UBC Theses and Dissertations
Study of within herd variability in milk fat, protein and lactose content of bulk milks in British Colunbia and factors affecting the design of herd milk sampling programs Williams, Christopher John
Three sets of data were used to estimate variation, from all sources, associated with bulk milk sampling, and testing programs. Three milk samples were taken from each shipment of 26 herds from March 14, 1970 to April 24, 1971 (Experiment I). The set of three samples was handled as follows: (1) one sample was used in the formation of a two-week composite; (2) one sample was used in the formation of a one-week composite; and (3) one sample was analysed fresh. Four milk samples were taken from each shipment of 22 different herds from November 17 to December 16, 1971. Three of the four samples were analysed fresh in duplicate (Experiment II). The fourth sample was divided into three parts and each part was used in the formation of a composite. Each composite was analysed in duplicate after a two-week collection period (Experiment III). Herd milk was shipped on alternate days. All milk samples (8,894) were analysed for milk fat, protein and lactose using Infrared Milk Analysers. Estimates, obtained from Experiment I by the analyses of variance of a hierarchal model (herds, periods within herds and shipments within herds and periods), of within herd-period (15 shipments per period) variances of percent milk fat, protein and lactose were; 0.01371 ± .00030, 0.00787 ± .00017 and 0.00548 ± .00012 respectively. Estimates were obtained from Experiment II of within herd-period variance and its components by the analyses of variance of a hierarchial model. The estimates of these variances for percent milk fat, protein and lactose respectively were: (1) within herd-period variance — 0.01329 ± .00064, 0.00507 ± .00031 and 0.00483 ± .00017; (2) biological (shipment to shipment) variance — 0.00607 ± .00061, 0.00340 ± .00029 and 0.00110 ± .00014; (3) sampling (within shipment) variance 0.00094 ± .00027, -.00021 ± .00006 and -.00033 ± .00013; and (4) testing (within sample) variance — 0.00628 ± .00029, 0.00167 ± 0.00006 and 0.00373 ± .00013. Estimates of within herd-period variance of percent protein from Experiment I were significantly different from estimates from Experiment II. Orthogonal polynomials were used to estimate the relationship between the serial correlations (calculated from Experiment I) of milk constituent percentage and the number of shipments separating two shipments for which the correlations were calculated. Only the linear term was significant for percent protein and lactose and accounted for 99.7 and 98.4 percent of the total sums bf squares for these two milk constituents respectively. Linear and quadratic after linear were significant for percent milk fat serial correlations and accounted for 98.4 and 1.3 percent of the total sums of squares respectively. Strata within periods was fitted as an effect (Experiments I and II) in a hierarchal model and was a significant source of variation. The variances of estimates of herd-period mean milk constituent percentages obtained from various simple and stratified random sampling schemes were calculated. Stratification resulted in a relatively small reduction in the variances of these estimates. Estimates of the variances associated with the formation of a composite sample obtained from Experiment III by the analysis of variance and from Experiments I and II were near zero. The variance of estimates of herd-period mean milk constituent percentages obtained from two two-week composites were 0.00368, 0.00110 and 0.00205 for percent milk fat, protein and lactose respectively. It was calculated that four random samples would estimate herd-period mean milk constituent percentages at least as precisely as two two-week composite samples. Two-week composite samples underestimated percent milk fat by 0.045 percent milk fat and overestimated percent protein and lactose by 0.023 and 0.010 percent respectively compared to corresponding estimates based on the fresh analyses of samples drawn from each shipment. Simple and multiple regression techniques were used in an attempt to predict herd differences in within herd-period variance from the average amount of milk shipped and percent milk fat, protein and lactose. In general, large within herd-period variances of milk constituent percentages were significantly associated with small herd milk shipments and high levels of milk fat and protein. However, the proportion of the total sums of squares accounted for by the various regression equations was relatively low; therefore the equations were not useful for predicting herd-period variances. Within herd-period variance of percent milk fat was highest in the spring and autumn; therefore sampling frequency may need to be greater at some seasons than at others. Differences among herds in within herd-period variance of milk constituent percentages were significant; therefore random sampling schemes may have to be modified to suit individual herds.
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