Determining the best mathematical function for describing the lactation curve and its coefficients heritability in Najdi cattle

To determine the best function for describing lactation of Najdi cow in Khuzestan, the day-based milk production test records, collected by Shushtar support station from 1990 to 2014, were used. Records included 2369 data related to 444 first parity cows. To determine the best mathematical function, six functions includind incomplete gamma, wilmink, inverse polynomial, complex logarithmic, Cobby and Le Du, and polynomial regression were evaluated. All functions were fitted using PROC NLIN procedure of SAS software and Gauss-Newton iteration method on day-based milk production test records; and compared based on coefficient of determination R2, corrected coefficient of determination, the mean square error and Akaike index. The results showed that the inverse polynomial function offers a better description for lactation curve in Najdi cattle.  The lactation curve parameters (a, b, c) were estimated 4.4841, 0.2514, 0.00273, and their heritability were 0.354±0.120, 0.280±0.11 and 0.276±0.155, respectively. Moderate heritability suggests the opportunity of genetic response via selection program. Heritability of these traits can be improved by correcting the known environmental impacts.