Comparison of Five Mathematical Functions for Prediction of Monthly Yield in Thai Multibreed Dairy Cattle Population

Abstract

Monthly yields of 32,583 records from 3,523 first lactation cows, collected by the bureau of Biotechnology in Livestock Production, Department of Livestock Development (DLD) were used in this study. These dataset were obtained between 1993 and 2003 in 777 farms throughout the country.
The objective was to evaluate five mathematical models for describing the phenotypic lactation curve of dairy cattle in Thai multibreed population. In the previous analysis, monthly milk yields were adjusted by the variation of herd-year-season of calving, Holstein Friesian (HF) fractions, calving age and first test-day after calving. The adjusted monthly milk yields were used to fit five mathematical functions. Five functions, i.e. Ali and Schaeffer polynomial (A&S), Schaeffer and Dekkers (S&D) logarithm, Wilmink exponential (WIL), Wood incomplete gamma (WD) and Legendre polynomials (LEG) functions were used in this study. For the whole data analysis, all functions showed few differences in comparison criteria. A&S fitted the actual yield better than other functions according to the adjusted coefficient of determination (R²_adj=0.39) and mean square error (MSE=6.84). For individual lactation analysis, A&S provided the smaller value of residual errors including means of absolute error (RES), means of mean square error (MMSE) and means of square prediction error (MSPE) than other functions. Ranking all functions from the best to the worst were A&S, WD, S&D, WIL and LEG, respectively. The results indicated that A&S function could be fitted well for the whole and individual data. Therefore, A&S could be applied to describe the phenotypic lactation curve in this dairy population.