Estimated model parameters of incomplete gamma and inverse polynomial functions and comparison of the models lactation yield prediction potential in Zebu and crossbred cattle

The study was conducted to estimate model parameters of Incomplete Gamma (IG) (b=1) and Inverse Polynomial ¢P) functions of a lactation curve and the models lactation yield prediction potential based on milk data from Bako Agricultural Research centre and Debre Zeit Research Station. The models were fitted to weekly total milk data of indigenous and crossbred cows. Five model parameters ("a", "c", "Ao", "Ai" and "AZ") of the two models, estimated from regression of weekly total milk data on weekly interval from calving, were analysed for the effects of genetic and non genetic factors. Based on the estimated model parameters for each cow, lactation yield was predicted and the deviation of the predicted from the actual yield estimated. The predicted lactation yield and percent deviation of the predicted from the actual lactation milk yield were analysed using the General Linear Model. The overall least square mean values of "a", "c", "Ad', "Ai" and "AY' were 2.559 t 0.01, 0.103 t 0.001, 0.379 t 0.024, 0.076 t 0.007 and 0.006 t 0.001, respectively. All parameters were significantly (p < 0.001) affected by sire breed and calving year. Besides, calving season (p < 0.001) and parity of the cow (at least p < 0.05) significantly affected "a" and "c" only. Crossbred cows had significantly (p < 0.001) higher "a" and "Al" and lower "c", "Ao" and "Az" values than the indigenous breeds. Horro, as a sire breed, had significantly higher "a", "Ad' and "Az" and lower "Ai" than Boran cows but not in the value of the parameter "c". Crossbred cows, however, were not significantly different among each other in the values of all parameters. Cows that calved in 1989 had significantly (p < 0.001) the highest "a"(2.750 t 0.097), "Ax" (0.019 t 0.004) and "c" (0.132 t 0.009), while the highest values of "Ao" (1.01 t 0.11) and the' lowest "Ai°( 0.238 t 0.03) were recoiled for cows that calved in 1987. Significantly (p < 0.001) highest values of "a" (2.543 t 0.023) and "c" (0.116 t 0'662) were' obtained for cows that calved during Arfasa (short rainy season). The lowest values of "a" (2.156 t 0.031) and "c° (0.102 t 0.003) were recorded for cows in the first parity (p < 0.001). The parameter "c" showed a linear trend with an increase in parity order. The overall mean actual lactation milk yield, and lactation milk yield predicted from IG (b = 1) and IP are 1522.3 t 17.18, 1540.3 t 15.91 and 1360.9 t 110.9 kg, respectively. The IG (b =1) over predicted the overall least square mean lactation milk yields by about 2.2 t 2.33 % while the IP underpredicted least square mean lactation milk yield by 15.5 t 9.61 °.6. The IG (b = 1) over predicted least square mean lactation yields by 1.1 to 5.0% for all sire breeds, dam breeds, locations and parities, while the IP under predicted least square mean lactation yield of all sire breeds except Horro and that of both dam breeds and locations. The significantly (p < 0.001) highest deviation was recorded for Homo cows (b.0 t 0.69 °.b) compared to the other sire breeds. Comparison of dam breeds, locations and parities indicated that the percent deviation was significantly (p < 0.05) higher for Horro than Boran cows (3.4 vs 1.1%); for Bako than Debre Zeit herd (3.1 va 1.5 %) and for cows in later than earlier parities. In the case of the IP, significantly (p < 0.05) highest deviation was observed for Boran cows (190.9 t 50.9 %) compared to the other sire breeds. From this study it can be concluded that the IG (b =1) better fitted to the weekly total milk data and 'enabled prediction of lactation milk yield with minimum biased compared to the IP and could be recommended for fitting to the lactation data of indigenous and crossbred cows of the study areas.