mastitis test records. I. Coded tests

A sample of 15,965 Holstein lactation records having California Mastitis Test scores for at least the first 9 mo of standard Dairy Herd Improvement production testing were studied for the effects of sire, parity, and year and month of calving. California Mastitis Test readings of "negative" or "trace" were coded normal while readings of "1", "2", or "3" were coded elevated. The frequency of elevated tests increased as parity increased. Effect of year of calving and a trend toward higher percentages of elevated coded test scores was significant. There was no distinct trend in elevated coded test score with month of calving. Sire effect on the incidence of elevation in the coded score was important. Heritability of first and second lactation monthly coded California Mastitis Test scores from a paternal half-sister analysis within herd, year, and season, for sires with at least 25 daughters ranged from .11 +/- .04 to .48 +/- .07. Genetic correlations between the third test and following tests of first and second lactations ranged from .25 +/-.15 to .58 +/- .18.