### INTRODUCTION

### MATERIALS AND METHODS

### Animals, records and Snell score transformation

_{j}the estimated boundary points for calving difficulty category

*j*; P

_{ij}is the observed probability of sex of calf

*i*in calving difficulty category

*j*; n

_{ij}is the frequency of scale values in sex of calf

*i*of calving difficulty category

*j*; N

_{j}is the sum of observations in calving difficulty category

*j*.

_{3}– X̂

_{2}), (X̂

_{2}– X̂

_{1}), …, (X̂

_{k-2}– X̂

_{k-1}). Once an arbitrary value of 0 was set to the first boundary point, subsequent boundary points for other categories was calculated by adding the previous category estimates. For the two extreme categories, scores are derived from the corresponding expected values under the two tails of the distribution. The scores for the first and last category are given by

*x̂*

*+ (log*

_{2}_{e}P

_{1}/Q

_{1}) and

*x̂*

*+ (log*

_{k-1}_{e}P

_{k–1}/Q

_{k–1}) where P

_{1}is the probability of a value greater than x

_{1}and Q

_{1}is the 1–P

_{1}, and P

_{k–1}is the probability of a value less than x

_{k–1}and Q

_{k–1}is the 1–P

_{k–1}. The Snell transformed CE scores for sex groups were computed following the above steps. Then, the derived score range of calving difficulty was forced to a scale spanning 0% to 100%, such that a score of 0% expressed the least of CE (an extreme difficulty calving) and 100% denoted the greatest of CE (a normal calving).

### Data analysis

**Y**is the vector of Snell transformed CE scores on a 0 to 100 scale;

**b**is the vector of fixed age at calving effect (in months);

**h**is the vector of random HYS effect;

**s**is the vector of random sire effect;

**mgs**is the vector of random MGS effect; and

**e**is the vector of random residual effect.

**X**,

**W**,

**Z**

**, and**

_{1}**Z**

**were incidence matrices relating the effects to phenotypes. Relationships among bulls were ignored for both sire and MGS effects.**

_{2}*σ*

_{s}_{,}

*) were converted to direct (D) and maternal (M) (co)variances using the relationship.*

_{mgs}*σ*

*is the additive genetic covariance between direct and maternal effects [15]. The phenotypic variance on the underlying scale was*

_{DM}*ŝ*

*and*

_{sire}*m̂*

*– 0.5*

_{mgs}*ŝ*

*, respectively, where*

_{mgs}*ŝ*is the sire and MGS solutions for the sire and

*m̂*is the solution for the MGS of the progeny or first-calving daughter. Secondly, the additive genetic trends of direct and maternal predicted transmitting ability (PTA) for the sires were also evaluated and plotted according to their birth years. The direct PTA (dPTA) was equivalent to the estimated solution for bull as sire (

*ŝ*). The maternal PTA (mPTA) was derived from

*m̂*– 0.5

*ŝ*, where

*m̂*is the solution for the bull as MGS.

### RESULTS AND DISCUSSION

### Descriptive statistics

### Genetic parameter estimates

^{2}) estimates for direct and maternal components from SCE based model were 0.11± 0.01 and 0.06±0.02, respectively. The daughter CE method, however, estimated a little lower h

^{2}for direct genetic effect (0.08±0.01) and maternal genetic effect (0.04±0.01). These overall differences in estimates were expected. The genetic variances due to direct and maternal effects were somewhat similar. The existence of direct genetic variances indicated the possibilities for selection responses towards a reduced calving difficulty, through a relative reduction of calf-size in relation to the dam’s pelvic openings. The correlation estimates between direct and maternal components were negative across models such as, −0.68±0.09 (SCE) and −0.71± 0.09 (DCE), possibly because of the negative covariances between them as it is commonly reflected by the relationships between calf size and dam’s pelvic dimension.

^{2}, 0.08; maternal h

^{2}, 0.04) in Dutch Holstein-Friesian cattle. The authors in a 2009 study [10], who also followed the Snell transformation of CE records and a linear model fit, reported very similar direct h

^{2}(0.14) and maternal h

^{2}(0.06) for calving ease in Charolais cattle. Likewise, a greater agreement was established with other studies irrespective of their choices for models of parameters estimations [5,15,16,19,20]. Despite the consistency for direct h

^{2}of CE from Heringstad et al [21], their h

^{2}estimate of maternal component was slightly higher (0.09). Some linear model studies [6,22], however, showed a trend where the linear models estimates were generally lower than those of the threshold models reports. To assert the differences between SCE and DCE model estimates in this study, a report by Weigel [23] greatly supported the present outcomes too.

_{GDM}) for calving ease was generally reported by others as well. A substantial harmony with similar estimates between these components was also reported by Mujibi and Crews [10]. In Canadian Holstein [22], a negative correlation between these genetic effects for CE (−0.16) was found as well. Similarly but within a slightly wider range (−0.04 to −0.44), some negative direct-maternal genetic correlations from animal and S-MGS models were also reported in Dutch Holstein Friesian cattle [18]. They evidently agreed, based on the outcome differences among the data subsets, that an accurate estimation of r

_{GDM}was rather difficult, even with about 100,000 records. Likewise, a fairly closer range of −0.08 to −0.47 in other dairy cattle studies was not unexpected [15,16]. In contrast, the study in Swedish Holstein [20] disagreed slightly by their weak positive or negative correlations, respectively, in calving difficulty trait. The magnitude at which reports differed might be attributed to the breed and population differences, in addition to the models of estimations. In support of the fact, an earlier work in 1996 [24] stated that estimates in beef cattle often tend to be more negative. The study of Mujibi and Crews [10], in support with Phocas and Sapa [25], illustrated that CE direct and maternal effects, that are genetically correlated in a negative way, could necessarily indicate the influences of physiological and biological factors of the heifer such as the size of pelvic opening at calf-birth. The work of Phocas and Sapa [25] treated CE as a trait of the dam.

### Phenotypic trends

### Genetic trends

### Choice of statistical models and CE evaluation approaches

^{2}estimates. The antagonistic correlation estimates between direct and maternal genetic components were also deemed high and indicated that there could be roles from maternal factors such as pelvic dimensions. However, evidence on sufficient genetic variances could reflect a selection improvement over time on CE. It is realized that direct genetic contributions resulting easier calving increased over time, whereas in overall, the maternal component was consistent and relatively low. A straightforward evidence of undesired and deteriorating maternal contributions on sires (sire EBV) were observed from the dams of sires, even though direct contributions were as desired. These outcomes were consistent with previous reports too. Thus, these results could be a good starting point for the development of selection and breeding plans for calving ease in the local Holstein population. A detailed future analysis with this trait alongside still-birth and birth weight of calves would validate present estimates with greater accuracies.