Prediction of Fortnightly Test-Day Milk Yields Using Four Different Lactation Curve Models in Indian Murrah Buffalo

| The present investigation was carried out using data on 18871 fortnightly test day milk yield (FTDMY) records during first lactation of 961 Murrah buffaloes calved during 1977-2012 maintained in an organized farm at National Dairy Research Institute, Karnal. The least squares means of the FTDMY ranged from 2.35kg to 7.92kg. The relative efficiency of four lactation curve models via. Gamma-type function (GF), Exponential function (EF), Mixed log function (MLF) and polynomial regression function (PRF) were compared. PRF described the highest coefficient of determination (R2) (99.78%) and with least value (0.02kg) of root mean squares error (RMSE), whereas, least coefficient of determination (93.13%) was observed in Gamma-type function having maximum (0.1kg) RMSE value suggesting PRF being best mathematical model for prediction of FTDMYs in Murrah buffaloes.


INTRODUCTION
L actation curve is the graphical representation of milk yield against time (Brody et al., 1923).Dairy cattle and buffaloes with more stable lactation curve are more persistent than those which show a rapid increase in the daily milk yield from calving to peak followed by a rapid decline.Very scanty work on lactation curve has been reported in Murrah buffaloes, the best dairy buffalo breed of India.Hence, the present investigation has been proposed to fit and compare the lactation curve models for describing the shape of the lactation curve in Murrah buffaloes and prediction of fortnightly test day milk yields.

MATERIALS AND METHODS
Data of 18871 fortnightly test day milk yield (FTD-MY) records during first lactation of 961 Murrah buffaloes calved during 1977-2012 at the National Dairy Research Institute, Karnal were collected.The climate of the farm is subtropical in nature.The lowest temperature falls to 2°C during the winter months, whereas the highest temperature goes up to 45°C during the summer.The annual rainfall is about 760 to 960mm, out of which most of the rainfall is received during the months of July and August.The relative humidity ranges from 41% to 85%.A total of 21 fortnightly test day milk yield records (6 th day, 20 th day, 35 th day,. . ., 305 th day) were taken at an interval of 15days from daily milk yield recording register.The data were used to estimate lactation curve parameters of the four lactation curve models via.Gamma-type function (GF), Exponential function (EF), Mixed log function (MLF) and polynomial regression function (PRF) for developing the prediction model for estimation of fortnightly test day milk yields in Murrah buffaloes.

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1. Gamma-type function: (Wood, 1967) Y t = at b e -ct In its logarithmic form, this reduces to ln (Y t ) = ln (a) + b ln (t) -ct 2. Exponential function (Catillo, 2002) Y t = a+be -0.70t +ct 3. Mixed log function (Guo and Swalve, 1995) Y t =a+bt 0.5 +clogt In the models, Y t = average daily yield in the t th test day of lactation; a = initial milk yield just after calving; b= ascending slope parameter up to the peak yield; c=descending slope parameter and t = length of time since calving.4. Polynomial regression function (Ali and Schaeffer, 1987) Y t =a+bx+cx 2 +dlog (1/x)+elog (1/x) 2 In this model, Y t = Average milk yield in t th week of lactation, a = Associated with peak yield, b & c = Associated with the decreasing slope, d & e = Associated with the increasing slope, x = t /305

RESULTS AND DISCUSSION
The least squares means of the Various lactation curve parameters (a, b, c, d and e) were estimated to fit into the mathematical models to obtain the prediction equation for FTDMYs (Table 1).The four lactation curve functions (Table 2) were developed after fitting the values of the lactation curve parameters for predicting FTDMYs.The overall observed and predicted FTDMYs for all 4 lactation curve functions were plotted graphically (Figure 1).The closeness of PRF was almost of simi

CONCLUSIONS
In the present investigation it was found that on an average, the peak yield from all lactation curves functions was found to be highest around 65 th day of lactation in Murrah buffaloes.PRF is the best function among four models studied followed by mixed log function explaining highest coefficient of determination with lowest root mean square error and therefore these two functions are recommended for prediction of FTDMYs in Murrah buffaloes.

Figure 1 :
Figure 1: Actual and predicted FTDMYs from various lactation curve functions in Murrah buffaloes lar order magnitude as the observed one.This may be due to the fact that this function accounted for rising and declining segments of the lactation curve.
FTDMYs were calculated for adjustment of effect of non-genetic factors (season, year of calving and age at first calving groups).

Table 1 :
Estimated lactation curve parameters of different functions in Murrah buffalo

Table 2 :
Different lactation curve functions with parameters for prediction of FTDMY in Murrah buffaloes

Advances in Animal and Veterinary Sciences December 2014 | Volume 2 | Issue 12 | Page 649Table 3 :
Predicted FTDMY and error (kg)of different lactation curve functions in Murrah buffaloes