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Estimating Holstein Lactation Curves with a Gamma Curve¹

Departments of Dairy and Experimental Statistics, New Mexico State University, Las Cruces, NM 88003

ABSTRACT

Milk production records of healthy Holstein cows were analyzed with the model:

where Y_i is milk production in kilograms at a specific time (t_i) in months. The parameters in this model were estimated with the techniques of intrinsically nonlinear regression. The milk production data came from four lactations of 36 cows and single lactations of 37 other cows which had completed at least one lactation. Production was collected monthly except that weekly means were used during the first 2 mo for the latter group. The first and third coefficients (ß^₁ and ß^₃) were lower for lactation 1 than for later lactations, i.e., estimated curves were lower and flatter for the first lactation than for later ones. Variances of deviations from the estimated curves were approximately equal after the 1st mo of lactation indicating that intrinsically nonlinear regression was the appropriate approach. Although coefficients varied for individual cows, most lactations were estimated closely by a gamma curve; coefficients of determination were close to 1.0 for means of cows but were not as consistent for individual cows. This technique allows statistical comparison of lactation curves of experimental groups of cows. This technique may be useful to extend incomplete lactation records, to compare daughters of sire groups, and to compare production of cows receiving different nutritional or physiological treatments.

¹ Journal article 610, Agricultural Experiment Station, New Mexico State University, Las Cruces 88003.

² Departamento de Recursos Pecuarios, Universidad National de Colombia, Medellin.