Influence of milking frequency on genetic parameters associated with the milk production in the first and second lactations of Iranian Holstein dairy cows using random regression test day models
- Moslem Moghbeli Damane^{1}Email author,
- Masood Asadi Fozi^{2} and
- Ahmad Ayatollahi Mehrgardi^{2}
DOI: 10.1186/s40781-016-0087-3
© Damane et al. 2016
Received: 3 November 2014
Accepted: 6 January 2016
Published: 1 February 2016
Abstract
Background
The milk yield can be affected by the frequency of milking per day, in dairy cows. Previous studies have shown that the milk yield is increased by 6–25 % per lactation when the milking frequency is increased from 2 to 3 times per day while the somatic cell count is decreased. To investigate the effect of milking frequency (3X vs. 4X) on milk yield and it’s genetic parameters in the first and second lactations of the Iranian Holstein dairy cows, a total of 142,604 test day (TD) records of milk yield were measured on 20,762 cows.
Results
Heritability estimates of milk yield were 0.25 and 0.19 for 3X milking frequency and 0.34 and 0.26 for 4X milking frequency throughout the first and second lactations, respectively. Repeatability estimates of milk yield were 0.70 and 0.71 for 3X milking frequency and 0.76 and 0.77 for 4X milking frequency, respectively. In comparison with 3X milking frequency, the milk yield of the first and second lactations was increased by 11.6 and 12.2 %, respectively when 4X was used (p < 0.01).
Conclusions
Results of this research demonstrated that increasing milking frequency led to an increase in heritability and repeatability of milk yield. The current investigation provided clear evidences for the benefits of using 4X milking frequency instead of 3X in Iranian Holstein dairy cows.
Keywords
Genetic parameters Random regression Milk production Milking frequency Iranian Holstein cowsBackground
The purpose of animal breeding is to genetically enhance the livestock production where more efficient animals are produced to guard against future circumstances. An important method for maximizing response to selection program is the accurate prediction of breeding values of animal [34]. In dairy cows, to implement an efficient breeding program, the estimates of genetic parameters for the production traits are required. In addition, to predict expected selection response and to achieve the predicted breeding value by the mixed model procedures, the accurate heritability, repeatability and correlation estimates are required. Various test day (TD) models have been recommended for genetic evaluation of dairy cows such as multiple-trait models, covariance function models and random regression models [33]. However, in many countries, the random regression model (RRM) has been widely demonstrated to increase the accuracy of breeding value predictions [31]. The use of RRM makes it possible to study changes in TD records over time and a better understanding of lactation genetics [32].
It has been found that the milk yield could be affected by the frequency of milking cows per day [16]. Erdman [14] demonstrated that the increase in milk yield due to the increased milk frequency is fixed, and is not dependent to the level of milk production at the time of increase milking frequency. In high producing dairy cows, twice a day milking interval of 10–14 h and 12–14 h are suggested, whereas, once a day or skipping milking is not acceptable, since it may arise several problems such as an increased in the somatic cell counts as well as poor udder health [30]. By increasing milking frequency from 2 to 3 times per day, an increase in milk yield from 6 to 25 % per lactation is observed [11, 14, 22] and there is also a decrease in somatic cell counts [17]. Moreover, Armstrong [1] reported that the milk production is increased by 8–12 % when four times (4X) a day milking is applied instead of three times (3X) a day. Three times-a-day milking is currently the most frequently used milking schedule in Iranian Holstein dairy cows, however, four times a day are also rarely applied. The objectives of this study were to estimate variance components for test day (TD) milk yield using a random regression TD model to evaluate the effect of milking frequency (3X vs. 4X) on genetic parameters associated with milk yield in the first and second lactations of Iranian Holstein dairy cows and determines how much milk yield changes with increasing in milking frequency in different lactation yield. It is expected that increasing milking frequency from 3X to 4X causes augmentation of genetic parameters of milk production and also increase in milk production, thereby would be more profitable for farmers.
Methods
Data
Summary of the pedigree information of milk yield data in 3X and 4X milking frequency
Number of | ||||||
---|---|---|---|---|---|---|
Trait | Milking frequency | Animal | Records | Sire | Dam | Herd |
Milk yield | 3 | 18,764 | 117,168 | 1002 | 16,458 | 112 |
4 | 2810 | 25436 | 296 | 2198 | 8 |
Descriptive statistics of the test-day records of milk yield (kg) for some selected days in milk with 3X and 4X milking frequency
3X Milking | 4X Milking | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Lact 1 | Lact 2 | Lact 1 | Lact 2 | |||||||||
DIM | N | Mean | SD | N | Mean | SD | N | Mean | SD | N | Mean | SD |
5–35 | 6392 | 29.7 | 4.9 | 7691 | 38 | 6.3 | 1142 | 32.5 | 5 | 1313 | 41.8 | 6.1 |
36–65 | 7022 | 33.4 | 4.9 | 8218 | 40.7 | 6.4 | 1298 | 37.3 | 4.8 | 1374 | 46.1 | 6.2 |
66–95 | 7097 | 33.9 | 5.1 | 8246 | 40.2 | 6.6 | 1292 | 38.6 | 4.9 | 1375 | 45.8 | 6.2 |
96–125 | 7430 | 33.4 | 5 | 8778 | 38.6 | 6.6 | 1336 | 38 | 4.8 | 1467 | 43.8 | 6.2 |
126–155 | 6816 | 32.8 | 5.3 | 7815 | 36.4 | 6.7 | 1330 | 37.2 | 4.8 | 1448 | 41.3 | 6.1 |
156–185 | 6293 | 32.4 | 5.4 | 7057 | 34.4 | 6.7 | 1375 | 36.4 | 4.8 | 1394 | 38.8 | 5.9 |
186–225 | 5234 | 31.8 | 5.6 | 5456 | 32.5 | 6.7 | 1336 | 35.4 | 4.7 | 1260 | 36.6 | 6.3 |
226–245 | 4287 | 31 | 5.6 | 4138 | 30.9 | 6.8 | 1324 | 34.4 | 4.6 | 1217 | 34.2 | 6.3 |
246–275 | 3105 | 30 | 5.7 | 2702 | 29.1 | 6.7 | 1318 | 39 | 4.5 | 1045 | 31.8 | 6.2 |
276–305 | 1938 | 29.2 | 5.8 | 1453 | 26.7 | 6.1 | 1045 | 31.9 | 4.8 | 747 | 29.8 | 6 |
Model
A single trait random regression model was applied to estimate genetic parameters of test day (TD) records of milk yield in the first and second lactations. The fixed effects of herd-test date, calving age and the number of days in milk were fitted in the model. Also the additive genetic effects and animal permanent environmental effects were added to the model analysis as the random effects. The data were analysed using ASReml software [15].
Where: y_{ ijnos } is the individual test-day records HTD_{ i } is i^{th} Herd-Test date, b_{ n } is fixed regression coefficient of age at calving, age_{ ijn } is calving age, c_{ n } is fixed regression coefficient of days in milk, dim_{ ijno } is days in milk, φ _{ n } is n^{th} Legender polynomial for days in milk, α _{ pn } is additive genetic effects, γ _{ pn } is animal permanent environmental effects and e_{ ijnos } is the residuals.
Where l is the Log likelihood values, K is the number of estimated parameters and n is the number of observations.
Results and discussion
Number of estimated parameters, log likelihood values and Schwarz’s Bayesian information criteria (BIC) for 3X milking frequency in the first and second lactations
Lactation | Ka^{a} | Kpe^{b} | Number of parameters | Log likelyhood | BIC |
---|---|---|---|---|---|
Lact 1 | 1 | 1 | 16 | −106,018.02 | 212,111.7 |
2 | 1 | 19 | −105,796.05 | 211,682 | |
2 | 2 | 22 | −105,772.28 | 211,648.6 | |
3 | 2 | 25 | −105,735.65 | 211,589.5 | |
3 | 3 | 28 | −105,703.71 | 211,539.9 | |
4 | 2 | 28 | −105,680.26 | 211,493 | |
4 | 3 | 31 | −105,656.98 | 211,460.6 | |
4 | 4 | 34 | −105,645.56 | 211,451.9 | |
5 | 2 | 31 | −105,661.18 | 211,469 | |
5 | 3 | 34 | −105,648.43 | 211,457.7 | |
5 | 4 | 37 | −105,635.52 | 211,446 ^{ c } | |
5 | 5 | 40 | −105,675.21 | 211,539.6 | |
Lact 2 | 1 | 1 | 16 | −131,871.6 | 263,819.6 |
2 | 1 | 19 | −131,569.2 | 263,229.1 | |
2 | 2 | 22 | −131,516.12 | 263,137.3 | |
3 | 2 | 25 | −121,394.82 | 242,909 ^{ c } | |
3 | 3 | 28 | −141,350.47 | 282,834.7 | |
4 | 2 | 28 | −131,347.03 | 262,827.8 | |
4 | 3 | 31 | −131,303.31 | 262,754.7 | |
4 | 4 | 34 | −131,275.85 | 262,714.1 | |
5 | 2 | 31 | −131,134.43 | 262,416.9 | |
5 | 3 | 34 | −131,086.81 | 262,336 | |
5 | 4 | 37 | −131,050.94 | 262,278.6 | |
5 | 5 | 40 | −131,041.94 | 262,274.9 |
Number of estimated parameters, log likelihood values and Schwarz’s Bayesian information criteria (BIC) for 4X milking frequency in the first and second lactations
Lactation | Ka^{a} | Kpe^{b} | Number of parameters | Log likelyhood | BIC |
---|---|---|---|---|---|
Lact 1 | 1 | 1 | 16 | −24,329.13 | 48,723.88 |
2 | 1 | 19 | −24,234.39 | 48,546.7 | |
2 | 2 | 22 | −24,226.59 | 48,543.4 | |
3 | 2 | 25 | −24,174.07 | 48,450.67 | |
3 | 3 | 28 | −24,171.08 | 48,456.99 | |
4 | 2 | 28 | −24,173.33 | 48,461.49 | |
4 | 3 | 31 | −24,169.18 | 48,465.49 | |
4 | 4 | 34 | −24,167.36 | 48,474.16 | |
5 | 2 | 31 | −24,112.26 | 48,351.65 ^{ c } | |
5 | 3 | 34 | −24,108.09 | 48,355.62 | |
5 | 4 | 37 | −24,100.91 | 48,353.56 | |
5 | 5 | 40 | −24,118.71 | 48,401.46 | |
Lact 2 | 1 | 1 | 16 | −27,021.36 | 54,108.25 |
2 | 1 | 19 | −26,923.09 | 53,923.99 | |
2 | 2 | 22 | −26,913.57 | 53,917.24 | |
3 | 2 | 25 | −26,859.41 | 53,821.2 | |
3 | 3 | 28 | −26,849.15 | 53,812.97 | |
4 | 2 | 28 | −26,857.37 | 53,829.41 | |
4 | 3 | 31 | −26,849.17 | 53,825.3 | |
4 | 4 | 34 | −26,845.67 | 53,830.58 | |
5 | 2 | 31 | −26,794.93 | 53,716.82 | |
5 | 3 | 34 | −26,787.09 | 53,713.42 ^{ c } | |
5 | 4 | 37 | −26,784.15 | 53,719.83 | |
5 | 5 | 40 | −26,791.15 | 53,746.11 |
Phenotypic analysis
For both the first and second lactations, similar patterns were observed in which the greatest milk yield was obtained from day 65 to 155 and thereafter, gradually reduced until the end of lactation period. In addition, the greatest difference (14 %) between milk yield with 3X and 4X milking frequency was obtained at day 95 and 125, for the first and second lactations, respectively. The lowest difference (9 %) between the values for milk yield with 3X and 4X milking frequency was obtained at day 275 and 305, respectively. Similar results were reported by Armstrong [1].
Estimation of genetic parameters
Additive genetic (σ ^{ 2 } _{ a }), animal permanent environmental (σ ^{ 2 } _{ pe }), residual (σ ^{ 2 } _{ e }) variances and heritability (h^{2}) of the test-day records of milk yield (Kg) for some selected days in milk and different milking frequency
Variances | Days in milk (DIM) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
5–35 | 36–65 | 66–95 | 96–125 | 126–155 | 156–185 | 186–215 | 216–245 | 246–275 | 276–305 | |
Lact 1 (3X) | ||||||||||
σ ^{ 2 } _{ a } | 5.0 | 5.7 | 4.9 | 5.2 | 6.1 | 8.1 | 9.1 | 8.0 | 8.5 | 21.7 |
σ ^{ 2 } _{ pe } | 9.2 | 11.0 | 11.7 | 11.3 | 11.9 | 13.4 | 15.2 | 17.8 | 20.0 | 18.1 |
σ ^{ 2 } _{ e } | 11.4 | 10.0 | 9.1 | 8.5 | 9.4 | 8.5 | 8.9 | 9.2 | 7.5 | 7.7 |
h ^{ 2 } | 0.20 | 0.21 | 0.19 | 0.21 | 0.22 | 0.27 | 0.27 | 0.23 | 0.24 | 0.46 |
Lact 2 (3X) | ||||||||||
σ ^{ 2 } _{ a } | 4.0 | 4.1 | 6.3 | 6.8 | 7.3 | 9.9 | 14.0 | 16.4 | 14.7 | 12.3 |
σ ^{ 2 } _{ pe } | 25.5 | 21.7 | 22.3 | 24.2 | 25.6 | 25.7 | 25.1 | 25.4 | 29.3 | 40.9 |
σ ^{ 2 } _{ e } | 20.9 | 19.0 | 15.7 | 14.3 | 13.4 | 12.7 | 12.5 | 11.5 | 11.2 | 10.1 |
h ^{ 2 } | 0.08 | 0.09 | 0.14 | 0.15 | 0.16 | 0.20 | 0.27 | 0.31 | 0.27 | 0.19 |
Lact 1 (4X) | ||||||||||
σ ^{ 2 } _{ a } | 10.1 | 8.9 | 12.0 | 11.6 | 11.5 | 11.2 | 11.0 | 9.5 | 9.1 | 13.5 |
σ ^{ 2 } _{ pe } | 20.3 | 14.3 | 11.6 | 10.7 | 10.6 | 10.9 | 11.4 | 12.7 | 15.6 | 21.6 |
σ ^{ 2 } _{ e } | 8.9 | 9.5 | 8.6 | 8.3 | 8.5 | 7.3 | 7.8 | 6.0 | 6.5 | 6.0 |
h ^{ 2 } | 0.26 | 0.27 | 0.37 | 0.38 | 0.38 | 0.38 | 0.36 | 0.34 | 0.29 | 0.33 |
Lact 2 (4X) | ||||||||||
σ ^{ 2 } _{ a } | 16.6 | 12.0 | 10.4 | 10.0 | 8.7 | 10.2 | 14.4 | 16.6 | 19.2 | 15.5 |
σ ^{ 2 } _{ pe } | 18.5 | 25.0 | 27.2 | 26.9 | 26.1 | 25.8 | 25.8 | 25.9 | 27.6 | 37.2 |
σ ^{ 2 } _{ e } | 21.6 | 16.4 | 15.2 | 11.6 | 12.3 | 11.4 | 8.9 | 8.0 | 7.9 | 6.7 |
h ^{ 2 } | 0.29 | 0.23 | 0.20 | 0.21 | 0.18 | 0.22 | 0.29 | 0.33 | 0.35 | 0.26 |
Variances tended to be larger at the beginning and the end of lactation, which is probably because of the smaller number of records that corresponded to these time periods, and are possible artifacts of Legendre polynomials.
Estimates of genetic (below diagonal) and phenotypic (above diagonal) correlations between milk yield on selected days in milk (DIM) for different milking frequency in the first and second lactations
MF^{a} Lactation and DIM | DIM | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
35 | 65 | 95 | 125 | 155 | 185 | 215 | 245 | 275 | 305 | ||
3X First | |||||||||||
35 | - | 0.34 | 0.29 | 0.27 | 0.23 | 0.19 | 0.17 | 0.18 | 0.19 | 0.10 | |
65 | 0.19 | - | 0.59 | 0.51 | 0.46 | 0.47 | 0.47 | 0.43 | 0.38 | 0.40 | |
95 | 0.14 | 0.87 | - | 0.62 | 0.57 | 0.55 | 0.52 | 0.50 | 0.46 | 0.41 | |
125 | 0.17 | 0.67 | 0.94 | - | 0.64 | 0.60 | 0.56 | 0.53 | 0.50 | 0.42 | |
155 | 0.07 | 0.74 | 0.95 | 0.97 | - | 0.66 | 0.62 | 0.56 | 0.51 | 0.49 | |
185 | −0.09 | 0.86 | 0.94 | 0.87 | 0.95 | - | 0.70 | 0.63 | 0.55 | 0.59 | |
225 | −0.18 | 0.89 | 0.94 | 0.81 | 0.88 | 0.97 | - | 0.69 | 0.63 | 0.63 | |
245 | −0.14 | 0.76 | 0.92 | 0.82 | 0.80 | 0.83 | 0.91 | - | 0.73 | 0.62 | |
275 | 0.03 | 0.54 | 0.80 | 0.81 | 0.72 | 0.65 | 0.71 | 0.92 | - | 0.63 | |
305 | 0.02 | 0.76 | 0.72 | 0.64 | 0.75 | 0.84 | 0.80 | 0.63 | 0.53 | - | |
3X Second | |||||||||||
35 | - | 0.51 | 0.43 | 0.38 | 0.35 | 0.33 | 0.31 | 0.29 | 0.27 | 0.22 | |
65 | 0.52 | - | 0.58 | 0.55 | 0.51 | 0.44 | 0.38 | 0.32 | 0.27 | 0.23 | |
95 | 0.29 | 0.96 | - | 0.65 | 0.61 | 0.55 | 0.46 | 0.39 | 0.32 | 0.26 | |
125 | 0.32 | 0.90 | 0.97 | - | 0.68 | 0.63 | 0.56 | 0.48 | 0.40 | 0.30 | |
155 | 0.45 | 0.73 | 0.79 | 0.92 | - | 0.70 | 0.66 | 0.59 | 0.50 | 0.36 | |
185 | 0.53 | 0.47 | 0.50 | 0.70 | 0.92 | - | 0.73 | 0.69 | 0.60 | 0.44 | |
225 | 0.54 | 0.27 | 0.28 | 0.50 | 0.80 | 0.97 | - | 0.75 | 0.69 | 0.52 | |
245 | 0.51 | 0.18 | 0.18 | 0.41 | 0.73 | 0.93 | 0.99 | - | 0.76 | 0.63 | |
275 | 0.43 | 0.20 | 0.23 | 0.44 | 0.73 | 0.91 | 0.96 | 0.98 | - | 0.75 | |
305 | 0.17 | 0.37 | 0.46 | 0.60 | 0.72 | 0.74 | 0.71 | 0.73 | 0.85 | - | |
4X First | |||||||||||
35 | - | 0.26 | 0.19 | 0.24 | 0.25 | 0.20 | 0.14 | 0.14 | 0.17 | 0.04 | |
65 | −0.71 | - | 0.67 | 0.55 | 0.49 | 0.51 | 0.50 | 0.45 | 0.33 | 0.37 | |
95 | −0.57 | 0.90 | - | 0.68 | 0.62 | 0.61 | 0.58 | 0.54 | 0.45 | 0.43 | |
125 | −0.18 | 0.67 | 0.90 | - | 0.71 | 0.68 | 0.61 | 0.58 | 0.52 | 0.45 | |
155 | 0.02 | 0.61 | 0.82 | 0.97 | - | 0.71 | 0.65 | 0.61 | 0.54 | 0.48 | |
185 | −0.01 | 0.75 | 0.83 | 0.90 | 0.95 | - | 0.73 | 0.68 | 0.58 | 0.55 | |
225 | −0.11 | 0.85 | 0.84 | 0.81 | 0.86 | 0.96 | - | 0.73 | 0.63 | 0.59 | |
245 | −0.09 | 0.75 | 0.80 | 0.79 | 0.80 | 0.86 | 0.94 | - | 0.74 | 0.63 | |
275 | 0.00 | 0.47 | 0.68 | 0.79 | 0.76 | 0.72 | 0.75 | 0.91 | - | 0.67 | |
305 | −0.41 | 0.67 | 0.74 | 0.72 | 0.73 | 0.77 | 0.73 | 0.61 | 0.55 | - | |
4X Second | |||||||||||
35 | - | 0.49 | 0.47 | 0.45 | 0.35 | 0.24 | 0.20 | 0.26 | 0.32 | 0.17 | |
65 | 0.40 | - | 0.67 | 0.60 | 0.54 | 0.49 | 0.45 | 0.39 | 0.31 | 0.30 | |
95 | 0.36 | 0.87 | - | 0.71 | 0.65 | 0.57 | 0.50 | 0.44 | 0.38 | 0.32 | |
125 | 0.31 | 0.61 | 0.91 | - | 0.73 | 0.64 | 0.56 | 0.52 | 0.47 | 0.37 | |
155 | 0.14 | 0.57 | 0.86 | 0.95 | - | 0.71 | 0.66 | 0.61 | 0.54 | 0.45 | |
185 | −0.04 | 0.63 | 0.72 | 0.70 | 0.87 | - | 0.76 | 0.71 | 0.60 | 0.55 | |
225 | 0.01 | 0.63 | 0.61 | 0.53 | 0.72 | 0.96 | - | 0.80 | 0.69 | 0.63 | |
245 | 0.27 | 0.55 | 0.56 | 0.55 | 0.70 | 0.86 | 0.93 | - | 0.80 | 0.69 | |
275 | 0.41 | 0.32 | 0.46 | 0.59 | 0.69 | 0.71 | 0.75 | 0.93 | - | 0.74 | |
305 | −0.29 | 0.17 | 0.29 | 0.42 | 0.73 | 0.97 | 0.97 | 0.88 | 0.73 | - |
The phenotypic correlations were smaller than the corresponding genetic correlations, but they followed a pattern similar to the corresponding genetic correlations for all traits (Table 6). The least phenotypic correlations between 5 and 305 DIM, were 0.10 and 0.22 for 3X cow and 0.04 and 0.17 for 4X cow for the first and second lactations, respectively.
Negative phenotypic and genetic correlations were observed between initial and final test-days. After calving, the cow suffers from post-calving stress and also from an energy deficit. This can be caused the negative values. Negative genetic correlations estimated by RRM using different functions have also been reported for Holstein cattle by Jamrozik and Schaeffer [19], Olori et al. [26], Brotherstone et al. [6] and Kettunen et al. [21], and in Brazil by Cobuci et al. [7], Costa et al. [9] and Bignardi et al. [3, 4]. Jakobsen et al. [18] reported genetic correlations estimates higher than 0.40 for first lactation test-day milk yield of Holstein dairy cattle, therefore slowly lower than some estimates observed in this study. However, lower estimates, even close to zero, were obtained for genetic correlations between test-day milk yields in first lactation by Cobuci et al. [7] and Biassus et al. [2].
Conclusion
The results of this study show the milk yield in the first and the second lactations is significantly affected by milking frequency. The results also indicate that the milk yield is more affected by milking frequency in the middle of the lactation periods. In the first lactation, the Phenotypic and genetic correlations between the 3X milk yields in the studied DIM were higher than those for the 4X while they were similar in the second lactation. In both lactations, the heritability estimated for milk yield in 3X was smaller than those for 4X, therefore the 4X cows could be genetically more accurately evaluated. However, because of the cost of other inputs like labor and failure in the marketing, the application of 4 times milking per day in Iranian Holstein cows should be investigated economically.
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
- Armstrong DV. Milking frequency. Proceedings of the 3rd Western Dairy Management Conference. 13–15 March 1997, Las Vegas, Nevada. 1997;79–84.Google Scholar
- Biassus IO, Cobuci JA, Costa CN, Roberto P, Rorato N, Neto JB, et al. Genetic parameters for production traits in primiparous Holstein cows estimated by random regression. Revista Brasileira De Zootecnia. 2011;40:85–94.View ArticleGoogle Scholar
- Bignardi AB, El Faro L, Cardoso VL, Machado PF. Random regression models to estimate test-day milk yield genetic parameters Holstein cows in southeastern Brazil. Livest Pro Sci. 2009;123:1–7.View ArticleGoogle Scholar
- Bignardi AB, El Faro L, Cardoso VL, Machado PF. Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models. J Dairy Sci. 2009;92:4634–40.PubMedView ArticleGoogle Scholar
- Bohlouli M, Alijani S. Estimation of genetic parameters of milk production traits of Iranian Holstein dairy cattle using multi-trait random regression model. Livest Res Rural Dev. 2012;24:11.Google Scholar
- Brotherstone S, White IMS, Meyer K. Genetic modeling of daily milk yield using orthogonal polynomials and parametric curves. J Anim Sci. 2000;70:407–15.Google Scholar
- Cobuci JA, Euclydes RF, Lopes PS, Costa CN. Estimation of genetic parameters for test-day milk yield in Holstein cows using a random regression models. Genet Mol Biol. 2005;28:75–83.View ArticleGoogle Scholar
- Cobuci JA, Costa CN, Neto JB, de Freitas AF. Genetic parameters for milk production by using random regression models with different alternatives of fixed regression modeling. Revista Brasileira De Zootecnia. 2011;40:557–67.View ArticleGoogle Scholar
- Costa CN, Melo CNR, Pacher IU, Freitas AF. Genetic parameters for test day milk yield of first lactation Holstein cows estimated by random regression using Legendre polynomials. Revista Brasileira De Zootecnia. 2008;37:602–8.View ArticleGoogle Scholar
- De Roos APW, Harbers AGF, de Jong G. Random regression test-day model in The Netherlands. Interbull Bull. 2001;27:155–158.Google Scholar
- DePeters EJ, Smith NE, Acedo-Rico J. Three or two times daily milking of older cows and first- lactation cows for entire lactations. J Dairy Sci. 1985;68:123–32.PubMedView ArticleGoogle Scholar
- Druet T, Jaffrezic F, Ducrocq V. Estimation of genetic parameters for test-day records of dairy traits in the first three lactations. Genet Sel Evol. 2005;37:257–71.PubMedPubMed CentralView ArticleGoogle Scholar
- El Faro L, Cardoso VL, Albuquerque LG. Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos Taurus Artiodactyla, Bovidae). Genet Mol Biol. 2008;31:665–73.View ArticleGoogle Scholar
- Erdman RA, Varner M. Fixed yield responses to increased milking frequency. J Dairy Sci. 1995;78:1199–203.PubMedView ArticleGoogle Scholar
- Gilmour AR, Gogel BJ, Cullis BR, Thompson R. ASReml User Guide Release 3.0 VSN International Ltd, Hemel Hempstead. HP1 1ES. UK. available at https://www.vsni.co.uk/downloads/asreml/release3/UserGuide.pdf 2009.
- Hale SAAV, Capuco TK, Erdman RA. Milk yield and mammary growth effects due to increased milking frequency during early lactation. J Dairy Sci. 2003;86:2061–71.PubMedView ArticleGoogle Scholar
- Hogeveen H, Ouweltjes W, de Koning CJAM, Stelwagen K. Milking interval, milk production and milk flow-rate in an automatic milking system. Livest Pro Sci. 2001;72:157–67.View ArticleGoogle Scholar
- Jakobsen JH, Madsen P, Jensen J, Pedersen J, Christensen LG, Sorensen DA. Genetic parameters for milk production and persistency for Danish Holsteins estimated in random regression models using REML. J Dairy Sci. 2002;85:1607–16.PubMedView ArticleGoogle Scholar
- Jamrozik J, Schaeffer LR. Estimates of genetic parameters for a test day model with random regressions for yield traits of first lactation Holsteins. J Dairy Sci. 1997;80:762–70.PubMedView ArticleGoogle Scholar
- Karacao B, Jaffrezic F, Kadarmideen HN. Genetic Parameters for Functional Traits in Dairy Cattle from Daily Random Regression Models. J Dairy Sci. 2006;89:791–8.View ArticleGoogle Scholar
- Kettunen A, Mantysaari EA, Poso J. Estimation of genetic parameters for daily milk yield of primiparous Ayrshire cows by random regression test-day models. Livest Pro Sci. 2000;66:251–61.View ArticleGoogle Scholar
- Klei LR, Lynch JM, Barbano PA, Lednor AJ, Bandler DK. Influence of milking three times a day on milk quality. J Dairy Sci. 1997;80:427–36.PubMedView ArticleGoogle Scholar
- Meyer K. Scope of random regression model in genetic evaluation of beef cattle for growth. Livest Pro Sci. 2004;86:68–83.Google Scholar
- Miglior F, Gong W, Wang Y, Kistemaker GJ, Sewalem A, Jamrozik J. Genetic parameters of production traits in Chinese Holsteins using a random regression test-day model. J Dairy Sci. 2009;92:4697–706.PubMedView ArticleGoogle Scholar
- Muir BL, Kistemaker G, Jamrozik J, Canavesi F. Genetic parameters for a multiple-trait multiple- lactation random regression test-day model in Italian Holsteins. J Dairy Sci. 2007;90:1564–74.PubMedView ArticleGoogle Scholar
- Olori VE, Hill WG, McGuirk BJ, Brotherstone S. Estimating variance components for test-day milk records by restricted maximum likelihood with a random regression animal model. Livest Pro Sci. 1999;61:53–63.View ArticleGoogle Scholar
- Penasa M, Cecchinato A, Battagin M, De Marchi M, Pretto D, Cassandro M. Bayesian inference of genetic parameters for test-day milk yield, milk quality traits, and somatic cell score in Burlina cows. J Appl Genet. 2010;51:489–95.PubMedView ArticleGoogle Scholar
- Razmkabir M. Estimation of genetic trend for production traits in Iranian Holstein cattle. MS Thesis 2005, Agriculture Faculty, University of Tehran. Tehran. Iran.Google Scholar
- Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;6:461–4.View ArticleGoogle Scholar
- Stelwagen K, Lacy-Hulbert SJ. Effect of milking frequency on milk somatic cell count characteristics and mammary cell damage in cows. Am J Vet Res. 1996;57:902–5.PubMedGoogle Scholar
- Strabel T, Ptak E, Szyda J, Jamrozik J. Multiple-lactation random regression test-day model for Polish Black and White cattle. Interbull Bull. 2004;32:133–6.Google Scholar
- Strabel T, Szyda J, Ptak E, Jamrozik J. Comparison of random regression test-day models for Polish black and white cattle. J Dairy Sci. 2005;88:3688–99.PubMedView ArticleGoogle Scholar
- Swalve HH, Guo Z. An illustration of lactation curves stratified by lactation yields within herd. Archiv 240 Tierzucht. 1999;42:515–25.Google Scholar
- Yousefi Golverdi A, Hafezian H, Chashnide Y, Farhadi A. Genetic parameters and trends of production traits in Iranian Holstein population. Afr J Biotechnol. 2012;11:2429–35.Google Scholar
- Zavandilova L, Jamrozik J, Schaeffer LR. Genetic parameters for test day model with random regression for production traits of Czech Holstein cattle. Czech J Anim Sci. 2005;50:142–54.Google Scholar