Prediction of First Lactation 305-day Milk Yield Based on Bimonthly Test Day Milk Yield Records in Murrah Buffaloes

The breeding programme in developing countries like India is mainly planned and evaluated based on the lactational 305-day milk yield of the animal which requires daily recording of the data. On contrary, daily milk recording is a tedious, time-taking, expensive and practically near-to-impossible task under field conditions. Studies conducted in the past revealed that the test day milk yield records could be an alternative to the daily milk yield recordings because there is a high genetic association between test-day records and complete milk production record (Rahayu et al., 2018; Singh et al., 2015; Torshizi and Mashhadi, 2015; Kokate et al., 2014). Though the accuracy of prediction of lactational milk yield is less for bimonthly milk yield records as compared to monthly milk yield records (Rahayu et al., 2018; Sahoo et al., 2015; Tailor and Singh, 2014; Chakraborty et al., 2010), yet bimonthly records could be used for economic prediction of 305-day milk yield under field conditions as data recording is further reduced.
 
Over the years, various conventional methods are in vogue for predicting the first lactation 305-day milk yield based on test-day milk yield records. Some of those methods are Test Interval Method (TIM), Centering Date Method (CDM), Ratio method (RM) and Multiple Linear Regression (MLR). Recently, a computational machine learning model which mimics the structure and functions of the biological neural network called Artificial Neural Network (ANN) has been introduced in animal breeding for the prediction of 305-day lactation yield (Singh et al., 2015; Murphy et al., 2014;  Sharma et al., 2013; Gorgulu, 2012; Gandhi et al., 2009; Grzesiak et al., 2003). The literature on prediction of lactational 305-day milk yield of buffaloes based on bimonthly is scanty till date, therefore, to bridge the knowledge gap, the present investigation was undertaken to evaluate the Murrah buffaloes based on bimonthly test day milk yield records and to find the best early test-day milk yields combination to predict the first lactation 305-day milk yield in order to make an early selection of the animals for breeding programme.

The study had been conducted on 2100 first lactation bimonthly test day milk yield (BTDY) records of 350 Murrah buffaloes calved in between 1993 and 2017 at ICAR-NDRI, Karnal, India. The records with lactation length less than 100 days, lactation yield less than 900 kg, culled in the middle of lactation, abortion, still-birth or any other pathological causes were considered as abnormal and thus, such records were not included for the prediction of the lactation yield. The outliers beyond three-standard deviation on both the tail ends of normal distribution were also excluded from the data. A total of 6 BTDY records were taken from each animal at an interval of 60 days. First BTDY was recorded on 6^th day (i.e. BTDY-1), BTDY-2 on 65^th day, BTDY-3 on 125^th day, BTDY-4 on 185^th day, BTDY-5 on 245^th day and the last BTDY (i.e. BTDY-6) was taken on 305^th day.

The prediction of First Lactation 305-Day Milk Yield (FL305DMY) was performed utilizing the following four conventional methods:
 
Centering date method (CDM)
In the case of intervening intervals, production credits (Likhi et al., 1995; O’ Connor and Lipton, 1960) were calculated by multiplying yield on intervening sample days with fixed sampling interval:
   
In first and last sample day yield production credits (PN) were calculated as follows: Where,
DIM = days from the first day of lactation to the first sample day in case of first sample day yield  and days between last sample day and terminal day of lactation in case of last sample day yield
LI = Sampling interval
P_n  = Production on n^th sample day
Production credits of all intervals were summed up to estimate lactation milk yield.
 
Test interval method (TIM)
 
TIM is also based on the calculation of prediction credit for all test-day yields and then summing up in order to know predicted milk yield (Likhi et al., 1995; Everett and Carter, 1968; Sargent et al., 1968). Basic formulae for all calculations were the same as in case of CDM, with sampling interval as follows:
For n^th   intervening interval:
 
                                LI = ½ (DIM_n+1 - DIM_n-1)
Where,
DIM_n+1 and DIM_n-1 were the days in milk up to and including the proceeding (n+1)^th  and preceding (n-1)^th sample days, respectively.
For first and last sampling intervals, sampling interval was the length of the first or last test period as the case may be.
 
Ratio method (RM)
 
It predicts the 305-day lactation yield by multiplying each test day with the ratio factor (Dass and Sadana, 2003). Where,
R = Y / X = Ratio of average 305-day milk yield to average test day milk yield.                  
   = Estimated 305-day milk yield of the i^th animal.
Xi     =   Test day milk yield of i^th animal.
Y    =   Average 305-day milk yield.
X    =   Average test day milk yield.
 
Multiple linear regression (MLR)
 
MLR was used to develop prediction equations by estimating the regression coefficients for the test-day milk yield records in different combination. The software used for MLR was SAS Enterprise Guide 4.3, 2003. Stepwise backward multiple linear regression analysis was used to estimate 305-day milk yield (Singh et al., 2015; Kokate et al., 2014; Chakraborty et al., 2010). Where,
    =  Estimated first lactation 305-day or less milk yield of the i^th animal.
x_i =   Test-day record of i^th animal.
a =   Intercept.
b_i =   Regression coefficient of first lactation 305-day or less milk yield on test- day records. The accuracy of fitting the regression models was calculated by using the following formula:                               
The comparison of the above mentioned conventional methods was made with newly evolved computational machine learning method that mimics human brain (neural network) called Artificial Neural Network (ANN).
 
Artificial neural network
 
ANN model is basically an intelligent data processing system which learns the predictive ability automatically from the data set presented while training the network. Such neural network consists of input layer, hidden layer(s) and an output layer. Each layer has a specific role in the execution of the neural network. In back propagation technique, input vector and the corresponding target vectors are used to train a network until it can approximate a prediction function (Ruhil et al., 2011; Gandhi et al., 2010).

A multilayer feed forward neural network with back propagation of error learning mechanism was developed using Weka software version 3.8.0 to predict the first lactation 305-day or less milk yield (FL305DMY). The network was trained and simulated using cross-validation of 10 folds, up to 2500 epochs or till the algorithms truly converged. Network parameters such as learning rate (0.3), momentum (0.5) and validation set size (0) were used as the default setting of the algorithms. Most of the time, it was observed that algorithms were truly converged which means that performance/error goal was achieved.
 
Estimation of error in prediction
 
The error in the prediction of first lactation 305-day milk yield was estimated as a deviation of predicted milk yield from the actual milk yield: Where,
E_i = Error in prediction.
      = Predicted 305-day milk yield of the i^th animal.
Y_i = Actual 305-day milk yield of the i^th animal.
 
Absolute error
 
Absolute error was estimated without considering the positive or negative signs as follows:
                                                          = | E_i |
 
Percentage absolute error
= (Absolute error / Mean of actual 305-day milk yield) × 100
 
Average error
 
                          = Sum of error / No. of observations
 
Percentage average error
= (Average error / Mean of actual 305-day milk yield) × 100
 
Root mean square error (RMSE)  
Where,
     = Predicted 305-day milk yield of the i^th animal.
Y_i = Actual 305-day milk yield of the i^th animal.
n = Number of observations.
 
Percentage RMSE 
  = (RMSE / Mean of actual 305-day milk yield) × 100

The first lactation 305-day milk yield of Murrah buffalo was predicted based on bimonthly test day milk yield records utilizing conventional and machine learning methods. The error was calculated as difference of observed value from predicted value, thus, the negative error indicated that the prediction method had under-estimated the milk yield and positive value indicated over-estimation. The efficacy of the prediction was also judged by absolute error, percentage absolute error, average error, percentage average error, root mean square error (RMSE) and percentage RMSE which has been presented in Table 1.



The deviation of predicted first lactation 305-day milk yield from actual 305-day milk yield utilizing CDM method was found to be 103.30 kg as absolute error (4.89%), -58.47 kg as average error (-2.77%) and 135.77 kg as RMSE (6.43%). Based on TIM, the deviation of predicted first lactation 305-day milk yield from actual 305-day milk yield was found to be 113.80 kg as absolute error (5.39%), 60.50 kg as average error (2.86%) and 146.13 kg as RMSE (6.92%). The deviation of predicted first lactation 305-day milk yield from actual 305-day milk yield utilizing Ratio method was found to be 104.96 kg as absolute error (4.97%), 2.11 kg as average error (0.10%) and 137.46 kg as RMSE (6.51%). The deviation of predicted first lactation 305-day milk yield from actual 305-day milk yield utilizing MLR method was found to be 93.49 kg as absolute error (4.43%), 0 kg as average error (0%) and 120.59 kg as RMSE (5.71%). The deviation of predicted first lactation 305-day milk yield from actual 305-day milk yield utilizing ANN method was found to be 93.99 kg as absolute error (4.45%), -0.58 kg as average error (-0.03%) and 121.82 kg as RMSE (5.77%). A perusal of Table 1 showed that the errors were least for MLR, followed by ANN, CDM, TIM and Ratio method. On contrary, Gandhi et al., (2010) reported ANN as best method for prediction as compared to MLR. Everett and Carter (1968) reported that TIM method overestimates actual first lactation 305-day milk yield by 91.4 kg of milk for bimonthly records. They also reported that estimation of actual 305-day production by CDM was more accurate than TIM.
 
he results clearly indicated that the multiple linear regression was the best amongst all the tested methods, therefore an attempt was then made to predict the first lactation 305-day milk yield based on early records. To select the best early BTDYs records amongst all six BTDYs records for prediction at an early stage, simple linear regression analysis with only one independent variable (BTDY) at one time was performed and the estimated intercept along with regression coefficients were estimated (Table 2). A perusal of the results showed gradual increase in the regression coefficient till BTDY-4, followed by gradual decline. Kokate et al., (2014) reported increase in regression coefficient till BTDY-3. The accuracy for prediction for different BTDYs varied from 19% to 62%. The accuracy was found to be higher in middle of the bimonthly records which was in agreement with Kokate et al., (2014).



The regression equation utilizing all the six bimonthly test day milk yield records was best with 121.8125 RMSE and 91.86% accuracy. But, in order to get early prediction, bimonthly test day yields were analysed by stepwise backward elimination regression method in SAS enterprise guide 4.3. For early prediction, with two variables (i.e. BTDY-2 and BTDY-4) the accuracy was 81.47%. On addition of one more variable the accuracy had increased to 85.29%. Further addition of bimonthly records were not leading to an increase in accuracy significantly. So, the equation with three bimonthly test day variables i.e. BTDY-2, BTDY-3 and BTDY-4 was found to be the best among early combinations with 163.7376 RMSE and 85.29% accuracy. The predicted equation showed more accuracy than reported by Kokate et al., (2014) in which the prediction equation include BTDY-2, BTDY-3 and BTDY-5 with 83% accuracy. The best prediction equations along with the estimated intercept values, regression coefficients, coefficients of determination (R²), AIC, BIC and RMSE values has been presented in Table 3.

The study revealed that the first lactation 305-day milk yield was observed to be best estimated by MLR, followed by ANN and CDM. Early prediction of FL305DMY using BTDY-2 (65^th day), BTDY-3 (125^th day) and BTDY-4 (185^th day) gave higher accuracy (85.29%), which was nearer to the one wherein all the test day records were utilized. Evaluation of the sires and dam based on early test day yields would eventually result in reduced cost incurred on milk records, reduced generation interval and increased response to selection.

The authors are thankful to the Director, ICAR-NDRI, Karnal and Head of Animal Genetics and Breeding section, ICAR-NDRI, Karnal for providing necessary facilities for conducting this study. The help rendered by Livestock Record Unit of ICAR-NDRI, Karnal is deeply acknowledged for providing the required data for the analysis.