Fitness of four different mathematical models to the lactation curve of Brown Swiss cows in Konya Province of Turkey

Abstract

Keskin, I., Dag, B. and Sariyel, V. 2009. Fitness of four different mathematical models to the lactation curve of Brown Swiss cows in Konya Province of Turkey. Can. J. Anim. Sci. 89: 195Á199. The aim of this study was to investigate the fitness of Incomplete Gamma (WD), Exponential (WIL), Mixed Log (MIL) and Polynomial Regression (AS) models to the lactation curve of Brown Swiss Cows. Data were collected from 143 Brown Swiss cows raised on the Altinova State Farm in Konya Province, Turkey. Milk yield was recorded monthly, and milk records were started at the third week of lactation (mean 0 16.9 day, SD00.7). Total milk yields estimated by the four models were very close to real total milk yield. The models were found to be adequate for estimation of milk yield. The MIL model underestimated the peak yield significantly. The differences between peak yields of the models and real peak yields were not significant and ranged from 27.70 to 29.01 L. All models forecasted peak time earlier than real peak time. The differences for the persistency values of the four models were significant. The AS model's persistency value was nearly equal to the real persistency value (77.56 vs. 77.59%). R 2 values of the models changed from 86.05 to 97.95%. The AS model gave the best R 2 and the least MSPE values. Consequently, the AS model showed the best fit to the lactation data of Brown Swiss cows and allowed a suitable definition of the lactation curve.Key words: Brown Swiss, cows, lactation curve, milk yield, mathematical model Keskin, I., Dag, B. et Sariyel, V. 2009. Ajustement de quatre mode`les mathe´matiques a`la courbe de lactation des Suisses brunes dans la province turque de Konya. Can. J. Anim. Sci. 89: 195Á199. L'e´tude devait e´tablir dans quelle mesure les mode`les Gamma incomplet (WD), Exponentiel (WIL), Log mixte (MIL) et Re´gression polynomiale (AS) refle`tent la courbe de lactation des vaches Suisses brunes. Les donne´es ont e´te´recueillies sur 143 vaches e´leve´es dans la ferme d'É tat d'Altinova, dans la province de Konya, en Turquie. Le rendement laitier a e´te´enregistre´mensuellement a`partir de la troisie`me semaine de lactation (moyenne 016,9 jours, É .-T. 00,7). Le rendement laitier total estime´par les quatre mode`les se rapproche beaucoup du rendement re´el. Les mode`les conviennent a`l'estimation du rendement laitier. Ne´anmoins, le mode`le MIL sous-estime sensiblement le rendement maximal. L'e´cart entre le rendement maximal indique´par le mode`le et le rendement maximal re´el n'est pas significatif et varie de 27,70 a`29,01 l. Tous les mode`les anticipent le moment oul e rendement maximal sera atteint, comparativement a`la re´alite´. La persistance varie sensiblement d'un mode`le a`l'autre. Celle du mode`le AS e´quivaut presque a`la persistance re´elle (77,56 c. 77,59 %). La valeur R 2 des mode`les varie de 86,05 % a`97,95 %. Le mode`le AS donne la meilleure valeur R 2 et la plus faible erreur de pre´diction au carre´. On en de´duit que ce mode`le est celui qui refle`te le mieux les donne´es de lactati...