Investigating the possibility of using Wood function (incomplete gamma function) in random regression model to fit on the test day records of milk yield

Although Wood function is of great importance to studying lactation curves because of its coefficients with biological interpretation, it has not been used under a random regression models. The objective of this study was to investigate the possibility of fitting Wood function on the test day records of dairy cows under a random regression model. Data was consisted of 743,205 test day records in first lactation of 81,192 Holstein cows from 46 herds in Iran which have been collected during 1991 to 2008. Linear form of Wood function which was a polynomial of 3 has been used. Three forms of Legendre polynomial functions with third order for additive genetic effects were also applied to evaluate the results of Wood function. Heritability estimates for daily milk yield obtained by linear form of Wood function were higher than those obtained by Legendre functions in most days indicating its advantage for genetic evaluations. Correlation between breeding values of animals predicted by linear form of Wood function and Legendre functions was 90%. In conclusion, Wood function can be employed in random regression models causing exploitation its desired characteristics and the advantages of random regression models to explain the genetic variations of dairy cows’ lactation curve.