Comparative efficiency of five mathematical functions in modelling the first lactation milk yield of Kankrej cattle

Modelling of first lactation milk yield of Kankrej cattle was done using five different non-linear mathematical functions viz., exponential decline function (EDF), gamma function (GF), inverse polynomial function (IPF), mixed log function (MLF) and parabolic exponential function (PEF). We compared their efficiency in describing variations in first lactation milk yield of animals maintained under field conditions. A total of 3994 fortnightly daily milk records of 203 Kankrej cattle calved during the years between 2011 and 2017 at farmers' herds in the Banaskantha region of Gujarat State, India were utilized for the study. The PROC NLIN procedure of Statistical Analysis Software (SAS) using Newton method of iteration was applied to generate the model parameters and corresponding standard errors. Different parameters like adjusted R-2-value, root mean square error (RMSE), Durbin-Watson (DW) statistic, Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to compare the efficiency of different models. Results inferred that mixed log function was the best non-linear mathematical function for explaining variations in the first lactation milk yield of Kankrej cattle followed by gamma function and parabolic exponential function. The exponential decline function was the least efficient in fitting the lactation curve in Kankrej cattle, followed by inverse polynomial function.