# Introducing a sinusoidal equation to describe lactation curves for cumulative milk yield and composition in Holstein cows.

Research paper by Navid N Ghavi Hossein-Zadeh, Hassan H Darmani Kuhi, James J France, Secundino S López

Indexed on: 08 May '20Published on: 08 May '20Published in: The Journal of dairy research

#### Abstract

The aim of the work reported here was to investigate the appropriateness of a sinusoidal function by applying it to model the cumulative lactation curves for milk yield and composition in primiparous Holstein cows, and to compare it with three conventional growth models (linear, Richards and Morgan). Data used in this study were 911 144 test-day records for milk, fat and protein yields, which were recorded on 834 dairy herds from 2000 to 2011 by the Animal Breeding Centre and Promotion of Animal Products of Iran. Each function was fitted to the test-day production records using appropriate procedures in SAS (PROC REG for the linear model and PROC NLIN for the Richards, Morgan and sinusoidal equations) and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination $\lpar {R_{{\rm adj}}^2 } \rpar$, root mean square error (RMSE), Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). $R_{{\rm adj}}^2$ values were generally high (>0.999), implying suitable fits to the data, and showed little differences among the models for cumulative yields. The sinusoidal equation provided the lowest values of RMSE, AIC and BIC, and therefore the best fit to the lactation curve for cumulative milk, fat and protein yields. The linear model gave the poorest fit to the cumulative lactation curve for all production traits. The current results show that classical growth functions can be fitted accurately to cumulative lactation curves for production traits, but the new sinusoidal equation introduced herein, by providing best goodness of fit, can be considered a useful alternative to conventional models in dairy research.