### INTRODUCTION

*r*>0.8) with blood levels (Andersson, 1988). Further, milk β-hydroxybutyric acid and milk acetone with information regarding the body condition score, milk fat and milk protein for energy balance can be used to establish ketosis in dairy cows (Koeck et al., 2014). Since April of 2012, Fourier transform infrared (FTIR) measurements for milk acetone and milk BHBA have been tentatively collected along with routinely evaluated milk measurements during dairy herd milk recording in Korea. Since ketosis is one of the most frequent diseases in dairy cattle, selective breeding for low incidence of hyperketonemia could be important to the dairy industry. Van der Drift et al. (2012) reported that there were moderate genetic relationships among concentrations of plasma BHBA, milk BHBA and milk acetone that may allow the use of milk BHBA and milk acetone in dairy cattle breeding. However, questions remain about whether the sensitivity of the records is sufficient to provide genetic information that can be used to select for low susceptibility to ketosis. Therefore, this study was conducted to investigate the heritabilities of milk BHBA and milk acetone and their genetic correlations, as well as the relationships with routinely evaluated test-day (TD) traits during first, second and third lactations.

### MATERIALS AND METHODS

### Data

### Statistical analysis

*y*

*is the TD record at*

_{ijkl:t}*t*DIM for one of the analyzed traits (milk BHBA, milk acetone, milk yield, fat, or protein %) of cow

*l*in a lactation (parity 1 to 3)

*k*th season within

*j*th age of calving at

*i*th herd TD, and

*t*is any DIM between 4 and 305;

*HTD*

*=*

_{i}*i*th herd TD effect, which takes the fixed effect of the lactation curve for each trait at t DIM into account;

*AgeSeason*

*is the effect of season*

_{jk}*k*of age

*j*at calving [age was categorized into 4 groups and calving seasons were defined as summer (May to October) and winter (November to April)];

*a*

*is the additive random regression coefficient of the*

_{ln:t}*l*th animal on

*t*DIM;

*p*

*is the permanent environmental random regression coefficient of the*

_{ln:t}*l*th animal on

*t*DIM;

*z*

*is the covariate associated with standardized DIM; and*

_{ln:t}*e*

*is a random residual effect. As*

_{ijkl:t}*z*

*is the Legendre polynomial that was recommended by Kirkpatrick et al. (1990),*

_{ln:t}*z*

_{1}−

*z*

_{3}were:

*t*

*is the smallest DIM and*

_{min}*t*

*is the largest DIM represented in the data.*

_{max}*b*is the vector of fixed effects;

*a*is the vector of additive genetic regression coefficients for each animal;

*p*is the vector of permanent environmental regression coefficients for each animal and

*e*is the vector of residual effect. The (co)variance matrices of random effect factors in

*a*,

*p*, and

*e*were assumed to be:

**is the (co)variance matrix of the additive genetic random regression coefficients of order 3;**

*G***is the additive genetic relationship matrix between animals;**

*A***is the (co)variance matrix of the permanent environmental random regression coefficients of order 3;**

*P***is the identity matrix; and**

*I**R*is the residual (co)variance.

### RESULTS AND DISCUSSION

### General description

^{2}= 0.2205) were as follows: