Modeling lactation curves and estimation of genetic parameters for first lactation test-day records of French Holstein cows

Several functions were used to model the fixed part of the lactation curve and genetic parameters of milk test-day records to estimate using French Holstein data. Parametric curves (Legendre polynomials, Ali-Schaeffer curve, Wilmink curve), fixed classes curves (5-d classes), and regression splines were tested. The latter were appealing because they adjusted the data well, were relatively insensitive to outliers, were flexible, and resulted in smooth curves without requiring the estimation of a large number of parameters. Genetic parameters were estimated with an Average Information REML algorithm where the average information matrix and the first derivatives of the likelihood functions were pooled over 10 samples. This approach made it possible to handle larger data sets. The residual variance was modeled as a quadratic function of days in milk. Quartic Legendre polynomials were used to estimate (co)variances of random effects. The estimates were within the range of most other studies. The greatest genetic variance was in the middle of the lactation while residual and permanent environmental variances mostly decreased during the lactation. The resulting heritability ranged from 0.15 to 0.40. The genetic correlation between the extreme parts of the lactation was 0.35 but genetic correlations were higher than 0.90 for a large part of the lactation. The use of the pooling approach resulted in smaller standard errors for the genetic parameters when compared to those obtained with a single sample.     

Genetic parameters for first lactation milk yields at three levels of herd production

A multivariate linear model was used to estimate sire variance and covariance components and residual variance components for first lactation milk yield and logarithms of yield at three herd production levels using Restricted Maximum Likelihood with the Expectation-Maximization algorithm. Data for four separate analyses were 305-d, mature equivalent first lactation milk records from cows sired artificially in the northeastern United States that freshened in 1970, 1971, 1976, and 1984. Respective numbers of records for each year were 42,618, 40,207, 33,581, and 34,196. Corresponding numbers of sires were 298, 289, 305, and 313. Herd production level was defined by mean yield of all cows freshening in same herd-year-season. For untransformed records sire and residual components of variance increased as mean increased, both within and between years. Correlations between sire effects at different production levels were all above .85. Heritabilities increased as production level increased. These results indicate that it may be necessary to account for heterogeneous genetic and environmental variance in sire evaluations. For logarithms of yield, sire components of variance were similar for each of the three production levels within a year. Residual components for logarithms decreased as production level increased. Change in variance from one production level to another was considerably more for logarithms than for untransformed yields.     

Genetic and environmental smoothing of lactation curves with cubic splines

Most approaches to modeling lactation curves involve parametric curves with fixed or random coefficients. In either case, the resulting models require the specification on an underlying parametric curve. The fitting of splines represents a semiparametric approach to the problem. In the context of animal breeding, cubic smoothing splines are particularly convenient because they can be incorporated into a suitably constructed mixed model. The potential for the use of splines in modeling lactation curves is explored with a simple example, and the results are compared with those using a random regression model. The spline model provides greater flexibility at the cost of additional computation. Splines are shown to be capable of picking up features of the lactation curve that are missed by the random regression model.     

Multitrait estimation of genetic parameters of lactation curves in Holstein heifers

Weekly milk yields of 1022 Holstein heifers from 61 sires were used to derive coefficients of the lactation curves using modified gamma and inverse polynomial functions. The natural logarithm of a modified gamma function was ln(yn) = ln (a) + b ln (n) + cn + u sin (x) + v cos (x), where a, b, c, u, and v are coefficients to be estimated; n is the day of lactation; and x is the day of year. Estimates of a, b, and c were combined to define persistency [-(b + 1) ln c], week of peak yield (b/c), and peak yield [a(b/c)be-b]. The inverse polynomial function was n/yn = A0 + A1n + A2n2, where A0, A1, and A2 are coefficients to be estimated. Variance and covariance components for the coefficients of the lactation curve were estimated by the multitrait restricted maximum likelihood method using canonical transformation. Heritability estimates were ln (a) .11, b .07, c .04 u .01, v .04, A0 .28, A1 .26, A2 .21, persistency .21, week of peak .18, peak yield .23, and 308-d milk yield .41. Genetic correlations indicated that selection for faster rate of increase to peak production would result in higher 308-d milk production, higher peak yield, and greater persistency.     

Genetic parameters for first and second lactation milk yields of Polish black and white cattle with random regression test-day models

Single- and two-trait random regression models were applied to estimate variance components of test-day records of milk, fat, and protein yields in the first and second lactation of Polish Black and White cattle. The model included fixed herd test-day effect, three covariates to describe lactation curve nested within age-season classes, and random regressions for additive genetic and permanent environmental effects. In two-parity models, each parity was treated as a separate trait. For milk and the two-parity model, heritabilities were in the range of 0.14 to 0.19 throughout first lactation and 0.10 to 0.16 throughout second lactation. For fat, heritabilities were within 0.11 to 0.16 and 0.11 to 0.22 throughout first and second lactations, respectively. For protein in the two-parity model, heritabilities were within 0.10 to 0.15 throughout most of first lactation and within 0.06 to 0.15 throughout the most of second lactation. For milk, genetic correlations between the first and second parities were 0.6 at the beginning of the lactation, rising to 0.9 in the middle, and 0.8 at the end of the lactation. For fat, the corresponding correlations were 0.6, 0.8, and 0.7, respectively, and for protein were 0.6, 0.8, and 0.8, respectively. Heritability estimates for all traits were flatter for the two-parity model. Relatively smooth genetic and permanent environmental variances with the two-parity model indicated that large swings of heritabilities could be artifacts of single-trait random regression models. High correlations between most of test day records across lactations suggested that a repeatability model could be considered as an alternative to a multiple-trait model to analyze multiple parities.     

Genetic parameters for fertility of dairy heifers and cows at different parities and relationships with production traits in first lactation

The objectives of this study were to estimate genetic parameters for fertility of Brown Swiss cattle, considering reproductive measures in different parities as different traits, and to estimate relationships between production traits of first lactation and fertility of heifers and first-parity and second-parity cows. Reproductive indicators were interval from parturition to first service, interval from first service to conception, interval from parturition to conception, number of inseminations to conception, conception rate at first service, and nonreturn rate at 56 d after first service. Production traits were peak milk yield (pMY), lactation milk yield, and lactation length (LL). Data included 37,546 records on heifers, and 24,098 and 15,653 records on first- and second-parity cows, respectively. Cows were reared in 2,035 herds, calved from 1999 to 2007, and were progeny of 527 AI bulls. Gibbs sampling was implemented to obtain (co)variance components using both univariate and bivariate threshold and censored linear sire models. Estimates of heritability for reproductive traits in heifers (0.016 to 0.026) were lower than those in first-parity (0.017 to 0.142) and second-parity (0.026 to 0.115) cows. Genetic correlations for fertility in first- and second-parity cows were very high (>0.920), whereas those between heifers and lactating cows were moderate (0.348 to 0.709). The latter result indicates that fertility in heifers is a different trait than fertility in lactating cows, and hence it cannot be used as robust indicator of cow fertility. Heifer fertility was not related to production traits in first lactation (genetic correlations between −0.215 and 0.251). Peak milk yield exerted a moderate and unfavorable effect on the interval from parturition to first service (genetic correlations of 0.414 and 0.353 after first and second calving, respectively), and a low and unfavorable effect on other fertility traits (genetic correlations between −0.281 and 0.295). Infertility after first calving caused a strong elongation of the lactation, and LL was negatively correlated with fertility of cows after second calving, so that LL can itself be regarded as a measure of fertility. Lactation milk yield depends on both pMY and LL, and, as such, is a cause and consequence of (in)fertility.     

Genetic parameters for clinical mastitis, somatic cell score, production, udder type traits, and milking ease in first lactation Holsteins.

Genetic parameters were estimated by restricted maximum likelihood with an animal model on first lactation data of 29,284 French Holstein cows for clinical mastitis, lactation somatic cell score, milking ease, production, and nine udder type traits. The heritability was low for clinical mastitis (0.024), moderate for lactation somatic cell score (0.17) and milking ease (0.17), and ranged from 0.17 to 0.30 for type traits. A high (0.72) but lower than unity genetic correlation was found between clinical mastitis and lactation somatic cell score and indicated that both traits were genetically favorably associated. The antagonism with production was stronger for clinical mastitis than for lactation somatic cell score (genetic correlations 0.45 and 0.15, respectively). Udder depth, fore-udder attachment, and udder balance were favorably associated with lactation somatic cell score and clinical mastitis with genetic correlations ranging from -0.29 to -0.46, whereas low correlations were found with teat length. Milking ease was found to be unfavorably correlated with lactation somatic cell score (genetic correlation 0.44) but not with clinical mastitis.     

Diversity of dairy goat lactation curves in France

A high level of production at the peak of lactation may be associated with animal health disorders, high feeding costs, and reduced milk supply throughout the year. The objective of this study was to typologize the lactation curves in French dairy goats and analyze the influence of environmental and genetic factors on these curves. The data set consisted of 2,231,720 monthly test-day records of 213,534 French Saanen and Alpine goats recorded between September 2008 and June 2012. First, principal component analysis classified the shape of the lactation curves into 3 principal components: the first component accounted for milk yield level throughout lactation, the second component accounted for lactation persistency, and the third component accounted for milk yield in mid-lactation. Then, from the principal component scores, the lactations were clustered into 5 different groups. Most lactations had a similar shape to the mean curve, except 30% of the lactations that fell into 3 clusters that had a high production level at the peak and then a different persistency according to cluster. Estimated breeding value for milk yield and home region of breeding were the factors most related to lactation production level. Month of kidding, breed, and gestation stage had the biggest effect on persistency. Month of kidding was the factor most strongly linked to mid-lactation production. A herd effect was observed on all 3 principal components.     

Genetic parameters of lactation cell counts and milk and protein yields in dairy ewes

A total of 3231 lactation records of somatic cell counts (SCC), milk yield, and protein percentage for 2379 Spanish Churra ewes from 10 flocks were used to estimate genetic and environmental parameters. Genetic parameters were estimated by REML with a multitrait repeatability animal model. A lactation measure of SCC was obtained as the mean of test day log SCC adjusted for stage of lactation. Heritabilities for SCC, milk yield, and protein percentage were 0.12, 0.24, and 0.17, respectively. The corresponding repeatabilities were 0.35, 0.49, and 0.38. Heritability and repeatability estimates of SCC obtained from this study fell within the range frequently reported for dairy cows. Therefore, as practiced for dairy cattle, future possibilities for sire evaluation to improve udder health status using lactation measures of SCC for dairy sheep are not rejected, although hygienic practices are regarded as more important. Genetic correlations of SCC with milk yield and protein percentage were -0.15 and -0.03, respectively. The genetic correlation between milk yield and protein percentage was -0.47. The low genetic correlations of SCC with milk yield and protein percentage may indicate that breeding decisions to improve milk and protein yields of Churra ewes are not expected to have an effective correlated response in SCC.     

Diphasic analysis of lactation curves in dairy goats

Milk production data on 5084 Alpine, 2052 LaMancha, 7024 Nubian, 2194 Saanen, and 2339 Toggenburg does were grouped into 90 subclasses: five breeds x three parities (1, 2, and 3) x two seasons of kidding (early, December to March; late, April to July) x three measures of 305-d milk production within breed (low, medium, and high). Subclass means of milk production for 100 3-d groups were smoothed and used to estimate parameters of a diphasic function, which is the sum of two logistic functions. Characteristics for each phase of the lactation curve (initial, peak, and 305-d yields, time of peak, and duration of phase), which are functions of parameters of the diphasic function, were then analyzed using a linear model including breed, parity, season, and mean of measure of production as a covariate, weighted by the number of observations in each subclass. Breed had little effect on the shape of the lactation curve in dairy goats. Parity affected primarily characteristics of the second phase of lactation. Season of kidding had the most consistent effect on the lactation curve: affecting characteristics of each phase. Measure of production affected characteristics of the second phase more than those of the first phase. First phase, with its proximity to overall peak and short duration, could be interpreted as a "peak" phase. Second phase, affected largely by parity, could be interpreted as a "persistency" phase.     

Effect of stage of lactation and parity on mammary gland cell renewal

Milk production is a function of the number and activity of mammary epithelial cells, regardless of stage of lactation. Milk yield is generally higher in multiparous cows than in primiparous cows, but persistency is usually greater in the latter group. We compared several measures related to metabolic activity, apoptosis, and endocrine control of mammary cell growth in 8 primiparous and 9 multiparous cows throughout lactation. Mammary gland biopsies were taken in early [10 d in milk (DIM)], peak (50 DIM), and late (250 DIM) lactation to evaluate gene expression and determine DNA and fatty acid synthase (FAS) content. Milk samples taken the day before the biopsies were used to detect protease activities and to determine stanniocalcin-1 (STC) concentrations. Blood samples served to measure insulin-like growth factor-1, prolactin, and STC concentrations. Milk yield was higher in multiparous cows than in primiparous cows at the 10 DIM (32.8 ± 1.3 and 25.2 ± 0.8 kg/d) and 50 DIM (38.0 ± 1.2 and 29.8 ± 1.1 kg/d), but it was the same for both groups at 250 DIM (23.9 ± 1.5 and 23.8 ± 1.1 kg/d). Except for stearoyl-coenzyme A desaturase, expression of genes related to milk synthesis was not affected by stage of lactation. However, gene expression of acetyl-coenzyme A carboxylase, β-casein, and FAS was lower in early lactation in primiparous cows. Expression of both proapoptotic bax and antiapoptotic bcl-2 genes was higher in primiparous cows, whereas the bax-to-bcl-2 ratio was not changed. Mammary DNA concentration was higher in multiparous cows, as was the amount of FAS protein in early lactation. Two bands of protease activity were found in milk samples, and one of the bands had an apparent molecular weight similar to gelatinase A and was dependent on the stage of lactation. Serum insulin-like growth factor-1 increased with day of lactation and was higher in primiparous cows. Serum prolactin decreased in late lactation, but peak values were observed in early lactation for primiparous cows and peak lactation for multiparous cows. Milk STC content increased with advancing lactation. The results are consistent with a lower degree of differentiation and a greater capacity for cell renewal in the mammary gland of primiparous cows.     

Short communication: reference values for blood parameters in Holstein dairy cows: effects of parity, stage of lactation, and season of production

Confidence intervals for blood parameters used for nutritional and metabolic profile testing in cattle were calculated for clinically normal lactating Holstein cows, taking into account the effects of parity, stage of lactation, and season. Blood samples were collected from 740 cows in 33 Italian dairy herds according to a predefined protocol. Herds were visited during summer and the following winter, sampling 12 lactating cows at each visit (4 primiparous and 8 multiparous). Six cows were selected from the early-lactation group (days in milk: 10 to 89) and the other 6 were selected from the mid-lactation group (days in milk: 90 to 215). Cow selection criteria excluded animals clinically exposed to periparturient diseases as well as animals not considered in good health by a veterinary clinical examination. For each blood variable, outliers were identified and discarded. Data were then analyzed for their Gaussian distribution and variables with not normal distribution were log-transformed to adjust for lack of normality. Herd mean values were calculated for each blood parameter according to 3 main classification factors: parity (primiparous vs. multiparous), stage of lactation (early vs. mid) and season of production (summer vs. winter). The resulting data set was statistically analyzed using a mixed model with the fixed effects of these factors, their interactions, and the random effect of herd. General 95% confidence intervals were calculated for blood variables that showed a relevant herd variance component such as albumin, triglycerides, aspartate, urea, glucose, alanine aminotransferase, lactate dehydrogenase, direct and total bilirubin, calcium, magnesium, and potassium. For the remaining parameters, specific confidence intervals were calculated for each level of the significant main factors. Parity affected blood concentration of total protein, globulin, creatinine, alkaline phosphatase, gamma glutamyl transferase, creatinine kinase, and phosphorus. Blood nonesterified fatty acids, aspartate aminotransferase, gamma glutamyl transferase, creatinine kinase and cholesterol were influenced by stage of lactation. The season of production had a significant effect on total protein, globulin, creatinine, alkaline phosphatase, phosphorus, sodium, and chlorine. The outcomes of this work will improve the accuracy of the biochemical profile as a tool for dairy practitioners to assess the metabolic status of lactating Holstein cows.     

Genetic parameters derived from using a biological model of lactation on records of commercial dairy cows

The object of this study was to investigate the genetics of lactation curve parameters derived from a biological model of lactation and the relationships among them. This biological model fitted 2 logistic curves to mimic the initial increase in milk secretory cell numbers in early lactation and the progression of apoptosis in late lactation. Records from 82,255 Holstein-Friesian heifers from commercial dairy herds in the United Kingdom, recorded from 1994 to 2003, were analyzed. The heritabilities of 2 lactation curve parameters, maximum secretion potential and relative cell death rate, were 0.27 and 0.08 respectively. Maximum secretion potential was highly genetically correlated with peak yield (0.99), and relative cell death rate was highly correlated with persistency of lactation (0.84). Heritability values for the traits analyzed showed a characteristic pattern. Total milk yield traits, maximum secretion potential, and peak yield had similar and moderate heritabilities (∼0.3). Traits associated with late lactation had lower heritability values (∼0.1), whereas day of peak yield and early lactation traits had little genetic variation. The permanent environmental variance of the various traits ranged from 0.08 to 0.26 of the phenotypic variance. Parameters from the 2 logistic curves were not highly correlated, suggesting that selection programs could be devised to exploit genetic variation in both aspects of lactation independently.     

Genetic parameters for first milk production and composition traits for Holsteins using multivariate restricted maximum likelihood

Heritabilities and genetic and phenotypic correlations among yields of milk, fat, protein, and percentages of fat and protein were estimated from 40,984 first lactation records of daughters of 488 young and 75 proven Holstein sires using multivariate REML and a sire model accounting for relationships and sire groups. Proven sires were treated as fixed effects. Heritabilities for yields of milk, fat, protein, and percentages of fat and protein were .29, .31, .25, .65, and .61, respectively. Genetic correlations of milk with yields of fat, protein, and percentages of fat and protein and correlations of fat yield with fat percentage were .45, .79, -.49, -.54 and .56, respectively. Genetic correlations among yields and among percentage of fat and protein were the same (.62). Genetic and phenotypic correlations of protein percentage with fat and protein yields and correlations of fat percentages with protein yield were small (-.13 to .11). Phenotypic correlations were .73 to .90 among yields of milk, fat, and protein; -.31 for milk and fat percentage; -.39 for milk and protein percentage; and .38 for fat yield and fat percentage. Estimates were consistent with an earlier study utilizing data from the same population and also with other reports.     

Genetic parameters across lactation for feed intake,fat- and protein-corrected milk,and liveweight in first-parity Holstein cattle

Breeding values for dry matter intake (DMI) are important to optimize dairy cattle breeding goals for feed efficiency. However, generally, only small data sets are available for feed intake, due to the cost and difficulty of measuring DMI, which makes understanding the genetic associations between traits across lactation difficult, let alone the possibility for selection of breeding animals. However, estimating national breeding values through cheaper and more easily measured correlated traits, such as milk yield and liveweight (LW), could be a first step to predict DMI. Combining DMI data across historical nutritional experiments might help to expand the data sets. Therefore, the objective was to estimate genetic parameters for DMI, fat- and protein-corrected milk (FPCM) yield, and LW across the entire first lactation using a relatively large data set combining experimental data across the Netherlands. A total of 30,483 weekly records for DMI, 49,977 for FPCM yield, and 31,956 for LW were available from 2,283 Dutch Holstein-Friesian first-parity cows between 1990 and 2011. Heritabilities, covariance components, and genetic correlations were estimated using a multivariate random regression model. The model included an effect for year-season of calving, and polynomials for age of cow at calving and days in milk (DIM). The random effects were experimental treatment, year-month of measurement, and the additive genetic, permanent environmental, and residual term. Additive genetic and permanent environmental effects were modeled using a third-order orthogonal polynomial. Estimated heritabilities ranged from 0.21 to 0.40 for DMI, from 0.20 to 0.43 for FPCM yield, and from 0.25 to 0.48 for LW across DIM. Genetic correlations between DMI at different DIM were relatively low during early and late lactation, compared with mid lactation. The genetic correlations between DMI and FPCM yield varied across DIM. This correlation was negative (up to −0.5) between FPCM yield in early lactation and DMI across the entire lactation, but highly positive (above 0.8) when both traits were in mid lactation. The correlation between DMI and LW was 0.6 during early lactation, but decreased to 0.4 during mid lactation. The highest correlations between FPCM yield and LW (0.3–0.5) were estimated during mid lactation. However, the genetic correlations between DMI and either FPCM yield or LW were not symmetric across DIM, and differed depending on which trait was measured first. The results of our study are useful to understand the genetic relationship of DMI, FPCM yield, and LW on specific days across lactation.     

Immunoglobulin isotype concentrations in milk as affected by stage of lactation and parity

Quarter milk samples were collected during lactation and analyzed for immunoglobulins from 32 first and 16 third lactation Holstein cows that were equally distributed progeny of sires selected for yield or merit. Variance component estimates indicated large variation for cow, quarter within cow, and stage of lactation. All immunoglobulin isotype concentrations were lowest at wk 21. Significant differences between first and third lactation cows were observed for milk immunoglobulin A (.012 and .018 mg/ml) and immunoglobulin M (.074 and .101 mg/ml). Quarters with cell counts above 1 X 10(6) cells/ml had higher concentrations of immunoglobulin G1, (.619 vs. .394 mg/ml) immunoglobulin G2 (.103 vs. .063 mg/ml), immunoglobulin A (.028 vs. .014 mg/ml), and immunoglobulin M (.117 vs. .087 mg/ml). There were no significant differences in immunoglobulin isotype concentrations due to genetic group (yield or merit), suggesting that selection for milk production has no significant effect on immunoglobulin concentration in milk. Degree of parity, however, must be considered when comparing immunoglobulin A and immunoglobulin M concentrations in milk.     

Measurement of mastitis in first lactation heifers and third to fourth lactation cows

The influence of lactation stage on susceptibility to mastitis infection in Friesian dairy cows was investigated. The cattle studied included third to fourth lactation cows and both summer and autumn calving groups of heifers. No increase in vulnerability to invasion by mastitis pathogens in recently calved cattle was demonstrated. Analysis of raw milk samples using ATP bioluminescence produced variation in results, suggesting that further work to develop the technique is required.     

Genetic improvement of total milk yield and total lactation persistency of the first three lactations in dairy cattle

The objective of this study was to compare 6 selection criteria in terms of 3-parity total milk yield and 9 selection criteria in terms of total net merit (H) comprising 3-parity total milk yield and total lactation persistency. The 6 selection criteria compared were as follows: first-parity milk estimated breeding value (EBV; M1), first 2-parity milk EBV (M2), first 3-parity milk EBV (M3), first-parity eigen index (EI₁), first 2-parity eigen index (EI₂), and first 3-parity eigen index (EI₃). The 9 selection criteria compared in terms of H were M1, M2, M3, EI₁, EI₂, EI₃, and first-parity, first 2-parity, and first 3-parity selection indices (I₁, I₂, and I₃, respectively). In terms of total milk yield, selection on M3 or EI₃ achieved the greatest genetic response, whereas selection on EI₁ produced the largest genetic progress per day. In terms of total net merit, selection on I₃ brought the largest response, whereas selection EI₁ yielded the greatest genetic progress per day. A multiple-lactation random regression test-day model simultaneously yields the EBV of the 3 lactations for all animals included in the analysis even though the younger animals do not have the opportunity to complete the first 3 lactations. It is important to use the first 3 lactation EBV for selection decision rather than only the first lactation EBV in spite of the fact that the first-parity selection criteria achieved a faster genetic progress per day than the 3-parity selection criteria. Under a multiple-lactation random regression animal model analysis, the use of the first 3 lactation EBV for selection decision does not prolong the generation interval as compared with the use of only the first lactation EBV. Thus, it is justified to compare genetic response on a lifetime basis rather than on a per-day basis. The results suggest the use of M3 or EI₃ for genetic improvement of total milk yield and the use of I₃ for genetic improvement of total net merit H. Although this study deals with selection for 3-parity milk production, the same principle applies to selection for lifetime milk production.