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The effect of milk pricing on genetic selection goals in British Columbia and Quebec dairy cattle populations Hird, Wendy Louise 1985

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THE EFFECT OF MILK PRICING ON GENETIC SELECTION GOALS LN BRITISH COLUMBIA AND QUEBEC DAIRY CATTLE POPULATIONS by WENDY LOUISE HIRD B.Sc, University of B.C., Vancouver, 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Animal Science) We accept this thesis as conforming to the .required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1985 © Wendy Louise Hird, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of (LnimaQ. SCJtQCL The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6 (3/81) -ii-ABSTRACT This study has compared the effect of milk pricing systems on the selection goals of dairy producers in two provinces of Canada, British Columbia (BC), and Quebec. These provinces were chosen for comparison as BC produces milk largely for a fluid market, while Quebec produces milk for a manufacturing market. Within BC, due to a higher utilization and higher milk price, the value/kg of skim on Van-couver Island was higher than that of the Vancouver Lower Mainland over the study period 1963-1982. Between the two provinces, the value/kg of skim in BC was found to be consistently higher than in Quebec over the 20 year period, while the value of fat was higher in Quebec than BC. In BC in 1980, the value of a kilogram of skim was approximately $0.30, whereas its value in Quebec was only $0.20. Dur-ing the 1960s in BC, the value of skim represented one half the value of milk, and in 1982 it comprised two thirds of the value of milk, as compared to Quebec, where fat represented 43% of the value of milk. Net economic values were calculated by sub-tracting the dollar cost of production associated with the components of milk (carrier, fat and protein), from the gross value/kg of skim and fat. These values showed that the value/kg of protein was negative and decreasing in both BC and Quebec. The economic value/kg of butterfat has been consistently positive and increasing over the study period in BC and Quebec to $3.27 and $3.34/kg respectively in 1982. The relative economic values of carrier, fat and protein in BC and Quebec in 1982 were 0.08:1.00:-0.10 and 0.06:1.00:-0.12 respectively, which puts moderate selection on carrier and fat, and negative selection on protein. Selection index weights for carrier, fat and protein revealed that the BC dairy industry has always applied positive selec-tion to the carrier and fat portion, and negative selection to the protein portion of milk. In 1982 the selection weights were 0.087:1.253:-1.189. The Quebec index has shown more fluctuation that BC, with less selection against solids compared to BC; -iii-(0.050:1.280:-0.657). Theoretical genetic goals of the BC dairy industry have been consistent at approximately 3.0% butterfat, 2.0% protein and 95.0% carrier. The genetic goals in Quebec have undergone wide fluctuations, but generally have sig-naled the dairy producer to increase both butterfat and protein. The goals of the two industries are now very similar, with the exception that Quebec continues to place higher value on solids than BC. -iv-Table of Contents Abstract ii List of Figures vi List of Tables vii List of Appendices viii Acknowledgements ix INTRODUCTION 1 REVIEW OF LITERATURE 8 Selection Index Theory 19 METHODS AND MATERIALS 29 Gross Value of Skim Milk and Butterfat 29 Prices Used to Calculate the Value of Skim Milk and Butterfat 30 BC Milk Prices 30 Quebec Milk Prices 31 Value in 100 kg of Milk 32 Net Economic Values 32 Factors Used to Calculate the Cost of Production 33 Metabolizable Energy Requirements 33 Feed Ratios 33 Hay and Feed Prices 34 Production Cost Calculation 34 Economic Value Calculation 36 Relative Economic Values 36 Selection Index Weights 37 -V-Relative Selection Weights 38 Genetic Goals of Selection Program 38 RESULTS AND DISCUSSION 41 Weighted Average Price of Milk 41 Cost of Hay and Dairy Feed 41 Value of Skim and Fat Within BC 49 Value of Skim in BC and Quebec 52 Value of Fat in BC and Quebec 52 Change in Value of Skim and Fat in 100 kg of Milk 59 Net Economic Values 62 Relative Economic Values of Components 70 Selection Index Weights of Components 75 Genetic Goals of Components 81 Use of Genetic Goals to Set Prices 87 SUMMARY 94 APPENDICES 98 LITERATURE CITED 107 -vi-List of Figures Figure 1. Weighted Prices of Milk 43 Figure 2. BC Feed and Hay Costs 45 Figure 3. Quebec Feed and Hay Costs 47 Figure 4. Value of Skim Within BC (1963-1975) 51 Figure 5. Value of Skim Within BC (1975-1982) 54 Figure 6. Value of Skim in BC and Quebec 56 Figure 7. Value of Butterfat in BC and Quebec 58 Figure 8. Change in Value of Fat and Skim in BC 61 Figure 9. Change in Value of Fat and Skim in Quebec 64 Figure 10. Economic Value of Milk Components in BC 67 Figure 11. Economic Value of Milk Components in Quebec 69 Figure 12. Relative Economic Values of Milk Components in BC 72 Figure 13. Relative Economic Values of Milk Components in Quebec 74 Figure 14. Selection Weights of Milk Components in BC 77 Figure 15. Selection Weights of Milk Components in Quebec 80 Figure 16. Genetic Goals for Butterfat and Protein in BC 83 Figure 17. Genetic Goals for Butterfat and Protein in Quebec 86 Figure 18. Genetic Goals for Carrier in BC 89 Figure 19. Genetic Goals for Carrier in Quebec 91 -vii-List of Tables Table 1. Heritabilities, genotypic and phenotypic correlations for milk production traits 8 Table 2. kx and ^  calculations 30 Table 3. Metabolizable Energy Requirements 33 Table 4. Phenotypic variance/covariance matrix 38 Table 5. Genotypic variance/covariance matrix 39 -viii-List of Appendices Appendix A. Milk prices in BC and Quebec 99 Appendix B. Feed and hay prices in BC and Quebec 100 Appendix C. Value/kg of skim and fat in BC and Quebec 101 Appendix D. Change in value/100 kg milk of fat and skim in BC and Quebec 102 Appendix E. Net economic value of milk components in BC and Quebec 103 Appendix F. Relative economic value of milk components in BC and Quebec 104 Appendix G. Selection index weights for milk components in BC and Quebec 105 Appendix H. Genetic goals for milk components in BC and Quebec 106 -ix-Acknowledgements I would like to acknowledge the efforts of several people who were helpful in the research and preperation of this thesis: my supervisor, Dr. R.G. Peterson, who in-spired me to begin this research, and who gave considerable time in discussing and evaluating the work; Dr. J.A. Shelford, for his encouragement and useful comments regarding the feed costs section of the thesis. I would like to express my manks to the wonderful people at Statistics Canada and to Mr. G. Thorpe, manager of the BC Milkboard, for their help in obtaining the data. Finally, many thanks to my husband, Donald Robinson, whose invaluable help as a critic, scientist, typist and friend en-abled me to complete this project. INTRODUCTION Milk pricing has become a controversial and confusing topic over the past few decades. In the past, milk was paid for on a butterfat basis, and this practice was rationalized by the low cost and ease of deterrnining butterfat content, the assumed constant proportion of fat to nonfat solids in milk, and the ease of elimination of fat from whole milk. The fluid milk price formula currently utilized in BC pays producers in different milk producing areas for their product based on a hectalitre (1 hi = 100 litres) with a butterfat differential. The pricing formula was developed to try to account for the costs of milk production, and includes such factors as the cost of feed, cost of farm labour, Consumer Price Index (an inflationary correction factor), and the price of farm inputs. Each factor is weighted in the formula, and the formula is adjusted rela-tive to a base year. This formula has been criticized in recent years, as some economists and animal scientists feel that it no longer correctly pays producers for the components of milk. The small butterfat differential does not appear to encourage producers to select for butterfat; and by paying mainly on volume only, encourages producers to choose sires that are high in milk volume and negligible in milk components; namely lactose, minerals, fat and protein. This means that farmers are paid a high price/kg for the water portion, and a low value/kg for the actual milk components. If, however, the energetic costs of the production of milk components is taken into account, the net economic values of the milk components can change drastically. Factors such as increasing feed prices or increasing butterfat differentials can further change the net or economic value of these components. Naturally, the net value of the components to the dairyman is the most important criterion for selection. - 1  -- 2 -A complicating factor in the development of selection criteria is the quota sys-tem utilized in Canada for supply management British Columbia (BC) is considered a "fluid" province, in that traditionally, 70% of the milk produced in BC has been used for fluid or Class I products such as packaged milk, sour cream, and table and whipping creams. The other 30% has been used in manufactured products such as yogurt and cheese. (BC Milk Board 1984, unpublished MS). BC dairy producers hold fluid production quotas which have steadily increased in value since 1972. These fluid milk quotas and prices have been controlled by the BC Milk Board since 1946. The manufacturing quotas were distributed by the BC Milk Board in accordance with a provincial allotment designated by the Canadian Dairy Commission (CDC). Manufacturing quotas were allotted in 1973 to insure supply management of manufactured products, and also to guarantee producers a fair return for their investment and labour. BC was allotted a 2.9% fraction of the national Market Sharing Quota (MSQ) based on a historically small manufacturing industry. The largest portion of the MSQ was allotted to Quebec and Ontario, based on historically large manufacturing indus-tries. After a period of withdrawal from the national milk marketing plan, BC reen-tered the plan with some strict guidelines. Producers demanded to be recognized as having an increasing manufacturing dairy industry, and to have MSQ allocated each dairy year on the basis of a total production ratio of 65% fluid and 35% industrial; using the average of the fluid milk sales of the two previous calendar years and the average mcoming butterfat test for each year. The 65:35 ratio is also used as a buffer for fluid and semifluid products in times of shortage. - 3 -A further factor affecting the economic value of products, and ultimately the selection goals, is the system of levies utilized in Canada. Canada has produced a surplus of dairy products for many years, and the excess protein has gone into low value products such as skim milk powder, which have been sold at a loss on the world market. The CDC has attempted to mimmize surpluses by the introduction of levies on manufactured milk. Every producer of manufacturing milk has paid an in-quota levy which has ranged from $2.27 to $5.14/hl over the past five years. This levy is necessary to provide funds to cover losses which occur when exporting skim milk powder not needed in Canada. Furthermore, producers who ship over their quota of MSQ are charged an over-quota levy which has ranged from $17.03 to $31.79/hl. The high over-quota levy was established both to discourage overproduc-tion and to market excess skim milk powder on the world market. In addition, farm-ers who produce fluid milk are charged a skim-off, or fluid levy which has ranged from $0.54 to $0.30/hl. The fluid levy was initiated to offset the extra butterfat taken out of the fluid milk, which is used in manufactured products (since the industry is based on 2% fluid sales). The in-quota levy has been widely criticized by dairy pro-ducers. Verdonk (1984) has argued that setting the standard for butterfat at 3.6 kg/hi and SNF (solids-non-fat) at 8.2328 kg/hi was a questionable decision. It was felt that the standard for SNF does not reflect the product, and should be raised. The problems and inconsistencies in the levies and pricing system have led to speculation regarding the effect of the pricing system on the producers' selection goals for milk. As the producer can only interpret his selection goals based on the provincial price-structure, it is reasonable to assume that producers in BC select against protein and fat, and put positive weight on milk yield only, whereas produc-ers in a manufacturing province such as Quebec would place more weight on fat and protein. . 4 -Unless the producer is paid the actual costs of producing the various milk com-ponents, he may as well select bulls which are negative for these components, since he pays an associated cost to produce each component. Hillers et al. (1979) con-cluded that in the development of selection indices, fat content should receive posi-tive weight, and protein and lactose negative weight, as producers realize a positive net return only for an increase in fat content. Given a theoretical metabolizable energy requirement for the formation of 1 gram each of the milk components to be 16.3, 8.5 and 6.6 kCals for fat, protein and lactose respectively, the expected net returns over feed costs from increasing fat, protein and lactose content by 0.10% for a cow producing 7272 kg of rnilk were: $12.78, -$2.51 and -$1.95 respectively. These figures were calculated given a fat differential of $0,242/0.1 kg, and assume no energy cost associated with water or mineral content. The price structure, and hence selection goals for milk in BC, do not appear to be stable from year to year, and this could pose a problem from a genetic point of view. It has been suggested (Peterson, unpublished MS) that as the relative economic weights of milk components change, the theoretical selection goals also change, and actual selection goals should change, were farmers able to interpret what they are. Changes in the milk price structure, such as an increase in the butterfat differential or in the settling rate, should result in an immediate change in the producer's selection goals. For example, Jeffries and Peterson (1980, unpublished MS) have pointed out that in the period from June 1978 to January 1979, a fat differential of $0.28 was used in BC. When the differential was raised to $0.30 in February 1979, the relative economic weights of carrier, fat and protein also changed. The industry was now asking for a higher fat level and consequently higher protein milk. - 5 -In reality, however, the results of genetic decisions in the dairy population are realized only 4 or 5 years later, and it would be impossible for a producer to make overnight changes in a selection program involving hundreds of animals; therefore there is a lag period between the time that the Milk Board changes the pricing struc-ture and the change in the producer's selection scheme. To minimize these fluctuations, a more useful method in a non-fluctuating sys-tem would be to hold the relative economic weights constant within the pricing struc-ture; for example 1.0:2.0:-5.0 for carrier, fat and protein respectively, and change the dollar value accordingly. In this way, the relative economic weights would remain constant, and a stable selection index could be utilized for a predetermined period of time. If this system were adopted the most important factor would be to develop better communication between the dairy industry and animal breeders in order to develop selection indices which would approximate the future selection goals of the dairy community. The milk pricing system rewards producers in way which may not realistically reflect the actual costs of producing milk components. This may lead in turn to con-fusion and contradictions in the establishment of genetic goals for the dairy industry. In order to detenriine the way in which the economic and genetic goals of the two provinces have moved in the past two decades, this study has focused on the follow-ing points: - 6 -• Due to the different producer prices paid to milk producing regions within BC, this study documents any differences between the $/kg value of fat and skim, as indicated by the milk price structure and the butterfat differential, in 3 milk pro-ducing regions of BC over the period 1963-1982. This information is used to compare BC values against those of Quebec. • To determine the change in the cost of production of a kilogram of carrier (whole milk-fat-protein), fat and protein based on variable monthly hay and feed prices, changing feed ratios and assumed estimates of the metabolizable energy requirements for the formation of one kilogram of each milk component. • To estimate the change in net economic values for a kilogram of carrier, fat and protein in BC and Quebec, and to estimate the change in economic weights (relative to fat) of the milk components, to observe fluctuations and trends in each province. • To calculate the selection weights for milk components and observe the change over time of the selection coefficient of each component, as indicated by the milk price structure utilized in BC and Quebec. These coefficients are used to test the hypothesis that BC dairy producers select against protein and fat, while Quebec producers select for protein and fat. • To calculate and compare the theoretical genetic goals of the BC and Quebec dairy industries utilizing the product of a matrix of genetic variances and covari-ances and the vector of economic weights. These parameters are studied in an effort to understand the way in which the - 7 -existing milk pricing system may affect the genetic selection goals of dairy pro-ducers from provinces which have different dairy marketing goals. - 8 -REVIEW OF LITERATURE Many factors determine the genetic goals of the dairy population. The largest contributing factor appears to be the economic aspect of the pricing structure. Another factor, however, is the biological constraints that affect milk production; namely the heritabilities and genetic correlations between traits. Table 1 (Jeffries et al. unpublished MS) shows the heritabilities, genetic correlations and phenotypic correlations for milk production traits. Table 1. Heritabilities (diagonal) genetic correlations (below diagonal) and phenotypic correlations (above diagonal) for milk production traits. Milk Skim Carrier Fat Protein Fat (%) Protein (%) Milk 0.26 1.00 1.00 0.74 0.89 -0.26 -0.33 Skim 0.99 0.26 1.00 0.72 0.88 -0.29 -0.34 Carrier 0.99 1.00 0.27 0.71 0.87 -0.30 -0.36 Fat 0.54 0.50 0.49 0.34 0.79 0.45 0.02 Protein 0.70 0.68 0.66 0.81 0.27 -0.04 0.12 Fat (%) 0.31 -0.34 -0.36 0.64 0.27 0.57 0.49 Protein (%) -0.42 -0.45 -0.40 0.32 0.35 0.75 0.73 A negative phenotypic correlation (relationship of observed values) between lactation milk yield and fat percentage of approximately -0.20 is generally accepted (Taylor and Van Home 1962). A similar relationship of the same magnitude exists for the SNF portion (-0.18). A positive genetic correlation between yield and protein is shown to be 0.70, with a phenotypic correlation of 0.89. The phenotypic and geno-typic correlations between fat and all other milk constituents are shown to be - 9 -positive, which means that an increase in protein and SNF will accompany an increase in fat by selection, whether this is desirable or not. The result is that pro-ducers cannot select for one milk component without an observed change in the other. Both the genetic goals and the biological constraints can affect the genetic gains made in a population. Several studies have evaluated genetic gains among dairy populations in Canada and the US to detenriine the effects of selection on milk con-stituents. Verde et al. (1972) reported a negative genetic trend of -0.034% fat per year among Florida Holsteins, while Powell and Freeman (1974) found a positive genetic trend for milk yield and a negative trend for percent fat in mid-western US Holsteins. In a comparison between Dairy Herd Analysis Service (DHAS) herds and the general population in Quebec, Kennedy and Moxley (1975) reported small nega-tive genetic trends for fat-test; -0.003% and -0.004% for the DHAS and general populations respectively. Protein showed annual genetic trends of -0.008% and -0.014% for the DHAS and the general populations respectively. The genetic merit of sampled Al-sires with respect to percent protein declined an average of 0.031% per year. As protein information has only recently been available in Quebec, no selection for protein percent could be direct. This indicates that even the high posi-tive genetic correlation between fat and protein percentage (Gaunt 1973) was not sufficient to prevent the depression in protein-test. A similar study by McColl and Peterson (unpublished MS) estimated some genetic trends in BC Holsteins. The percent-fat and percent-protein changes were estimated to be 0.0098% and -0.0014%. The extent to which testing for milk protein (introduced by the BCDHIA in 1968) has affected milk protein in BC is not clear. There appears to be a very slight selec-tion against milk protein by producers, but this is essentially zero. - 10 -Although there has been concern over the declining protein percentage, protein yield has itself increased due to the increase in total milk yield realized in Canada. Because of the large manufacturing milk industry in Quebec and Ontario, Canada has experienced a surplus of protein, which in the form of skim milk powder, is sold at a loss on the world market. Grueble (1979) has postulated that the skim milk problem is a dislocation of resources, and that standards for fluid milk should be increased to absorb the excess SNF and improve palatability. In order to raise standards of products and allow a more equitable payment to producers, all-component pricing of milk has been established in a few parts of the world. California introduced component-pricing of milk in 1962 to increase stan-dards for fat and SNF in low fat milk. Grueble (1979) has attributed the higher stan-dards in fluid products under component pricing to the increased per capita Class 1 sales from 1971 to 1978 in California. Since 1979 the California standards have been set at a rninimum of 12.2% total solids in whole milk, where the minimum milk fat is 3.4% and minimum SNF content is 8.6%. For 2% milk, milk fat solids must lie between 1.9% and 2.1%, and SNF must be 10%; skim milk must contain 0.25% milk fat and 9% SNF. These standards exceed the US federal government standards and result in less excess butter and powder being made. In 1977, if California had been on federal standards, Grueble estimated that they would have made 7.5% more butter (11.7 million pounds) and 12% more powder (21 million pounds), and this would have been marketed by the government at a loss. California producers believe that the higher standards for fluid products under component pricing have led to increased per capita Class I sales in the 1970s. A similar claim has been made by Zurborg (1978), based on the experience of a Mississippi co-op which implemented a protein differential to improve palatability and yields for manufactured products. On hard cheeses, Zurborg reports an average yield increase of 2 to 2.5 pounds of finished -11 -product for each additional pound of protein in the raw milk. In the case of cottage cheese manufacturing, each extra pound of protein resulted in approximately six extra pounds of cottage cheese. In another study, Lebaron and Brog (1968) reported higher yields for powdered milk and cheese from milk with higher percentages of SNF. For example, for each 0.1% increase in SNF, powdered milk yields rose by 0.1 lb; cheddar cheese yields increased by 0.14 lb for each 0.1% increase in protein in milk. Redelmeier (1983) found that for the past 20 years, most milk in Holland has been purchased from farmers based on a weighted combination of fat and protein. The weights given to fat relative to protein, were in the 66:33 range during the 1960s, and changed to 60:40 in the mid 1970s. The weighting factors change from region to region depending on the end-product use of the milk; the highest being 5.70:5.35 (fat:protein). A negative base price has been introduced in the Netherlands, where the cow which produces the most solids is the most profitable. In Canada, Ontario has employed a butterfat differential providing for SNF since the early 1970s (Gould 1984a). Rather than actually measuring SNF or protein, the system assumes a fixed relationship between SNF and fat. For every 0.1% increase in butterfat, they assume an increase of 0.045% in SNF, as increases in butter yield also imply a higher skim milk powder yield. Gould (1984b) points out that the but-terfat component accounts for 81.7% of the butterfat differential and the non-fat solids accounts for the remaining 18.3%. Under this method, producers receive the true value of the milk they produce only if that milk has the average ratio of SNF to butterfat. The butterfat differential used in July 1984 was $0.5977/0.1 kg, and this included approximately $0.13 for SNF. - 12 -However, one disadvantage that processors with higher rninimum standards face is the possibility of receiving milk below the rninimum SNF standard which they must then fortify with SNF, thus putting them at a possible cost disadvantage. Grue-ble (1979) has pointed out that producers can increase their SNF test by increasing the protein in the feed. Schultz (1973) and Rook (1976) note that decreasing the par-ticle size of dietary roughage and increasing soluble carbohydrate depressed milk fat content and increased milk protein due to the increased uptake of propionic acid. Emery (1978) found that milk protein increases 0.02% for each 1% increase of dietary crude protein. This practice, however, has not been demonstrated to be economically efficient. Graf (1973) cites further reasons for component pricing as being the increased market-value of SNF relative to fat, and a shift of consumer preference to low fat products. He also points out that a reliable SNF test using the lactometer, the infrared milk analyser (to test for protein, fat and lactose) and the Mojonnier are inexpensive. Zurborg (1978) discussed the changes in commodity values in the US over the period 1950-1975. The increase in values of non-fat dry milk and skim milk in the US both exceeded 500%, whereas the value of butter and fluid milk-fat increased only 14% and 4% respectively. Johnson (1975) also considered the sharp rise in value of water-nonfat solids mixture relative to the fat. In a ten year period from 1965-1975, non-fat dry milk value rose from $0.15/lb to $0.60/lb, whereas butterfat rose from $0.10 to $0.59/lb. The effect of component pricing systems on producer-income has been studied by Hillers et al. (1970, 1980) and by Jacobson and Walker (1973). Hillers et al. - 13 -(1970) evaluated seventeen systems which included different values for fat, protein, SNF and water. Each system was constrained to distribute a fixed sum of money for the total pool of milk. Mamtaining a fat differential of 8.3 cents and adding value to either SNF or protein favoured producers of milk with high fat-test; lowering the fat differential to either 6.5 cents or 4.5 cents, and adding value to SNF favoured pro-ducers of milk with low fat-test. Placing a differential on protein, and lowering the fat-differential to 6.5 cents favoured producers of high fat. Systems with a fat-differential of 4.5 cents, and lower values for protein favoured producers of milk with low fat-test. In a later study Hillers et al. (1980) evaluated three pricing-systems, including fat-only, fat-protein and the Froker-Hardin system, in which producers are paid on fat percentage, utilising a regression of protein percentage on fat percentage to compen-sate producers for expected differences in protein content. Significant differences in payment occurred between the Froker-Hardin system and the fat-protein system for milk from different producers containing the same fat content because of differences in protein content This suggests that the Froker-Hardin system may cause economic errors. Jacobson and Walker (1973) discussed the Jack relationship (Jack 1957) between butterfat and SNF (measured in percent) in milk where: SNF = 7.07 + OMBF This equation assumes that for a given amount of milk-solids, 30% will be fat and 70% will be SNF, and is similar to the assumed relationship incorporated in the Ontario differential scheme. It assumes that a butterfat differential will accurately - 14 -reward the producer, and that all farmers produce the average relationship of SNF to BF. Jacobson and Walker (1973) argue that in commonly used butterfat differential pricing, the SNF and water differentials are not considered, and milk is treated as though it had the same content of SNF and water. They introduced a BF, SNF and water pricing-plan, where water is determined by: BF + SNF + W = 100 The individual producer-price per hundredweight (Pm) for milk of any test could then be determined by: P„ = Pb + PbJ(BF - 3.5) + P^SNF - 8.63) + PJIO0 - BF - SNF) - 87.87 = Pb + (Pbf~ PJ(BF - 3.5) + ( * V - PW){SNF - 8.3) where Pb is the blend price for milk containing, in this example, 3.5% BF, 8.63% SNF, and 87.87% water. Pw is determined as a residual price after the value of but-terfat and SNF have been determined and subtracted from the total value of the milk. Jacobson and Walker conclude that implementation of this plan would solve the equity problem in producer payments, but that the problem of which value to apply to the components remains unresolved. Fallen (1980) points out that the demand for fluid milk by consumers is rela-tively inelastic. That is, the percentage change in the quantities of rnilk taken in response to percentage increases or decreases in price is small relative to the percen-tage change in price. He also states that the demand for soft dairy products such as yogurt, is more elastic than for fluid, and that demand for hard products such as cheese, is more elastic still. Brog (1969) maintains that since the demand for rnilk products is largely a function of price, the price of rnilk contained in manufactured - 15 -dairy products should be directly related to the value of the milk components plus other non-dairy additives used in their production. In hopes of discovering a milk accounting system capable of quantifying the cost of milk components in consumer packages, Brog examined milk-pricing models and milk supply. He points out the difficulty of pricing complexes containing more than one entity within a single price. For example, the effect of the lumping of lactose and minerals is recognized as a potential loss in pricing efficiency. His work attempted to make quantitative esti-mates of the pricing efficiency of six selected milk pricing systems using an "academic" tri-component model as the optimum standard. The component values selected as pricing indices for all models were derived from the retail market values of butter, cheese and edible whey powder. After considering manufacturing and marketing costs, the ratios of the retail values were used to establish the value of the components in producer's milk. Based on an r2 value of 0.993, the fat-protein model was judged superior in its explanatory ability, as it possessed the optimal capability of aligning the value of fat and protein in the producer's milk with the value of these two components in the consumer-packaged dairy products. By the choice of equations deterniining the value of cheese and whey-powder, Brog assumed that the two protein fractions, soluble and insoluble, were equal in value. This is not necessarily true, but the procedure was justified by stating that the two proteins are found in a relatively constant ratio in the cow's milk, allowing one to price the two proteins as a single entity. Brunner (1981) characterized the proper-ties of the important proteins, noting that the caseins account for 75-85% of milk proteins. cc-Sl- and <x-S2-casein account for 39-46% and 8-11% respectively, while B-casein accounts for 25-35% of total protein. K-casein accounts for 8-15%, and y-casein for 3-7%. The remainder of the rnilk proteins (15-22%) are found to be whey proteins, namely B-lactoglobulin, a-lactalbumin, serum albumin and finally, - 16 -immunoglobulins (1.9-3.3%). The proteins themselves contain numerous genetic polymorphs, and can be distinguished by molecular weight, amino acid residues, and factors such as the sensitivity to calcium ions. Based on this information, it does not seem wise to assume that proteins will be found in a constant ratio in cow's rnilk. Ng-Kwai-Hang et al. (1984) have shown that of the different milk proteins, the casein fraction is the most important in deterrnining the yield of manufactured products. Their study showed that 97% of Holsteins produced a-Sl-casein, and that this form of casein is associated with higher milk and fat yields They point out that cows that produced higher amounts of K-casein and p-lactoglobulin produced higher protein content The yields of manufactured products using milk with the correct forms of casein were much higher than those with the incorrect composition. The potential effect of protein and fat pricing on milk prices for the five major US dairy breeds was evaluated by Smith and Snyder (1978). Given varying protein and fat differentials, they attempted to evaluate the percentage of herds that would "lose or gain" within each breed. Jersey herds experienced gains at all ranges, fol-lowed by small losses in Guernsey, Brown Swiss and Ayrshire breeds. The Holstein herds accounting for 90% of the US dairy cattle population, experienced predom-inantly large losses up to 77%. Smith and Snyder expect owners of Holstein herds to be skeptical of payment plans which include differentials in addition to fat, especially SNF. They maintain that testing for protein-only is necessary as it is more accurate and less expensive than testing for SNF. Alternately, they point out that one advan-tage of basing differentials on SNF rather than protein is that a definite price for non-fat dry milk powder is established in the national market - 17 -Johnson (1975) asserts that non-fat solids can be valued more precisely, since they are an identifiable dairy product, whereas protein is not. He maintains that pro-tein is not separable from milk, as is fat, and cannot be removed from its low-value use and transferred to a high-value use. Hence, the highest market value in its low-value use tends to set the upper limit for a common differential for all uses. In the future it may be possible to utilize protein in a more cost-effective manner. Mem-brane filtration units which segregate protein are used in Europe. This technique would allow the industry to channel protein away from low value products such as skim milk powder, and utilize it in high value products such as cheese. Lactose is also generally ignored even though its concentration in milk is larger than that of fat or protein, and although it contributes directly to the yield of non-fat dry milk, and to the palatability of fluid milk (Wahid-ul-Hamid 1960). Small varia-tions in lactose content, and the utilization and marketing problems that it has presented as a major constituent of whey, explain the insignificance of lactose as a price-detennining component of milk. Hillers et al. (1980) further studied the value of fat and protein, asserting that the economic value of a solids component of milk should be a function of net returns from products in which the milk solids are used. They divided manufacturing costs into fixed (those that remain constant regardless of solids) and variable costs (those that change with the solids content of milk). Fixed costs, in $/100 kg milk, included factors such as transportation, processing and labour, and packaging. They calculated the economic value of changing either the fat or protein content of milk by 0.1% as the difference in net returns. These were computed by comparing net returns from two levels of fat and protein content in standard yield formula, and applying current market-prices and costs of processing. - 18 -Hillers et al. state that the economic value of the fat and protein components of milk is a function of the prices of the manufactured products into which they are made, the influence of each component on product yields, and different manufactur-ing costs associated with the manufactured product. The values of a 0.1% increase in the protein content in 100 kg of milk used to manufacture hard cheese, non-fat dry milk and cottage cheese were $0.30, $0.14 and $0.45 respectively. The values of a 0.1% increase in the fat content in 100 kg of milk used to manufacture hard cheese and butter were $0.36 and $0.24. Hillers et al. concluded that values of this nature could be used in a multiple-component plan by weighting each value by the proportion of the milk supply used for that product Ladd and Dunn (1979) considered the effect on plant profits of an increase in protein test in milk. They argued against methods of calculating the value of the marginal product assuming that the increased product costs nothing to produce. They developed a procedure for measuring protein premium, first by considering the firm's revenues, costs and profits; then considering the effect upon the firm's profits of vari-ation in its total receipt of protein. This effect is converted into a measure of the effect upon profits, of variation in protein test, to determine the maximum premium that the firm can afford to pay for milk that has a higher protein test without reducing its profits. Application of differential calculus results in a complete accounting for all effects of a change in one variable. This is useful when computing the total change in three variables, and in deterrnining the proportion of the total change which can be accounted for by variation in the first two variables. An important question when designing a selection scheme is to determine how much emphasis to put on selection for protein or SNF percentages. Kelso (1979) - 19 -feels that dairymen should continue to select for milk yield with only enough emphasis in the components to prevent dropping below minimum market standards. Hardie (1978) has suggested that selection for fat or protein percentage decreases rnilk yields, and that selection for milk yield after one generation should result in 50 to 90% of the genetic gain from direct selection for yields of fat, protein and solids-not-faL Van Vleck (1978) recommends ignoring percentage values under the present scheme, and selecting for dollar value, which correctly considers fat percentage, milk yield and SNF percentage, with the proper emphasis on each. Selection Index Theory The selection index (I) that is widely used in plant and animal breeding, refers to a linear, weighted combination of observed measurements that is used to calculate a criterion for selection and genetic gain. The first description of the use of the selection index in plant breeding was by Smith (1936), and was first applied to ariimal breeding by Hazel (1943). According to formulae established by Hazel and Lush (1942), selection for an index which gives proper weight to each trait is more efficient than selection for one trait at a time, or for several traits with an indepen-dent culling level for each trait. Many studies have utilized the selection-index procedure to perform several different functions. Legates and Lush (1954) used a single trait selection index for butterfat production in dairy cattle using fat yields of the individual cow and her close relatives. Young and Tallis (1961) used an index to select for lifetime produc-tion, which has been termed the "Performance Index," while Van Vleck (1970,1976) - 20 -expanded the index procedure to select for traits, each having direct maternal and grandmaternal genetic traits. Hazel first discussed the construction of an index in relation to the relative economic values of several traits which have economic importance. It was suggested that the gain made for each trait y be weighted by the relative economic value of the trait a H = + CC2Y2 + • • • + anyn The relative economic value for each trait depends upon the amount by which profit may be expected to increase for each unit of improvement in that trait, and is defined as the partial regression of H, the aggregate index, on y. Relative economic values can be obtained from longtime price averages and cost of production figures. These have been estimated in two ways: direct economic analysis of a production system (Hogsett and Norskog 1958), or by a multiple regression analysis by regress-ing estimates of profit on phenotypic traits (Andrus and McGilliard 1975). The usual difficulty with the regression analysis method is that the relative economic weights vary depending on how profit is defined, the number of traits considered, and the sampling variability. Lin (1978) postulates that a certain degree of variation in economic weights will not change expected response very much and Brim (1959) found that the expected genetic gain was also little affected by changes in price ratios. Usually changes in economic values signify a change in net merit, the selec-tion goal, thereby reducing the overall selection gains, which is a major deterrent to genetic progress from index selection; however, several authors (Pearse et al. 1967; Vandepitte and Hazel 1977; Smith 1983) have reported that the efficiency of index selection is not sensitive to changes in the economic weights. Large changes, - 21 -(±200%) in some traits resulted in losses of efficiency. Changes in efficiency of selection depend on traits or groups of traits that dominate the index. Smith con-cluded that fine tuning of economic weights will not improve index selection. This is reassuring, since change by selection is a long term process, and a stable set of selec-tion objectives is required for improvement to occur. The selection index I can be defined as: I = + P2*2 + • • • + P„*» Where I is the selection index prediction of true genetic value, (often the additive genetic value), the x's represent phenotypic performance for the traits, and the p's represent the weights, or multiple regression coefficients. Van Vleck (1974) pointed out the desirable properties of the p values: to use the selection index to predict some true value T, the weights should rnmimize the expected squared difference between T and its predictor I, and maximize the correla-tion between the true values of T and I. The regression coefficients can then be cal-culated from n simultaneous equations where: pioi, + faa^ + • • • CesxJ + P»o v. = Cax2T • • • + P„< = CaxJ - 2 2 -with a constant C which does not affect the relative sizes of the p's: C = o I^/aH = 1 These equations are similar to multiple regression equations with the exception that the true variances and covariances are assumed known, and replace the sums of squares and products used in multiple regression. The usual methods of interclass and intraclass correlations are used to calculate the phenotypic covariance (ax^ and variance (oi.), but the covariance (axT) is the true covariance between xt and T which cannot be measured directly, and which must therefore be estimated indirectly. T is the portion of the genetic covariance between relatives which is due to additive genetic effects in common between the relatives, and is estimated by a . c c o i o , where a , is the additive relationship between the relative with record x, and the individual under evaluation and ofo is the additive genetic variance. When we redefine T to select for other values, for example additive plus dominance variance, the right hand sides must be redefined. The usual procedure (Van Vleck 1974) for calculating I from the economic values is to calculate the relative economic values of standard deviation units, and by setting up the right hand side, solve for the p values directly. If V/ is the economic value per standard deviation of trait i, then T = + + V 'G f = / ' = P i ' v i + pYy 2 + • • • + P » ' y » where Therefore - 23 -° * P i ' + ay^' + • • • + < * „ * P « '= <sy\T O^PY + <p2' + ••• + <xWllpV= qy2r < ^ , P i ' + o^k' + • • • + o?J3,. = oy»r Lin (1978) expanded the general selection index procedure of Henderson (1963). The selection index I and the aggregate genotype H are defined by Lin as: I = f p * = x ' P t=i H = fc«i = g'a where: x' = (XU *2> ' ' ' » xm) a' = ( a j , otj, • • • , a „ ) g' = (gl> 8l> " -  'in) P ' = < P l . P * ••• ,PJ where x ' , a', g' and P ' are the row vectors of m known phenotypic values, n known relative economic values, n unknown genetic values and m index coefficients, respec-tively. The following relationships exist from the above definitions: oi = p-pp c& = aTa, O m = P'Ga where Var(x) = P, the mxm phenotypic variance-covariance matrix; Var{g) = F, the n x n genetic variance-covariance matrix; and Cov(x,g) = G, the mxn genetic covariance matrix between the phenotypic values in I and the genotypic values in H, the - 24 -aggregate genotype. If m = n, then G and F are identical. The correlation between I and H is: = p"Ga  r m VpTp VaTFa Maximizing log rlH is equivalent to rnaximizing rlH. Thus rm = log(P'Ga) - -jlogCpTR) - |log(aTa) and the maximum likelihood of p is given by 3 logr™ i i i 1 -Ga- ^ — i — 2 Pp = 0 9P P'Ga 2 pTp Pb = Ga P'Ga The scalar pTp/p'Ga can be dropped without affecting the proportionality of the p/s. This means that Pp*=Ga are the index equations which have solutions p=P~1Ga. When the vector p is a solution the following statistical properities exist (Van Vleck 1974): °"IH = Pra = ^nV^i = 1 rm = CWO-ICTH = oi/a^H = oyaH Jeffries et al. (unpublished MS) addressed the problem of calculating economic weights in an index including yields of whole milk, fat and protein. The weights were previously difficult to calculate, as increases in whole milk due to selection also increase the yields of fat and protein due to correlated responses (Taylor and Van Home 1962). The appropriate economic weights for fat and protein apply only to increases or decreases in the yield of these components in relation to the result obtained by selecting for whole milk. The economic weights for fat and protein - 25 -would be constant and not change with selection, however, the weights for whole rnilk change with response to selection, since the relative proportions of fat and pro-tein in the whole rnilk change. If fat and protein have values different from the car-rier portion of the milk then the value of whole milk changes due to selection, and a constant economic weight is not appropriate. Jeffries et al. proposed that milk be expressed in terms of fat- and protein-free milk (carrier). An index of carrier, fat and protein can then be defined with constant economic weights for each variable. Then the decision to select for whole milk alone, or use an index of carrier and one or more constituents, depends on the dollar returns for each alternative, where: in which p,- is the row vector of selection index weights pertaining to base milk (m), fat(f) and protein (p), and X, is the vector of the phenotypic expression of each trait. Estimates of ft (Henderson 1963) are obtained ft = P - ' G K where P and G are phenotypic and genotypic variance-covariance matrices, and K is a column vector of economic weights. Using economic weights relative to base rnilk, and setting Xf and KP to 1.0, the response to whole rnilk and to carrier, fat and protein can be evaluated. Williams (1962a) has suggested the use of a base index in which the economic weights are used directly as the index weights, instead of the index being computed from the estimated parameters. This suggestion was expected to counteract the effect of errors in the parameter estimates and the loss of efficiency in terms of the size of sample used for estimation. This scheme has been further considered by Williams (1962a, 1962b), Harris (1964) and Sales and Hill (1976a, 1976b). For two variables, Williams showed that unless progress from the optimal index is substantially greater -26-than that from the base index, there is a high probability that the estimated index will yield a poorer response than the base index. He concluded that the base index should be used unless a large amount of data is available for parameter estimation. When the selection index has been constructed, several useful properties arise (Lin 1978). When selection is on I, the genetic gain in H due to truncation selection is given by AH = p f f l ( L - V = ^ i = R I H L C T H in which Ty. and I, are the mean index values for the population and the selected indi-viduals, and i~is the selection intensity factor, ie: The genetic gain in H is proportional to rm, which reaches a maximum when B = P~!Ga. The genetic gain in the i'th index trait due to selection on I is: AG1 = BG;Io;-T(J = g<'B(^ CTI) where g', is a row vector of genetic covariances between the i'th trait and each com-ponent trait incorporated in the index. In matrix notation this is expressed A = G8(i7cri) where A is a column vector of genetic gains corresponding to each trait of the index. AH can be expressed as: = a'GB^ CTx) = ZciiAG, Therefore, AH is a linear combination of genetic gains in the index trait, each - 27 -weighted by its relative economic weight The column vector of genetic gains, A, can be expressed as A = Gp, as Hal is a scalar constant. Based on this property, it has been suggested (Peterson 1984, pers. commun.) that this may be a useful measure of the genetic goals of the population. Lin (1978) and Young (1961) have suggested that the efficiency of index selec-tion may increase by dropping a trait in the index, even though it is an economically important trait. Tallis (1962) and Lin (1978) have discussed the use of the restricted selection index to optimize genetic gains in some traits while holding others constant. By setting unit increases and decreases in some traits while holding others constant, the index coefficients can be derived by p = G _ 1 A , where A is a column vector of units of gain. Lin has pointed out that this is an easy method as the phenotypic variances, covariances and relative economic values are not needed, but the genetic changes can be adjusted by substituting the a values for A in the equation. Morley (1955) and Abplanalp (1963) developed a backward solution to the res-tricted selection index for the special case in which the breeder wants to improve one trait and hold another constant The index coefficients can be derived from p = G. An index can be derived which bypasses the problems of estimating the relative economic values and phenotypic variance-covariance parameters. However, the genetic change in each trait can be regulated according to its relative economic value by substituting a for p in the above expression. Although it usually is assumed that an individual's merit can be expressed as a linear combination of values weighted by relative economic values, some traits are functions of other traits and are best expressed as nonlinear functions. Smith (1967) transformed data on composite traits such as feed efficiency to a logarithmic scale, so - 28 -that the effect of the component traits was linear. In this case, genetic and pheno-typic parameters were also estimated on a logarithmic scale. Kempthorne and Norskog (1959) have recommended using squared traits as a new variable to account for non-linear situations, as well as cubic, quadratic, and higher powers. Selection indices are also often derived in retrospect after the conclusion of selection. The retrospective index weights can be obtained from p = P^ A*, where A* is a column vector of phenotypic gains in each index trait. With the retrospective index determined, the aggregate genotype in retrospect can be determined by A* = Pp* = Go' Hence, a* = G^ A* = G^PP* where a is a vector of relative economic values in retrospect (Van Vleck 1974). - 29 -METHODS AND MATERIALS Gross Value of Skim Milk and Butterfat (k values) The method used to study the problem of fluctuating selection goals was to first calculate the gross dollar value of a kilogram of skim milk and a kilogram of butter-fat, as dictated by the producer milk price. These values were later used to calculate the economic weights by subtracting the cost of production of each component. In this case the dollar value of skim included the protein fraction. To calculate the gross value of skim and fat ( * i and k2), it was necessary to solve a system of simul-taneous equations with two unknowns (Peterson 1979, unpublished MS). Utilizing these equations it was possible to convert the milk price from a dollars/hectalitre ($/hl) basis with a butterfat differential expressed in $/0.10 kg to a price per kilogram of skim milk and butterfat The butterfat differential is the price added to or sub-tracted from the price per hectalitre based on a tenth of a kilogram of butterfat above or below the standard; in this case 3.6 kilograms of butterfat/hi. Using a specific gravity for milk of 1.032 (which is only true for typical milk and changes, for example, as the proportion of fat or other components change), milk volumes were converted from hectalitres to kilograms for the equations given in Table 2. The right hand sides of the equations give the price paid for a hectalitre of milk with 3.6 and 3.7 kg fat/hl, and the constants on the left are the kilogram of skim and fat in a hectalitre of milk. - 30 -Table 2. Equations to calculate ky and k2. 99.6*1 + 3.6/fej = base price + d2 (3.6 - 3.6) x 10 99.5*i + 3.7*2 = base price + d2 (3.7 - 3.6) x 10 Parameter Units base price $/hl 1 hi 103.2 kg *i Dollar value of skim/kg *2 Dollar value of fat/kg dt butterfat differential; d2 = 0.1*2 - 0.l*i, which represents the value of sub-stituting 0.1 kg of fat for 0.1 kg of skim Prices Used to Calculate the Value of Skim Milk and Butterfat British Columbia Milk Prices The base prices used were the monthly weighted average of quota and excess prices paid over the twenty year period from 1963-1982. The weighted average price is calculated from the accounting value of each class of milk, multi-plied by the utilization in hectalitres. These were totaled and the pool charge deducted, including handling and transportation costs. To calculate a weighted aver-age price per hectalitre, the total value is divided by the total number of hectalitres utilized. - 31 -The BC rnilk prices were abstracted from the BC Milkboard Annual Reports, 1963-1982. Three areas of BC were originally used for the study: Vancouver Island, BC Mainland area and Kamloops (until 1975 when the Kamloops area prices were eliminated). Thorpe (1984) has stated that because of the initiation of Dairy Income Assurance the government amalgamated the regions of Kamloops and Vancouver area. The butterfat differentials were abstracted from the BC Milkboard Annual Report and other unpublished Milkboard records, as butterfat differentials were not always published in the annual reports. The butterfat differentials were calculated from the Federal Government Support Price for butter/kg. Currently, for every one-tenth of a kilogram that a producer's raw milk shipments is above or below the stan-dard 3.6 kg fat/100 litres, one tenth of the support price is added or subtracted accordingly. However, from January 1963 to May 1968, qualifying milk was paid for based on 100 lbs of qualifying milk of 4% butterfat. In May 1968 the rnilk price was changed to 3.5% butterfat standard. Finally, in January 1977, the milk price was changed to a standard of 3.6 kg of butterfat per 100 litres (hi), thus eliminating the percentage differential figure. BC milk prices were changed from dollars per hun-dred pounds to dollars per hectalitres in January 1977. In this study, prices prior to 1977 were converted to $/hl by multiplying the $/100wt by 2.27008, while butterfat differentials were converted to $/kg by multiplying the $/lb price by 2.204. Quebec Milk Prices Quebec milk prices (1971-1982) were obtained from Cansim Statistics Canada files. Producer prices for fluid and manufacturing milk were obtained from the Farm Income and Prices section, Agriculture Statistics Division, Statistics Canada. It is - 32 -assumed that shipping and handling charges for milk are already removed, as reported in BC Quota and Excess Prices. The standard butterfat percentage for Que-bec was 3.5% up until 1964; following this it changed to 3.4% from 1964-1978. From 1978-1980, the differential was 3.5%, and changed to 3.6 kg/hi when the metric system became effective in 1980. Fluid prices paid to Quebec dairy producers are calculated by a provincial board (the Quebec Agricultural Marketing Board) through a formula which evaluates the cost for each factor of production and adds them to obtain a production cost. Value in 100 kg Milk The monthly dollar/kg values of skim (*i) and fat (*2) were multiplied by their average proportions in whole milk; 96.4% and 3.6% for skim and fat respectively. These values were used to evaluate the contribution of skim and fat to the value of 100 kg of whole milk over time. Net Economic Values Economic values are generally difficult to compute since increases in whole milk due to selection include increases of fat and protein due to correlated responses. Therefore carrier was considered to be a more useful component of a selection index than whole milk (Jeffries et al. 1980, unpublished MS), where: kg carrier = kg wholemilk - kg fat - kg protein In this study, by eliminating the part/whole relationship and expressing milk yields in terms of fat and protein-free milk (carrier), this problem was eliminated. The cost of production figures were subtracted to obtain the net economic weights. - 33 -Factors Used to Calculate the Cost of Production Metabolizable Energy Requirements To calculate the net economic values of the three components, several costs of production were calculated, using an estimate of the metabolizable energy (ME) requirements necessary to produce milk. Based on estimates by Hillers et al. (1979), the metabolizable energy required to produce rnilk constituents are given in Table 3. Table 3. Metabolizable energy requirements. 1 kg fat 16.3 Meal ME 1 kg protein 8.5 Meal ME 1 kg lactose 6.6 Meal ME 1 kg water and minerals 0.0 Meal ME Feed Ratios In this study the feed costs for producing each component were calculated by utilizing a changing ratio of roughage to concentrate in the ration. Goertzen (1983) has suggested that in the 1960s farmers in the Fraser Valley were feeding essentially no grain in the summer and minimal grain in the winter (approximately 10 pounds per day). This would result in a 75:25 roughage to concentrate ratio. He has stated that farmers began to feed more concentrates in the early 1970s, after MSQ (Market Share Quota) was introduced, resulting in a 60:40 ratio. Goertzen also indicated that -34-high rnilk producing cows are today being fed 20-22 lbs of concentrate per day; or one half of their ration (50:50 ratio). By incorporating these three estimates of the ration components, a curve was generated by the UNIX spline utility program, pro-ducing an estimated monthly roughagexoncentrate ratio for the period 1963-1982. The spline method allows the smooth interpolation of points between supplied values, and is based on the calculation of a continuous derivative of a curve which passes through the supplied data points. Hay and Feed Prices The BC hay (roughage) prices were abstracted from the BC Milkboard Annual Report from 1963-1982. Prior to June 1977 dairy feed prices reported in imperial Tons were converted to metric Tonnes by multiplying by 1.01605. Prior to November 1970 hay prices were reported as local and alfalfa hay. As dairy producers began utilizing more imported alfalfa hay, these prices were changed to the price of imported alfalfa hay in November 1970. Dairy feed prices (16% protein) were abstracted from the BC Milkboard Annual Report until May 1973, when feed price listings were changed to an index of dairy feed utilizing a Statistics Canada Index for BC. For the period 1973-1982, prices of 14-16% protein dairy feed were obtained from Grain Facts, a publication of the Canadian Livestock Feed Board. Feed prices for Quebec were abstracted from Grain Facts 1970-1982 and the Canadian Livestock Feed Board Annual Report, 1963-1969. Quebec hay prices were collected from Sta-tistiques Agricoles du Quebec, 1963-1982. Production Cost Calculation Costs for Production of an additional kilogram of each milk constituent were - 35 -calculated using the following parameters: 1. A roughage (hay) to concentrate (dairy feed) ratio ranging from 75:25 to 50:50. 2. Roughage in $/kg @ 2.20 Meal ME/kg (NRC 1978). 3. Concentrate in $/kg @ 3.00 Meal ME/kg (NRC 1978). 4. Cost of complete ration/tonne: $ CRITonne =(roughage fraction/tonne ration) x ($lkg roughage) + (concentrate fraction!tonne ration) x ($/kg concentrate) 5. Cost of complete ration/kg: $ CRIkg = ($CRITonne)ll000 6. To calculate the cost of a complete ration in Meal ME: A = $IMcal ME A = ($ CRIkg)!(Meal ME/kg CR) 7. The cost of production for each kilogram of component, assuming 10% feed was-tage and a constant percentage of lactose/kg of carrier (5.36%) is: a. Carrier milk/kg: (0% Fat, 0% Protein, 5.36% Lactose) $ cost/kg = 1.1 xAx (0.0536 x 6.6) - 36 -b. Fat/kg: $ cost/kg = 1.1 xAx 16J c. Protein/kg: $ cost/kg = 1.1 xAx8J Economic Value Calculation A monthly vector of economic values (al5 a^, 0 3 ) were calculated by: Net economic value of component = Gross value - Cost of production Where: Cost/kg carrier (aj) = k{ - cost/kg carrier Cost/kg fat (02 ) = *2 - cost/kg fat Cost/kg protein (a3) = kx — cost/kg protein Since it does not have a differential payment, protein does not have any gross value in the rnilk price. Therefore, the value of protein was assumed to have the same low value as carrier. The cost of production was subtracted from the value of carrier to compute an economic value for protein. Relative Economic Values To view the change in relative economic values of the three components, the value of carrier and protein were expressed relative to fat by: - 37 -Ctj/Oj = relative economic value of carrier to fat 0(2/02 = relative economic value of fat relative to fat = 1.0 0 3 / 0 2 = relative economic value of protein relative to fat Selection Index Weights The monthly selection index weights that were applied to each of the com-ponents were calculated (Henderson 1963) by: B, = p-'Ga where G is a genetic variance/covariance matrix; a is a column vector of relative economic values relating to carrier, fat and protein; P"1 is the inverse of the phenotypic variance/covariance matrix; and Bf- is a row vector of selection index weights relating to carrier, fat and protein. The coefficients of the nxn P matrix of phenotypic variances and covariances for carrier, fat and protein, as calculated by Jeffries et al. (1980, Unpublished MS) are given in Table 4. The inverse of the P matrix was calculated utilizing UBC SYMSOL. It was useful to use an inverse as the value of the economic weights changed monthly but the pheno-typic matrix did not As P and G are full rank, P"1 and G - 1 are uniquely defined by P and G. To complete the calculation, the two square matrices G and P~ l were multi-plied utilizing MULT, a subroutine of UBC Matrix. The product matrix was - 38 -Table 4. Phenotypic variance-covariance matrix. Carrier Fat Protein Carrier 579984.08 16858.83 16386.09 Fat 16858.83 963.26 599.53 Protein 16386.09 599.53 601.14 multiplied by the monthly a vectors to obtain the vectors of p values (Pi, p2, p3); the selection index weights of carrier, fat and protein respectively. Relative Selection weights The p values were expressed relative to one component (butterfat) in order to view the relative selection pressure which has been exerted on the milk components over time. Where P1/P2 = relative selection weight on carrier relative to fat P 2 / P 2 = relative selection weight on fat relative to fat P3/P2 = relative selection weight on protein relative to fat Genetic Goals of Selection Program The genetic goals of the selection program which the industry indirectly set through the milk price were calculated by (Lin 1978): - 39 -A=GS in which A is a vector of genetic goals for carrier, fat and protein; B is a vector of selection index weights for carrier, fat and protein, and G is an nxn matrix of genetic variances and covariances for carrier, fat and protein as shown in Table 5. Table 5. Genotypic variance-covariance matrix. Carrier Fat Protein Carrier 155601.31 3510.98 3355.80 Fat 3510.98 330.95 188.43 Protein 3355.80 188.43 164.27 The diagonal elements represent the genetic variances of carrier, fat and protein in the BC dairy population, and the off-diagonals are genetic covariances. These were estimated from first lactation records of BC Dairy Herd Improvement herds. The presumed genetic goals of the selection program were calculated for carrier, fat and protein by multiplying the G matrix by the column vector of monthly selec-tion weights (B x, B2, B 3) utilizing MATVEC, a subroutine of UBC MATRIX. This routine solves the three simultaneous equations and optimizes the profitability of the equation at each economic weight. By multiplying the economic values by the G matrix the values are weighted by the variance and covariance of the trait. Assuming that the variance/covariance matrix is constant, and that only the economic weights change over time, the presumed goals of selection can be estimated. The genetic - 40 -goals were scaled into percentages of the sum of the three goals. The same analysis was performed on the Quebec data, and since no variance/covariance matrix for carrier, fat and protein was available from the litera-ture for the Quebec data, it was assumed that the variances and covariances were the same as BC's. However, there is evidence to indicate that dairy populations vary somewhat in their genotypic and phenotypic variances. Everett (1985, pers. com-mun.) has found that Eastern US dairy herds show genetic variances ( kg2) for milk, fat and protein of 242451, 356 and 200 respectively. In comparison, BC herds show similar genetic variances: 330.95 and 164.27 for fat and protein (Table 5). Although the variances are similar at the present, this similarity may not have existed in the early years of this study, therefore the Quebec data should be interpreted cautiously. - 41 -RESULTS AND DISCUSSION Weighted Average Price of Milk The weighted average producer prices of qualifying rnilk in BC and Quebec are shown in Figure 1. Yearly averages of these data are given in Appendix A. BC pro-ducers have received a consistently higher price for their milk over the 20 year period shown. This is largely the result of BC producing a much higher percentage of its milk for the fluid industry than Quebec, and receiving a higher price for its fluid than manufacturing milk. Quebec producers have, however, received a con-sistently higher butterfat differential than BC producers, which would partly serve to offset the differences in prices received. In general, Quebec producers have lower costs of inputs than BC producers: 1979 Statistics Canada figures indicate that the value of farm capital per farm in Quebec was $125,000; including $15,000 for land and building, $25,000 for machinery and equipment and $24,000 for livestock. The same farm in BC was estimated to cost $243,000 due to a $198,000 land and build-ing cost, and in 1980, the land value in BC was $902/acre, compared to only $466 in Quebec. Costs of farm inputs have risen faster in BC than Quebec, in particular fac-tors such as seed, grain and fluid quota. Cost of Hay and Dairy Concentrate Feed As the cost of hay and feed was the highest variable cost utilized in the calcula-tion of economic values, it was important to evaluate the effect of fluctuating feed prices on the economic values for carrier, fat and protein. Yearly averages of dairy feed costs are given in Appendix B. In general, dairy feed costs, shown in Figure 2 and Figure 3, were consistently higher in Quebec than BC, reflecting higher shipping costs to Quebec. Traditionally almost all eastern grains are moved to the Eastern Terminal by water (Canadian Livestock Feed Board 1969). -42-Figure 1. The weighted average producer prices ($/hl) of qualifying milk produced in BC and Quebec, 1963-1982. a or U J o_ < _ i _ i O Q 50 40 30 H 20 10 r* • Q 6 •/ / A/ P • ' • O O : P 0 O ° o 0 o o -o o o o o 1963 ' 1965 1967 1969 1971 ' 1973 ' 1975 1977 ' 1979 1981' 1983 oo PROVINCES • BC O QUEBEC YEARS -44-Figure 2. The price of alfalfa hay and 16% protein dairy feed ($/Tonne) in BC, 1963-1982. 250-i LU 200 O CrT 150 cr U J 0 _ in cr < 100 o -a . o Q O : o . • o 0 o Q o ° o o o P o o Q 50 o . o i • -•rm-*-m-J o 1963 ' 1965 ' 1967 ' 1969 ' 1971 ' 1973 ' 1975 ' 1977 ' 1979 ' 1981 ' 1983 COMPONENT • ALFALFA  O CONCENTRATE YEARS -46-Figure 3. The price of alfalfa hay and 16% protein dairy feed ($/Tonne) in Quebec, 1963-1982. 250 200 o o cn 150 LY. U J Q_ CO < 100 •O o o o o o . o v o . p . o o o 0 o Q 50-o o ° o o o - 0 ° 0 ° ° ' • • • • COMPONENT • ALFALFA  O CONCENTRATE 0 H — i — i — i — i — i — i — \ — i — \ — i — i — \ — i — i — i i i i i i 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 YEARS -48 -Dairy concentrate (14-16% protein) prices in the early 1960s were quite con-sistent in BC and Quebec and fluctuated around a price of $60/Tonne, while BC hay prices, at $45/Tonne rose slightly faster than those in Quebec. Domestic prices of grains were low in the early 1970s following record North American feed grain pro-duction. Both feed and hay prices rose dramatically during the crop year of 1972-1973 (Canadian Livestock Feed Board Annual Report, 1973). Prices of Canadian feed grains doubled during the year and ingredient costs rose by 250%, resulting in much higher feed costs for livestock producers. The high costs were a result of several suc-cesive problems on the world market. Grain became scarce with a shortfall of grain production in Russia, China, India and Australia. Coupled with these supply shor-tages was the failure of the Peruvian fishing industry due to warm water temperatures and overfishing. Peru had previously provided a large proportion of the world's livestock protein needs, and the loss of the Peruvian fishmeal led to a heavy demand for soybean meal. This factor contributed to raising the price of soybean meal to approximately $470/Tonne; nearly 4 times higher than in August 1972. Another factor which contributed to the rise in North American prices was the international currency alignment and the instability of the dollar. The devaluation of the US dollar affected the Canadian dollar and made Canadian products appear inex-pensive. In 1974 the average feed prices in Canada were still double those of 1973, but prices of protein ingredients declined sharply to one-third of those in 1973. Dairy feed prices continued to climb in 1974, partly due to cumulative increases in the costs of minor components such as urea. - 49 -Hay prices also rose sharply in 1972-1973 following severe winter weather and drought. BC livestock producers faced a shortage of forage crops during the 1973-74 winter, and similar shortages in Washington State reduced the import of Alfalfa hay from Washington. To assist producers trying to obtain hay, the BC government paid a transportation subsidy of up to $15/ton on hay shipped from the Peace River and Alberta. To further stabilize the livestock industry, the BC government implemented Farm Income Assurance in 1973. The plan called for producer and government con-tributions to a fund from which payments were made to producers when market returns fell below a specific level. Quebec feed prices began to increase more rapidly than BC prices during 1974-1975. Because of labour problems, deliveries of feed grains to the eastern market were continually disrupted. Rail rates increased by $0.12/100 lbs to Quebec, and shipping rates from the Prairies to BC increased by 20% in July 1975. Following production increases in all areas, hay prices began to level off in 1975. Canadian feed grain prices decreased in 1976-1979, reflecting a downward trend of world grain prices and an adjustment to levels which were competitive with US corn. In 1979-1981, after several bumper crop years, Canadian grain production dropped sharply, especially in the Prairies, resulting in price increases. Value of Skim and Fat Within BC The gross value of skim ($/kg) between the milk producing regions of BC, namely Vancouver (Lower Mainland), Kamloops and Vancouver Island can be seen in Figure 4. The value of skim in Vancouver Island has been consistently higher than that of Kamloops (shown only until 1975) and Vancouver. This is largely due -50-Figure 4. The value of skim ($/kg) in Vancouver, Kamloops and Vancouver Island, 1963-1975. 0.20 < LY O O _J ^ LY UJ Q_ GO LY < _ J _ l o 0.15 H 0.10 0.05 0.00 i i 1 1 \ 1 1 1 1 r 1963 1965 1967 1969 1971 1972 — i ; 1 1974 1975 REGION • KAMLOOPS O VANISLAND X VANCOUVER YEARS - 52 -to a higher weighted average milk price received on Vancouver Island, which in turn results from a higher utilization of their Class I milk. For example, in 1982 the weighted average price received by Vancouver Island farmers was consistently $3-4/hl higher than the Vancouver price, resulting in a higher value of skim than the Lower Mainland. Vancouver Island farmers also have higher costs of transportation of feed and other supplies, which are felt to be barely covered by the higher price. The value of skim in Kamloops was virtually identical to the value of skim in the Vancouver area. As discussed previously, Kamloops area prices were discontinued in 1975. Therefore, Figure 5 shows only the value in the Vancouver Island area and Vancouver area from 1975-1982. The value of skim was higher in the Vancouver Island area in this period. For the remainder of this study, only Vancouver prices will be used when referring to British Columbia. Value of Skim in BC and Quebec Figure 6 shows that the gross value of skim (these k values are reported in Appendix C) in BC has been consistendy higher than Quebec throughout the 20 year period, reflecting a higher milk price and lower butterfat differential. This is consistent with the hypothesis that a manufacturing-oriented industry such as Quebec would put less emphasis on the skim portion of their milk than a fluid-oriented industry. In 1980 in BC, the value of 1 kg of skim was approximately $0.30, whereas a kilogram of skim in Quebec was worth only $0.20. Value of Fat in BC and Quebec Figure 7 shows the value of butterfat/kg in Quebec and BC. Early in the 1960s there were observable differences between the two provinces, as Quebec had a much -53-Figure 5. The value of skim ($/kg) in Vancouver and Vancouver Island, 1975-1982. 0.45 0.40 < § 0.35 O cr U J Q_ tn cr < _ J _ i o 0.30 0.25 0.20 H o • O Q/ O 0 O o • o. 0.15 -| 1 1 — i 1 1 1 r 1975 1976 1977 1978 1979 1980 1981 1982 1983 REGION • VANISLAND O VANCOUVER YEARS -55-Figure 6. The value of skim ($/kg) in BC and Quebec; 1963-1982. 0.35-1 0.30 < 0.25 OH O O ^ 0.20 CC Ld CL (/) 0.15-| cr < O 0.10 Q • o O o Q, O # 7 6 ° O 0.05 Q' o.oo 4 o o o o o o o 0 o i i r i i i i 1 1 1 1 1 1 1 1 1 1 1 1 1 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 PROVINCE • BC O QUEBEC YEARS -57-Figure 7. The value of butterfat ($/kg) in BC and Quebec; 1963-1982. OJ of o J o o 0 o o .o o o o o o o o o o Jo o • • •-• i H i i i i i i i i i \ i T — i — T — i — i — i — i — i — I 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 PROVINCE • B C _ O QUEBEC YEARS -59-higher initial value of fat than BC: $1.50 versus $1.10/kg respectively. The value in 1966 and 1967 rose to $2.00/kg and then dropped to $1.50/kg. From 1973-83 the value of fat rose in a linear fashion in both provinces, from $1.50/kg to $4.75/kg. The reason for the similar trends in value of butterfat is due to the butterfat differentials in the provinces. Quebec paid a much higher butterfat differential than BC in the early 1960s, but the margin has since narrowed, and Quebec now pays only slightly more than BC for its butterfat. Change in Value of Skim and Fat in 100 kg of Milk Figure 8 shows the change in the value of fat and skim in 100 kg of average milk (96.4% skim, 3.6% fat) over time in BC (Appendix D). The value of skim and fat were similar in the 1960s, both contributing about one half of the total milk price; $6 and $4 respectively. The value of butterfat rose slowly during 1973-1982 from $6.62 to $16.12/100kg of milk. The value of skim fluctuated in the 1960s, but rose sharply in the early 1970s as large increases in milk prices, with a corresponding lower increase in the value of butterfat, caused the value of skim to double from 1973-1975 and to rise to a high of $27.95/100 kg of milk in 1982. The value of skim at this time was more than double the value of butterfat as represented by the milk price and the relative amounts of the two components. This means that BC dairy producers were being paid $10/100kg in 1963, while in 1982 the same producer was receiving $44/100 kg, of which $28 was for skim and $16 for butterfat Two thirds of the rnilk price in 1982 is represented by skim, which is mostly water but also contains protein and lactose, while one third is represented by fat. Given that the metabolic cost of production of fat is much higher than skim, it is difficult to support a system which puts such a high value on water and a low value on solids. These findings are consistent with changes in commodity values discussed by -60-Figure 8. The change in value of butterfat and skim in 100 kg of average milk (96.4% skim, 3.6% fat) in BC, 1963-1982. o o 30 n 25 20 3 »• < 10 A O Q hr o o o o o 5 *^ V# ~ ~ o' o o o o o o O O O o o o . o o o 0 COMPONENTS • SKIM O BUTTERFAT I 1 1 1 1 1 1 1 1 1 1 I I I I I I I I 1 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 YEARS - 62 -Zurborg (1978), who reported a 500% increase in the value of skim rnilk over a 25 year period, while the value of butter and butterfat increased only 14% and 4% respectively. The companion to Figure 8, Figure 9 shows the change in value of fat and skim in 100 kg of milk in Quebec. The value of skim in 100 kg was low in Quebec ($0.96) through the early 1960s, and began to rise sharply in the 1970s. The value of skim in 100 kg of milk doubled between 1970 and 1971 and then declined to approximately $ll/100kg in 1977. It then continued to increase up to a value of $21.20/100 kg in 1982. The value of butterfat in Quebec was initially much higher ($6/100 kg) than that of skim, and represented approximately 86% of the milk price in 1963. The value of butterfat did not increase, and fell to about 50% of the rnilk price by 1972. After 1974, butterfat made small gains to a high of $16.27/100 kg in 1982. Due to a lower weighted average price for whole milk, butterfat represented only 43% of the value of 100 kg of milk in 1982. Quebec dairy producers still receive a large proportion of their milk cheques from the value of butterfat in the milk. As the average ratio of fluid to industrial milk produced by Quebec farmers is 78% MSQ and 22% fluid (Federation des Producteurs dii lait du Quebec 1983), it can be seen that the Quebec dairy industry continues to place a higher value on solids relative to BC. Net Economic Values Net economic values were calculated by subtracting the dollar cost of produc-tion associated with producing carrier, fat and protein. The cost of maintaining the cow was not considered, as it is not possible to partition the cost of maintenance into the three rnilk components. Therefore the production costs were adjusted based on a -63-Figure 9. The change in value of butterfat and skim in 100 kg of average rnilk (96.4% skim, 3.6% fat) in Quebec, 1963-1982. 30 - I O 25 20 3 o-CH < _j 10 H o -4> v r ° o 0 o o-5 H 0 o o .o o o o O O O O , ,• p o o • • • • COMPONENTS • SKIM O BUTTERFAT o H — i — i — - i — i — i — i — i — i — i — i — i — i — i — i — i i i i i i 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 YEARS - 65 -change in ration composition and on a changing hay and concentrate feed price. The cost of hay comprised approximately 75% of the ration in the early 1960s, and this lead to low costs of production and consequently higher economic values. As the ration composition approached 50% concentrate in the late 1970s, the cost of produc-tion increased sharply. Butterfat has the highest cost of production per kilogram, since it has a higher metabolic cost associated with it (16.3 MCal ME/kg). As pro-tein is ignored in the price structure, it has a value equal to carrier. In this study the value of protein was determined by setting the value of protein to the value of carrier and then subtracting the production costs. Therefore, the gross value of protein is always tied to the value of carrier. As the economic value of carrier grew along with the increasing importance of water in the rnilk price, the economic value of protein decreased, since there was no protein differential associated with the rnilk price. Fig-ures 10 and 11 (Appendix E) show the net economic values of carrier, fat and protein in BC and Quebec. The value of carrier in BC has been consistently higher than in Quebec. The value of carrier in Quebec was essentially zero until the 1970s, when its value increased to a high of $0.15/kg in 1978. This can be explained by observ-ing Figure 6, which shows the change in the value of skim in Quebec. Although representing over 95% of the content of milk, the value of skim was very low, and represented less than one fifth of the value of 100 kg of milk. Because of the associ-ated metabolic cost of production, and higher feed costs in Quebec, a negligible economic value was the result. In BC, the value of fat was low in the 1960s (less than $1.00/kg), but had doubled by 1978. In Quebec, the value of fat represented essentially 100% of the value of milk until the 1970s. The value of fat still remains higher than in BC, presumably due to Quebec's large manufacturing industry. Both BC and Quebec's milk pricing systems have resulted in negative economic values for protein throughout the study period; ranging from -$0.21/kg to -$0.41/kg. From this data it appears that the economic values of the solid component of milk are not -66-Figure 10. The net economic value ($/kg) of carrier, butterfat and protein in BC, 1963-1982. 4-i < or: O O _ j cr Ld o_ GO cr: < o O ,0 o o o o o ° • o o o o o o o. o 6 0 0 0 x — * — * — X — X - — X — X — X — X - - X — x . * - - X - x ^ * ^ x - ~ * COMPONENT • CARRIER  O FAT X PROTEIN _•) _| ! j ( ! ( j j ( ! ( ( ( ( ^ ( } ( ( ( ( 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 YEARS -68-Figure 11. The net economic value ($/kg) of carrier, butterfat and protein in Que-bec, 1963-1982. 4 3H < LY O o LY UJ 0_ CO LY < o O o o "O" o •o o ;0-0 6 o o o o o ° o o o . o o 0 x — x — * — X — X — X — x ~ x — x — x _ - 1 1 i i i i i 1 r — — i 1 1 1 1 1 i i i i r i i 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 COMPONENT • CARRIER  O FAT x PROTEIN YEARS - 70 -related to the net returns from the products in which they are used (Hillers et al. 1980). Currently there is no economic benefit to either the BC or Quebec dairy pro-ducer for selecting for protein, and this study estimates that producers will pay $0.33/kg and $0.41/kg in respective production costs to produce protein. Under this pricing system (Kelso 1979), dairymen should select for milk yield with only enough emphasis on butterfat to prevent dropping below rninimum market standards. Relative Economic Values of Components The relative economic values of carrier, fat and protein in BC are shown in Fig-ure 12. The values of carrier and protein have been computed relative to the value of fat, which is assigned a constant value of 1.0. The relative economic value of each component depends upon the amount by which profit (ie., the marginal return above variable costs) may be expected to increase for each unit of improvement in the component. The relative economic values for carrier and fat in BC have under-gone little change during the study period (Appendix F). In 1963 fat was approxi-mately twelve times more valuable than carrier (0.08:1.00); identical to its relative value in 1982. Carrier rose in relative value in the 1970s, but otherwise has remained quite constant in relation to butterfat. Protein, while still having a negative value, increased in value relative to fat. Again, this can be viewed as the result of a consistently lower dollar value for butterfat and an increased dollar value for skim, of which carrier forms the major component. The relative economic values of the three components in Quebec can be seen in Figure 13. The value of fat relative to carrier ranged from fat being 100 times more valuable than carrier in 1967, to 10 times more valuable in 1976. The relative value of protein was generally related to the value of skim and the relative cost of protein. The relative economic values in BC -71-Figure 12. The relative economic values (butterfat = 1.00) of carrier, butterfat and protein in BC, 1963-1982. 1.5 - i 1-6 O O O O O O O O O O O O O O O - O O - O O O 00 > _ J U J cr 0 . 5 H 0 - 0 . 5 COMPONENT 9 CARRIER  O FAT X PROTEIN -1 -| i i | 1 1 r~—I 1 1 1 1 1 1 1 1 1 1 I I I 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 YEARS -73-Figure 13. The relative economic values (butterfat = 1.00) of carrier, butterfat and protein in Quebec; 1963-1982. 1.5-1-6 O O O O O O O O O O O O O O o o o o o o CO I— •=2_ 0.5 Ld > Ld DC 0 X- .x—x- /X— -0.5 -X_ X ^ X V COMPONENT e CARRIER  O FAT * PROTEIN -1 ~ l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 YEARS - 75 -and Quebec in 1982 were 0.08:1.0:-0.10 and 0.06:1.00:-0.12 respectively. This shows that the relative economic values appear virtually identical, but are quite different if the percentage of each component in milk is accounted for. These figures show weights which differ dramatically from those of the Holland pricing scheme (Redelmeier 1983), in which the fatprotein weighting factors are as high as 5.7:5.35. The actual effect of changes in relative economic values upon longterm selec-tion is unresolved. Smith (1983) has reported that the efficiency of index selection is not sensitive to changes in economic weights, although large changes (± 200%) in some traits may result in a loss in efficiency. Over the study period changes of this magnitude have occurred in the value of carrier and fat, signifying a change in selec-tion goals. These changes may have resulted in a reduction in overall selection gains among BC and Quebec dairy populations. Selection Index Weights of Components The results of the selection index weights (p values) for carrier, fat and protein in BC can be observed in Figure 14. These selection weights can be used to weight observed measurements in a selection index I, and calculate criteria for selection and genetic gain. In this situation, the selection weights are those which should have been used if perfect information were available. Therefore the p values calculated are similar to a vector of retrospective index weights. For example, based on this study, the selection index which would have been applied to the BC dairy population in 1963 was: / = 0.016X! + 0.235x2 + -0.283*3 where xu x^ and x^ are the respective phenotypic values for carrier, fat and protein. These index weights put a low weight on carrier, a positive weight on fat and -76-Figure 14. The selection index weights for carrier, butterfat and protein in BC, 1963-1982. 1.5 O .0 Q :0 •o- O' CO \— 3Z O O h-o U J _ i U J CO 0.5 o t G O 0 -0.5 0 ° o O O O o O; 0... o - H -1.5 A "~1 I I I I I I I I 1 1 1 1 1 1 1 1 1 1 I 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 COMPONENT • CARRIER  O FAT X PROTEIN YEARS - 78 -negative weight on protein. This index remained quite stable until 1973, when the selection pressure for carrier and against protein began to increase. The BC dairy industry has always applied a positive selection pressure on the fat portion of the milk, and this pressure increased after 1975. The selection pressure on carrier has also been consistently positive and has increased over the 20 year period. The weight on protein has been negative, and increased sharply after 1972. The selection index in 1982 approximated: / = 0.087*! + 1.253x2 + -1.189x3 The results of the selection index weights for carrier, fat and protein in Quebec are shown in Figure 15. Quebec had a fairly constant positive selection weight for butterfat until 1977, after which the selection for butterfat increased sharply. In con-trast to the BC situation, Quebec exerted a positive selection pressure on protein in the period 1963-1970. This is the period when the genetic goals for protein in Que-bec exceeded 4%. Carrier experienced negative selection pressure until 1969, when the value began to increase. The selection against protein experienced in the Quebec dairy industry was not as strong as in BC over the study period, but fluctuated widely due to a varying pressure on the carrier portion. The selection index pertaining to Quebec in 1963 was: / = -0.012*! + 0.427x2 + O.I86X3 By 1982 the index weights had changed dramatically to an index of: / = 0.050*! + 1.280x2 + -0.657x3 This index is similar to the BC index, with the exception that a cow producing high solids would still fare better in the Quebec industry than the BC dairy industry. In general, the Quebec industry showed more fluctuation than its BC counterpart. It appears from these figures that the trend of decreasing selection against protein may -79-Figure 15. The selection index weights for carrier, butterfat and protein in Quebec, 1963-1982. 1.5 H CO h— o o h-o Ld _ i Ld CO 0.5 O o o o o o o o id o o o o o o o 0 o o o -0 .5 -H -1.5 7\ I I I I I I I I I I 1—r~i 1 | i i ~T r I I 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 COMPONENT • CARRIER  O FAT X PROTEIN YEARS - 81 -be levelling off in both provinces. The selection against protein has fluctuated in Quebec since 1976, but has remained fairly constant in BC. It is possible that an increasing commitment to solids in BC may alter the selection weights for solids over the next few years. Genetic Goals of Components Figure 16 (Appendix H) shows the the genetic goals for fat and protein in BC, as estimated by the selection weights of each component. The genetic goals were calculated by multiplying the genetic variance/covariance matrix by a monthly vector of selection weights to arrive at a monthly goal for the three components which the industry was indirectly asking of producers. The g vector was scaled to yield percen-tage figures. In essence, if the industry had perfect knowledge, these are the values that they would have published as their goals. The goal for butterfat in BC shows some surprising trends. In 1963 the goal was 3.14%, and by 1966 increased to 4.58% due to qualifying milk being paid for based on 4% butterfat. The goals for butterfat have fluctuated widely, and are a reflection of a change in the butterfat differential without a corresponding increase in the total milk price. In 1974, when prices of feed inputs escalated, the goal for fat decreased to 2.25%, reflecting an even stronger pressure on the carrier portion of rnilk. After 1975 the goal for fat increased slowly to a goal of 3.36% fat in 1982. It seems clear that the fluctuation of the theoretical goals for butterfat would lead to a loss in genetic progress. It is also pos-sible that the higher theoretical goal of 3.36% in 1982 shows an increased commit-ment to milk solids due to the expansion of the dairy manufacturing industry in BC. The goal of protein has also changed somewhat over the 20 year study period. This goal in 1963 was 2.06% protein, and increased to 2.84% in 1966. As the -82-Figure 16. The theoretical genetic goals for butterfat and protein in BC, 1963-1982. 6-i YEARS - 84 -genetic variance/covariance matrix is constant, the protein line shows very similar trends to the fat line. The goal for protein decreased to a low of 1.62% in 1974 and increased to a high of 2.25% in 1982, reflecting a slowly increasing trend to solids in BC. Although large fluctuations have occurred during the study period, the goals for protein appear to have stabilized in BC since 1978. These data agree with values reported by McColl et al. (1982, Unpublished MS), who found a negligible change in genetic gain for fat and protein in BC over a 10 year period. This conclusion is supported by the fairly constant genetic goals shown in Figure 16. The genetic goals for fat and protein in Quebec are shown in Figure 17. The genetic goals prior to 1972 are not reported here, as it is thought that the variance/covariance matrix used for this study may not pertain to Quebec during this period, resulting in goals that were biologically unlikely for dairy cattle. In 1973 the goal for fat in Quebec was 3.78%, compared to 3.01% in BC. The decreasing com-mitment to fat in Quebec can be seen as the goal dropped to 2.58% in 1974, and continued to decline until 1976. From 1978-1980, the butterfat differential was changed to 3.5%. The goal for fat did not sink to as low a level as BC during the critical price increases of 1973-1975, and recovered quickly in 1977 to a goal of 4.53%. After 1975 the goal for butterfat levelled off at value greater than 4%. The goals for protein have also shown dramatic changes over the 20 year period, and generally follow the trends shown by fat. In Quebec, the genetic goals for protein were approximately 2.38% in 1973 and dropped below 2% until 1977, when they recovered to a high of 2.82%. These findings are consistent with those of Kennedy and Moxley (1975), who reported negative genetic trends for fat- and protein-test in DHAS and the Quebec dairy population in general. The goal for pro-tein remained fairly constant at 2.4-2.8% during the 1977-1982 period. Although the -85-Figure 17. The theoretical genetic goal for butterfat and protein in Quebec, 1972-1982. 6-i COMPONENT • FAT A PROTEIN H —I I I | 1 -j | 1 1 1 , 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 YEARS - 87 -Quebec dairy industry is shrinking, and losing a small percentage of the market share quota (MSQ) per year, their $600 million dairy industry appears to have main-tained a stronger commitment to milk solids compared to BC as reflected in the rnilk pricing structure. Due to large dairy cooperatives such as Agropur, which holds 60% of the entire cheese market in Canada, it is likely that the actual goals for solids will remain higher than those of BC in the future. The genetic goal for carrier in BC can be observed in Figure 18. In 1966 the goal fell to 92.58%, indicating an increasing commitment to solids via the milk price and butterfat differential. The goal has fluctuated widely over short intervals of time, creating a problem in goal setting from the dairy producer and animal breeder's point of view. It increased steadily from 92.58% carrier to a high of 96.13% in 1974, indi-cating a genetic goal of only 3.87% fat and protein. The goal for carrier remained fairly constant for the remainder of the study period. The goal for carrier in Quebec is shown in Figure 19. It is interesting to note that the goals for carrier in Quebec have more fluctuations over short periods of time compared to BC, but that Quebec has remained consistent in its goals for carrier since 1977. Use of Genetic Goals to Set Prices The merit of this study lies in pointing out some inconsistencies of milk pricing systems such as the one in BC, which continues to place a high value on carrier and a low value on protein and butterfat. This study also pointed out the very real prob-lem of fluctuating genetic goals for rnilk constituents. A practical application of these results would be to approach the milk pricing system from a preconceived goal -88-Figure 18. The theoretical genetic goal for carrier in BC, 1963-1982. YEARS -90-Figure 19. The theoretical genetic goal for carrier in Quebec, 1972-1982. 97-i u~1 i 1 1 1 1 1 1 1 1 1 1 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 YEARS - 92 -mutually agreed upon by industry and breeders. The goal for selection would be cal-culated from long-term averages of production on dairy products and projected pro-duction figures and by calculating the percent carrier, fat and protein needed in each product. Once the goals were agreed upon, the vector of selection weights and rela-tive selection weights used in a selection programme could be calculated. From these, a vector of economic values, used to set prices in a multiple component pricing scheme could also be calculated. For example, assume the industry desires rnilk which is 94.45% carrier, 3.32% fat and 2.23% protein:1 g = Gp = (94.45, 3.32, 2.23) Therefore P = G"'g Using G"1 from the Methods and Materials section, p = (5.943, 8.389, -8.188) P«to,« = (0.07084, 1.0, -0.97610) Since PP = Ga and a = G_1Pp Therefore a = (1.818, 2.188, -2.300) This vector of economic values or relative economic values could be used to guide the producer toward the desired goal for milk production in the industry. It is impor-tant that the genetic goals for milk are expressed publicly and that the pricing system reflects these goals. The industry should reevaluate its goals for milk every five to 1 I am indebted to R.G. Peterson for this example ten years. - 93 --94-SUMMARY This study evaluated the effect of British Columbia and Quebec's milk pricing system upon several parameters relating to genetic selection. Based on an introduc-tory study by Peterson (1980), the hypothesis was that the selection goals of the dairy population would change dramatically when the milk price or butterfat differential was changed, as this would alter the relative emphasis that producers would put on the milk components. BC and Quebec were chosen for comparison because BC pro-ducers supply milk primarily for fluid consumption, while Quebec produces milk for a large manufacturing industry. To calculate the effect which the milk pricing system had upon genetic goals, several parameters were first estimated. Within BC, the value of fat and skim in different milk producing areas was evaluated. Due to a higher weighted average pro-ducer price, the value of skim on Vancouver Island was found to be consistently higher that the value of skim in the Lower Mainland. Given the higher cost of tran-sportation of feed and other supplies to Vancouver Island, it was felt that the net values were not actually different between these two areas, and the remainder of the study evaluated from BC and Quebec only. The results indicated that the small but-terfat differentials paid in BC and Quebec place a heavy emphasis on the skim por-tion and less on the butterfat portion of milk. Due to higher overall weighted aver-age rnilk prices, the BC pricing system placed more emphasis on the skim portion than Quebec. Observing the change in value of fat and skim in 100 kg of average milk (96.4% skim and 3.6% fat) proved a useful method of evaluating trends. For example, in BC, approximately one half of the price of milk in the early 1960s was represented by skim; the other half by butterfat. By 1982, two thirds of the price was accounted for by skim, and one third by butterfat. Due to a lower weighted average price paid for whole milk in Quebec, butter still represented 43% of the - 95 -value of 100 kg of milk in 1982, and it is clear that the Quebec milk pricing system puts more emphasis on the solids portion of rnilk than BC. To calculate the net, or economic value of milk components as represented by the rnilk price, cost of production calculations were utilized. The cost of production calculation accounted for changes in the concentrate:roughage ratio and changes in feed prices in the two provinces. Given both increases in feed and hay prices and in the concentrate:roughage ratio, the production costs increased over time. The costs of production were calculated in MCal ME/kg, multiplied by the metabolic cost of production of each component, and subtracted from the gross value to arrive at the economic value. Feed costs were generally higher in Quebec; resulting in higher costs of production. As protein has no gross value in the milk price, but does have an economic cost of production, there resulted a negative economic value for protein in BC and Quebec. Currently there is is no economic benefit to either BC or Quebec producers for selecting for protein, and this study estimates that in 1982 BC and Quebec producers paid $0.33/kg and $0.41/kg in respective production costs to pro-duce protein. Both BC and Quebec now place more relative emphasis on protein that in the early 1970s. In 1982, the relative economic values of milk components in BC and Quebec were 0.08:1.00:-0.10 and 0.06:1.00:-0.12 respectively, which places a moderate value on carrier and fat and a negative value on protein. This emphasis may not be appropriate in Quebec, as milk with a higher proportion of solids requires less energy (transportation, drying, cooling, separation) and labour costs to process each unit of end product, compared to BC (Hillers et al. 1978). Since 1977, the relative economic weights have remained fairly constant, due to small changes in ration composition, feed prices and rnilk prices. However, a large change in any of the components would change the relative emphasis dramatically. -96-The selection index weights, which would be used in a selection index in order to calculate selection criteria, were also shown to fluctuate in both provinces. In this study, the selection weights are those which would have been used if perfect infor-mation were available. The BC dairy industry has always applied positive selection pressure on the carrier and fat portion of milk and increasingly negative pressure on the protein portion. In contrast, the Quebec industry placed positive selection pres-sure on protein in the early 1960s, but dropped sharply after 1977. In 1982 the selection weights in BC and Quebec were similar, with the exception that BC has more negative selection on protein and lower selection on fat compared to Quebec. This means that a cow producing higher solids would be evaluated higher under the Quebec index. These selection weights were used to calculate the theoretical genetic goals of the dairy industry; that is, the type of milk that the market is indirectly requesting through its milk price. In BC, the goals for carrier, fat and protein have signaled to produce high amounts of carrier and low levels of fat and protein. In 1982, the goals were 94.39% carrier, 3.36% fat and 2.25% protein. The goals for Quebec producers signaled to increase both butterfat and protein. In BC and Quebec the goals for solids varied widely over the study period, indicating that the industry has not clearly denned its goals to dairy producers. If these were the actual goals desired by the dairy industry, the large fluctuations experienced from year to year would be unreal-istic to apply to dairy populations. A practical application of these results would be to develop important lines of communication between industry and breeders, and to develop genetic goals in each province which would account for current and pro-jected needs of the market. From these goals a set of selection weights could be developed to use in a selection program, and a set of economic values developed and used to price milk components. Component pricing of milk, per se, does not provide - 97 -direction to dairy producers unless translated into a multiple trait selection scheme. The problem of deciding which values to apply to milk components will remain unresolved until the industry calculates the value of the components in dairy pro-ducts, and arrives at a genetic goal for its selection programs. - 98 -APPENDICES - 99 -Appendix A. Y e a r l y w e i g h t e d a v e r a g e s o f r n i l k p r i c e s i n $ / h l , a n d b u t t e r f a t d i f f e r e n t i a l s i n $ / k g . BRITISH COLUMBIA QUEBEC Milk differential Milk differential $/hl $/kg $/hl $/kg 1963 10.37 0.11 7.01 0.16 1964 10.45 0.11 7.29 0.16 1965 11.21 0.12 7.64 0.17 1966 11.97 0.15 7.72 0.19 1967 12.72 0.14 8.20 0.17 1968 12.52 0.14 8.30 0.16 1969 12.78 0.14 8.50 0.16 1970 13.15 0.14 8.74 0.16 1971 13.70 0.14 10.44 0.16 1972 14.83 0.14 11.99 0.16 1973 17.46 0.17 14.22 0.17 1974 22.26 0.19 18.80 0.19 1975 25.65 0.21 22.41 0.20 1976 28.08 0.23 21.20 0.20 1977 29.82 0.26 22.32 0.27 1978 31.16 0.27 28.20 0.28 1979 34.15 0.30 29.09 0.34 1980 38.60 0.33 31.11 0.36 1981 42.13 0.38 35.26 0.40 1982 45.45 0.42 38.08 0.43 - 100 -Appendix B. Yearly averages of the price of hay and dairy concen-trate (16% protein) in $/tonne. BRITISH COLUMBIA QUEBEC Hay Concentrate Hay Concentrate $/tonne $/tonne $/tonne $/toime 1963 49.61 76.91 45.10 76.91 1964 48.68 73.09 45.71 73.09 1965 49.84 74.47 44.79 74.47 1966 53.68 78.72 44.79 78.72 1967 58.28 81.11 50.16 81.11 1968 60.50 82.61 45.32 82.61 1969 82.60 80.41 40.62 80.20 1970 62.17 83.56 40.96 83.80 1971 60.90 88.09 48.95 85.89 1972 69.08 88.83 51.41 84.79 1973 91.79 123.38 61.68 120.08 1974 125.77 151.62 125.77 159.50 1975 118.63 155.29 118.63 163.19 1976 120.50 155.58 120.50 160.42 1977 119.27 152.82 119.27 158.33 1978 111.35 138.92 111.35 159.67 1979 135.82 149.92 135.82 185.17 1980 176.19 177.00 176.19 214.17 1981 156.98 214.08 156.98 241.92 1982 148.75 199.30 148.75 229.42 - 101 -Appendix C. Yearly averages of gross values of skim milk and but-terfat (k values) in $/kg. BRITISH COLUMBIA QUEBEC Skim $/kg Fat $/kg Skim $/kg Fat $/kg 1963 0.06 1.16 0.01 1.61 1964 0.06 1.16 0.01 1.61 1965 0.07 1.24 0.01 1.76 1966 0.06 1.53 0.01 1.91 1967 0.07 1.52 0.02 1.70 1968 0.07 1.47 0.03 1.60 1969 0.07 .1.47 0.03 1.63 1970 0.08 1.48 0.03 1.63 1971 0.08 1.48 0.05 1.65 1972 0.09 1.49 0.06 1.66 1973 0.11 1.84 0.08 1.76 1974 0.15 2.05 0.12 1.98 1975 0.18 2.28 0.15 2.15 1976 0.19 2.52 0.13 2.17 1977 0.20 2.77 0.12 2.82 1978 0.21 2.91 0.17 3.01 1979 0.23 3.26 0.16 3.54 1980 0.26 3.58 0.18 3.80 1981 0.28 4.08 0.20 4.19 1982 0.29 4.48 0.22 4.52 - 102 -Appendix D. Y e a r l y a v e r a g e s o f the c h a n g e i n v a l u e o f s k i m a n d f a t i n 100 k i l o g r a m s o f m i l k . BRITISH COLUMBIA QUEBEC S k i m Fat Total S k i m Fat Total $/100 kg $/100 kg $/100 kg $/100 kg $/100kg $/100kg 1963 5.78 4.17 9.95 0.96 5.79 6.75 1964 5.78 4.16 9.95 0.96 5.79 6.75 1965 6.74 4.46 11.20 0.96 6.33 7.29 1966 5.78 5.50 11.28 0.96 6.87 7.83 1967 6.74 5.47 12.21 1.92 6.12 8.04 1968 6.74 5.29 12.03 2.89 5.76 8.65 1969 6.74 5.29 12.03 2.89 s 5.86 8.76 1970 7.71 5.32 13.03 2.89 5.86 8.76 1971 7.71 5.32 13.03 4.82 5.94 10.76 1972 8.67 5.36 14.04 5.78 5.97 11.75 1973 10.60 6.62 17.22 7.71 6.33 14.04 1974 14.46 7.38 21.84 11.56 7.12 18.68 1975 17.35 8.20 25.56 14.46 7.74 22.20 1976 18.31 9.07 27.38 12.53 7.81 20.34 1977 19.28 9.97 29.25 11.56 10.15 21.71 1978 20.24 10.47 30.71 16.39 10.83 27.22 1979 22.17 11.73 33.90 15.42 12.74 28.16 1980 25.06 12.88 37.94 17.35 13.68 31.03 1981 26.99 14.68 41.67 19.28 15.08 34.36 1982 27.95 16.12 44.07 21.20 16.27 37.47 - 103 -Appendix E. Y e a r l y a v e r a g e s o f net e c o n o m i c v a l u e s o f m i l k c o m p o n e n t s ( a v a l u e s ) i n $ / k g . BRITISH COLUMBIA QUEBEC Carrier Fat Protein Carrier Fat Protein $/kg $/kg $/kg $/kg $/kg $/kg 1963 0.05 0.64 -0.21 0.00 1.09 -0.26 1964 0.05 0.67 -0.19 0.00 1.12 -0.24 1965 0.06 0.75 -0.19 0.00 1.27 -0.25 1966 0.05 1.01 -0.21 0.00 1.39 -0.26 1967 0.06 0.98 -0.21 0.01 1.16 -0.26 1968 0.06 0.93 -0.21 0.01 1.95 -0.26 1969 0.06 0.94 -0.20 0.01 1.09 -0.25 1970 0.07 0.93 -0.21 0.02 1.08 -0.26 1971 0.07 0.93 -0.21 0.03 1.09 -0.25 1972 0.08 0.92 -0.21 0.05 1.08 -0.24 1973 0.09 1.06 -0.30 0.06 0.98 -0.33 1974 0.13 1.05 -0.37 0.10 0.98 -0.40 1975 0.15 1.29 -0.34 0.13 1.16 -0.37 1976 0.17 1.54 -0.32 0.11 1.18 -0.38 1977 0.18 1.80 -0.30 0.10 1.88 -0.38 1978 0.19 2.03 -0.25 0.15 2.19 -0.29 1979 0.20 2.26 -0.30 0.14 2.56 -0.36 1980 0.23 2.35 -0.38 0.15 2.57 -0.46 1981 0.25 2.79 -0.40 0.17 2.90 -0.47 1982 0.27 3.27 -0.33 0.19 3.32 -0.41 - 104 -Appendix F. Yearly averages of relative economic values of milk components in $/kg. BRITISH COLUMBIA QUEBEC Carrier Fat Protein Carrier Fat Protein $/kg $/kg $/kg $/kg $/kg $/kg 1963 0.08 1.00 -0.33 0.00 1.00 -0.24 1964 0.08 1.00 -0.29 0.00 1.00 -0.22 1965 0.08 1.00 -0.26 0.00 1.00 -0.20 1966 0.05 1.00 -0.21 0.00 1.00 -0.19 1967 0.06 1.00 -0.21 0.01 1.00 -0.23 1968 0.07 1.00 -0.23 0.01 1.00 -0.25 1969 0.07 1.00 -0.22 0.01 1.00 -0.23 1970 0.07 1.00 -0.22 0.02 1.00 -0.24 1971 0.08 1.00 -0.22 0.03 1.00 -0.23 1972 0.09 1.00 -0.23 0.04 1.00 -0.22 1973 0.09 1.00 -0.29 0.06 1.00 -0.34 1974 0.12 1.00 -0.35 0.10 1.00 -0.42 1975 0.12 1.00 -0.27 0.11 1.00 -0.31 1976 0.11 1.00 -0.21 0.10 1.00 -0.32 1977 0.10 1.00 -0.17 0.05 1.00 -0.21 1978 0.09 1.00 -0.12 0.07 1.00 -0.13 1979 0.09 1.00 -0.13 0.05 1.00 -0.14 1980 0.10 1.00 -0.16 0.06 1.00 -0.18 1981 0.09 1.00 -0.14 0.06 1.00 -0.16 1982 0.08 1.00 -0.10 0.06 1.00 -0.12 * Carrier and protein are expressed relative to butterfat, which is assigned a value of 1.0. - 105 -Appendix G. Y e a r l y a v e r a g e s o f the s e l e c t i o n i n d e x w e i g h t s (P v a l u e s ) o f m i l k c o m p o n e n t s . BRITISH COLUMBIA QUEBEC Carrier Fat Protein Carrier Fat | Protein 1963 0.016 0.235 -0.283 -0.012 0.427 0.186 1964 0.017 0248 -0.278 -0.011 0.440 0.178 1965 0.018 0.278 -0.289 -0.014 0.499 0.231 1966 0.013 0.386 -0.198 -0.018 0.549 0.293 1967 0.017 0.373 -0.261 -0.008 0.452 0.141 1968 0.018 0.349 -0.276 -0.005 0.409 0.082 1969 0.019 0.354 -0.289 -0.005 0.424 0.085 1970 0.021 0.352 -0.316 -0.004 0.421 0.067 1971 0.023 0.347 -0.356 0.006 0.419 -0.049 1972 0.028 0.341 -0.435 0.008 0.415 -0.149 1973 0.032 0.389 -0.505 0.018 0.359 -0.319 1974 0.050 0.373 -0.801 0.035 0.369 -0.631 1975 0.059 0.468 -0.912 0.047 0.418 -0.753 1976 0.063 0.567 -0.948 0.041 0.427 -0.656 1977 0.063 0.674 -0.934 0.025 0.714 -0.369 1978 0.065 0.768 -0.923 0.045 0.842 -0.627 1979 0.069 0.858 -0.984 0.036 0.986 -0.474 1980 0.082 0.881 -1.201 0.040 0.985 -0.564 1981 0.084 1.049 -1.202 0.048 1.108 -0.669 1982 0.087 1.253 -1.189 0.050 1.280 -0.657 - 106 -Appendix H. Yearly averages of the genetic goals dictated by milk prices. BRITISH COLUMBIA QUEBEC Carrier % Fat % Protein % Carrier • % Fat % Protein % 1963 94.79 3.14 2.06 n/a n/a n/a * 1964 94.62 3.25 2.13 n/a n/a n/a 1965 94.47 3.34 2.19 n/a n/a n/a 1966 92.58 4.58 2.84 n/a n/a n/a 1967 93.36 4.06 2.57 n/a n/a n/a 1968 93.73 3.83 2.45 n/a n/a n/a 1969 93.84 3.75 2.41 n/a n/a n/a 1970 94.10 3.58 2.32 n/a n/a n/a 1971 94.45 3.35 2.21 n/a n/a n/a 1972 95.00 2.98 2.02 91.52 5.29 3.19 1973 94.98 3.01 2.01 93.84 3.78 2.38 1974 96.13 2.25 1.62 95.67 2.58 1.75 1975 95.97 2.34 1.69 95.78 2.48 1.74 1976 95.64 2.56 1.81 95.43 2.72 1.86 1977 95.24 2.81 1.95 92.66 4.53 2.82 1978 94.92 3.02 2.07 93.75 3.78 2.46 1979 94.80 3.10 2.11 92.66 4.51 2.84 1980 95.20 2.84 1.96 92.96 4.32 2.72 1981 94.80 3.10 2.10 93.17 4.17 2.65 1982 94.39 3.36 2.25 92.87 4.36 2.77 * The genetic goals for Quebec prior to 1972 are not reported here, as it is thought that the variance/covariance matrix used for this study does not pertain to Quebec during this period. - 107 -LITERATURE CITED Abplanalp, H.F., Ogasawara, F.X. and V.S. Asmundson. 1963. Influence of selection for body weight at different ages on growth of turkeys. Poultry Science 4:71-82. Andrus, D.F. and L.D. McGilliard. 1975. Selection of dairy cattle for overall excel-lence. Journal of Dairy Science 58:1876-1879. Brim, C.A., Johnson, H.W. and C.C. Cockerham. 1959. Multiple selection criteria in soybeans. Agronomy Journal 51:42-46. Brog, R.A. 1969. Quantitative analysis of seven selected milk pricing systems. Journal of Dairy Science 52:1485-1489. Brunner, R.J. 1981. Cow milk proteins: twenty-five years of progress. Journal of Dairy Science 64:1038-1054. Cunningham, E.P. 1969. The relative efficiencies of selection indexes. Acta Agricul-turae Scandinavica 19:45-48. Emery, R.S. 1978. Feeding for increased milk protein. Journal of Dairy Science 61:825-828. Fallart, R.F. 1980. Milk pricing, the past, present, the 1980's. Journal of Dairy Sci-ence 64:1105-1112. - 108 -Gaunt, S.N. 1973. Genetic and environmental changes possible in milk composition. 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Effects of changes in economic weights on the efficiency of index selection. Journal of Animal Science 56:1057-1064. Smith, B.J. and S.D. Snyder. 1978. Effects of protein and fat pricing on farm milk prices for the five major U.S. dairy breeds. American Journal of Agricultural Economics 60:126-131. Smith, H.F. 1936. A discriminant function for plant selection. Annals of Eugenics (London) 7:240-250. Tallis, G.M. 1962. A selection index for optimum genotype. Biometrics 18:120. Taylor, W.R. and H.H. Van Horn. 1962. Genetic and environmental influences on pro-tein and solids-not-fat. Iowa State University Cooperative Extension Service: 1-10 Thorpe, G. 1984. Pers. commun. Manager, B.C. Milkboard. Burnaby, B.C. Vandepitte, W.M. and L.N. Hazel. 1977. The effect of errors in the economic weights on the accuracy of selection index. Annals of Genetic Selection 9:87. - 114 -Van Vleck, L.D. 1970. Index selection for direct and maternal genetic components of economic traits. Biometrics 26:477-483. 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