<div style="text-align: justify;">In this study, four lactation curve models viz. Gamma-type function (GF), Mixed log function (MLF), Exponential function (EF) and Polynomial regression function (PRF) were fitted to predict the weekly test-day milk yields pertaining to 961 Murrah buffaloes progeny of 101 sires spread over a period of 36 years (1977-2012) maintained at ICAR-NDRI, Karnal. The PRF was the best fit with highest R2 (99.3%) and lowest RMSE (0.3%) which was used subsequently to estimate the first lactation 305-day or less milk yield (FL305DMY) from weekly test-day milk yields. The sires were evaluated using four linear models viz. Least Squares(LSQ), Simple Regressed Least Squares (SRLS), Sire (BLUP-SM) and animal (BLUP-AM) models from actual as well as PRF predicted FL305DMYs. BLUP-AM was the most efficient, among the sire evaluation models, in predicting the breeding values. Sire evaluation on the basis of predicted data (using PRF) was similar to that on the basis of actual data indicating that the best fitted lactation curve function can be used as an alternative for early animal evaluation and reduction of generation interval.</div>

Modeling lactation curve for genetic evaluation of Murrah buffaloes

<div><strong>Background: </strong>Lactation curve patterns are currently integrated in dairy cow&rsquo;s management software. Lactation curve modeling is useful for monitoring individual yields for diet planning, determining optimum strategies for insemination and genetic evaluation. It also helps for predicting expected missing values on field records and gives concise summary of biological efficiency and persistency of dairy cows.<br />
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<strong>Methods:</strong> The study was aimed to characterize the lactation curve pattern for crossbred dairy cattle using different non-linear models. During the period 1991 to 2018, daily milk yield (DMY) consisted of 281698 records of 750 crossbred dairy cows maintained at Livestock Farms. GADVASU, Ludhiana, were collected for the study. Different non-linear models <em>viz</em>. exponential decline function (EDF), parabolic exponential model (PEM), inverse polynomial model (IPM), gamma-type function (GTF), mixed log function (MLF) and Ali and Schaeffer model (ASF) were used for the analysis. The model(s) that best fit and describe the curve characteristics was selected on the basis of coefficient of determination (R<sup>2</sup>), coefficient of variation (CV), Akaike information criterion (AIC)&nbsp;and mean square error (MSE).<br />
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<strong>Result: </strong>The study clearly revealed that the PRM gave highest fit to DMY data with R<sup>2</sup>, MSE, AIC and CV values of 98.10%, 0.087, -743.31 and 2.37%, respectively. The IPM had also best fitted the observed DMY data with highest R<sup>2 </sup>(98.05%), lower MSE (0.089), low AIC (-735.8972) and lower CV (2.40%) values. The fitting of observed DMY data with predicted DMY were also found to be higher in the MLF (R2= 96.46%, MSE= 0.159, AIC= -558.16 and CV= 3.21%) and GTF (R2= 95.85%, MSE= 0.190, AIC= -505.24 and CV= 3.50%), whilst the EDF and PEM Models depicted relatively low fit to the DMY data when compared with the other non-linear models. However, IPM and GTF models can be used for accurate prediction of daily milk yield in the crossbred cattle population because they were typical standard lactation curves.</div>


<div>Characterization of Lactation Curve Patterns using Non-linear Models in Crossbred Dairy Cattle</div>


<div style="text-align: justify;">The present investigation was carried out on 838 weekly test day milk yield records of first lactation pertaining to 411 HF x Deoni (Holdeo) crossbred cows spread over 38 years located at Cattle Cross Breeding Project, Vasantrao Naik Marathwada Krishi Vidyapeeth, Parbhani (Maharashtra). The comparison of four lactation curve models viz, Parabolic exponential function, Wood&rsquo;s gamma function, Quadratic model and Mixed log function was made in the present investigation. Mixed log function described as an excellent model for prediction of WTDY with the highest coefficient of determination (99.01 %) with comparatively lowest root-mean-square error (0.16 kg) value. The quadratic model was least fit model with the lowest coefficient of determination (90.76 %) and the highest root-mean-square error (0.51 kg) among the four models in Holdeo. The predicted error in WTDY in Parabolic exponential function, Wood&rsquo;s gamma function and mixed log function were the highest in WTDY5 and in Quadratic model it was highest in WTDY6. The errors between the observed values and predicted values were highest during the peak phase in all four models. The errors in estimated and predicted WTDMY values in initial milk yield of Holdeo cows were lower than the peak yield. The ascending phase of lactation curve was shorter than the descending phase. The gamma type function when compared to mixed log function, explained low peak yield and it is recommended that this function can give the best fit for the low yielding cows.</div>

<div style="text-align: justify;">Comparative study of fitting various lactation curve models in Holdeo crossbred cattle</div>

<div><strong>Background: </strong>Various mathematical models have been tried by different researchers to fit the lactation curves in indigenous, exotic and crossbred cows maintained in organised farms only. Hence, this study was aimed to fit various lactation models and to identify the best fit model (s) for prediction of milk production in crossbred dairy cows in field conditions.<br />
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<strong>Methods:</strong> Multistage random sampling procedure was used for selection of 100 dairy cows for the purpose of data collection. The monthly milk yield data (up to 10 months of lactation) of the selected crossbred cows reared in field conditions of Tamil Nadu State, relating to the period from 2017-20, were collected for lactation curve modelling. The milk data so collected were used to fit 14 lactation curve models in the study. The highest Coefficient of Determination (R&sup2;) value and the least Root Mean Square Error (RMSE) value were used as the criteria to select the best fit model(s).<br />
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<strong>Result:</strong> The overall average total milk production was estimated to be 2223.19 kg per lactation in 10 months of lactation in the selected crossbred cows. Average daily milk yield at the first month of lactation was 9.16 kg and the highest daily milk yield of 9.56 kg was observed at the second month of lactation. At the end of the lactation, the lowest yield was 5.01 kg per day and hence the overall average daily milk yield was found to be 7.41 kg. Based on the selection criteria, the Mitscherlich X Exponential model was identified as the best fit model, followed by Ali and Schaeffer and Morant and Gnanasakthy model for prediction of milk production in crossbred dairy cows reared in field conditions and the estimated lactation curve model parameters a, b, c and d values for the best fit model were 331.71, 1519.82, 9.56 and 0.07 kg, respectively.&nbsp;</div>


<div>Comparative Evaluation of Lactation Curves of Crossbred Dairy Cows in Field Conditions in Tamil Nadu, India&nbsp;</div>


<p><strong>Background: </strong>The present study was aimed to investigate the lactation curve and factors influencing persistency in Ongole cattle, utilizing the daily milk production records and history sheets available in the Livestock Research Station, Mahanandi.<br />
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<strong>Methods:</strong> Key parameters such as peak yield (PY), day of peak yield (DPY), average weekly yield (AWY), lactation length (LL), standard lactation milk yield (SLMY), total lactation milk yield (TLMY) and persistency indices given in three prominent reports (denoted as P1, P2 and P3 in the ascending order of reporting years) were computed using the milk production records. Other parameters such as parity, age at first calving (AFC), season of calving (Rainy, Autumn, Winter, or Summer), sex and birth weight of calf were extracted from the history sheets.<br />
&nbsp;<br />
<strong>Result:</strong> The findings revealed that the lactation curve typically displayed a concave downward shape, with the peak of milk production occurring around the eighth week of lactation. The mean values of P1, P2 and P3 were 75.799&plusmn;0.979, 88.038&plusmn;0.929 and 57.897&plusmn;0.775 per cent, respectively. All the three persistency indices (P1, P2 and P3) showed a significant positive correlation with SLMY and TLMY. The P1 and P2 had a significant positive correlation with DPY, LL and AFC. Further, P1 exhibited a significant negative correlation with parity, while P2 was significantly influenced by the season of calving. The coefficients of determination for the regression models of P1, P2 and P3 were 0.622, 0.282 and 0.223, respectively. In conclusion, the study suggests that the lactation curve in Ongole cattle follows a typical concave downward shape with the peak milk yield occurring in the eighth week of milking. Furthermore, lactations characterized by higher LMY tend to have greater persistency.</p>


<p>Lactation Curve and Factors Affecting Persistency in Ongole Cattle</p>


<p>The purpose of this study was to classify Anatolian buffalo using Gaussian mixture regression model according to discrete and continuous environmental effects. Gaussian mixture model performs separately regression analysis both within and between groups. This is an important property of Gaussian mixture models which makes it different from other multivariate statistical methods. The data were obtained from 1455 Anatolian buffalo lactation milk yield records reared in seven different locations in Bitlis province, Turkey. Age of dam, lactation duration and locations were considered as environmental effects on lactation milk yield. Data set was divided into three homogenous subgroups with respect to AIC and BIC in the Gaussian mixture regression, based on environmental effects on lactation milk yield. Estimated mean for lactation milk yields and mixing probabilities for the first, second and third subgroups were determined as 1494.33 kg (16.9%), 540.33 kg (45.2%) and 847.61 (37.9%), respectively. The numbers of buffalo in each subgroup according to mixing probability were obtained as 159, 756, and 540 for the first, second, and third groups, respectively. The effects of lactation period, age of dam and villages were found statistically significant on lactation milk yield in subgroup 1 that was highest mean for lactation milk yield (p&lt;0.01). &nbsp; In conclusion, results showed that Gaussian mixture regression was an important tool for classifying quantitative traits considering environmental effects in animal breeding.</p>


<p>Modeling with Gaussian mixture regression for lactation&nbsp;milk yield in Anatolian buffaloes</p>


<div style="text-align: justify;">he aims were to identify the body weight of the several age groups in Norduz lambs and its correlations between these traits were to determine the best non-linear growth curve models for the growth performance of the Norduz sheep breed. A total of 91 male and female of Norduz lambs were evaluated under extensive system conditions. The least square means for weights at birth and at 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195 and 210 days of age periods were 4.51&plusmn;0.56, 9.28&plusmn;0.25, 11.14&plusmn;0.29, 14.99&plusmn;0.37, 18.21&plusmn;0.43, 22.54&plusmn;0.54, 22.33&plusmn;0.25, 23.59&plusmn;0.54, 25.58&plusmn;0.55, 28.07&plusmn;0.58, 29.45&plusmn;0.60, 29.98&plusmn;0.84, 32.44&plusmn;0.61, 32.03&plusmn;0.59 and 31.45&plusmn;0.57 kg, respectively. There were differences in favor of lambs of four-year old dams at 15 days of age and also lambs born single at 90 days of age for the body weight. The effect of weight of dam at birth, 30, 45, 60 days of age was significant (P&lt; 0.05-P&lt;0.01) and the birth weight in lambs importantly effected the weights at 15, 30, and 45 days of age.<br />&nbsp;&nbsp; &nbsp;All correlations between the body weights of several age periods were significant as statistical (P&lt;0.01). As for the growth models, distinguished models were compared using the coefficient of determination and mean square error for both sexes. As a result, we concluded that von Bertalanffy model were the best model in comparison with the other models for biological growth curves in Norduz male and female lambs.</div>

Effects of some factors on growth of lambs and the determination of growth curve models

<p><strong>Background:</strong> Breeding programme is mainly structured and evaluated on the basis of first lactation 305-day milk yield (FL305DMY) of dairy animals. Early prediction of 305-day milk yield using test-day records is crucial for early evaluation of elite animals and to reduce the cost of data recording and animal rearing.&nbsp;<br />
<br />
<strong>Methods:</strong> In the study, the prediction efficiency of conventional models viz. centering date method (CDM), test interval method (TIM), ratio method (RM) and multiple linear regression (MLR) was compared with the newly evolved machine learning connectionist model named Artificial Neural Network (ANN). Data on 3,850 monthly test-day milk yield (MTDY) records of 809 Murrah buffaloes were utilized for the prediction of FL305DMY. The prediction efficiency of the models was compared based on absolute error, average error, root mean square error (RMSE) and their respective percentages. An attempt was thereafter made for the early-stage prediction of FL305DMY.&nbsp;<br />
<br />
<strong>Result:</strong> MLR was identified as the most accurate model with least error in prediction (4.19% RMSE), followed by ANN model (4.28% RMSE). The prediction accuracy for the regression equation incorporating all the 11 MTDY records was found to be 95.68 per cent. The optimal regression equation for early-stage prediction of FL305DMY consisted of four variables viz. MTDY-3 (65<sup>th</sup> day), MTDY-4 (95<sup>th</sup> day), MTDY-5 (125<sup>th</sup> day) and MTDY-7 (185<sup>th</sup> day) showed a R<sup>2</sup> value of 87.02 per cent. It was inferred from the study that the most effective early-stage prediction of FL305DMY could be achieved by 185<sup>th</sup> day of lactation, offering a valuable tool for early and efficient selection of elite animals using monthly test-day milk yield records.</p>


<p>Comparative Efficiency of Conventional and Connectionist Models in Prediction of First Lactation 305-day Milk Yield in Murrah Buffaloes</p>


<div>The present study was conducted to estimate and compare the three types of growth models in Hanwoo steer (Bos aurus coreanae). The Gompertz, Von Bertalanffy, and Logistic nonlinear models were used. A total of 2,239 Hanwoo steers (Bos taurus coreanae) from 6 months to 24 months old (2003 to 2014) and 8,916 growth data from the Hanwoo improvement Center were used to estimate the growth model which included three parameters. These parameters were A, mature body weight; b, growth ratio; and k, intrinsic growth rate. Regression equations using the Gompertz, Von Bertalanffy, and Logistic models were calculated as respectively. The mean square errors (MSEs) for each model were 1945.9, 1958.7, and 1935.0, respectively. The equation using the Logistic model showed the lowest value among three models. The estimated birth weights from the Gompertz, Von Bertalanffy, and Logistic models were 50.35 kg, 36.94 kg, and 74.13 kg, respectively. Furthermore, the estimated mature weights from the Gompertz, Von Bertalanffy, and Logistic models were 919.0 kg, 1043.3 kg, and 770.0 kg, respectively. In addition, the estimated age and body weight at inflection from the Gompertz, Von Bertalanffy, and Logistic models were 349.0 days and 338.1 kg, 317.9 days and 308.2 kg, and 397.8 days and 385.0 kg, respectively. Based on the results, we concluded that the regression equation using the Logistic model was the most appropriate among the growth models for measuring data. However, further studies would be needed in order to obtain more accurate parameters using a much wider period of data from birth to shipping age.&nbsp;</div>


<div>Comparison and estimation of the growth curve models of Hanwoo steer (<em>Bos taurus coreanae</em>)</div>


<div>First lactation records of 351 Karan-Fries cows born to 27 bulls, having 3 or more progeny were used to evaluate sires by animal model (AM). Heritabilities, genetic and phenotypic correlations between the traits were estimated by univariate and bivariate linear animal models. The heritability estimates for 305 days or less milk yield (305MY), fat based energy corrected milk yield (FECMY), fat protein based energy corrected milk yield (FPECMY) and fat protein lactose based energy corrected milk yield (FPLECMY) were 0.23, 0.65, 0.11 and 0.39, respectively. There was a high (0.99) genetic and phenotypic correlation between 305MY, FECMY and FPLECMY. The high and positive genetic correlations between energy traits are indication of common genetic and physiological mechanism governing these traits. Comparison of ranks of the sires based on 305MY, FECMY and FPLECMY by animal model depicted a notable100 per cent level of similarity except for FPECMY in which the ranks were entirely different. There was a high heritability and genetic correlation between FECM and FPLECM. Genetic evaluation of Karan-Fries bulls based on energy corrected milk yield will increase the accuracy of selection than the conventional mil yield evaluation. It can help in mitigating the nutritional insecurity of the country in the long run.</div>


Modeling lactation curve for genetic evaluation of Murrah buffaloes

Characterization of Lactation Curve Patterns using Non-linear Models in Crossbred Dairy Cattle

Comparative study of fitting various lactation curve models in Holdeo crossbred cattle

Comparative Evaluation of Lactation Curves of Crossbred Dairy Cows in Field Conditions in Tamil Nadu, India

Lactation Curve and Factors Affecting Persistency in Ongole Cattle

Modeling with Gaussian mixture regression for lactation milk yield in Anatolian buffaloes

Effects of some factors on growth of lambs and the determination of growth curve models

Comparative Efficiency of Conventional and Connectionist Models in Prediction of First Lactation 305-day Milk Yield in Murrah Buffaloes

Comparison and estimation of the growth curve models of Hanwoo steer (Bos taurus coreanae)

Genetic Parameters and Animal Model Evaluation of First Lactation 305-d Milk Yield and Energy Traits in Karan Fries Cattle