### INTRODUCTION

### MATERIALS AND METHODS

### Animals, data recording and data transformation

_{2}(SCC/100)+4. Instead of a constant 3 which most studies used, a constant 4 was used to avoid the problem of negative value in the data (Martins et al., 2011). Each of the test-day SCS was adjusted by Wilmink’s (1987) function for milking stage of the cow due to the changing pattern of SCS within its production trajectory. The adjustment function used was

*y*

_{ij}*=a*

*+*

_{0}*a*

_{1}

*t*

*+*

_{ij}*a*

_{2}

*exp*(−0.05

*t*

*)*

_{ij}*+e*

*, where*

_{ij}*y*

*is a record of SCS for*

_{ij}*i*

^{th}animal at

*j*

^{th}test-day,

*e*

*is the residual errors,*

_{ij}*t*

*is the difference in days between*

_{ij}*j*

^{th}test-date and calving-date of the

*i*

^{th}animal, and

*a*

_{0},

*a*

_{1}, and

*a*

_{2}are the regression coefficients of SCS (

*y*

*) on*

_{ij}*t*

*and*

_{ij}*exp*(−0.05

*t*

*) estimated within each lactation stage. An average lactation SCS (LSCS) was obtained from all test-day SCSs which were finally adjusted for lactation age groups (5 groups/parity; at 5 months interval each).*

_{ij}### Animal pedigree

### Data analysis

**y**is the vector of observations,

**b**is the vector of fixed effects and covariates,

**u**is the vector of random additive effects,

**q**is the vector of random HY effects,

**e**is the vector of random residual effects, and

**X**,

**Z**, and

**W**are known design matrices relating observations to the fixed and random effects

**b**,

**u**and

**q**respectively. The assumptions for distribution of

**y**,

**u**,

**q**and

**e**can be described as

**G**is the variance-covariance matirx of the random effects vector

**u**,

**H**is the variance-covariance matrix of the random effects vector

**q**, and

**R**is the matrix of residual variances and covariances. The

**G**,

**H**, and

**R**matrices are described as

**G**=

**A**⊗

**G**

**, where**

_{0}**A**is the animal relationship matrix,

**G**

**is the additive genetic variance-covariance matrix between traits, and ⊗ is the direct product operator,**

_{0}**H**=

**I**⊗

**H**

**and,**

_{0}**R**=

**I**⊗

**R**

**, where**

_{0}**I**is the identity matrix of the same order as

**y**,

**H**

**is the matrix of HY variance-covariance between traits,**

_{0}**R**

**is the matrix of residual variance-covariance between traits,**

_{0}**0**is the null vector, and

**Φ**is the null matrix.

^{2}) for traits using (co)variance estimates of sire and animal models. Genetic and phenotypic correlations were calculated from the (co)variance estimates of the multivariate sire models only. To obtain h

^{2}from sire model, the estimated sire variance for a trait was multiplied by 4, as it is known that sire model can obtain only 1/4

^{th}of the total genetic variances. Genetic trends for LSCS in dataset 1 were obtained from estimated breeding values (EBV) for all animals using (co)variances obtained by sire-models, which were derived by PEST software package (Groeneveld et al., 1990).

### RESULTS AND DISCUSSION

### Descriptive statistics of the datasets

### Heritability estimates

^{2}) among parities obtained through sire model analyses were more or less similar among datasets, especially for h

^{2}of LSCS

_{2}and LSCS

_{3}. In contrast, the univariate animal model heritabilities were higher than those from sire model estimates and, the observed differences in h

^{2}estimates among datasets were negligible too. However, the analyses using all datasets yielded lowest heritabilities for LSCS

_{5}trait. This is probably because of the bias caused by noticeably fewer records from 5th parity cows as compared to other parities, and resulted underestimated genetic variances for the respective trait; whereas, gradually increased genetic variances were noticed from parity 1 to 4 traits. Another source of bias in the 5th lactation estimates (LSCS

_{5}) using animal model might be associated with the presence of noticeably fewer dams than other parities, which was less influential to sire model estimates as expected. With the parity number increases, the proportional increases of variance for herd-year and residual effects deemed relatively higher than the additive genetic variance, indicating more environmental influences on SCS increase. A higher SCS also indicates the consequences of more infection of mastitis in the udder. Environmental variances were found to be relatively lower in the animal model analyses than those found in the sire models, as an opposite of the genetic variances, and those are possibly due to the presence of complete pedigree relationships in the animal model analyses.

^{2}estimates for LSCS between 0.10 and 0.27 (Monardes et al., 1990; Mrode and Swanson, 1996; Rupp and Boichard, 1999; Mark and Sullivan, 2005). Rupp and Boichard (2003) reviewed that LSCS trait, obtained by averaging the individual test day records, shows consistently higher h

^{2}estimate around 0.15. Estimates of heritabilities in this study deemed very consistent with most of these earlier studies. Further agreement is found in Austrian Fleckvieh cows which showed a mean h

^{2}of 0.09 to 0.13 for SCS traits in first five lactations (Koeck et al., 2010). Heritabilities obtained by Kadarmideen (2004) and Charfeddine et al. (1997) are also comparable (0.13 to 0.14). Our estimates in first three lactations are concordant with Swedish Holstein (Carlen et al., 2004), and Polish Holstein (Rzewuska et al., 2011), even though traits were defined differently. Similar h

^{2}estimates were obtained from the repeated measures test-day SCS model for first three lactations (Reents et al., 1995). However, some disagreements were observed from several reports (Haile-Mariam et al., 2001; Mrode and Swanson, 2003; Heringstad et al., 2008; Dube et al., 2008; Martins et al., 2011; Ivkić et al., 2012), where h

^{2}estimates tend to be higher or lower than those estimates found in this study. Increase of genetic variances and heritability estimates along with the increment in parity numbers have also been reported in earlier studies (Schutz et al., 1990; Samore et al., 2002; Muir et al., 2007; Ptak et al., 2007; Martins et al., 2011).

### Genetic and phenotypic correlations

_{4}and LSCS

_{5}(0.99) whereas, the lowest genetic correlation was found between LSCS

_{1}and LSCS

_{5}(0.62). Genetic correlations were generally strong between successive lactations (0.82 to 0.99), and tended to decrease between distant lactations. Sire model analysis using dataset 2 also derived similar estimates (Table 5). The phenotypic correlations among LSCS traits, however, were expectedly low to moderate. The highest phenotypic association of 0.54 was observed between LSCS

_{4}and LSCS

_{5}in the study. Phenotypic correlations between other lactations ranged between 0.22 and 0.51. Genetic trends of LSCS traits were shown in Figure 2. Even though it was found that heritabilities increased slightly with more parity records per cow (dataset 2), their genetic correlations rather deemed less influenced. In fact, more animals with at least two successive parity records were sufficient to obtain similar correlations as estimated from animals having more than 2 successive parity records.

_{1}using EBV of animals from dataset 1 (Figure 2) showed fairly consistent and very low EBVs in animals across the years for the same trait. Estimated breeding value of LSCS

_{2}, LSCS

_{3}and LSCS

_{4}, although higher than EBV of LSCS

_{1}, showed somewhat similar trends, indicating less degradations over time. The observed EBVs indicate that genetic merit for high SCS (susceptibility to mastitis) in the first lactation of Holsteins is negligible but increases as lactation number progresses. Evidently, these results seem to be in line with the claim that first lactation trait probably is a different trait from second and later lactations (Reents et al., 1995). They found more incidence of mastitis in later lactations which is also similar to our study. Reents et al. (1995) further suggested that SCS from later lactations might be a better indicator for mastitis susceptibility than only first lactation SCS. Shook and Schutz (1994) also suggested use of later lactation records, ideally in a multiple-trait model.