A comparison of different models of the lactation curve in dairy cattle

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Abstract
A study of 468 lactations in two herds of British Friesian cows sampled weekly between 1976 and 1979 was undertaken to investigate seasonal variations in milk yield and to compare four models of the lactation curve: (i) logey(n)=loge a + b logen—cn; (ii) y(n) = anbe-cn; (iii) y(n)= ae-pn—ae-qn; and (iv) y(n) = a—p'n—ae-q‘n.Model (i) was fitted by unweighted linear regression and the remainder by maximum likelihood. Average peak yield was 29 kg/day and 305-day yield was 5720 kg.Model (ii) fitted the data slightly better on average than models (iii) and (iv), and all were better than model (i). Compared with model (i), model (ii) reduced the average residual mean square proportionally by 0-10 in cows and 004 in heifers (first calvers). Model (iv) described the initial rise in milk yield up to week 5 better than models (i) or (ii) but reached a maximum value slightly early. Models (i), (ii) and (iv) slightly underestimated and (iii) slightly overestimated maximum milk yield, but model (ii) provided the best estimate of the position of maximum yield.Peak yields for heifers occurred on average at approximately 10 weeks post calving compared with 7 weeks for cows. Mean persistency of lactation, calculated as s= -(b+1) logec, did not vary from the second lactation onwards, whereas the average rate of decline p' in model (iv) increased with parity.When milk yields were adjusted for stage of lactation, significant variations were found that were related to the week of recording but this seasonal variation in milk production was smaller than that found nationally in the United Kingdom.