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Appropriate mathematical models for describing the complete lactation of dairy sheep

  • G. E. Pollott (a1) and E. Gootwine (a2)


Despite milk being an important product from sheep, there are very few reports of milk production from the complete lactation of dairy sheep. The Improved Awassi in Israel is kept under an intensive system of management with lambs being weaned soon after birth. Records from one such flock were analysed to investigate the suitability of various mathematical functions for describing milk yield from the complete lactations of dairy sheep. This included a consideration of whether the functions could cope with short lactations, a characteristic of dairy sheep, and a limited number of test-day records per lactation.

Four non-linear mathematical functions were investigated (Wood, Morant, Grossman and Pollott), two of which could also be fitted in a linear and a linear weighted form (Wood and Morant). These functions were fitted to weekly data from a ‘typical Awassi lactation curve’, represented by least squares means of daily milk yield from each week of a 40-week lactation derived from an analysis of 25605 test day records. Characteristics of the lactation were calculated from the functions, such as total milk yield, day and level of peak yield and persistency. These functions were also fitted to 1416 individual lactation records of up to 10 test-day records per lactation. The value of the functions was investigated using the residual mean square (RMS) of the fitted curve as an indicator of how well each function described the lactation. Forms of these functions with a reduced number of parameters were also investigated.

The non-linear functions always fitted the data with a lower RMS than their linear equivalent and the weighted form of the linear functions always had a lower RMS than the unweighted form. Of the linear functions, Morant fitted better than Wood. Of the non-linear functions Grossman, Morant and Pollott (additive and multiplicative) fitted the data equally as well but better than Wood. The various functions predicted characteristics of the lactation curve differently; the Wood functions tended to overestimate yield in early lactation and the Morant functions underestimated peak yield.

No function was better suited to short lactations than another. However the three-parameter function of Morant, Pollott multiplicative and Pollott additive were considered to be the most suitable for describing the complete lactation of dairy sheep.



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Appropriate mathematical models for describing the complete lactation of dairy sheep

  • G. E. Pollott (a1) and E. Gootwine (a2)


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