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Genetic and environmental parameters of milk protein yields in Holsteins Ahunu, Benjamin Kwadjo 1978

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GENETIC AND ENVIRONMENTAL PARAMETERS OF MILK PROTEIN YIELDS IN HOLSTEINS by BENJAMIN KWADJO AHUNU B.Sc. (Agric.) University of Ghana, Legon, 1975  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 August, 1978 © Benjamin Kwadjo Ahunu, 1978  In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representative.  It is understood that copying or publication of this  thesis for financial gain shall not be allowed without my written permission.  Benjamin K. Ahunu  Department of Animal Science University of British Columbia 2075 Wesbrook Place Vancouver, B.C., Canada V6T 1W5.  ii  ABSTRACT  Milk, fat and protein first lactation records of 27,137 British Columbia Dairy Herd Improvement cows were analysed for gross genetic and environmental influences. The average production was 5,663 kg of milk containing 3.59% fat and 3.23% protein. Age at freshening accounted for 3.0, .3.7, 3.7, .0.28 and 0.15% of the variance in milk, fat, protein, percent fat and percent protein respectively. Cows freshening in the winter had higher average milk, fat and protein yields than those freshening in summer; however, the percentage constituents of both fat and protein were higher for the summer cows than for the winter cows. Heritability of each characteristic and the phenotypic and genetic correlations between different characteristics were derived from paternal half-sib analyses with 100 sire groups. Heritability values were: milk 0.18; fat 0.24; protein 0.21; % fat 0.38, and % protein 0.47. Within herd-year-season phenotypic correlations between milk yield and the percentages were both negative, whereas the correlation between the constituent percentages was positive. Genetic trends in the cow population averaged 51.5 kg, 2.77 kg, 1.87 kg, 0.015% and -0.049% for milk, fat and protein yields and fat and protein percentages respectively. The dollar returns from incorporating milk, fat and protein yields and/or the constituent fractions in various selection indices were estimated for different levels of protein payment. Higher dollar returns will be expected from selection based on total yields than from selection based on either fat or protein percentage. Measuring protein for a genetic  iii  program will be feasible only when unrealistically high prices are paid for protein.  iv  TABLE OF CONTENTS Page ABSTRACT  ii  LIST OF TABLES LIST OF FIGURES LIST OF APPENDICES ACKNOWLEDGEMENTS  ...  v vii viii ix  INTRODUCTION  1  LITERATURE REVIEW  5  SOURCE OF DATA  13  PART I:  ANALYSIS OF ENVIRONMENTAL PARAMETERS  15  MATERIALS AND METHODS  15  RESULTS AND DISCUSSION  17  PART II: ESTIMATION OF GENETIC PARAMETERS  29  MATERIALS AND METHODS  29  RESULTS AND DISCUSSION  34  PART III: APPLICATIONS  45  DIRECT AND CORRELATED SELECTION  45  SELECTION INDICES  50  RESULTS AND DISCUSSION  56  SUMMARY AND CONCLUSIONS  58  LITERATURE CITED  60  APPENDIX  65  V  LIST OF TABLES Table  Page  1. Summary of the Analysis of Variance: Lactational Yields and Composition  18  2. Least Squares Means and Standard Errors for Lactational Yields and Composition: Different Years  19  3. Least Squares Means and Standard Errors for Lactational Yields and Composition: Different Seasons  23  4. Least Squares Means and Standard Errors for Lactational Yields and Composition: Year-Seasons  25  5. Classification of Season of Calving  35  6. Number of Sires in Each Group  35  7. Summary of Analysis of Variance: Lactational Yields and Composition  36  8. Least Squares Means and Standard Errors of Lactational Yields and Composition: Different Sire Groups  36  9. Phenotypic and Genetic Correlations and Estimates of Heritability for Milk Yields and Composition  41  10. Genetic Correlations and Heritability Estimates from Wilcox et a l (1971)  41  11. Heritability Estimates of Milk, Fat and Protein Yields and Milk Constituents for Hoi steins from Various Sources 12. Direct and Correlated Responses from Single Trait Selection  43 47  13. Correlated Responses Expressed as Percent of Direct Selection Response  47  Table 14. Dollar Gain or Loss for Different Protein Differential Prices Following One Generation of Direct and Correlated Selection 15. Phenotypic and Genetic Correlations and Heritability Estimates for Base Milk, Fat and Protein Yields 16. Coefficients o"f Selection Indices for Different Levels of Protein Differentials of Payment 17. Gross Dollar Returns per Generation of Selection for the Indices, Considered for Various Protein Differentials Prices 18. Gross Dollar Returns of Indices 2 Through Index 4 Relative to Index 1 and Index 5 Relative to Index 6. - Units are Expressed as Percentages  vii  LIST OF FIGURES Figure  Page  1. Yearly Trends for Lactational Yields  20  2. Yearly Trends of Milk Constituents: (% Fat and % Protein)  21  3. Year-Season Trends for Lactational Yields  26  4. Year-Season Trends for Lactational Composition  27  5. Sire Group Trends of Lactational Yields  37  6. Sire Group Trends of Lactational Constituents: (% Fat and % Protein)  38  vi i i  LIST OF APPENDICES Appendix 1.  Derivation of Variance-Covariances of Base Milk (BM) from Whole Milk (WM) Variance-Covariance  2.  4. 5.  65  Relative Economic Weights Used in Analysis for Base Milk, Fat and Protein Yields  3.  Page  66  Relative Economic Weights Used in Analysis for Whole Milk, % Fat and % Protein  67  Genetic and Phenotypic Variances of Traits Analysed Genetic Correlations with Standard Errors  68 69  ix  ACKNOWLEDGEMENTS  I would like to express my appreciation to all those who have been helpful to me in completing this thesis. Special mention, however, needs to be made of Dr. R.G. Peterson of the Department of Animal Science, under whose supervision this work was done. His patient assistance, advice and suggestions throughout all the stages of the work are greatly appreciated. I am indebted to Mrs. Mabel Striker for skilled technical assistance. I am most grateful to Diane J. Green for typing the manuscript. I sincerely thank B.C.D.H.I, for permission to use their data for the analysis. Behind the scene stood My Lord Jesus Christ who gave me the strength and wisdom I needed to finish the work.  1  INTRODUCTION  Many investigations have been carried out on the more important parameters of dairy records. Most authors have, however, confined their work to the estimation of genotypic and environmental parameters of milk and milk fat.  The estimates obtained exhibit a rather wide range and  suggest that the parameters may vary considerably from one population to another. Latest trends in consumption patterns and the high prices currently obtainable for non-fat milk products have caused attention to be directed towards the non-fat solids (SNF) of milk. There seems to be adequate justification for this due to apparent consumer interest in the protein content of dairy products. Sales of low fat and fat-free dairy products have increased, indicating a decline in the importance of butterfat. Shute and Yankowsky (1973) estimated that per capita consumption of dairy products in Canada dropped from 207 kg in 1949 to 162 kg in 1971.  Particularly notable  was the 20% drop in fluid milk consumption from 1960 to 1972.  It was  suggested that this decline may have been due in part to the apparent concern with cholesterol and saturated fat content in human diets. Consumption of skim milk rose by 11% between 1972 and 1973 while whole milk dropped 2%. Consumption of cheese, yoghurt and ice milk has been increasing. Milk protein is a high quality protein containing an excellent balance of amino acids for human nutrition. In 1971, about 22% of the protein in diets of the average American came from milk (Graf, 1971). Milk protein is also relatively inexpensive under current marketing practices. Based  2  on 1973 retail prices in Canada, McFarlane and Fisher (1974) stated that protein in skim milk powder, on a unit weight basis, was cheaper than all other protein sources evaluated in the study. Dry beans, cheddar cheese, egg, fresh milk and meat were all found to be more expensive sources of protein than powdered skim milk. A kilogram of protein from steak was found to be several times more expensive than the same quantity of protein from any of the dairy products, Thus, from a nutritional viewpoint, the decreasing demand for milk fat and increased emphasis on the non-fat fraction suggests that the pricing structure of milk should no longer be based on fat ignoring other constituents such as protein. Multiple Component Testing and Pricing (MCTP) of milk is now being strongly considered in many dairying countries. Testing for milk protein content started on a large scale in the Netherlands in 1957 (Politiek, 1968) and by 1972 as many as 10,000 protein determinations per day were being made to provide a broader basis of payment (Anonymous, 1972). Since then, Denmark, Poland and Switzerland have followed the Dutch example by paying for both protein and fat content in milk supplied to the cheese industry (Cerbulis and Farrel, 1975). These economic trends and the world protein shortages suggest that future selection goals for dairy cows should include milk protein. In Finland, the breeding value of bulls for protein content is currently being evaluated through progeny testing. The importance of milk protein has made i t necessary to investigate the alternatives of breeding for protein content or protein yields in general (Maijala, 1974). In the United States, Graf (1974) observed that several dairy cooperatives and farm organizations have recently adopted protein pricing while more are  3  ready to do so. Leuenberger (1976) reported that a protein payment program has been so successful for Mississippi Valley members that Scott County Dairy Herd Improvement Association in southeastern Iowa has started testing for protein in member herds. California already includes protein in their pricing method. Protein payment of raw milk is particularly justified from an economic point of view in cheese and fresh cheese manufacture where the direct relationship of milk protein content to the conversion rate to cheese is readily apparent. Compositional quality can have a direct bearing on price paid by manufacturers, and this is becoming more important as the proportion of milk used in manufacturing tends to increase. Payment for milk on the basis of fat content alone would only be satisfactory in a diversified industry i f there were a perfect relationship between fat and non-fat yields and industrial requirements. The first decision to be made in devising a scheme for payment is selection of the milk constituent or constituents on which i t is to be based. In practice, the choice lies between fat, protein, lactose, SNF and total solids, singly or in combination. Such considerations should be made from the point of view of market requirements, consumer protection, animal breeding, economics of production and ease of testing at acceptable cost. A protein price differential is preferred for a number of reasons. An abbreviated comparison may be as follows: 1. Protein is the most variable part of the SNF and is the most valuable nutritionally and industrially. In addition, reliable protein tests are now available at a relatively low cost. 2, Protein content of milk can be changed more by breeding and  4  selection programs than other SNF components. The analysis described in this thesis will document some of the variability associated with protein, as well as fat and milk yields of first lactation Holstein cows. The protein content of milk will change little unless the price differential offered for increased protein content is large enough to make i t profitable. As shown by Tabler and Touchberry (1959) and subsequently verified by other workers (Gaunt, 1973; Van Vleck, 1977), the dairyman benefits more by selecting for increased milk yield than for milk containing a higher percentage of protein. To develop breeding plans to change the composition of milk requires a knowledge of heredity and environmental components of these constituents. To gain information on the effectiveness of selecting for one trait and the concurrent change in other traits, the correlations among traits must be known. Estimates of these parameters will influence to a great extent the choice of future breeding plans. The purpose of this work is to estimate from field data the genetic and environmental parameters of milk constituents and to determine the probable consequence of selecting for total yields of milk, fat and protein individually or in combined indices.  5  LITERATURE REVIEW  The sources of variation which affect protein and solid-non-fat (SNF) yields in the milk of normal lactating cows have been established and include breed, stage of lactation, climatic environment and level of nutrition. Protein and SNF, as well as fats, are under genetic control and cam.be changed through breeding practices. Far more information, however, exists on the fat content than on the SNF content of milk produced by commercial cattle. This may be due to the ease of technology of fat determination and pricing scheme of fluid milk. Selection for compositional quality has thus mainly been based on fat percentage. Of the two fractions making up the total solid content (SNF and fat), fat is much more variable and under payment systems based on total solids selection for fat content would give greater economic gain than selection for any non-fat constituent. Protein is generally accepted as being the most variable of the SNF components. This has been shown in a recently published study by Herrington et al_ (1973). Earlier studies with limited data, gave some indications of the genetic variations in the protein content of cows milk (Pontous, 1964; Robertson et al_., 1956; Von Krosigh et al_., 1960, and Wunder and McGilliard, 1964), and heritability estimates from these studies ranged from .08 to .48. More recently, Armstrong et al (1971), obtained monthly samples over 2 years for SNF and protein content of herds in Canada. The averages and standard deviations were 8.733 ± .336 for SNF and 3.428 - .247 for protein content. Results of a comparable New York study by Herrington et al (1973) were 12.018 - .626 for total  6  solids, 3.530 ± .250 for fat and 3.127 ± .143 for protein. Butcher et al (1967) obtained means and standard deviations of 3.67 ± .29, 3.16 ± .19 and 12.23 ± .45 for percents fat, protein and total solids, respect tively. The possibility of increasing the protein content of milk by breeding requires a knowledge of both gentic and environmental influences on the trait. To increase milk yield or to change milk composition, selection for genetically superior sires and dams must be practiced. Accuracy of genetic selection is improved by adjusting for the environmental factors affecting lactation records. Since total milk yields and total solids percentages are inversely related, improvement in yield is difficult to achieve when the concehtration-of the solids has to be maintained or improved and since correlations are negative between these, improvement of both yields and percentages cannot be obtained (Barnard et al_., 1970). The nutrition of the cow has been shown to have markedly affected the milk composition. In many areas, cows placed on lush pasture in the spring .exhibited increases in SNF content mainly due to increases in the protein percentages (Politiek, 1957) which were attributable to an increase in the plane of nutrition (Rook et al_., 1960). Some studies have shown that the forage quality and quantity may affect SNF. The study by Murdrock and Hodgson (1967) showed that high intake of grass silage was associated with a fall in milk yields and SNF. These decreases were largely due to a reduction in energy intake on a high silage ration since when equal dry matter of silage or hay from the same field were fed, reductions in yields and SNF did not occur. It has been well documented that very little change in milk protein or SNF  7  can be expected from increasing dietary protein to levels considerably above recommended standards. Typical of such studies was that of Rook and Line (1962) who varied ration protein from 70 to 160% of standard and observed no differences in the SNF or true protein. Alterations of the physical form of the rations have had variable effects on milk SNF. Cornell workers (Bishop et al_., 1963, and Loosli et_ a]_., 1963) have investigated the effect of pelleting concentrates on milk composition. Their results indicated that pelleting caused little change in milk SNF or protein but may cause a decrease in milk fat at low forage intake. Seasonal influences on lactation percent fat were reported by Blanchard et a l (1966), Gacula et aj_ (1968) and Waite et a l (1956). Late summer calving cows had higher lactational average fat tests.  Environmen-  tal temperature ranges of 10-30°C tended to cause decreases in fat percentage but beyond this range sharp decreases can be expected not only in fat percentage but also in SNF and protein percentages as well. Age had a significant effect on milk composition with a gradual reduction in percentages as the total yields increased with age (Waite ejt al., 1956). The effect became more pronounced as cows exceeded their third lactation with SNF decreasing more than fat ( Gacula ejb a^L, 1968; Sargent e l aj_., 1967). First lactation yield increased with age at calving but within the limits normally encountered in practice (20-36 months), age at first calving did not have a marked effect on either yields of milk, fat or protein or the composition of the milk produced in the first lactation. Such evidence as exists (Barnard et aj_., 1970) suggests that heifers reared on a very high level of feeding and calving very young may produce appreciably lower total yields in the early lactations compared with their  8  counterparts calving for the first time at a later age. The expected genetic gain per generation resulting from selection for a single trait lactation yield of milk is given by the equation AG = i h m am 2  2  where h m is the heritability of the lactational yield,m a is the phenotypic standard deviation and i is the intensity of selection. To make J  J  r  significant genetic changes in future generations, heritabilities of the milk constituent fractions must be considerably above zero and show some variation. Many studies have documented high heritability and repeatability values for milk constituent fractions. However, variances associated with protein yields and percentages are smaller compared with corresponding fat and percent fat values. It is therefore less efficient to select for protein through breeding than in the case of fat, and the progress in breeding for protein percent will be slower than in breeding for total protein yields (Gaunt, 1973). It is therefore important that Artificial Insemination (A.I.) bulls, which potentially are used as service sires on a large number of cows, be superior for fat and protein potential. Contrary to what would be the ideal situation, Van Vleck (1977) contended that there were not enough bulls high for both milk predicted difference (P.D.) and SNF percentage to make selection effective for both simultaneously. He estimated that about twice as many bulls would have to be sampled to find as many high for both milk and SNF percentages as can be found for milk alone or for SNF alone. The important question to breeders then is how much emphasis, i f any, should be put on selection for protein or SNF percentages. Van Vleck  9  (1977) suggested that under the current pricing system the answer would be to ignore the percentage values and i f the price of protein or SNF became great enough, then selection should be for dollar value and not for direct protein or SNF percentages. The phenotypic and genetic correlations between milk yield, fat yield and fat percentage have been studied by several workers. The genetic correlation between milk and fat yield has«' in most cases been found to be close to .7 whereas estimates of the genetic correlation between milk yield and fat percent varied from practically zero (Robertson et al., 1956) to -0.77 (Farthing and Legates, 1957). Systrad (1971) estimated the correlated response of milk yield from selection on fat yield to be about 10 kg per generation for Danish data. Other studies on protein by Barnum et al_. (1969), Butcher et al_ (1967) and Wilcox et a l (1971) also suggested that attempts to increase the protein percentage would be an effective method but not as effective as increasing total protein yield. As observed by Blanchard ejt aj_ (1966), selection for any of the percentage traits would be expected to decrease milk yield and have comparatively little effect on total yields of SNF,  although the percentage  composition would be expected to change. Sargent (1970) asserted that selection for SNF percent would inevitably necessitate some sacrifice in total SNF yield and a larger sacrifice in milk yields. Gacula et al (1968) found that selection for milk yield alone generally had a lowering effect on the percentages;.of milk constituents, Further, it was concluded that if breeding programs were desired for increasing one or more constituents, an index was needed that would not cause depression in yield as a correlated consequence of selecting for constituent percentages.  10  If selection were based on protein percent alone, there would be a decrease in amount of milk,', but fat percent would increase, and vice versa. However, i t has to be pointed out that Gacula et al_ (1968) and other workers, primarily discussed the improvement in the percent of milk constituents while Venge and Christensen (1969) showed that better economic returns may be achieved by using the total amount of milk,fat and/or amount of protein as a criterion for selection. This study will seek to document such findings. Using their parameter estimates in Holsteins, Butcher et_ al_ (1967) examined the direct and correlated responses to selection for milk constituents and concluded that due to the high genetic correlation between milk fat and protein (r = 0.77) and the greater genetic variance of fat percent, larger increases would be obtained by selecting for fat. Von Krosigh (1960) indicated similar results. It appears, therefore, that breeding for fat yields hitherto has also served to increase protein yield, and correspondingly the transition to selection for protein yield would mean no essential alteration in the progress of fat yields.  Nevertheless,  progress for protein yields will be greater (about 20% more) i f selection is directly for i t , but the difference is not so large as many would be inclined to believe (Maijal.a and Vilva, 1976). In fact, selection for milk yield alone would generally result in a correlated increase in protein and SNF yields which are about 90-100% as effective as direct selection for;protein. Indeed, the majority of recent studies concerning protein selection have been based on comparisons between selection for the single milk traits (eg. Bergman, 1971; Systrad, 1971; Wi 1 cox ejt al_., 1971). The results in  11  general showed that direct selection gave the greatest improvement for the trait in question. However, selection for fat or protein percent would not be profitable, because the indirect improvement in fat and protein quantity would only be relatively small. Furthermore, the cost of demanding replacement of a butterfat test plus selection by a corresponding protein test, seems to be unprofitable because of the high correlation between these two traits and the fact that butterfat will continue to be a valuable product.  The most realistic alternative to a  single trait selection seems to be a combined selection for milk, butterfat and protein yield. A study by Brascamp and Minkema (1972) cited by Petersen (1975) indicated that extensive selection and testing for protein as a basis for an index selection would not be profitable. Economic conditions, however, change quite often in cattle breeding and in addition the change in response to selection of individual traits may be unknown. Therefore, i t seems better, from time to time, to reexamine the relationship between the important characteristics in order to plan the breeding policy for the coming few generations.  There is already  an increasing interest on the part of dairy cattle breeders in some countries for specific information on the non-fat components of milk (Rennie, 1974). Such information is being requested in order that effective breeding and management programs can be developed. There will likely be an increasing demand in Canada for recorded information on bulls and cows with respect to non-fat components, particularly protein, in order to compete in world markets in cattle and semen. The desirability of maintaining high levels of quality protein in the diet of our human populations is so important that i t would seem wise  12  to emphasize protein percent sufficiently to prevent decreases below market standards and possibly in the future to increase both protein content of milk and total protein yield.  13  SOURCE OF DATA  Data used in this investigation were obtained from British Columbia Dairy Herd Improvement Association (B.C.D.H.I.A.) milk production records and were made available for research through the courtesy of the Dairy Herd Improvement Division of the B.C. Ministry of Agriculture. Data accumulated during the period of April 1970 to March 1976 form the basis of this study. The data base included 88,000 lactations from 58,000 Hoi stein cows in 630 herds with lactation totals for milk, fat and protein. Since incomplete records were not identified, all records less than 275 days in length were excluded from the analyses. Records from 275 days to 305 days were considered as 305-day lactation but no adjustments were made for records less than actual 305-day lactation. Records with age to lactation start from 20-36 months with no recorded dry period, were considered as first lactations since lactation number was not reliable. Transfer of records from the old testing scheme to the current D.H.I, program took place prior to July 1971 during which period herds were transferred from the Babcock testing to the Infra Red Milk Analyser (IRMA). Records made before July 1971, therefore, had complete lactation information on milk and fat yields but not necessarily complete protein tests. The mean lactational yield for milk, fat and protein percentages from reliable sources (Wilcox et aJL, 1971) for Hoi steins were 7073 kg, 3.70% and 3.11% with standard deviations of 1425 kg, 0.39% and 0.25% respectively. A minimum level of acceptance of a record for inclusion in  14  the analyses was therefore set at overall fat and protein content of 2.0% for each constituent while the upper limits were correspondingly 6.0% and 5.0% in a lactational yield of 3636 kg to 12,273 kg of milk. These limits were well outside ± 2 standard deviations and therefore permitted more than 95% of the total records for each trait to be included in the analyses.  15  PART 1: ANALYSIS OF ENVIRONMENTAL PARAMETERS MATERIALS AND METHODS  The first analysis of 27,137 first lactations gave estimates of yearly trends and seasonal effects for milk, fat, protein lactational yields and percent fat and percent protein. A year-season was defined as the year and season of a lactation based on date of lactation start. Months were thus grouped into 12 year-seasons with 2 seasons of six months each year. Season 1 included April through September and Season 2, October through March. These periods were chosen rather than the conventional Record of Performance (R.O.P.) classification of March through August and September through February, because they agree more closely with summer pasture grazing and winter feeding in the Lower Fraser Valley of B.C. which included the bulk of the data. Further restrictions were imposed by eliminating records from those herds With less than six complete lactations in three consecutive seasons. These restrictions left lactations from 584 herds out of an initial 630 herds for the analyses. The fixed effectsmodel assumed for all measures of lactational yield was as follows: ykl  +  e  ijkl  (1)  where X...-, = the actual lactational yield for milk, fat, protein, percent fat or percent protein. U  = the population mean for the trait under study.  16  H.  = a constant common to all cows in the i ^ * herd. 1  Y. • = the effect of the j  year of freshening.  A. L.  S^  = the effect of the k  season of freshening.  YS^  = the joint effect of the.ik*'' season in the j ' year when 1  t  1  the effect of season and year are held constant. A^.^i = the age in months at parturition of the 1  cows of the  i ^ * herd freshening in the j ^ year and in the k^ season. 1  e  ijkl  ' "f associated with the 1^ cow of the i ^ herd herd freshening in the j * * year and in the k' season, which is assumed to be independent and normally distributed 2 with.mean equal to zero and variance a e.  = a ranc  om e T  e c t  1  t  1  All effects in the model except ^-j^-j were regarded as fixed. Since :. the number of herds (584) was too large for existing programs at the University of B.C. Computing Centre, a least squares technique for absorbing one main effect with a large number of levels was employed. This technique depends on sorting data and absorption in a sequential manner. The reduced model was as follows: X.ljkl .. , = U + Y. . +e.ijkl j + S.k +YS.. jk + A.. jkl  (2)  The sum of squares for the herd effects was obtained from the difference R(U,h,y,S,Y ,S,A) - R(U,y,S,YS,A) where R(U,h,y,S,YS,A) and R(U,y,S,YS,A) indicate the reduction in sums of squares due to fitting constants for the effects included in the parentheses.  17  RESULTS AND DISCUSSION  A summary of the results of the least squares analysis of variance for milk, fat, protein yields and % fat and % protein are presented in 2 Table 1. This table also shows the value of R for the statistical model 1, that is the proportion of the total variation in each trait that was 2 accounted for by fitting the full model 1. Partial R values are also shown for the individual effects in the model. For lactation yields and composition, the statistical model accounted for 32, 32, 36, 19 and 16 percent of the total variation for milk yield, fat yield, protein yield, % fat and % protein respectively; all effects, except the year by season interaction, were significant for all traits. Year by season interactions were significant for protein, % fat and % protein but not for milk and fat yields. Year The overall least squares means and least squares standard errors for the yields and composition are reported in Table 2. Figures 1 and 2 show the yearly trends in yields and percentages of the constituents. The graphs were made by plotting the least squares constants of each dependent variable associated with years against year of lactation start. They are, therefore, estimates of year effects removing the other effects in the model. Over this comparatively short period of time, there was an increasing trend-in all the three yield traits studied. This may in part be due to  18  Table 1. Summary of the Analysis of Variance: Lactation Yields (kg) and Composition  Categories Herd  Year x Season Season  Age  Trait Milk  .323  2.7396 X 10  Fat  .323  0.40186 X 10  0.2663* .0154* .0030* .00038 .0374*  Protein  .364  0.29566 X 10  0.3078* .0127* .0062* .0009* .0369*  % Fat  .194  995.84  0.1799* .0082* .0017* .0012* .0028*  % Protein  .164  350.795  0.1246* .0316* .0004* .0060* .0015*  26542  D.f.  9  Total CSS  Year  Total Fitted  b  8  8  8  26541  0.2770* .0081* .0077* .0002  582  5  1  5  a. Fraction of the total sums ofsquares accounted for by fitting the effects in the statistical model equation (2). b. Total corrected sums of squares (kg )• c. Fraction of the total sums ofsquares accounted for by each effect in the statistical model. *  Significant source of variation (P * .05).  .03*  1  19  Table 2. Least Squares Means (X) and Standard Errors (SE) for Lactational Yields (kg) and Composition for Different Years  Years  Number of Observations  Milk X±SE  Fat X±SE  Protein X±SE  % Fat X±SE  % Protein X±SE  1970-71  2504  5572+20 202.1*0;. 8 174.4±0.73.64*0.01 3.13*0.01  1971-72  4313  5548+15 197.3*0.6 182.1*0.5 3.57*0.01 3.29*0.00  1972-73  4633  5627*15 197.7*0.6 182.3*0.5 3.53*0.01 3.25*0.00  1973-74  5631  5675*14 201.7±0S5 182.4*0.4 3.57*0.01 3.22*0.00  1974-75  6136  5699±13 205.2*0.5 183.8*0.4 3.62*0.01 3.23*0.00  1975-76  3930  5852*17 211.1*0.6 188.7±0.5 3.63*0.01 3.23±0.00  OVERALL  27137  5663.2  202.5  182.3  3.59  3.23  20  RG.1.  YEARLY TRENDS FOR LACTATIONAL YIELDS  MILK FAT PROTEIN  -O —D  •a-  21  FIG.2.  YEARLY  TRENDS OF MILK CONSTITUENTS:  (%fat and % protein)  °/o PROTEIN  -A  A-  22  genetic improvement and partly to improved feeding and management. No attempt is made here to differentiate between these two sources of improvement. Burnside and Legates (1965), working with first lactation records of Holstein-friesian heifers, reported a mean milk production of 5635 kg in 1954 and 6660 kg in 1962, thus giving an annual trend of 128 kg milk. Similarly, Gacula e_t al_ (1968) recorded 5955 kg milk in 1960 and 6452 kg in 1962 which gave an annual trend of 124 kg milk. In the present study, the least squares subclass mean (u + yi) in 1970 was 5575 kg and 5852 kg in 1975.  The annual trend was 55 kg milk. Van Vleck  (1966) and Gacula et a]_ (1968) used different lactation records, while the present study limits itself to first lactation records only. Trends for fat, protein, % fat and % protein were 2.25 kg, 3.5 kg, -.0025% and -.025% respectively. Results of more recent workers using first lactation records were as follows: Halgrave and Legates (1971) showed 53 kg milk per year and Hintz et al_ (1978) had 36 kg milk per year, while Kennedy and Moxley (1975) obtained 57 kg milk, 1.9 kg fat, 1.1 kg protein, -.003% fat and -.014% protein per year. Verde et aj_ (1972) also reported annual trends of 90 kg milk, 1.1 kg fat and -.052% fat. Complete transfer of herds from the Babcock test was not completed before July 1971.  Records made before this time therefore may contain  incomplete protein tests. Even though screening was employed to remove suspicious data, i t appeared that not all of such data were effectively removed. This explains the unusually low protein yields and percentages for the first year (1970), otherwise a downward trend was observed for % protein which could be explained by selection for increased milk yield while ignoring protein. There was no apparent trend in % fat.  23  Table 3. Least Square Means (X) and Standard Errors (SE) for Lactational Yields (kq) and Composition for Different Seasons  Seasons  Number of Observations  Milk X±SE  1  13343  2 TOTAL  Protein X±SE  Fat X+SE  Protein -X±SE  % Fat X±SE  5592±9  201±0.4  180±.3  3.60±.004  3.,23±.002  13794  5735±9  204±0..3  184±.3  3.56±.004  3.,22±.002  27137  5663  182.3  3.59  3..22  202.5  %  Using the year constants in Figure 2, downward trends over the period were from +.065 to -.093 for % protein and .046 to -.065 for % fat. Gacula ejt al_ (1968) over a five-year period, reported downwards of 0.08 to -.10 for % fat and .07 to -.04% for % protein. Season Season of calving was a significant source of variation for all the traits under study. The season of calving least square means and standard errors are reported in Table 3. Season of calving accounted for 7.7, 3.0, 6.2, 1.7 and 0.04 of the variation of lactation averages for milk fat and protein yields and % fat and % protein respectively. In terms of percentage of total.'variation, season effects estimates for the constituent percentages were small. Cows freshening in the winter had higher average milk, fat and protein yields than those freshening in summer; however, the constituent percentages were higher for the summer cows than  for the winter cows. Year by Season Interaction Year by season interaction was not significant for milk and fat yields but was significant for protein yield and the constituent percentages. The variances accounted for by the interaction effects were, however, minimal. The year-season subclass means are graphed in Figures 3 and 4. The results indicate that spring grazing tends to decrease fat and protein constituents while increasing milk yield as reported by Waite et al_ (1956). The results of year, season and year-season effects are in general agreement with the findings of other workers (Bereskin and Freeman, 1965; Gacula et al_., 1968; and Van Vleck, 1966). Herd Herd effects were highly significant for all traits.  In terms of  percentage of total variance, herd was the most important of the effects fitted in the statistical model. Herd estimates accounted for 27.77, 26.6, 30.8, 18.0 and 12.45 percent of the total variances for milk, fat yield, protein, % fat and I protein respectively. Age 2 Age effects were significant for all traits under study. The R values were 3.0, 3.7, 3.7, 0.28 and 0.15 percent for milk, fat, protein, fat and % protein respectively. The partial regression coefficients from least squares regression  analyses  were 0.102, 0,117, 0,117,  0.037 and 0.033 for milk, fat, protein, % fat and % protein respectively.  25  Table 4. Least Square Means (X) and Standard Errors (SE) for Lactational Yields (kg) and Composition for Each Year-Season  Number of Year Season Observations Summer 70  942  Mi 1 k X±SE  Fat X±SE  Protein X±SE  % Fat X±SE  % Protein X±SE  5516+32 201+1.2 171 ±1 .06  3.66±.014 3.10+.008  Winter 70-71  1562  5635+25  178± .86  3.62+.011 3.17+.006  Summer 71  1994  5481+22 197+ .85 181± .73  3.6U.009 3.30+.006  Winter 71-72  2319  5615+20 198+ .77 184+ .68  3.51+.009 3.28+.005  Summer 72  2298  5527+21 195+ .79 180+ .68  3.55+.009 3.271.005  Winter 72-73  2335  5729+21 200+ .78 184+ .68  3.50±.009 3.22±.005  Summer 73  2552  5628+20 200+ .75 180+ .64  3.57±.008 3.2U.005  Winter 73-•74  3079  5723+18 203+ .68 184+ .60  3.57+.008 3.23t.004  Summer 74  3043  5624+18 203+ .68 183+ .60  3.63±.008 3.25+.005  Winter 74-•75  3093  .68 185+ .60 5775118 207+ .  3.61±.008 3.21+.004  Summer 75  2514  5773+20 207+ .76 187+ .65  3.61+.008 3.25+.005  Winter 75-•76  1406  5931+26 215+1.01 190+ .87  3.61+.0112 3.2lt.007  TOTAL  27137  5663  203+.J .96  203  182  Summer =Freshening from April through September Winter = Freshening from October through March  3.59  3.23  27  FIG. 4.  YEAR SEASON TRENDS FOR LACTATDNAL COMPOSITION  0-10T  YEAR-SEASONS  FAT  ~*a  &  °/c PROTEIN  -A  ^.  "lo  28  This is an indication that cows calving late produce higher milk, fat and protein yields and also higher fat and protein fractions than their counterparts calving for the first time at a younger age, Summary Herds, years, seasons and age were significant sources of variation for all the traits studied. Year-season interaction was a significant source of variation for protein yields, % fat and % protein but not for total milk and fat yields. Differences in lactational averages and composition were related to the season in which lactation started. In general, i t appeared that cows freshening in a season resulting in depression of lactation milk yield had above-average lactation percentages of fat and protein. Over the six-year period, total milk production increased with a corresponding lowering in the protein content while the fat content remained fairly constant. Environmental variance is a source of error that reduces precision in genetical studies and i f these are not removed, smaller genetic estimates are obtained. This is a result of an increase in the environmental variance not accompanied by a proportionate increase in genetic variance.  29  PART II: ESTIMATION OF GENETIC PARAMETERS MATERIALS AND METHODS  The second analyses were based on a subset of the previous data. It had been determined from the analyses in Part I that the protein levels recorded for the first year 1970 were low due to incomplete protein tests. It was therefore decided to exclude records from the first year and thus eliminate the first two year-seasons as well as records with no sire identification. A total of 19,213 275-305 day first lactation records for cows with identifiable sires who calved during 1971-76 were obtained from the 27,137 original records. This new data represented records involving 100 sires. The following restrictions were imposed to isolate the new data from the bulk of the data base. i) Cows were milked for 275 days and up to 305 days, ii) Age at first calving was between 20 and 36 months, i i i ) Only sires with 10 or more daughters distributed among 5 or more herds were used. iv) Only herds with 20 or more first lactation records representing three or more sires with at least six records in a year-season were included. These restrictions were designed to limit records to sires widely and extensively used in Artificial Insemination (A.I.) and to eliminate confounding sire with herd and/or season effects. A total of 4182  30  herd-year-seasonSo(HYS) for 547 herds were formed. A herd-year-season was defined as a year or season within a herd. For example, two cows occurring in the same herd but freshening in different years or seasons were classified into different HYS. Similarly, two cows in different herds but freshening in the same year or season were also separated into different HYS. Sires were grouped according to the year in which their first daughter's record appeared. A group was defined as a set of sires entering service during the same period of time. For example, sire group 1 (Gl.) included all sires which had their daughters calving for the first time prior to September 1972, while sire group 2 (G2) represented sires which had their daughters calving for the first time between October 1972 and September 1973. Table 6 shows the complete classification 6f;the'Sire grouping. The reason for grouping was to define populations with different means around which sire genetic values were distributed. According to Schaeffer ejt a l (1975), year groupings are logical since sires selected for A.I. in 1971 were conceptually drawn from a population of all possible zygotes from matings made in that time, while sires selected in 1976 were drawn from a population of all possible zygotes from more recent matings. Since genetic trend has been upward with milk production (Miller et a l . , 1969), the average merit of sires sampled in 1976 should be greater than that of sires sampled in 1971. The grouping procedure was also important in removing bias (Henderson, 1975) because evaluation of sires that continue in service over a long period of time after being returned to service generally tended to decline  31  and also sires of later generations appeared to be under-evaluated relative to older sires. The model assumed to describe the 305-day first lactation record was: Y.ijkl ., i = HYS. + G. + S/G.. + e, i j jk ijkl where Y..., = the actual 305-day lactation yield or composition. 1J KI  HYS. = the effect due to the i herd-year-season of calving, considered fixed and common to all records in the i ^ HYS. t  G-  n  = a constant common to all records of daughters in the  J genetic group (year) in which a sire's first daughter calved, considered as fixed. S/G.. = a random sire effect common to daughters of the k^ sire in JK  the j  group. The breeding values of sires in the same  group are regarded as a random sample from the same population, and  ^-jjki  dom variable mutually uncorrelated with any other  = a ran  variable, in the model. In sex-limited inheritance such as milk production, breeding values of sires are based on the performance of their offspring. If the records of progeny of sires are made on a comparable basis, the genetic covariance between members of a sire's progeny is primarily a function of the additive genetic variance: a2 Therefore, a2 is an estimate of a2 s  This is because sire effects are the only genetic effects common to a daughter of a sire and another daughter of the same sire. Heritabilities, genetic and phenotypic correlations, were calculated using the paternal half-sib intra-class correlation method. The sire  32  component of variation, a2 for each dependent variable was calculated by the formula: . - MSerror a 2 = MS sires Ki  5  K-| is the weighted number of progeny per sire. The value of K-jwas calculated to be 186.76 by the method described by Becker (1975) for unequal number per subclass (unbalanced design).. That is: K  l  ~ [ '' n  EE  -  i j i j I / df (sires per group) n. n  Heritability was then estimated as: h  4a  -  2  2 s  /(s  2  + s  o\)  2  where h is an estimate of heritability in the narrow sense, 2 a  = the error component of variance and contains both environmental variance and genetic variance  and a  2  = the component of variance for sires.  The standard error of the heritability estimates were obtained by the approximate method of Swiger et al_ (1964) when normality of the intraclass correlation t is2(n-l)(l-t) assumed. [l + ( K l ) t] S.E. (h ) K*(n-s)(s-l) 2  r  2  where t is the intra-class correlation calculated as +t. = a2/ ( a 2 + ,a 2) x s  s  e  and n = the number of observations  s = the number of sires involved and K-j = a coefficient determined as already noted. Traits are influenced by both genotype and environmental factors. The relation can be expressed simply as: P =G+ E where P is the observed phenotype of an individual, G denotes the mean value for that genotype over the environment-.typical; of the population and E is the deviation from G of the actual phenotype of the individual The statistical model assumes that the correlation between the genotype and the environment are zero. Genetic correlations were estimated by the formula rg =  Cov X,Y  where o2x and a2y are the sire components for traits X and Y respectively and Cov'X,Y is the covariance of traits X and Y. The covariance (Cov X,Y) was arrived at by the expression a2(x+y) = a2x + o2y + 2 Cov X,Y 2  where a (x+y) is the sire component of the sum of traits x and y. Phenotypic correlations were obtained directly from the LSA8 computer program output (Peterson, 1965).  34  RESULTS AND DISCUSSION  Classification of the season of calving is shown in Table 5. Grouping of sires, the number of sires represented in each group and the total number of records analysed for the various groups are entered in Table 6. A summary of the analysis of variance of yields of milk, fat, and protein and the fractional constituents of fat and protein is presented in Table 7. The table shows the R values for the statistical model, that is, the proportion of the total variation in each trait that was accounted for by fitting the effects of herd-year-season, sire group, sires and age (as a covariable). For lactation yields of milk, fat and protein, percent fat and percent protein, the statistical model accounted for 46, 44, 50, 36 and 31 percent respectively of the total variation. All effects were significant (P - .05) except the effect of sire groups in the percent protein analysis. Table 8 shows the least squares means of yields and fractional components with their standard errors. Lactation production and constituents are represented graphically in Figures 5 and 6. Very few records (only 58) were represented for the two sires in group 5 out of the total data of 19,213. This small number of observations was reflected by the considerably larger standard errors associated with the group for all the traits analysed. Weighted regression analysis based on the number of sires in sire groupings gave increasing trends for milk, fat and protein yields and fat percent but a negative trend for percent protein. The  35  Table 5. Classification of Season of Calving  Table 6. Number of Sires in Each Group  Sire Group.  Year in Which First Daughter Calved  Number of Sires Represented  Number of Lactations  Gl  Prior to September 1972  64  15,031  G2  October 1972-September 1973  14  2,518  G3  October 1973-September 1974  8  718  G4  October 1974-September 1975  12  825  G5  October 1975-September 1976  2  58  100  19,213  TOTAL  36  2 Table 7. Summary of the Analysis of Variance: R Values for Lactation Average Yields and Composition  Component  Total Fitted  HYS  d.f.  1912  4181  Milk  .553  Fat  Groups  Si res/Groups  Age  4  95  1  .458*  .0019*  .056*  .037*  .562  .444*  .0035*  .071*  .046*  Protein  .617  .503*  .0020*  .063*  .049*  % Fat  .475  .357*  .0010*  .114*  .003*  % Protein  .453  .310*  .0004"  140*  .0021  * Source of variation significant (P * .05)  Table 8. Least Square Means (X) and Standard Errors (SE) of Lactation Yields (kg) and Composition (%) for Different Sire Groups  Group  Milk (kg) X±SE  Fat (kg) X±SE  Protein (kg) X±SE  % Fat X±SE  7o Protein X±SE  1 2 3 4 5  5716.7*33.6 5676.7+31.1 5913.1+49.7 5920.2+46.2 5626.2+99.9  205.85+1.29 204.97+1.46 216.12+1.96 217.16+1.77 199.21+3.82  183.88+1.03 183.26+1.17 188.71+1.66 191.61+1.42 182.34+3.07  3.62+.007 3.63+.008 3.68+.010 3.69+.009 3:53+.020  3.23+.004 3.24+.004 3.20+.005 3.24+.005 3.24+.Oil  208.66  185.96  3.63  3.23  OVERALL 5770.6 MEANS  37  FIG. 5.  SIRE GROUP TRENDS OF LACTATIONAL YIELDS  SIRE GROUPS MILK  -O—• —O—  FAT  —O  PROTEIN  A—  •VoPROTEIN  —A  j£r  39  annual genetic trends were 51.53 kg milk, 2.77 kg fat, 1.87 kg protein, 0.015% percent fat and -0.049% for percent protein. Results of most authors (Gacula et al_. 1968; Kennedy and Moxley 1975, and Verde et_ al_. 1972), however, showed negative genetic trends in both percent fat and percent protein. The results from this study showed, therefore, that fat percent has increased while protein percent decreased. Estimates of heritabilities, genetic and phenotypic correlations, have been reported in Table 9.  Phenotypic Correlations Phenotypic correlations among the traits ranged from -.24 to +.86 (Table 9). Milk yield was negatively correlated with the two constituent fractions and the values are in close agreement with the comprehensive studies of Wilcox ejt al_ (1971) whose values have been reported in Table 10. Gaunt ejt al_ (1966) reported correlation values of -.28 and -.27 for milk with % fat and milk and milk with % protein, respectively, while Thompson and Loganathan (1968) had -.26 for milk with % fat and -.11 for milk with % SNF.  Blanchard et al_ (1966) also obtained -.25 and -.16  for milk with % fat and milk with % SNF respectively. Thus, a negative phenotypic correlation between lactation milk yield and fat percentage of approximately -.20 is rather generally accepted (Legates, 1960). A negative relationship of about the same magnitude appears to exist for the SNF constituents. The value for the current study (-.24) was similar to the accepted values. Robertson (1956), however, obtained a very low  40  correlation of only -.14 between milk and % fat. Since the phenotypic correlation between SNF or protein and milk yield is negative and ranges from -.08 to -.26, a tendency for high yielding cows to produce milk which is slightly lower in the fractional constituents would be expected. The correlation between fat and protein percentages was .54 in data of Gaunt et al_ (1966) and for Robertson et al_ (1956), the figure was .40,and a value of .52 from Politiek (1957). These are much lower than the value reported by Von Krosigh et_ al_ (1960) of nearly .70. The correlation found in this study was .56 for % fat -.r% protein. In summary, the phenotypic correlation between the percentage contents of fat and protein was positive and of the order of magnitude similar to other workers. Yields were highly correlated with each other, the values ranging from .73 to .86 (Table 9). This underlines the great opportunity for improvement by direct selection. Other workers (Thompson and Loganathan, 1956) reported slightly higher phenotypic correlations for corresponding yields. Their values ranged from .75 to .97.  Genetic Correlations Genetic correlations (rg) among yields (Table 9) were not only high and positive but also similar to the phenotypic values. The remaining genetic correlations were considerably larger in absolute values than the corresponding phenotypic correlations. The values for genetic correlations that could be compared were similar to those reported by other workers.  By way of comparison, the genetic correlations between milk  constituentswhich were recorded by Wilcox ejt al_ (1971) in their comprehensive study, have been reproduced in Table 10. The genetic correlation  41  Table 9. Phenotypic Correlations, Genetic Correlations and Estimates of Heritability for Milk Yields and Composition  Milk Milk  Fat  Protein  .73  .86 .80  a  Fat  .60  Protein  .75  .82  -.26  .62  .27  % Protein -.33  .34  .37  b  % Fat  % Fat  % Protein  h  -.24  -.31  .18*.03  .48  .09  .24*.04  .04  .18  .21*.03  .56  .38*.05 .47*.06  .74  a. Elements above the main diagonal are phenotypic correlations b. Elements below the main diagonal are genetic correlations.  Table 10. Genetic Correlations and Heritability Estimates: Holsteins from Wilcox et al (1971)  Milk  Fat  Protein  % Fat  h  2  .23  Milk  ' .25  Fat  .70  Protein  .82  .81  -.30  .46  .13  % Protein -.30  .17  .28  % Fat  .% Protein  .21 .57 .54  .37  42  between milk yield and constituent factors were both negative; -.26 and -.33 for mi.lk-% fat and milk-% protein respectively. Corresponding figures obtained by Gaunt et al_ (1966) were -.28 and -.27. These negative values would be expected since high milk production has been associated with low percentage of the constituents, both within and between breeds by several workers. It appeared, however, that genetic correlations obtained for the percentage composition in this study were slightly larger than those reported by Wilcox et al_ (1971).  In particular, rg (% fat and % protein)  of .62 for this study and that of .46 by Wilcox and coworkers. Nevertheless, the observed rg value of .62 was s t i l l smaller than that reported by Johnson (1957) who estimated a value of .69 for Holstein. The correlation between % fat and % protein was positive and large, A breeder selecting for a higher percentage for one of the constituents would thus automatically be selecting for a higher percentage composition in the other constituent.  Heritability Reliable estimates of heritability require the use of a large number of records. In general, milk constituent fractions have high heritabilities. Table 11 is a summary of the heritability estimates by various workers on Holstein populations. The heritabi1ities from this study using paternal half-sib analysis were slightly lower than most of the results reported by other workers, most of whom used daughter-dam regression analysis for their estimates. Studies by Van Vleck and Bradford (1965) have shown that genetic estimates from daughter-dam  43  Table 11. Heritability Estimates of Milk, Fat and Protein Yields and Milk Constituents for Hoi steins from Various Sources  Milk  Fat  Protein  % Fat  Gacula et al. 1968  .37  .45  .30  .45  Blanchard et al. 1966  .29  .29  Gaunt et al. 1968  .24  .24  .20  .57  .45  Wilcox et al. 1971  .23  .25  .17  .57  .37  .44  .37  Van Krosigh et al. I960 Thompson & Loganathan 1968 .23  .09 .  % Protein .75  .68  .45  regressions were larger than estimates obtained from paternal half-sib analysis on the same set of data. However, the values from this study are similar to those obtained by Wilcox et al^ (1971) in their comprehensive study. Heritability for milk seemed low, (.18)-, but Wunder and McGilliard (1964) had earlier reported a heritability value of only .17. One reason for this low estimate could be due to the removal of genetic trends which parallel increasing mean production (Van Vleck, 1966).  45  PART III: APPLICATIONS DIRECT AND CORRELATED SELECTION  Genetic progress is expressed as: A G = 1  x °x x P  h2  where i is the intensity of selection. This is the difference between X  the average value of a quantitative character in the whole population and the average value of those selected to be parents of the next generation expressed in standard deviation units. ap is the phenotypic standard deviation and h2X is the heritability of the trait. v  Correlated response arises from the fact that traits may be genetically correlated.  A change in a trait y due to selection for trait x  can be predicted from the expression: CRy = ixhxhyr9xya Py n  D  where CR is the correlated response in trait y when selection pressure y  has been placed on trait x, h and h are the square roots of the resy pective heritabilities, rg is the genetic correlation between the traits xy and is the phenotypic standard deviation of the trait y. x  If i t is assumed that only 5% of the sires and 80% of the dams are used, the intensity of selection (i ) after Pirchner (1969) would be 1.205. A  For comparative purposes, i t is convenient to express the responses anticipated from selection as the change in yield for a selection differential on a single lactation basis. This eliminates the need for  46  specifying the selection intensity in illustrating the comparative magnitude of the response to alternative selection models. With a selection differential of one standard deviation, the expected genetic change may thus be expressed as: AG  = h ap 2  x  x  and the expected correlated change in trait y may be expressed as: AGC  y = hxhyr yxyan Q  Estimates of expected genetic changes from single trait selection and expected genetic changes are presented in Table 12. These expected values are based on estimates of genetic correlations and heritability values from Part II analysis. In Table 13, the expected genetic changes have been expressed as percentages of direct single trait selection. Table 12, for example, shows that an increase of 305 kg in milk yield could be expected in one generation of selection for milk yield alone while correlated responses in milk yield from selection for fat and protein yields would be 211 kg and 247 kg respectively. These correlated responses in yields of milk represent 69% and 81% of the expected yield in milk from direct selection for milk. On the other hand, decreases of 115 kg (-38%) and 162 kg (-53%) in milk yield would be expected from selection for percent fat and percent protein. Direct selection for fat was expected to give the highest response in fat yields. Expected correlated responses from the other traits were all positive and were 8.1 kg, 11.9 kg, 12.2 kg, and 7.4 kg respectively for correlated responses from selection for milk, protein, percent fat and percent protein. The results indicate that selection for protein  47  Table 12. Direct and Correlated Responses from Single Trait Selection (kg)  Response to Selection  Trait Under Selection  Milk  Milk Fat Protein % Fat % Protein  305* 211 247 -115 -162  Fat  Protein  % Fat  8.1 15.6 11.9 12.2 7.4  7.6 9.6 10.9 4.0 6.0  -.023 .063 .026 .130 .105  % Protein -.018 .021 .023 .058 .081  *Direct responses are shown on the main diagonal and are under!ined.  Table 13. Correlated Responses Expressed as Percent of Direct Selection _ Response  Response to Selection Trait Under Selection  Milk  Fat  Milk Fat Protein % Fat % Protein  100* 69 81 -38 -53  52 100 76 78 47  Protein 68 88 100 37 55  % Fat -18 48 20 100 81  *Direct selection on the main diagonal (underlined).  % Protein -22 26 28 72 100  48  yield and % fat are nearly as effective in increasing fat yields as direct selection for fat yield. Direct selection in fat yield was also expected to give correlated responses of 211 kg in milk yield (69%), 9.6 kg (88%) in protein yield and slight increases (48% and 26%) in fat and protein percentages as direct selection for the individual traits would give. Direct selection for protein showed that this would be effective but the variability in protein is much less than that for fat. Therefore, the potential for genetic progress in increasing protein content is much less in absolute terms than i t is for fat. For example, direct selection for protein was expected to give 10.9 kg which in absolute terms was only 70% of the value of direct selection for fat (15.6 kg) even though the heritability values for fat and protein yields are essentially the same. Correlated responses in protein yield from selection for milk, fat, percent fat and percent protein were 7.6 kg, 9.6 kg, 4.0 kg and 6.0 kg which are correspondingly 68%, 88%, 37% and 50% of direct selection for protein. Direct selection for protein was also expected to give increases of 81% (247 kg) in milk yield, 76% (11.9 kg) of fat yield and 20% and 28% for the percentages relative to direct selection of the individual traits. Direct selection for percent fat and percent protein gave the greatest responses in the constituent fractions in each case.  Correlated  responses from selection for milk were both negative. Also, correlated responses in milk yield when selection was for percent fat and percent protein were negative. This means that selection for percent composition would decrease milk yield and vice versa.  However, selection for percent  49  fat and percent protein would give slight correlated increases in fat and protein yields. The expected genetic gain in milk yield per cow per year is 45 kg i f selection is for milk alone (Anderson et_ al_. 1978). This corresponds to a selection intensity of 0.148. Using quota milk prices in British Columbia ($33.39 per 100 kg milk and 28<£ differential for a point of fat above 3.5%), gross dollar gain or loss following one generation of selection were calculated for varying prices for a point of protein above 3.2% at $.00 to $.42.  The results are reported in Table 14, The results show that selection for the yield traits resulted in pos-  itive dollar returns with selection for milk yield returning the highest. Gross dollar returns from selection for milk decreased as the price for protein payment increased. This is due to the negative correlation between milk yield and % protein. On the other hand, the gross dollar returns from selection for fat and protein yields increased with increasing payment for protein. Selection involving percent fat and percent protein resulted in negative dollar returns, the magnitude decreasing with increasing payment for protein. This means that even though selection for percent fat and percent protein increase fat and protein percentages in the milk, the dollar returns for the increased percentages are not enough to make up for the correlated decreases in milk yield.  Table 14. Dollar Gain or Loss for Different Protein Differential Prices Following one Generation of Direct and Correlated Selection  Protein Differential Trait Under Selection $.00  $.07  Milk  14.73  14.62  14.50  14. 38  Fat  12.03  12.16  12.29  Protein  13.09  12.18 .  % Fat  -3.16  % Protein  -5.54  $.35  $.42  14.27  14.15  14.03  12.42  12.55  12.68  12.81  13.40  13.48  13.62  13.75  13.88  -2.35  -2.00  -1. 65  -1.31  -0.96  -0.61  -5.08  -4.62  -4.15 - -3.70 - -3,24  -2.78  $.14 •  $.21  $.28 •  50  SELECTION INDICES  Selection indices are the optimal methodsof selection for an aggregate of several traits. Such an index combines the different traits in a way that maximizes the probability of progress in the aggregate economic value. In general, the index is defined as: I.l = b,X, 1 1 + b2X2 + ... + bnXn 0  0  where the b.'s are the derived optimum weighting coefficients for the i  t h  trait. Hazel (1943) defined the genetic-economic value of an index as: H = a g, + a g + ...a n  0  PI  0  22 3  i gi  +ag nn 3  where the a. s are the economic values corresponding to one unit of X... 1  Subsequently, Henderson (1963) showed that an estimate of b. is given by: b = P" G A 1  where P is a phenotypic variance-covariance matrix of the traits involved in the payment scheme, G is a genotypic variance-covariance matrix of all the traits under selection and A is a column vector of relative economic weights. Genetic changes for the individual traits may not necessarily be continually in the direction considered desirable. Greater utility of the selection index would appear possible i f in the derivation of the coefficient b.'s, restrictions might be imposed which would ensure that certain specified traits are not changed in the wrong direction. The derivation of the solution to this problem was given by Kempthorne and  51  Nordskog (1959). The desired set of b^'s is obtained from the following matrix equations: b = [I* - P" G* (GP" G* )G*]p" GA 1  1  1  1  1  where I* is the identity matrix with ones on the diagonals and zero elsewhere, G* is the rows of G for which the traits are not to change, G*^ is the transpose of G and p~^, G, and A are the same matrices previously defined. Using current Quota Milk prices in British Columbia ($33.39 per 100 kg milk and $.28 differential for a point of fat above 3.5%), gross monetary benefits or Dollar Returns (DR) of milk and its constituent yields and fractions were estimated for various selection indices. With the b's computed, an estimate of DR through an index I-j is DR = yCb^P.b.)-  5  i  where y is a factor of selection intensity, y was set equal to 0.148 which corresponds to a genetic gain of milk yield of 46 kg per cow per year when selection is for that trait alone. In the analysis, whole milk (WM) was differentiated from base milk (BM). Base milk is the product obtained after fat and protein have been removed from whole milk. Since whole milk contains fat and protein, the price per kilogram will be different at any given fat and protein percentage. Base milk will, however, maintain a constant price per kilogram and would only chan in like manner as fat and protein when the differentials of payment for fat and protein change. This was important in selecting economic weights for the analysis. A variance-covariance matrix of the relationships between whole milk, fat and protein was used to derive the variance-covariance matrix of base milk, fat and protein. The procedure is outlined in Appendix 1. The  52  Table 15. Phenotypic (Above Diagonal) and Genotypic (Below Diagonal) Correlations and Heritability Estimates for Base Milk, Fat and Protein Yields  Trait  Base Milk  Fat  Protein  h  .74  .89  .19  .80  .24  Base Milk Fat  .56  Protein  .72  .82  11  .21  phenotypic and genotypic correlations of base milk, fat and protein yields and the corresponding heritabi 1 ities are presented above in Table 15. Six selection indices were considered, Index 1 = b, 1mmX + bI X, f f+ b,IpX p m  lf  n  Index 2 = b2m Xm + b2fJ(, f 0m  m  9  Index 3 = b, 3m Xm + b-3p Xp m  Index 4 = b I n d e x  4f  5wmwm  5 = b  X  •k  m  X + b X f  +  4p  b  5%f hf  p  +  5%p %p  b  X  ~k  ~k  Index 6 = b6wm.„X wm + b 6%tX„AT+ b 6%p , X/,p Clim  Mf  /f  co  0  0  where the b. s are row vectors of selection index weights pertaining to 1  the traits base milk (m), fat (f), protein (p), percent fat (%f), percent protein (%p) and whole milk (wm). Payment was always based on all three traits but may have a value of zero for an individual component. The  53  selection indices are interpreted as follows: Index 1 is an index based on selection for base milk, fat and protein yields; Index 2 is based on selection for base milk and fat; Index 3 is selection for base milk and protein while Index 4 is selection for fat and protein yields. These first four indices were constructed based on relative economic weights for one kilogram of each trait entered in the analysis. The relative economic weights are reported in Appendix 2. Index 5 is a selection index based on selection for whole milk yield, percent fat and percent protein. Index 6 is selection for whole milk yield while keeping percent fat and percent protein constant.  Indices  5 and 6 were constructed based on relative economic weights for one kilogram of whole milk, 0.1% fat and 0.1% protein,increases.  The coefficients  of the various indices for different protein differential prices are reported in Table 1.6-  Relative economic weights for comparisons between  the different Dollar Return (DR) values were calculated for varying protein prices with quota milk price and fat differential at current British Columbia levels and for a point for protein above and below 3.2% protein content at $.00 to $.42.  In Table 18, the gross dollar differences  in selection for base milk, fat and protein yields (Index 1) have been converted to percent dollar advantage relative to selection for base milk and fat (Index 2), base milk and protein (Index 3), and fat and protein (Index 4), by the formula ( i i Ii  ^) x 100%, where I. is the corresponding dollar 1  return for indices 2 through 4. In the last row of Table 18, dollar differences have been contrasted for Index 5 vs. Index 6. Thus, in Table 18, for example, a value of 0.0 means no selection advantage, While a value of 5.1 means a selection advantage of 5.1% in the appropriate contrast.  54  Table 1 6. Coefficients of Selection Indices for Different Levels of Protein Differential Payment 9  Protein Differential $.00  Index  h  U  $.14  $.21  $.28  $.35  $.42  BM) F) P)  .047 1.085 -.678  .034 1.085 - .200  .022 1.040 .176  .011 1.020 .551  -.001 1.000 .927  -.012 .979 1.302  -.023 .959 1.677  BM) F)  .035 .830  .030 .986  .026 1.107  .021 1.227  .016 1.348  .011 1.469  .006 1.590  BM) P)  .040 .706  .027 1.154  .015 1.503  .004 1.852  -.007 2.202  -.019 2.551  -.030 2.901  F)  .916 .791  .939 .856  .960 .875  .981 .893  1.001 .911  1.022 .928  1.043 .946  .048 15.140 57.341  .043 13.852 51.557  .038 12.564 45.773  .034 11.276 39.989  .029 9.988 34.205  .029 9.828 32.859  .020 7.412 22.637  P  h  £.07  <  )  ;;;WM) ;  %FAT) %PR0)  .022 .016 .023 .026 .029 .033 .036 WM) %FAT*) 255.071 236.866 206.662 182.457 158.253 153.526 109.844 %PR0*) -555.748 -502.926 -450.105 -397.283 -344.462 -334.099 -238.819 a  Relative economic weights for the traits considered are reported in Appendices 2 and 3.  Table 17- Gross Dollar Returns per Generation of Selection for the Indices Considered for Various Protein Differential Prices*  Price for Protein Differential $.00  Index  $.07  $.14  $.21  $.28  $.35  $.42  16.52 16.19 15.88 16.47 8.15 6.88  16.98 16,44 16.39 16.80 5.83 4.92  ~>  Index Index Index Index Index Index  1 2 3 4 5 6  (I,)  (I ) (I ) (I ) (15) (16) 2  3  4  15.30 15.20 14.44 14.46 13.55 11.45  15.58" 15.58 14.78 15.16 12.27 10.36  15.67 15.67 14.91 15.49 10.98 9.27  15.86 15.80 15.14 15.82 9.69 8.18  16.15 15.98 15.46 16.15 8.40 7.10  * Relative economic weights for the traits considered are reported in Appendices 2 and 3.  Table 18. Gross Dollar Returns of Indices 2 Through Index 4 Relative to Index 1 and Index 5 Relative to Index 6. Units are Expressed as Percentages  Price for Protein Differential Contrast  $.00  $.07  $.14  $.21  $.28  $.35  $.42  II vs I I] vs I Ii vs I I5 vs 16  0.66 5.96 5.81 18.34  0.0 5.40 2.77 18.43  0.0 5.10 1.16 18.45  0.38 4.76 0.25 18.46  1.06 4.46 0.0 18.31  2.05 4.03 0.30 18.46  3.28 3.60 1.07 18.50  2  3 4  56  RESULTS AND DISCUSSION  In all cases when protein was included in the index, the coefficient associated with protein increased as the price differential increased. The relative value of the coefficients for other traits in the indices decreased progressively as expected. Individual animal selection for milk and fat produced a gross progress of $15.20 per generation in the absence of protein payment. By selecting for milk, fat and protein but without protein payment, a gross progress of $15.30 per generation resulted. The difference of $.10 per generation was due to the correlated responses in milk and fat yields by including protein in the selection index. As the relative economic value of protein was increased, the differences between selection for base milk, fat and protein (Index 1) and selection based on only base milk and fat (Index 2) narrowed until these two indices were equal at protein differentials of $.07 and $.14 and then increased, thus describing a curvilinear relationship. These observations parallel the results of Anderson et a l (1978). A general pattern of gradual decrease and an eventual increase in the differences between dollar return for Index 1 on one hand and dollar returns from Indices 2, 3 and 4 on the other hand, with increased payment of protein, was apparent from the results. Selection for base milk, fat and protein (Index 1) was equal or superior to all the other forms of selection in gross dollar return at all levels of protein differential. The Dollar Return values also show that measuring protein has its greatest  57  advantage in selection for base milk and protein (Index 3) and selection for fat arid protein (Index 4) at unrealistically high prices for protein as in the case of selection for base milk and fat (Index 2). There did not seem to be any advantage, therefore, of including protein in a selection index except when the price differential was equal to or greater than that of the fat differential, Dollar Returns for selection involving whole milk and the constituent fractions (Indices 5 and 6) continued to decrease with increased protein payment. The gross dollar returns were considerably smaller at all levels of protein differential. This means that gross dollar return, from selection based on total yields of milk, fat and protein is expected to be greater than income from selection based on milk yield and fat and protein percentages. Comparison between Index 5 and Index 6 showed that a selection advantage of 18% for Dollar Return from the unrestricted selection (Index 5) over the restricted selection (Index 6) existed.  58  SUMMARY AND CONCLUSIONS  The analyses in part I showed that cows freshening in the winter season had above average lactational yield but below average lactational values for the constituent fractions. Differences in lactational averages and composition can therefore be related to the season in which lactation started. Annual trends from part I analyses included both environmental and genetic components. Trends from part II analyses based on sire groupings gave estimates of genetic trends to be 51.5 kg milk, 2.77 kg fat, 1.87 kg protein, 0.015% percent fat and -0.049% percent protein, thus indicating a genetic improvement in all traits except protein percentage. This can be explained by selection for milk and fat content ignoring protein. Heritability estimates and genetic and phenotypic correlations from part II analyses agreed with the literature. Genetic and phenotypic correlations among the yields of milk, fat and protein were all strongly positive. The size of these genetic correlations attest to the importance of milk in determining the yield of fat and protein. The values further indicate that yield of the components such as fat is rather closely tied genetically to the yield of protein. It can therefore be said that genes affecting one trait were also responsible for positive changes in the other traits. The breeder selecting for any of the yield traits would automatically be selecting for the other two traits, though with less pressure.  It is antici-  pated, however, that attempts to increase protein percentage by selection on fat content would not be efficient even with the high genetic correlation of 0.74.  The reason being that in the Netherlands there has been indirect  58A  selection for protein percentage through selection for fat percentage but the responses obtained have fallen far below expectations from the regression of fat on protein (Politiek 1957, 1968). The impression is that protein percent hardly increased with fat content. The Dutch experience in commercial breeding suggests that if an increase in protein content is wanted, it may only be obtained by direct selection for this trait. The expected selection responses in the yield traits would be about 5.4% to 8.0% of the lactational yield per generation. Selection for milk yield, however, would result in decreases in the functional composition but selection for fat and protein yields would result in slight to moderate elevation in the fractional composition. The small variation in percent fat and percent protein reflect the futility of attempting to change the relative amounts of fat or protein content in milk. In general, the heritabilities for the percentages are approximately twice that of the lactation yield traits. This is evidence that environment has less effect on the percentages of fat and protein content of milk than on the lactational yields of milk, fat and protein. Despite the high heritabi1ities, however, single trait selection to increase the percentage constituents would result in a significant reduction in the yield traits while leading to very little change or improvement in actual milk composition. The parameter estimates from part II analyses were used in the computations for direct and correlated selection responses in part III. The • results suggest that selecting for milk alone is a relatively efficient means for improving yield of fat and protein. Joint selection for yield of milk, fat and protein would result in more yield of fat and protein than selection for milk alone and would subsequently result in more farm income.  59  If the desired r e s u l t i s for higher y i e l d s of fat and p r o t e i n , then s e l e c t i o n should be based on those t r a i t s .  Current p r i c i n g systems give a r e l a t i v e l y  high value to the base milk f r a c t i o n which d i c t a t e s i t s i n c l u s i o n i n any p r a c t i c a l s e l e c t i o n program.  Selection should not be directed toward i n -  creased percent f a t or percent protein since such a program would cause a decrease i n milk y i e l d r e s u l t i n g in lower d o l l a r r e t u r n s . indices are used, milk y i e l d i s s t i l l  Even when s e l e c t i o n  the most important t r a i t with regard  to d o l l a r r e t u r n s . There was, as expected, an economic advantage of programs employing measurements on m i l k , f a t and protein over programs employing only p a r t i a l measurements.  Based on the B r i t i s h Columbia p r i c i n g system, the value of  base milk was $.236 per kilogram and $3,036 per kilogram of f a t with no payment for p r o t e i n .  When payment for protein was imposed with various d i f f e r -  e n t i a l s of $.00 to $.42 per point of protein above 3.2%, the price per k i l o gram of base milk dropped progressively.  There was, therefore, a decreased  advantage of a three t r a i t s e l e c t i o n over base milk and f a t or base milk and protein or an index with f a t and protein y i e l d s , as the price of prot e i n increased.  Selection for t o t a l y i e l d s of base m i l k , f a t and protein  resulted i n higher d o l l a r returns than s e l e c t i o n for whole milk, and composition. Despite the decreasing demand for milk f a t and the increased demand for cheese and milk protein products, dairymen should s e l e c t for t o t a l milk y i e l d and ignore both f a t and protein y i e l d s as the a d d i t i o n a l d o l l a r returns for m u l t i p l e t r a i t s e l e c t i o n are minimal under current p r i c i n g schemes.  From a n u t r i t i o n a l point of view, the goal could as well be to  increase the t o t a l y i e l d s of f a t and protein rather than j u s t t h e i r percentage f r a c t i o n s or p r o p o r t i o n a l i t y i n m i l k .  Standardization of these  59A  constituents during processing could be used to attain the most desirable composition of the final product to enhance flavour and marketability. However, such a selection program would require changes in the pricing scheme for milk in order to give a financial incentive to the breeder. The analyses discussed in this thesis were empirical derivations and did not consider costs of measurements of fat or protein testing program. Economic justification could be reached only when costs of measurement and testing have been entered into the genetic program and found feasible for implementation.  60  LITERATURE CITED  Anderson, R.D., R.W. Everett and L.D. Van Vleck. 1978, Economic analysis of protein testing for selection. J. Dairy Sci. 61: 102-108. Anonymous. 1972. Editorial comment. New Z, J. Dairy Sci. Tech. 7(3) September. Armstrong, J.G., D.A. Hill and V,W. Kadis. 1971. A study of the composition of Alberta milk. Can. Institute Food Technol. J(4) 9. Barnard, C.S., R.J. Halley and A.H. Scott. 1970. Milk Production. Illife Books Ltd., London. Barnum, D.A., D.A. Biggs, D.M. Irvine and J.C. Rennie. 1969. A study of milk composition in Ontario. Ontario Dept. Agric. Canada. Part 1. Becker, W.A. 1975. Manual of Quantitative Genetics. 3rd ed. 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Schaeffer, L.R., M.G. Freeman and E.B. Burnside. 1975. Evaluation of Ontario dairy sires for milk and fat production. J. Dairy Sci. 58: 109-115. Shute, D.M. and Z.Y. Yankowsky. 1973. Trends in per capita food consumption in Canada (1949-1971). Canadian Farm Economics, Vol. 8, No, 2, April 25-31, 1973. Swiger, L.A., W.R. Harvey, D.0. Everson and K.E, Gregory. 1964. The variance of intraclass correlation involving groups with one observation. Biometrics 20: 818-826.  Systrad, 0. 1971. Selection for protein content in milk. Meld. Nor. Landbrukshogsk 50(27): 119. Tabler, K.A. and R.W. Touchberry. 1959. Selection indices for milk and fat yield of Hoistein-Friesian dairy cattle. J. Dairy Sci. 42: 123,  64  Thompson, N.R. and S. Loganathan. 1968. Composition of cows' milk. II. Genetic influences. J. Dairy Sci. 51: 1933-1935. Van Vleck, L.D. 1966a. Change in variance components associated with milk records with time and increase in mean production. J. Dairy Sci. 49: 36-40. Van Vleck, L.D. 1966b. Heritability estimates of milk production with different numbers of records per sire by herd subclass. J. Dairy Sci. 49: 53-55. Van Vleck, L.D. 1977. Should you select sires for solids-not-fat? Dairy Herd Management, p. 36, 40. Van Vleck, L.D. and G.E. Bradford. 1965. Comparison of heritability estimates for daughter dam regression and paternal half-sib correlation. J. Dairy Sci. 48: 1372-1375. Venge, 0. and K. Christensen. 1969. Expected genetic gain in amount of protein by selecting for butterfat in Red Danish cattle. Acta Agric. Scandinavica 19: 99-102. Verde,. O.G., C.J. Wilcox, F.G. Martin and C.W. Reeves. 1972. -Genetic trends in milk production in Florida Dairy Herd Improvement Association herds. J. Dairy Sci. 55: 1010-1012. Von Krosigh, CM., J.0. Young and G.A. Richardson. 1960. Genetic influences on the composition of cow's milk. J. Dairy Sci. (Abstract). 43: 877. Waite, R., J.CD. White and A. Robertson. 1956. Variations in the chemical composition of milk with particular reference to the solids-not-fat.' I. The effect of the stage of lactation,,season of year and age of cow. J. Dairy Res. 23: 65-81. Wilcox, C.J.,- S.N. Gaunt and B.R. Farthing. 1971. Genetic interrelationships of milk composition and yield. Southern Cooperative Series Bull. No. 515. Agric. Exp. Sta. University of Florida, Gainesville, Florida. Wright, J.A., 0.*A.F. Rook and J.J. Panes. 1969. The winter decline in the solids-not-fat content of herd bulk-milk supplies. J. Dairy Res. 36: 399-407. Wunder, W.W. and L.D. McGilliard. 1964. Heritabilities and genetic correlations for components of milk in Hoi steins and Guernseys. (Abstr.) J. Dairy Sci. 47: 700.  APPENDIX 1  Derivation of variance-covariances of base milk (BM) from whole milk (WM) variance-covariance. Whole milk = BM + Fat + Protein = BM + F + P •-•WM =BM F P Now V  V  C O V  + V  +V  (WM,F)  BM,F  + 2 C0V  =  C O V  BM,P  + 2 Cov  (BM;F)  +  C  0  ™  + 2 C o vF P  V  F  '  P  +  V  F  and (WM,P) ° (BM,P)  C0V  = C  C O V  (BM,F)  =  V  C O V  + C 0 VP  (WM,F)  "  ' P  C 0 V  F +V  (P,F)  " F V  and (BM,P) (WM,P) " (P,F) " P  C0V  = C0V  Cov  V  From (1) V  BM  WM  =  V  " F " P V  = WM  =  WM  V  -  " F " P  V  2  V  V  L  +  C 0 V  V  2  "  V  C 0 V  F  +  V  P  "  2  [  2  (WM,P) "  (BM,F)  C O V  C 0 V  C 0 V  "  2  C  (WM,F) "  F,P  " P]  (WM,F)  2  C 0 V  (BM,P) "  V  C 0 V  "  V  "  O  2  P,F  C  0  V  (WM,P  2  C  ° F,P V  " F] " V  F  }  '  +  P  2  C  0  V  P  '  F  66  APPENDIX 2  Relative Economic Weights ($) at Various Protein Differential Prices 2 for 1 kg each of Base Milk , Fat and Protein  Protein Differential Trait  $.00  $.07  $.14  $.21  $.28  $.35  $.42  Base Milk  0.2359  0.2135  0.1911  0.1689  0.1463  0.1239  0.1015  Fat  3.0359  3.0359  3.0359  3.0359  3.0359  3.0359  3.0359  Protein  0.0  0.8890  1.5421  2.1952  2.8483  3.5014  4.1545  Economic weights based on $33.39/100 kg milk and 28<£ fat differential. Base milk = Whole milk - (Fat + Protein).  67  APPENDIX 3  Relative EconomicWeights ($) at Various Protein Differentials for 1 kg of Whole Milk, and 0.1% each of Fat and Protein Content  Protein Differential Tra i t  $.00  $.07  $.14  $.21  $.28  $.35  $.42  Whole Milk  0.2359  0.2135  0.1911  0.1689  0.1463  0.1239  0.1015  % Fat  0.28  0.28  0.28  0.28  0.28  0:28  0.28  % Protein  0.0  0.07  0.14  0.21  0.28  0.35  0.42  Economic weights based on $33.39/100 kg milk and 28<£ fat differential.  APPENDIX 4  Genotypic and Phenotypic Variances of Traits Analysed (kg )  Trait  Genetic  Phenotypic  Milk  524,00  2883782  Fat  1062.24  4231.22  Protei n  589.12  2725.42  % Fat  .04749  .11394  % Protein  .018148  .03426  69  APPENDIX 5  Genetic Correlations with Standard Errors  Milk  Fat  Fat  .60 ± .075  Protein  .75 ±.048  %  Fat  % Protein  -.26S±  .107  -.33 ± .092  Protein  % Fat  .82 ± .036 .62  ±  .065  .34 ± .091  .27  ±  .090  .37 ± .082  .74 ± .041  

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