# Genetic Parameters Estimation of Milking Traits in Polish Holstein-Friesians Based on Automatic Milking System Data

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

^{2}for milk yield (MY), milk protein and fat percentage in Holstein cows using RRM and Legendre polynomials of orders 3 to 6, assuming fixed residual variances during successive days of lactation. It should be highlighted that in this study, genetic variations for milk yield and protein and fat contents, as well as the heritability indicators of these traits followed a similar trend regardless of the order of the polynomial, and the possible differences concerned the beginning and the end of lactation. Similar findings were presented by Costa et al. [15], i.e., variation in AG, PE, h

^{2}of milk yield depending on Legendre polynomial as well as the need to use polynomial of 5th order. Moreover, the same authors [15] evaluated the quality of the models and showed the best fit for a model assuming heterogeneity of variance in different lactation periods. Higher order polynomials for modeling the effect of AG and PE than in previous studies were proposed by Bignardi et al. [25] namely seventh- and twelfth-order polynomials, respectively. Contrary results were reported by Naderi at al. [19] for Holstein-Friesian cattle in Iran—out of the different order Legendre polynomials (3rd to 6th), the best fit of the model for the AG and PE effect was obtained for third-order polynomial.

## 2. Materials and Methods

#### 2.1. Data

- Milk yield (MY) (kg)—daily milk yield of cow summed during 1 day in milk,
- Milk frequency (MF) (no.)—number of milking per cow per day,
- Milking speed (MS) (kg/min)—average milk flow rate during milking (Table 1).

#### 2.2. Statistical Model

## 3. Results

## 4. Discussion

^{2}obtained using two RRM models differing in the mode of PE treatment (fixed or random effect). The model accounting for PE as a fixed effect during the entire lactation period resulted in high h

^{2}values in early lactation unlike the model with random PE. Literature on the subject provides several studies which present a completely different shape of the curve for h

^{2}values of milk yield per lactation. Kheirabadi [7] and Cobuci et al. [41] presented a curve that showed an upward trend throughout the lactation for h

^{2}of milk yield. Yet another trend for h

^{2}of MY during successive days of lactation was shown by Bignardi et al. [25] and Nixon et al. [20]. The curves from these studies, showing the values of these heritability values, at first showed a downward trend, followed twice by an upward and a downward trend until the end of lactation. A very similar shape of the curve for daily MY heritabilities, compared to Bignardi et al. [25] and Nixon et al. [20] was obtained by Naderi [19]. The only difference was that there was no downward trend in the initial shape of the curve. Our daily MY heritabilities ranged from 0.131 to 0.345. A similar range of fluctuations for daily heritabilities during lactation to ours, estimated based on TD, was obtained by Biassus et al. [6] (0.14–0.31) and Cobuci et al. [41] (0.15–0.31), and different ranges by Strabel and Misztal [23] (0.14–0.19), Costa et al. [41] (0.27–0.42), Jamrozik and Schaffer [9] (0.40–0.59), Naderi [19] (0.45–0.60) and Moretti et al. [42] (0.14–0.53). In the study by Nixon et al. [20] using 24-h AMS data, the range of daily h

^{2}was narrower (0.14 to 0.20) than in our study. In the context of these results, it is necessary to highlight the results obtained by Piwczyński, Sitkowska and Ptak [32] in AMS herds for MY heritability estimated only from the test-day data. The MY heritabilities in this study ranged from 0.162 to 0.338, which is in strict compliance with the range presented here. The averaged MY heritability, calculated from 300 daily indicators (0.257), falls within the ranges reported by other authors (0.12–0.34): Gray et al. [43], Nixon et al. [20], Kirsanova et al. [44], Sasaki et al. [8] and Kheirabadi [7].

^{2}of average milk flow (kg/min) for Irish Holstein herds using test-day records was 0.21. Gäde et al. [35], Gäde et al. [54], Wethal and Heringstad [31], Carlström at al. [49] and Santos et al. [30] made the estimations in German, Norwegian and Swedish barns with automatic milking. Heritability estimates were based on single milking or 24-h milk yields and ranged from 0.25 to 0.55.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Genetic (AG), permanent environmental (PE) variances for milking frequency (MF) and milking speed (MS) of primiparous cows.

**Figure 3.**Heritabilities of milk yield (MY), milking frequency (MF) and speed (MS) in subsequent days in milk.

**Figure 4.**Genetic covariances for controlled pairs of traits primiparous cows, where MS-MY—milking speed and milk yield covariance, MF-MY—milking frequency and milk yield covariance, MF-MS—milking frequency and milking speed covariance.

**Figure 5.**Genetic correlations (rG) for controlled pairs of traits primiparous cows, where MS-MY—milking speed and milk yield covariance, MF-MY—milking frequency and milk yield covariance, MF-MS—milking frequency and milking speed covariance.

Trait | Number of 24-h Records | $\overline{\mathbf{x}}$ | Standard Deviation | Coefficient of Variation (%) |
---|---|---|---|---|

Milk yield (kg) | 538,688 | 28.591 | 8.823 | 30.859 |

Milking frequency (no.) | 538,688 | 2.915 | 0.886 | 30.420 |

Milking speed (kg/min) | 538,688 | 2.526 | 0.908 | 35.931 |

**Table 2.**Number of parameters (P), log-likelihood value (Log L), Akaike’s information criterion (AIC) and Bayesian information criterion (BIC) for different models in single trait random regression analysis.

Model | Order of fit | Log L | AIC | BIC | p |
---|---|---|---|---|---|

Milk yield (kg) | 1 | −1,081,429.608 | 2,162,883.216 | 2,163,016.482 | 12 |

Milk yield (kg) | 2 | −1,062,894.572 | 2,125,825.144 | 2,126,025.042 | 18 |

Milking frequency (no.) | 1 | −25,033.237 | 50,090.474 | 50,223.738 | 12 |

Milking frequency (no.) | 2 | −10,201.294 | 20,438.588 | 20,638.484 | 18 |

Milking speed (kg/min) | 1 | 382,535.783 | 765,047.566 | 764,914.300 | 12 |

Milking speed (kg/min) | 2 | 415,176.076 | 830,316.152 | 830,116.254 | 18 |

**Table 3.**Estimates of additive genetic variance (diagonal), covariance (lower diagonal) and correlations (upper diagonal) between random regression coefficient and percentage of variance associated with each eigenvector (EV%).

Trait | Regression Coefficients | Intercept | Linear | Quadratic | EV% |
---|---|---|---|---|---|

Milk yield (kg) | Intercept | 24.13 | 0.19 | −0.73 | 81.66 |

Linear | 2.14 | 4.84 | −0.04 | 14.72 | |

Quadratic | −5.97 | −0.17 | 2.74 | 3.63 | |

Milking frequency (no.) | Intercept | 0.20 | −0.12 | −0.53 | 67.35 |

Linear | −0.016 | 0.086 | −0.31 | 27.73 | |

Quadratic | −0.043 | −0.016 | 0.032 | 4.92 | |

Milking speed (kg/min) | Intercept | 0.61 | 0.3144 | 94.66 | |

Linear | 0.048 | 0.038 | 5.34 |

**Table 4.**Log-likelihood value (Log L), Akaike’s information criterion (AIC) and Bayesian information criterion (BIC), number of parameters (P), for different models in two-trait trait random regression analysis.

Model ^{1} | Order of Fit ^{2} | Log L | AIC | BIC | p |
---|---|---|---|---|---|

MY-MF | 1 | −1,036,614.637 | 2,073,247.274 | 2,073,353.46 | 9 |

MY-MF | 2 HOM | −923,334.831 | 1,846,715.662 | 1,846,987.03 | 23 |

MY-MF | 2 HET | −907,256.912 | 1,814,589.824 | 1,815,038.17 | 38 |

MY-MS | 1 | −909,037.893 | 1,818,093.786 | 1,818,199.972 | 9 |

MY-MS | 2 HOM | −728,555.075 | 1,457,156.15 | 1,457,427.518 | 23 |

MY-MS | 2 HET | −711,685.300 | 1,423,446.6 | 1,423,894.946 | 38 |

MF-MS | 1 | −671,185.362 | 1,342,388.724 | 1,342,494.91 | 9 |

MF-MS | 2 HOM | 337,838.394 | 675,630.788 | 675,359.422 | 23 |

MF-MS | 2 HET | 348,202.475 | 696,328.95 | 695,880.604 | 38 |

^{1}MY—Milk yield (kg); MF—Milking frequency (no.); MS—Milking speed (kg/min);

^{2}HOM: homogeneous residual variance; HET: heterogeneous residual variance.

**Table 5.**Estimates of additive genetic covariance between random regression coefficients in two-trait random regression analysis.

Milking Speed (kg/min) | Milk Yield (kg) | ||||
---|---|---|---|---|---|

Intercept | Linear | Intercept | Linear | ||

Milking frequency (no.) | intercept | 0.015 | 0.055 | 1.240 | 0.210 |

linear | −0.033 | −0.047 | −0.020 | 1.250 | |

Milk yield (kg) | intercept | 0.063 | −0.610 | ||

linear | 0.470 | −0.410 |

Trait | AG | SE | PE | SE | R | SE | P | SE | h^{2} | SE |
---|---|---|---|---|---|---|---|---|---|---|

MY | 15.853 | 3.091 | 19.681 | 2.752 | 26.789 | 0.135 | 62.323 | 1.311 | 0.257 | 0.047 |

MF | 0.164 | 0.030 | 0.175 | 0.027 | 0.369 | 0.002 | 0.709 | 0.013 | 0.230 | 0.041 |

MS | 0.325 | 0.061 | 0.367 | 0.054 | 0.078 | 0.000 | 0.770 | 0.025 | 0.420 | 0.074 |

^{2.}

**Table 7.**Genetic correlations between milking frequency and milk yield in different days of lactation.

Milk Yield (kg) on Different Days of Lactation | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Days | 5 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 305 | |

Milking frequency on different days of lactation | 5 | 0.638 | 0.632 | 0.613 | 0.573 | 0.495 | 0.364 | 0.188 | 0.010 | −0.134 | −0.237 | −0.318 |

30 | 0.619 | 0.617 | 0.606 | 0.577 | 0.513 | 0.398 | 0.236 | 0.068 | −0.071 | −0.173 | −0.255 | |

60 | 0.582 | 0.587 | 0.589 | 0.577 | 0.536 | 0.448 | 0.312 | 0.161 | 0.031 | −0.068 | −0.150 | |

90 | 0.519 | 0.534 | 0.553 | 0.564 | 0.556 | 0.506 | 0.407 | 0.283 | 0.167 | 0.074 | −0.005 | |

120 | 0.416 | 0.444 | 0.484 | 0.526 | 0.561 | 0.564 | 0.518 | 0.433 | 0.341 | 0.260 | 0.186 | |

150 | 0.262 | 0.304 | 0.368 | 0.447 | 0.532 | 0.603 | 0.626 | 0.597 | 0.539 | 0.478 | 0.416 | |

180 | 0.067 | 0.121 | 0.208 | 0.321 | 0.458 | 0.597 | 0.696 | 0.731 | 0.717 | 0.683 | 0.639 | |

210 | −0.124 | −0.062 | 0.039 | 0.175 | 0.349 | 0.543 | 0.707 | 0.800 | 0.829 | 0.823 | 0.801 | |

240 | −0.275 | −0.211 | −0.104 | 0.044 | 0.239 | 0.467 | 0.674 | 0.810 | 0.873 | 0.891 | 0.888 | |

270 | −0.381 | −0.317 | −0.209 | −0.058 | 0.146 | 0.391 | 0.624 | 0.788 | 0.875 | 0.911 | 0.922 | |

305 | −0.461 | −0.399 | −0.294 | −0.144 | 0.063 | 0.317 | 0.567 | 0.751 | 0.855 | 0.906 | 0.929 |

**Table 8.**Genetic correlations between milking frequency and milk speed in different days of lactation.

Milk Speed (kg/min) on Different Days of Lactation | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Days | 5 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 305 | |

Milking frequency on different days of lactation | 5 | −0.255 | −0.199 | −0.126 | −0.050 | 0.025 | 0.096 | 0.162 | 0.221 | 0.273 | 0.318 | 0.362 |

30 | −0.261 | −0.205 | −0.131 | −0.054 | 0.021 | 0.093 | 0.160 | 0.219 | 0.272 | 0.317 | 0.362 | |

60 | −0.268 | −0.212 | −0.138 | −0.061 | 0.015 | 0.088 | 0.154 | 0.214 | 0.267 | 0.313 | 0.359 | |

90 | −0.272 | −0.217 | −0.144 | −0.068 | 0.006 | 0.078 | 0.144 | 0.203 | 0.255 | 0.301 | 0.346 | |

120 | −0.267 | −0.215 | −0.147 | −0.076 | −0.005 | 0.062 | 0.124 | 0.181 | 0.230 | 0.273 | 0.317 | |

150 | −0.244 | −0.200 | −0.141 | −0.080 | −0.020 | 0.038 | 0.092 | 0.141 | 0.184 | 0.222 | 0.260 | |

180 | −0.198 | −0.166 | −0.124 | −0.079 | −0.034 | 0.009 | 0.049 | 0.085 | 0.118 | 0.147 | 0.175 | |

210 | −0.139 | −0.121 | −0.097 | −0.072 | −0.046 | −0.020 | 0.004 | 0.025 | 0.045 | 0.063 | 0.080 | |

240 | −0.081 | −0.076 | −0.069 | −0.061 | −0.052 | −0.043 | −0.034 | −0.026 | −0.018 | −0.011 | −0.003 | |

270 | −0.034 | −0.039 | −0.045 | −0.051 | −0.055 | −0.059 | −0.062 | −0.064 | −0.066 | −0.066 | −0.067 | |

305 | 0.006 | −0.007 | −0.024 | −0.041 | −0.057 | −0.071 | −0.084 | −0.095 | −0.104 | −0.112 | −0.120 |

Milk Yield (kg) on Different Days of Lactation | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Days | 5 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 305 | |

Milking speed on different days of lactation (kg/min) | 5 | −0.137 | −0.149 | −0.166 | −0.186 | −0.204 | −0.213 | −0.204 | −0.178 | −0.148 | −0.120 | −0.094 |

30 | −0.090 | −0.101 | −0.119 | −0.140 | −0.161 | −0.177 | −0.179 | −0.166 | −0.146 | −0.126 | −0.107 | |

60 | −0.028 | −0.039 | −0.056 | −0.078 | −0.104 | −0.129 | −0.145 | −0.148 | −0.142 | −0.133 | −0.122 | |

90 | 0.034 | 0.024 | 0.007 | −0.015 | −0.045 | −0.079 | −0.109 | −0.128 | −0.136 | −0.137 | −0.135 | |

120 | 0.095 | 0.085 | 0.069 | 0.046 | 0.013 | −0.029 | −0.072 | −0.107 | −0.128 | −0.140 | −0.147 | |

150 | 0.151 | 0.143 | 0.128 | 0.105 | 0.069 | 0.019 | −0.037 | −0.085 | −0.119 | −0.141 | −0.156 | |

180 | 0.203 | 0.196 | 0.182 | 0.158 | 0.120 | 0.064 | −0.003 | −0.064 | −0.110 | −0.140 | −0.163 | |

210 | 0.248 | 0.242 | 0.229 | 0.206 | 0.166 | 0.105 | 0.029 | −0.044 | −0.100 | −0.138 | −0.168 | |

240 | 0.288 | 0.283 | 0.271 | 0.248 | 0.207 | 0.141 | 0.057 | −0.026 | −0.090 | −0.136 | −0.171 | |

270 | 0.322 | 0.317 | 0.306 | 0.284 | 0.242 | 0.173 | 0.082 | −0.009 | −0.081 | −0.133 | −0.173 | |

305 | 0.355 | 0.351 | 0.341 | 0.319 | 0.277 | 0.204 | 0.107 | 0.009 | −0.071 | −0.128 | −0.174 |

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**MDPI and ACS Style**

Aerts, J.; Piwczyński, D.; Ghiasi, H.; Sitkowska, B.; Kolenda, M.; Önder, H.
Genetic Parameters Estimation of Milking Traits in Polish Holstein-Friesians Based on Automatic Milking System Data. *Animals* **2021**, *11*, 1943.
https://doi.org/10.3390/ani11071943

**AMA Style**

Aerts J, Piwczyński D, Ghiasi H, Sitkowska B, Kolenda M, Önder H.
Genetic Parameters Estimation of Milking Traits in Polish Holstein-Friesians Based on Automatic Milking System Data. *Animals*. 2021; 11(7):1943.
https://doi.org/10.3390/ani11071943

**Chicago/Turabian Style**

Aerts, Joanna, Dariusz Piwczyński, Heydar Ghiasi, Beata Sitkowska, Magdalena Kolenda, and Hasan Önder.
2021. "Genetic Parameters Estimation of Milking Traits in Polish Holstein-Friesians Based on Automatic Milking System Data" *Animals* 11, no. 7: 1943.
https://doi.org/10.3390/ani11071943