Modeling and evaluation of lactation curve functions in Gir cattle

Abstract

The aim of the study was to model and evaluate five different non-linear lactation curve functions for their efficiency of explaining the variations in first lactation milk yield of Gir cows maintained in the farmers herds. Information on 4,334 fortnightly test day yields of 223 cows calved during the period from 2013-2017 were used for the study. Twenty fortnightly yields starting from the day 15 of lactation were used for fitting the five different non-linear mathematical models, viz. Exponential decline function (EDF), Gamma function (GF), Inverse polynomial function (IPF), Mixed log function (MLF) and Parabolic exponential function (PEF). The curve functions (a, b and c) with standard errors and different evaluation parameters, viz. adjusted R2-value, Akaike information criterion (AIC), Bayesian information criterion (BIC), Durbin watson (DW) statistic and root mean square error (RMSE) were estimated by non-linear regression analysis using PROC NLIN procedure Newton method of SAS (SAS Institute, 2010). The adjusted R2 value of the models ranged from 69.28 (exponential decline function) to 99.36% (parabolic exponential function). All the DW estimates were positive ranging from 0.1573 for exponential decline function to 0.7707 for parabolic exponential function. The RMSE (0.1453) and AIC (4.9152) estimates were also lowest for parabolic exponential function while highest for exponential decline function. Based on the results, it may be concluded that among five functions, parabolic exponential function is the best fitted lactation curve model followed by mixed log function, gamma function, inverse polynomial function while exponential decline function was the least efficient in explaining the variations in first lactation daily yield in Gir cattle.