SELESTWN 0F DAIRY CATTLE EFGR OVERALL EXCELLENCE i’hesés far the Degree of Pb. E}. MECHEGAN STATE UfliVEfiSEW DEVGN FRANKUR ANDRUS 1m This is to certify that the .' . . ~ thesis entitled SELECTION OF DAIRY CATTLE FOR OVERALL EXCELLENCE presented by DeVon Franklin Andrus has been accepted towards fulfillment of the requirements for Ph.D. :19pr in Dairy 5&0ch mafl/th on D. McGilliard Majorprofeuor Date Oct. 2' 1972 0-7639 ABSTRACT SELECTION OF DAIRY CATTLE FOR OVERALL EXCELLENCE By DeVon Franklin Andrus Traditionally, selection of dairy cattle has been for milk production. Profitable production is actually desired. Profit is a complex variable which should allow application of index selection. Such selection has been limited in dairy cattle. Chief deterrents have been volume of data required, high costs for collection and pro- cessing, large standard errors of estimates and ignorance of relative economic weights of contributory traits. This study seeks to discover relative economic weights for several important traits and suggest means for applying a widely used method of constrUction of indexes for plant breeding to selection of dairy cattle. Data were from the lifetime production, health and feed consumption records of 111 cows in the Michigan State University re- search herd. Seven traits were studied; milk production, butterfat test, mastitis cases, live freshenings per opportunity, milking time, body weight and herd life. Lifetime profit was computed for each cow from income and eXpense records. Lifetime data were submitted to a least squares, multiple regression analysisvfith profit as dependent variable and traits studied as independent variables. Partial regression co- efficients indicated the following contributions to profit per year of herd life: one live freshening, $70; one year of herd life, $7.74; increase of .1% in butterfat test, $75.80; increase of 454 g in body weight, 8 cents; increase in milking time of one minute per milking, $3.74; increase of one case of mastitis per year,-—$13.l6; and increase of 454 g per year in milk production, 2.6 cents. Relative economic weights were indicated by corresponding standard partial regression coefficients of .22, .10, .31, .09, .03, -.38 and .64. Profit per year of herd life was predicted with an equation using the derived coefficients. Rankings by the prediction equation and actual profit were compared. Agreement was generally good. Four variables, milk production, butterfat test, mastitis cases and live freshenings per opportunity were statistically significant contributors to profit. Heritability estimates from the literature were applied to economically significant traits to determine which might be included in a genetic selection index. Live freshenings per opportunity dropped out due to zero heritability estimates. Rankings by economically significant traits, final index, actual milk production and mature equivalent milk production were com- pared. The reduced and final indexes were both more accurate in pre- dicting profit than either measure of milk production. Actual milk production was more accurate than mature equivalent milk production. Of variation in profit, 68, 66 and 56% was accounted for by the prim- itive, reduced and final indexes. Effects of culling or selection for special mating by reduced index, final index and two different measures of milk production were M compared. Profit from culling bottom 20% of herd was increased most by the final index. The final index increased profit least when sel- ecting the top 20% of cows. The final index was more accurate in determining profit than any measure currently in use. Progress in selection for profit could be made by means of the index. Milk production would not increase as rapidly as under selection for milk production alone but other import- ant economic traits would improve more rapidly. Butterfat test would increase. This might be an undesirable effect. Other behavioral and type traits should be included to account for more of the variation. The methods of Grafius (1965) could probably be applied more fully by substituting a subjective rating for actual profit in the regression equation. SELECTION OF DAIRY CATTLE FOR OVERALL EXCELLENCE By DeVon Franklin Andrus A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Dairy 1972 La ‘ ACKNOWLEDGMENTS I wish to express my gratitude to Dr. Lon D. McGilliard, my major professor, for his patience with my failures, perse- verance in the face of my confusion, and endurance of my plodding. He has always been available to listen with a sympathetic ear, encourage with a stout spirit, and advise with a gentle tongue. I also wish to thank the other members of my graduate committee, Dr. James C. Braddock, Dr. John E. Grafius, Dr. John T. Huber, and Dr. William E. Magee for their patience, advice, and encouragement. I am especially grateful to Dr. Grafius whose work inspired the approach taken in this study. Many others helped me in many ways. I am indebted to Dennis V. Armstrong, A1 Thelen, Dr. Clinton E. Meadows, Dr. John L. Gill and other members of the staff of the Michigan State University Department of Dairy. I drew a lot of inspiration, help and suggestions from my fellow graduate students, particularly Yu Yu and the boys in room 17, Gurdas Dass, Russel Erickson, Charles Goeke, Lee Kucker, Frank Roche, Philip Spike, and Evans Wright. Of course, I am thankful for the assistantship provided through the agency of Dr. Charles A. Lassiter, Chairman of the Department of Dairy. Without it I would never have passed this way. ii Most of all, once more and forever, I am grateful beyond my power of expression to my wife, Joanne, and my eight children, Marie, Robyn, Dawn, Kyle, Mark, Jay, Sylvia, and Ford, for their sacrifices, their understanding, and their support throughout the entire period of my doctoral study. iii TABLE OF CONTENTS INTRODUCTION..................................................... REVIEW OF LITERATURE............................................. History and development of index selection....................... Single trait indexes..................................... Multiple trait selection................................. Income over feed cost.................................... Interrelationships among traits ................................. SOURCES AND TREATMENT OF DATA.................................... Sources of data.................................................. Overall excellence............................................... Income........................................................... Income from sale of calves............................... Income from sale of milk................................. Income from salvage...................................... Expenses......................................................... Rearing costs............................................ Forage costs............................................. Concentrates costs....................................... Breeding costs........................................... Labor costs for milking.................................. Labor costs other than for milking....................... Housing, overhead and miscellaneous costs................ iv 18 18 20 21 21 22 23 24 25 26 27 27 28 29 29 Fixed veterinary costs................................... Variable veterinary costs................................ Interest on alternative investment costs................. Relating profit to time.......................................... Construction of the selection index.............................. Milk production.......................................... Butterfat test........................................... Mastitis................................................. Live freshenings per opportunity......................... Milking time............................................. Body weight.............................................. Herd life.OOOOOIOOCOOOOOOO00.0.0...OOOOOOOOOOOOOOOOOOOOOO Other possible index traits.............................. Determination of economic importance............................. Comparisons of rankings.......................................... Comparison of means and effects on profit........................ RESULTS AND DISCUSSION........................................... Comparison of profit and ranking................................. Relative economic importance of independent variables............ variables dropped from index...O000......OOOOOOOOOOOOOOOOOOOOOOO. Herd lifeOOOOOOOOOOOOO0..00......OOOOOOOOOOOOOOOOOO00.... BOdy weight.O0..OI.O0.00.0.000000000000000.000.000.000... Milking time............................................. Economically important traits.................................... Milk production.......................................... Mastitis................................................. Butterfat test........................................... V 30 30 32 32 32 33 34 34 34 36 37 38 39 40 43 43 44 44 49 54 55 56 57 58 60 60 60 Live freshenings per opportunity......................... Comparison of different indexes.................................. Effects of index selection on other traits....................... Analysis based on M.E. milk production........................... SUMMARY AND CONCLUSIONS.......................................... LIST OF REFERENCES...00.0.0000...0.000......OOOOOOOOOOOOOOOOOO0.. vi 61 62 67 71 73 78 Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table 10. 11. 12. l3. 14. 15. 16. LIST OF TABLES Milking time to assess labor for milking charges........ Distribution of cows by milking time, as rated from memory by farm manager and herdsman..................... Milk prices to determine income from sale of milk....... Rearing Costs Of Calves..0...0..OOOOOOOOOOOOOOOOOOOOOOOO Rates charged for variable veterinary services.......... Partial regression coefficients and their standard error-8000......OOO...O0....000......OOOOOOOOOOOOOOOOOOOO Standard partial regression coefficients with their Standard errors.I0.00..OOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOO Comparison of estimated profit, profit, and rank according to eaChOO0.0.0...0..OOOOOOOOOOOOOOOOOO00...... Proportion of profit explained by various selection indexeSOOOOOOOOOOOIO.IOOOOOOOOOOOOOOOOOOOOOO0.00.00.00.00 Ratios of standard partial regression coefficients of each other variable to milk production.................. Partial correlation coefficients and R2 deletes......... Simple phenotypic correlations.......................... Comparison of rankings based on four different measures 0f worthOOOOCOO....0OOOOOOCOOOIOOOOOOOOOOOOOOOOOOOOOOOOO Means of primitive index traits under various culling SChemeSOOOOO0......OOOOCOOOOOOOCOOOOOCOOOO0.00....COO... Means of primitive index traits under various selection SChemeSOOOOOOOOOO00....0.....00..OCOOOOOOOOCOOOIOOOOOOO. Standard partial regression coefficients with their standard errors and significance, mature equivalent milk prOdUCtionO...OO...OOOOOOOOOOOOOOC0.000000000000000 vii 20 20 23 26 31 41 42 45 49 50 51 52 64 67 70 71 Table 17. Partial regression coefficients and their standard errors, mature equivalent milk production........................ 72 Table 18. Partial correlation coefficients and R2 deletes, mature equivalent milk production............................... 72 viii Figure 1. Figure 2. LIST OF FIGURES Regression of income over feed cost on average first lactation bOdy weightOOOOOOOOOOOO0.0000000000000000000. Distribution of milking time as remembered by farm manager and herdsmaHOOOOOOO0.0.0.0000...OOOOOOOOOOOOOOO ix 14 59 INTRODUCTION Scientific breeding of dairy cattle has been devoted, primarily, to the increase of milk production. The reason is milk is the main saleable product of the dairy cow. However, the single goal of increasing milk production may not always be the most desir- able objective of a sound breeding program. The fact is often over- looked that cows are not usually kept only to produce milk but to return a financial profit. Milk production is closely linked to profit. Even so, other important factors may make significant con- tributions to profit. Examples are butterfat test, susceptibility to disease, reproductive efficiency, ease of milking, temperament, efficiency of feed utilization, type characteristics, herd life, salvage value, etc. Index or total score is the most efficient method of selection for progress in overall worth (Hazel and bush, 1942). Methods of index construction, including means of estimating necessary parameters have been available for a relatively long time (Hazel, 1943). Exten- sive applications have been to poultry breeding and other species where production is concentrated in a relatively few large establishments, offspring per parent are many, generation interval is short, and unit cost per animal is relatively small (Kempthorne and Nordskog, 1959; Cunningham et a1., 1970). Applications to large animals have not been anywhere near so extensive. In spite of urgings from such a noted authority as Lush (1960), "To make selection more accurate, we need sounder and simpler selection indexes," use has been limited. This has been especially true of multitrait selection for overall excellence. Reasons for this slow advance are many. Conventional index construc- tion requires many data, standard errors of estimates are high, costs are great, and results are a long time in coming. Relative economic weights of various traits are rarely known. Often, few people other than the person constructing a particular index take the trouble to learn how the index was constructed or how it can be used. This study was undertaken with the goal of attaining three main objectives. 1. Develop a simple index for evaluating cows on overall excellence. 2. Discover the relative economic importance of some common traits. 3. Apply the index to selection of cattle and suggest means of improving overall excellence. Even partial attainment of these goals may help speed adoption of index selection to improvement of large animals. REVIEW OF LITERATURE Selection for overall excellence involves simultaneous selection for more than one trait. Total score, or index selection, is a modern development, application of which has increased steadily but relatively slowly. The greatest practical obstacle to widespread adoption was pointed out by Hazel and Lush (1942), "the difficulty of knowing how much importance should be given each trait in making up the score." This review traces briefly the history of index selection with emphasis on work with dairy cattle and details efforts to under- stand interrelationships among traits in this study. Choice of traits and interrelationships among traits chosen are factors which determine "how much importance should be given each trait." History andcievelopment of index selection Even though index selection is superior to two popular alternative methods, independent culling levels and tandem (Hazel and Lush, 1942), few applications have been made to breeding dairy cattle or other large animal species. Smith (1936) developed a discriminant function for selection of plant varieties on their genotypes in the presence of errors of observations. Since his arguments applied to selfing varieties, there was essentially no genetic theory involved. The genetic basis for index construction and a method for calculation of genetic correlations were outlined by Hazel (1943). He listed phenotypic and genetic constants needed and detailed instructions for finding them by con- structing several examples of indexes. 3 4 Many sophisticated refinements have been added to the theory of index construction since then. A method of restriction of selec- tion indexes has been used extensively in poultry breeding. The idea is to hold one of the important traits constant while making progress by selection for overall merit (Kempthorne and Nordskog, 1959). Recently, a further refined and simplified method of index restric- tion was introduced to permit simultaneous control of one or more traits (Cunningham et a1., 1970). These and other contributions to simultaneous multitrait selection require the same basic information listed by Hazel and Lush (1942). Application has been widest to species producing large numbers of offspring in multiple births and possessing short generation intervals. Single trait indexes In dairy cattle breeding, surprisingly most index selection has been for single traits. An index permits consideration of effects of relatives, contemporaries, and other factors, such as environment on the trait under selection. Many examples of use of this type of index are available: Intraherd selection for butterfat production in Jerseys utilizing records of the cow, her dam, daughters, and sisters (Legates and Lush, 1954), intraherd selection of milk production cor- rected to 3.5% butterfat for Holsteins (McGilliard, 1954), utilizing information about milk production from parents and grandparents in assessing the genetic potential of young Holstein bulls (Barr, 1962), evaluating cows on their own records, records of their dams, daughters, paternal sisters, and maternal sisters (Deaton, 1964), estimating average transmitting ability by utilizing milk production records of 5 relatives on both sides of the pedigree (Eastwood, 1968), and estimat- ing the transmitting ability of a bull on his daughters performance relative to contemporaries of the same breed freshening in the same herd, year, and season (Agricultural Research Service, USDA, 1970). Indexes for selection of a single trait have been widely used because of the relative ease of assembling and processing data. They do not require the kind of genetic correlations nor economic values described and calculated by Hazel (1943). Multiple trait selection Studies indicate the possibility of genetic gain per year in milk production of 1% to 2% of the average. To realize potential gains, sounder and simpler indexes are needed (Lush, 1960). Four types of in- formation are needed for multitrait index construction, phenotypic correlations, genetic correlations, heritabilities, and economic import- ance. A great deal is known about phenotypic correlations, quite a lot about heritabilities, but little about genetic correlations. Economic importance deserves much closer scrutiny than it has received (Lush, 1960). Many indexes have been constructed with more or less arbitrary economic weights. 0f two indexes on type and butterfat production in Jerseys, one rated type and production equally, the other rated produc- tion at three times the value of type (Harvey and Lush, 1952). In a series of indexes calculated for Jerseys from value of milk on the Chicago fluid market and value of butterfat on the Boston cream market, 1 kg of fat was equal to 17.57 kg of 5.3% milk (Tabler and Touchberry, 1955). In similar indexes for Holsteins 23.5 kg of 3.6% milk was equal in value to 1 kg of butterfat (Tabler and Touchberry, 1959). In both 6 studies butterfat test was given an arbitrary economic weight of zero. Workers have commented on shifting economic weights from herd to herd and time to time as prices change (Legates and Lush, 1954; Cunningham et a1., 1970). Income over feed cost Most studies of selection on net merit or overall excellence use income over feed cost as an indicator of excellence. Feed cost has been recognized as the single item contributing most to the cost of milk production (Davis, 1962). For this reason, income over feed cost has been included in most DHIA reports for many years. Of 14 factors contributing significantly to net income on 340 Michigan dairy farms over 5 years, the six most important were milk production per cow, milk price per 45.36 kg, dairy cattle sales per cow, grain consumed per cow, feed cost per cow, and hay equivalent consumed per cow. They had coefficients of determination of .066, .043, .043, .031, .013, and .013. Milk production per cow and grain consumed per cow were linearly related to profit (Speicher and Lassiter, 1965). To determine replacement policies which would maximize income over feed, six culling criteria at various prices were compared by computer simulation of 15 years. Criteria compared were mature equiv- alent (M.E.) milk (305 days), mature equivalent gross income from milk, actual milk (305 days), actual gross milk sales (305 days), actual in- come over feed costs (365 days) and present value of expected gross income of cow and her subsequent replacements. There were no signif- icant differences between criteria in generating income. A change in prices did not dictate a change in strategies. Genetic ability to 7 produce milk was highest at the end of 15 years when culling was on M.E. milk production, but differences between strategies in return over feed were minor (Rundell, 1967). McDaniel et a1., (1968) studied income over feed cost for individual cows from lactation records of 57 Ayrshires, 68 Brown Swiss, and 57 Holsteins in the same herd. Effects of milk prices, feed prices, production and physical size on ranking cows for income over feed cost were investigated. Eleven sets of milk prices and feed prices had correlations with income over feed cost ranging from .97 to 1.00 in- dicating that all ranked cows in about the same order. Milk production was the best single indicator of income over feed cost at average prices. Precision in estimating income over feed cost was improved when body weight, weight gain during lactation, and forage intake were included with milk production. An estimate of income over feed costs was sig- nificantly bettered by adding body weight and feed consumption to pro- duction as compared to production alone. Ranking of cows from DHIA records of income over feed cost based on milk yield, body weight, weight gain, and feed intake appeared to be accurate for culling cows on profitability. This conclusion would hold only if DHIA records of income over feed cost were reasonably accurate. If incorrect feed consumption data were reported for individual cows, rankings of DHIA income over feed cost would be of little use regardless of results by research workers. This is an important point because individual owners and herdsmen have been notoriously careless in reporting feed consumption data. Also, feed consumption data are virtually unknown for the individual cow in many large herds where feeding is by group. 8 In 1,801 Holstein herds in the northeastern United States, milk yield accounted for about half the total variation in income over feed cost. The only measure of feed closely related to income over feed cost was amount of concentrates fed. Amount of hay fed had little in- fluence on production or income over feed cost. This led to the con- clusion that estimates of feed costs other than for concentrates were of little help (Miller et a1., 1968). Milk production, feed consumption, and body weights in first lactation of 425 Holstein cows were studied by Miller et a1. (1971) for associations among several arbitrary measures of economic efficien- cy, 4% fat corrected milk yield, income over feed cost, feed efficiency, and feed cost per 45.36 kg of milk. Two milk prices with a single but- terfat test differential ($.08 per .l%) and four feed price conbina- tions were used. High forage prices reduced income over feed cost more than high grain prices. Body weight was positively related with feed cost and feed cost per 45.36 kg of milk but negatively related to in- come over feed cost. "Milk price, feed price, and milk yield were the most important factors affecting income over feed cost." They account- ed for 60, 12, and 19% of the variation. Interrelationshnnsamong traits Assignment of economic weights to traits depends upon which traits are considered and interrelationships among them. Only traits under consideration in this study are reviewed here. Relationships between milk production, butterfat production, and butterfat test have been so extensively researched and so widely published as to be common knowledge. Hence,they are not reviewed. They have been mentioned, perhaps superficially, in a few cases where their relationships with other traits were encountered. Because cross breeding improves reproductive performance of cows and livability of calves in beef cattle (Cartwright et a1., 1964; Gaines et a1., 1966), it has become accepted for increasing performance. Cross breeding has not been as acceptable or popular with dairy cattle breeders. Wide differences between breeds in milk composition and pro- duction have acted as deterrents even though the same benefits in re- production and livability in beef cattle are available. Dickinson and Touchberry (1961) compared livability of purebred Holsteins and Guernseys and crosses between the two. More than twice as many purebreds were lost as cross and 3/4 breds. Overall death losses to calving age were 32.7% for purebreds and 13.4% for crossbreds and criss-crosses. There was no significant difference between liv- ability and production. The improved livability was sufficient to merit the conclusion that there is a place for crossbreeding in manage- ment plans of commercial grade herds. This agrees with the observation of Lush (1960) that rotational crossing might become profitable if heterosis is important enough. In seven measures of reproductive performance, services per conception, age at first calving, interval from first service to con- ception, gestation length, calving interval, calving date to first heat, and calving date to first service, Verley and Touchberry (1961) found length of gestation the only one significantly heritable. Rela- tionships of all other factors to mating system were consistent, small and nonsignificant. Data came from a selected group of animals capable of conceiving, maintaining pregnancy, and successful parturition. Wilcox et a1. (1966) analyzed lifetime reproductive performance 10 records of more than 1,000 cows in Florida institutional herds. No genetic relationship between production and livability was detected. However, abortion rates were 5.3% for purebreds and 3.5% for cross- breds. Though "losses due to reproductive failure, mastitis, lameness, and other diseases were twice as great among purebreds as crossbreds, no evidence of heterosis was detected." The latter finding disagrees with findings of Dickinson and Touchberry (1961) cited earlier. Defi- .nitions of parameters as well as treatment of data and the population under study were decidedly different. In disagreement with most other workers, Wilcox et a1. (1957) found heritability of breeding efficiency of .32 and longevity .37 in the Overbrook Hospital Holstein herd in New Jersey. Breeding efficien- cy was defined as calving interval. Correlation between the two traits was near zero. Parker et a1. (1960) attributed heritability in the Overbrook herd to heritability for production and favoritism to daugh- ters of high producing cows. Generally, findings of research workers have indicated herit- ability of reproductive traits is low. Pou et a1. (1953) found repeat- ability and heritability of fertility near zero when measured by non- returns to first service, services required per conception, and calving interval. Many workers have noted a positive relationship between pro- duction and calving interval (Rennie, 1952). However, Smith and Legates (1962) found intraherd-year-season phenotypic correlations between 90-day production and days open were not significant. They concluded that production has little effect on this measure of fertil- ity. 11 Relationships between production and longevity and reproduc- tion and longevity have been attributed to factors other than additive genetic effects (Verley and Touchberry, 1961; Andrus, 1968). Herd life has been largely dependent upon management decisions. For a re- view of literature related to herd life see Andrus (1968). Body weight is easy to measure. The high accuracy with which it can be estimated by its almost interchangeable substitute, heart girth, has made this even more true. Therefore, it has been the favorite indicator of body size. There is a voluminous literature, reaching back many years, on the relationship of body weight to pro- duction. Large differences in size between breeds and size as an easy way of increasing production have fanned the flames of numerous controversial results. The real differences in market value of in- dividual bull calves and similar differences between salvage cows of different sizes have been main contributors to the arguments. McDaniel and Legates (1963) found a positive linear regression of milk yield on weight, estimated from heart girth measurements, in- dependent of age. Though regressions were statistically significant and consistent, they were small ranging from 1.011: .31 to 1.81 ii .56 kg of milk for each increase of one kg in body weight. Clark and Touchberry (1962) found milk production increased 1.34 kg for each kg increase in body weight (scale weight) when age was held constant. Erb and Ashworth (196l)compared the relative effects of age and weight on yield in an experimental herd of Holstein, Jersey, and Guernsey cows. When effects of age and breed were removed, they found weight did not affect production significantly, though there was still a positive relationship. Intrabreed age was more than twice as important as 12 weight in determining production. This is in contrast to Clark and Touchberry (1962), who found weight more important than age. Erb and Ashworth (1961) found striking differences between breeds. They con- cluded that "the effects of weight on yield are interpreted too highly if differences due to age and breed are not removed." They cited ex- amples of herds where the larger cows were the lower producers indicat- ing the possibility of lowering production if selection is on size alone. In Michigan DHIA data from herds of the same three breeds with greater numbers, Miller and McGilliard (1959) found intraherd partial regressions of about 34.02 kg of milk per month of age and 2 kg of milk per kg body weight at first calving. Heritabilities from paternal sister correlations ranged from .4 to .8 for weight and .3 to .6 for production. These are higher than those found by Clark and Touchberry (1962). The latter workers obtained estimates of .29, .44 and 0 for body weight, milk production, and but- terfat production from first lactation data. When all lactations were included, estimates were .19,.43, and .41. Miller and McGilliard (1959) found genetic correlations of .3 between weight and production. This disagreed with Clark and Touch- berry (1962), who obtained values ranging from near zero in first lactation to -.53 in second lactation. When they combined the first four lactations, genetic correlation between body weight and milk production was-.12, leading to the observation that selection for greater size might lead to a reduction in milk production. In the same study genetic correlation between milk and butterfat production was .90. Relationships between yield and age cannot be estimated without bias. Older cows are selected cows. Effects of age are combined with 13 effects of culling. Weight isla further confounding factor (Lush and Shrode, 1950). Clark and Touchberry (1962) pointed out that environ- mental conditions which are conducive to large size also contribute to higher milk production. Kelley and Butcher (1967) concurred in this view. They found average weight of animals in a herd might be useful in evaluating environmental differences between herds. Large correla- tions between herd averages of weight and production provide further supporting evidence (Miller and McGilliard, 1959). Body size, as such, is not the important consideration. Milk production, regardless of how attained, is not the goal. Profitability of each cow is the desired end. Small cows remaining in a herd after culling on production regardless of size, produced more efficiently than large ones in the same herd (Clark and Touchberry, 1962). In attempting to relate size and several other factors directly to profit, Miller et a1. (1971) found the regression of income over feed cost on body weight was curvilinear (Figure 1). Maximum income over feed cost was reached at about 530 kg body weight, 50 kg below herd average. This relationship was apparently due to reduced effi- ciency of feed utilization at heavier weights. Rate ofnfilking has always been recognized as an important economic factor. Adoption of machines for milking intensified in- terest. Most studies have been from an engineering viewpoint to improve chore routine or equipment. Early workers claimed most cows could be trained to milk in essentially the same amount of time. Four minutes was often suggested as an appropriate time (Peterson, 1944; Hopson, 1944). Most studies have centered around the rate of milk flow which has been shown by Donald (1960) and several other workers to be INCOME OVER FEED COST (3) 14 400 360 r ‘— 320 b - 280 b '- 240 b ._ 200 l _J l l 450 500 550 600 650 700 AVERAGE BODY WEIGHT (K.G.) Figure 1. Regression of income over feed cost on average first lactation body weight.3 a After Miller et a1. (1971) 15 highly heritable. Few studies have analyzed variation of time required to milk. Rate of milking was investigated by Lamb (1969a, 1969b). Sire effects were highly significant. Milk production was the most import- ant factor affecting rate of milking. Touchberry and Markos (1970) agreed that milk production was the most important factor affecting milking time. They found that time required to milk could be predicted with accuracy from yield of milk per milking and rate of flow. "Milk- ing time increased .51 min for each increase of 1 kg of milk per milk- ing, independent of maximum rate of flow." Differences among cows of the same breed accounted for 55.7% of the variance in time required to milk and 52.2% of the variance in rate of flow. Markos and Touchberry (1970) found heritabilities of .54 i .12 for rate of flow and .22.i .13 to .27.: .14 for milking time. They reasoned that many slower milking cows would also be lower producers; hence, selection for milk produc- tion tends to apply pressure for improved milking time. Milking time is apparently at least moderately high in herit- ability but is closely associated with milk production. Research on mastitis has been extensive in volume; however, most of this has been directed toward improving environmental practices or prescribing treatments for its cure. Relatively little has been done from a genetic standpoint. It is generally conceded that mastitis is a major disease problem and one of the most costly disease problems of the dairy industry. Janzen (1970) gives an extensive review of economic losses from mastitis. Possible genetic origins of susceptibility to mastitis or udder disease were noted early. From data from the Annual Report of 16 the New Zealand Dairy Board for 1945, Lush (1950) estimated heritability by intraherd regression of daughter on dam was .38 for susceptibility to mastitis. He indicated that many cases of apparent heritability of mas- titis had been called to attention before that time, usually on an in- dividual basis, because of their peculiarity. The work of Murphy et a1., (1944) was cited as an example. Legates and Grinnells (1952) estimated heritability of resistance to mastitis was .27, in substantial agreement with Lush (1950). Legates and Grinnels (1952) found small, positive, nonsignificant phenotypic correlations between susceptibility to masti- tis and milk and butterfat production. Genetic correlations were not interpretable. Schmidt and Van Vleck (1965), in a different approach, found an heritability within herd of number of quarters infected with Streptococcus agalactiae of .20. They also cited other smaller herit- abilities of various measures of mastitis and pointed out possible reasons for the lack of agreement. Infection with S. agalactiae was positively correlated with milk production and milking time, but values were small and nonsignificant. Correlation with age was moderately high. Heritabilities ranging from —.03 to .12 were reported for presence of various mastitis causing organisms and secretion of abnormal milk by Wilton and Van Vleck (1969). The diversity of results and the fragmentary nature of avail- able information about relationships between various traits underscore the difficulties associated with construction of a meaningful selec- tion index. Deploring the failure of plant breeders to make wider use of selection indexes but recognizing probable reasons for their apathy, l7 Grafius (1965) developed a simplified method of index construction for breeding small grains. It permitted use of large volumes of accumulated data on multiple traits and comparison of a relatively large number of lines. He termed it a “backward approach." This designation was meant to describe the manner in which one of the most serious problems of index construction was circumvented, assigning economic weights. The usual approach is to assign economic weights arbitrarily or analyze voluminous statistics to estimate them. Grafius (1965) rated various strains for overall excellence by comparing them, trait by trait, with a standard or "yardstick" variety. Economic weights for individual traits were then determined by submitting the raw data, with the over- all ratings as right hand sides, to a least squares computer routine for solution of regression coefficients. The index was completed by applying heritabilities to traits significant economically. Genetic correlations, calculation of which is another deterrent to applied use of selection index theory, were assigned zero. Since this method has been useful in practical application to breeding of small grains, it may be applicable to animal breeding problems as well. SOURCES AND TREATMENT OF DATA Sources of data For traits desired in the index extensive records of cows that had completed their careers in a herd were needed. All registered Hol- steins freshening for the first time in the Michigan State University herd after August 1, 1959, and completing their careers in the herd by December 31, 1970, were included,lll cows. August 1, 1959, was the first date for which individual grain feeding records were available on the DHIA reports. December 31, 1970, was when processing of data commenced. Birth and freshening dates and milk and butterfat production records were from the Michigan DHIR card file and DHIA annual herd summary reports. Average forage fed, individual grain feeding records, and most of the body weights were from DHIA monthly herd summary reports Individual sickness, veterinary treatment, calf livability, mastitis cases, etc. were from the individual health record card files. The herd book required by the Holstein Friesan Association of America for main- taining a herd of registered cattle was the source of identification numbers and a check on production and reproduction records and body weights. It proved to be a more complete and reliable source of body weights than the DHIA monthly herd summary reports. All sources were checked and cross checked where information was duplicated. Milking times were not recorded. Milking time was approximated by the farm manager and the herdsman independently ranking the 111 cows in one of five groups. 1. Much faster milking than average. 2. Faster milking than average. 18 l9 3. About average in milking Speed. 4. Slower milking than average. 5. Much slower milking than average. They were instructed to rate only those cows they could definitely re- member. After rating all the cows independently, they were asked to resolve any differences in their individual independent ratings. Both these men had been with the herd throughout the entire period covered by this study and had worked with every cow. They would be most like- ly to remember the extremes. Hence, any cow not listed in any group by them was included in group 3. The works of Touchberry and Markos (1970) and Lamb (1969b) were used to approximate milking times for each of the five groups. From their means and standard errors together with the distribution in the survey of the farm manager and the herdsman, the following times were assigned: group 1) <. 2.5, group 2) 2.5 to 4.0, group 3) 4.0 to 6.0, group 4) 6.0 to 8.0, and group 5) :> 8 min. Means were set for each group at 2.5, 3.25, 5.00, 7.00 and 10.00 min. When these means were applied to the double 4 herringbone parlor system to determine how much of a man's time was occupied in milking each cow, the resulting labor efficiency was too large to be realistic. Milking time only does not account for time changing machines. By trial and error, I found that adding one min to each of these mean times would bring the labor requirement into realistic range. This procedure seemed reasonable since each cow should share approximate- ly equally in time required to change machines regardless of her milking speed. The final figures to determine milking time in assessing labor charges are listed in Table 1. 20 Table 1. Milking time to assess labor for milking charges. Group Milkinngi e (min) 1. Much faster milking than average ' 3.5 20 Faster milking than average 4.25 3. About average in milking Speed 6.00 4. Slower milking than average 8.00 5. Much slower than average 11.00 ' Table 2 shows the distribution of cows in the five groups as actually remembered by the farm manager and herdsman and when cows not remembered are included in group 3. The latter distribution approxi- mates those found by Touchberry and Markos (1970) and Lamb (1969b). Table 2, Distribution of cows by milking time, as rated from memory by farm manager and herdsman. Cows actually Cows not remembered Group remembered included in group 3 1. Much faster 7 7 2. Faster 12 12 3. Average 14 84 4. Slower 10 10 5. Much slower 1 1 Heritabilities for the application of the index to selection of cows as parents of the next generation were from the literature. Most often quoted or most recent figures were used to gain most realism. Overall excellence The first problem in constructing a selection index on overall excellence was to define overall excellence. Since cows are kept for profit, it seemed most appropriate to define overall excellence as 21 profit, simply income minus expense. Time is always relevant so the definition was refined by placing profit on unit time by dividing prof- it by years of herd life. The final definition of overall excellence or net merit was profit per year of herd life. The equation was: Profit per year of = {Income during life - Expense during life productive herd life Years of productive herd life Both elements in the numerator of this equation are complex and tedious to determine. The denominator is relatively simple to obtain. Procedures are eXplained in detail. Income Three variables that contribute to income are sale of calves, sale of milk, and salvage value of the cow. Income from sale of calves Income from sale of calves from a cow depends upon two factors number of calves born to the cow which are sold and price received for each calf. Since many of the calves produced by these cows were not sold but were kept for replacement heifers it was necessary to consider the potential sale value of these calves. Also, whether a cow has a heifer or a bull calf is a matter of chance. It was not desired to give credit for favorable chance nor to discriminate for unfavorable chance where such possibilities could be removed. Market prices, dif- ferential management practices that affect the calf's chances of liv- ing or alter its market value and season of birth are other factors associated with income from sale of calves. A COW'WaS credited with a salgflfle calf at average value every time she had a live freshening, regardless of the sex of the calf. The average value of a saleable calf allowed $30 as the value of a 3-day-old bull and $130 as the value of a 3-day-old registered 22 heifer calf. These values were averaged to arrive at $80 as the average value of a saleable calf. The values were obtained in consultation with the farm manager. Thus, income from sale of calves was $80 times the number of live freshenings. Income from sale of milk Actual income from milk is a function of amount sold in kil- ograms and price per kilogram. Since they are not accounted for else- where, transportation and marketing charges must be deducted from this gross value to arrive at a net income from sale of milk. The price of milk during the period covered by this study was based upon butterfat test. A base price was established for milk testing 3.5% butterfat. Milk varying in test from the 3.5% base was paid for at the base price plus or minus a differential for each .1% above or below the 3.5% base test. Monthly milk prices for southern Michigan were from the Michigan Milk Messenger, volumes 42 to 51, June, 1960 to May, 1970. The super pool, adjusted blend prices for the Jackson, Lansing Zone (3c zone) were base. Marketing charges were deducted from these prices. The remainders were then summed and divided by the number of months to give an average price of $4.435 per 45.36 kg f.o.b. the farm. Farm records showed hauling costs of $.20 per 45.36 kg in 1960 and $.30 per 45.36 kg in 1970. The weighted averaged for the total period was approximately $.235 per 45.36 kg. When this was deducted from the average price f.o.b. the farm, it left an average price, f.o.b. the processing plant, of $4.20 per 45.36 kg for milk testing 3.5% butterfat. The differential also varied from $.065 to $.08 during the 10 years for which records were consulted. The weighted average 23 differential was $.0707. This was rounded to $.07 per .1% butterfat in determining prices used to calculate income from sale of milk. To avoid giving any cow an advantage in income because of price changes during her life in the herd, each cow was credited with her total lifetime milk production at the price for the average butterfat test of her milk on her individual DHIR record cards. The average test was calculated by dividing total lifetime fat production by total life- time milk production. Table 3 gives the milk prices used to determine each cow's individual income from sale of milk. Table 3. Milk prices to determine income from sale of milk. Butterfat Milk Price Butterfat Milk Price Test % $/45.36 kg Test % $/45.36 kg 2.1 3.22 3.7 4.34 2.2 3.29 3.8 4.41 2.3 3.36 3.9 4.48 2.4 3.43 4.0 4.55 2.5 3.50 4.1 4.62 2.6 3.57 4.2 4.69 2.7 3.64 4.3 4.76 2.8 3.71 4.4 4.83 2.9 3.78 4.5 4.90 3.0 3.85 4.6 4.97 3.1 3.92 4.7 5.04 3.2 3.99 4.8 5.11 3.3 4.06 4.9 5.18 3.4 4.13 5.0 5.25 3.5 4.20 5.1 5.32 3.6 4.27 Income from salvage Salvage value is determined by weight and price of sale. Since actual sale weights and sale prices were available for only a few of the cattle, it was necessary to devise other means of determining salvage 24 value. In any case, it was not desirable to give cows credit for the fortunate chance of going to market when the price happened to be high or to penalize them for the misfortune of going to market when the price happened to be low. Hence, a reasonable average price for the 11 years was sought. Libby (1971) gives the average prices for utility cows 1957 to 59 as $16.07 per 45.36 kg at Detroit. He lists only the price during a single month in 1970, $20.03 for November. Prices actually received for 39 cows sold to a small packer in Lansing ranged from $11.50 to $19.50 and averaged $15.20. Thirty- five of these cows were sold during the first 6 years of the period or before 1966. Considering the known facts and the probable cost of delivery, the net price in calculating income from salvage should be $16.00 per 45.36 kg. Actual salvage weights were available for the same 39 cows. However, a few cows were sold for dairy purposes and many were sold in groups at a truck load weight and price. If these groups had not often had other breeds mixed with them, it might have been possible to get reasonable approximations of individual weights and prices for all cows. After realization that individual sale weights were hopelessly confounded, weight at the beginning of the terminal lactation was the sale weight for all cows. Expenses Expenses were divided into 10 categories: rearing, forage, concentrates, breeding, labor for milking, labor other than for milk- ing, housing, overhead, and miscellaneous, fixed veterinary services, variable veterinary services, and interest on alternative investment. 25 These categories were chosen for convenience in calculating expenses of each cow. Rearing costs The cost of rearing is a complicated expense which differs markedly from locality to locality or even from farm to farm. From detailed cost accounting records on the University farm the average cost of rearing an individual heifer could be calculated. Because research facilities must be maintained and labor is unionized on the farm, rearing costs seemed far too large to make results applicable to commercial dairy farm operations. All costs, which include extra labor at $3.96 per hour and interest and overhead on such expensive items as digestion stalls, experimental silos, and laboratory facilities, are approximately $600 per calf year, $400 per heifer year, and $1200 per cow year. After consultation with the farm manager, two of the Michigan State University calf rearing experts, and reviewing Hillman et a1. (1965), Jack (1963) and many other written reports,it was assumed the article by Bechtel (1962) represented costs of calf and heifer rear- ing on well managed farms in this area during the period under study. All costs were summarized by age of calves. The general costs of $3 per month were distributed over the entire growing period of 24 months. Age group costs (Table 4) of $174.90 and general costs of $72 were summed to make a total cost of $246.90 for rearing a calf to 24 months of age. This was rounded to the nearest $50 to obtain a base cost for rearing of $250 to 24 months of age. Charges for the second year of rearing were obtained by add- ing the age group costs of $59.80 (Table 4) to the general charges of 26 $36 ($3 per month). The total of $95.80 for the second year was round- ed to the nearest $5 to obtain the figure of $95 which was used to- gether with the base figure of $250 for 24 months to derive the rear- ing cost of each cow as she entered the milking herd at first freshen- ing. Fraction of a year over or (Rearing cost) = $250 i $95 under 24 months of age at first freshening. Rearing costs were not related to body size or efficiency. All differences in rearing costs were determined solely by age at first freshening. Table 4 is a summary, by age of calf, of rearing costs accord- ing to Bechtel (1962). Table 4. Rearing costs of calves Age in Rearing months Costs $ 0 - 2 $64.95 3 - 6 26.55 7 - 12 21.60 13 - 24 59.80 Total to 24 months 174.90 Forage costs Average hay fed per cow per day and average silage fed per cow per day as reported on the DHIA monthly reports were used for the forage costs. These figures, 9.07 kg of hay per cow per day and 13.60 kg of silage per cow per day, were multiplied by 365 to get the average hay and silage fed per cow per year, 3,311 kg of hay, and 4,787 kg of silage. These figures were converted to the average hay and silage II 27 fed per 454 kg cow per year by dividing by the average body weight from the DHIA records (590 kg) and multiplying by 454. Average forage fed per 454 kg cow per year was 2,547 kg of hay, and 3,821 kg of silage. Hay was priced at $25 per 907 kg and corn silage at $8.26 per 907 kg (Hildebrand et al. 1969). With these prices and the average forage consumed as indicated above, the annual forage cost for a 454 kg cow was $104.97. This was rounded to $105 and then divided by 454 to obtain $.23l per kg body weight per year as the cost of forage. The average cost of forage for one year was calculated for each cow by multiplying her average body weight by $.231. Final cost of forage for each cow was obtained by multiplying her cost of forage for one year by her number of years of herd life. Forage = ($ 231) average years of costs ° body weight herd life Concentrates costs Each cow was charged for concentrates actually fed her as indi- cated in DHIA monthly reports. The price of concentrates was taken as $.066 per kg. (Concentrates costs) = ($.066) (kg of concentrates fed) Breeding costs The herd was bred on contract with Michigan Animal Breeders Cooperative at $4 per service. To approximate more nearly what the costs would have been to a well managed commercial dairy farm in the area, it was decided to charge $9 per first service, $1.50 per return up to the 4Ch service, which was again charged at $9, and so on. These charges were set to include cost of semen, technician, and herdsman's time in locking up the cow, turning her loose, etc. The total costs of breeding charged, thus approximated closely the amount actually paid under the contract but tended to favor easy breeders and to penalize repeat breeders more than the flat charge. Number of Number of lst, 4th, 7th + $1.50 additional Breeding - ($9) etc. services repeat services costs A 28 Labor costs for milking Cows were milked in a stanchion barn by one man using an around the barn pipe line milker with three units. At times additional help was employed for various experiments. All labor was by members of the AFLCIO local 1585, a union for maintenance and service employees of Michigan State University. In an attempt once more to approximate more closely costs on a typical, well managed farm, published figures compiled by the Agricult- ural Economics Department were relied upon. (Speicher et a1., 1970; Hoglund, 1970). A double 4 herringbone parlor with 4 milker units per man was assumed. (This was a common type of milking arrangement in the area for the size herd involved during the time under consideration) Milking time per milking, determined as previously described, was converted to milking time per day by multiplying by .5. (A cow must be milked twice daily, but since one man is operating four units, his time required by a single cow is only 1/4 of her total milking time per day or 1/2 her milking time per milking.) Milking time per day was then converted to total milking time by multiplying the number of days in milk. This was converted from minutes to hours by dividing by 60. Labor cost for milking was obtained by multiplying time in hours by $2. The wage of $2 per hour was derived from Hoglund (1967) with the aid of personal consultation with Hoglund. The total annual salary of dairy farm hired labor (Hoglund, 1967) was divided by the number of hours of work usually required. The result of approximately $2 per hour was settled upon as a reasonable average for the 11 years. Labor costs Milking time days in = o o ' o 2 (for milking) ('5) 4per milking mllk ($22 29 Labor costs other than for milking From Table 4 of Speicher et al. (1970) times for barn chores, open lot, which included collection into holding pen, roughage feed- ing, and manure and bedding handling, were added to total 11.6 hr per cow per year. To this total, 6.4 hr per cow per year were added for clean up portion of the time allotted for milking and clean up. This final sum of 18 hr per cow per year was multiplied by years of herd life to obtain hours of labor for other than milking for each cow. This labor was also charged at $2 per hour as determined previously. Years of herd life) ($2) Housing, overhead, and miscellaneous costs other than (18) milking Labor costs ( Cattle were housed in a stanchion barn and milked by pipe- line as previously mentioned. Actual housing, overhead, and equipment costs were available. However, as also previously indicated, these figures included substantial increments due to the experimental and instructional nature of the facilities. Such items as digestion stalls, laboratory, class room, individual feeding stalls, etc., are not re- quired on the ordinary, well managed dairy farm. Because of this pub- lished data approximated housing, overhead, and miscellaneous costs. Each cow was charged $86 per year of herd life. This represent- ed 85% of the cost of such services in a cold, covered building with 80 free stalls and conventional manure disposal system (Hoglund et al. 1969). The 85% was decided by consultation with Hoglund as to the aver— age costs over the 11 years. The published costs were current at the time of publication near the end of the period. Inflation during the 11 years was considerable. 30 Housing, overhead and miscellaneous ($86) Years Of herd life costs Fixed veterinary costs These costs were derived from veterinary services applied routinely to every cow. Rates charged for these services were obtained from consultation with Dr. Wayne Oxender and Dr. Christian Miller, vet- erinarians in charge of veterinary services to the herd during the lat- ter portion of the period. Rules from consultations for assessing fixed veterinary charges were: 1. Each cow was charged with: a) one magnet at $2 b) immunizations at $2 c) dehorning and extra teat removal at $1 2. Each cow was charged $.75 for each annual brucellosis test and an annual tuberculosis test while she was in the herd during Jan- uary of that year. 3. Each cow was charged for the number of pregnancy checks and post-partem examinations of her as recorded on her health record card. Ordinarily, such checks and examinations were routine on each cow. Pregnancy checks were 60 to 90 days after last service and post- partem examinations within a few days of delivery. Irregularities in breeding or calving would produce differing numbers of examinations. (fixed veterinary) ___ (service ) (cost of) + (service )(cost. of)+ costs performed service performed service ... Variable veterinary costs All veterinary services not charged under fixed veterinary costs were charged as variable veterinary costs. Each cow was charged 31 for services performed on her as recorded on her health record card. Prices in Table 5 were used to assess charges. These prices were obtained from consultation with Dr. Oxender and Dr. Miller. variable . . , serV1ce cost of serV1ce cost of veterlnary = , + . + costs performed serV1ce performe serV1ce ... Table 5. Rates charged for variable veterinary services. Service Rate $ Mastitis $ 1 per quarter Uterine infusion 2 Rectal examination 1.5 A.C.G. 10,000 units 3 Milk Fever 10 Retained Placenta 6 Ketosis 8-10 Hoof Trimming 6 per cow Anti-biotic injection (pneumonia, high temperature, etc.) 2 Cesarean section 40 Hardware operation 50 Indigestion bolluses 2 Dystocia (calf delivery) 10 Pink eye 2 Septicemia 10 Acute mastitis 10 Emergency calls 10 Follow up calls 2 Professional veterinary services performed by the hour 20 per hour For mastitis treatments an additional charge covered cost of milk rendered unsaleable by the treatment. Income from milk was credit- ed for all a cow produced regardless of saleability. Since milk from a cow treated with most antibiotics is not saleable for 72 hr after treatment, loss of income was charged to that cow. Unsaleable milk is not necessarily thrown away but may be fed to calves. Therefore, when- ever a cow received a mastitis treatment, she was also charged for the 32 value of one half of her milk for 3 days. Average production through- out herd 1ife, average test throughout herd life, and price from Table 3 were used to assess these charges. Interest on alternative investment costs Interest on housing, equipment, etc., was accounted for in assessing housing, overhead, and miscellaneous costs. Interest on the value of individual animals was not considered elsewhere. The approach is that of charging to each animal the amount that could have been earn- ed had the money invested in her been invested in some alternative enterprise. Interest was charged at the rate of 6% per annum simple interest on the value of the cow upon entry into the herd. This value was the rearing cost of the individual. Interest was charged for the cow's herd life. interest) ___ (6‘7) rearing) years of costs ° cost herd life Relating profit to time The denominator in profit per year of productive herd life equation is years of productive herd life. Date of first freshening was subtracted from date of leaving herd and the difference expressed in years. Years of date of date of productive = leaving - first herd life herd freshening Construction of the selection index One of the main objectives of this study was to develop a selec- tion index which would be simple to construct and easy to apply to practical situations. To attain this objective, methods of Grafius (1965), which have been applied successfully to small grains, were "- 33 employed. The key to success with Grafius' methods is the ability of trained plant breeders to rate varieties correctly for net merit or overall worth by subjective means. If they are unable, any index de- veloped by this method is meaningless. Application to animal problems is similar. An answer was sought to the question can trained animal breeders correctly identify traits that contribute to overall excellence. In the choice of variables to include in an index, those traits which are usually measured or can be measured easily, those which affect economic profit significantly, and those which are capable of showing response to selection would be most desirable. Measures closely asso- ciated with production, reproduction, efficiency of feed utilization, health, and behavior are implied. Thus, variables were picked sub- jectively on available data on presumed relationship to form, function, or temperament, and on knowledge of the herd and its environment. Milkgproduction Since the biggest source of income from most cows is from sale of milk, milk production should be included in any index seeking to in- crease profit. Milk production is moderately heritable, most estimates being about .25 (Wilcox et al. 1971). Thus, it is subject to improve- ment by selection. It is also easily measured with accurancy and is highly responsive to manipulation of the cow's environment. Milk pro- duction records were available on all cows in this study. Milk pro- duction throughout herd life, unadjusted for age or season of calving, was divided by years of herd life to obtain milk production per year of herd life. milk production lifetime milk per year of herd = production ife years of‘fierd lite 34 Butterfat test Milk has been priced and is still being priced on percentage of butterfat it contains. Percentage of butterfat is highly herit- able, about .55 (Wilcox et al. 1971). It is easily and routinely measured, and data were available. An average lifetime butterfat test was obtained for each cow by dividing lifetime butterfat production by lifetime milk production. average lifetime butterfat butterfat = production test lifetime milk production Mastitis Mastitis has been called the number one problem of the dairy industry and "the most costly disease affecting dairy cattle" (Davis, 1962). It is widely recognized as costly to the dairy farmer (Janzen, 1970). Methods of detection and measurement are not universal nor uniformly developed. Heritability of susceptibility to specific organ- isms is relatively low to moderate, estimates ranging from 4L.l to .2 (Schmidt and Van Vleck, 1965). From treatments for mastitis recorded on health records for individual cows, the number of cases of mastitis requiring treatment per year of herd life was obtained by dividing total lifetime cases by years of herd life. average number of total cases of mastitis cases of mastitis = during lifetime per year years of herd life Live freshenings per opportunity Next to low production, the biggest single cause of involun- tary culling of cows on most dairy farms is breeding problems, usually failure to settle (Meadows, 1966). For this reason some measure of 35 breeding efficiency should be in a selection index. Heritability of re- productive traits in general and of such traits as measure breeding ef- ficiency in particular is low, most estimates not differing significant- ly from zero (Rennie, 1952). Therefore, response to selection will be insignificant. However, this trait is subject to considerable varia- tion through manipulation of the environment by man. The potential economic importance and ability of man to affect breeding efficiency by management decisions merited inclusion of some measure of breeding efficiency in the list of index variables. Learning more about the specific economic importance of breeding efficiency was worth the ef- fort to devise a measure and process the data. An adequate measure of breeding efficiency is difficult to find. What is wanted is a cow that will reproduce regularly with a minimum of attention. Breeding cows costs money. Milk production is a function of motherhood. Cows that do not freshen do not produce milk. Calves have value. Cows that do not freshen do not produce calves. Cows that freshen with dead calves do not produce saleable calves. It has generally been conceded by many dairy scientists that average calving interval in dairy cows is longer than desirable (Rennie, 1952). Therefore, a measure of breeding efficiency that would reflect calving interval, repeat breeding,and livability of calves was sought. The measure chosen was live freshenings per op- portunity. Live freshenings per year of herd life was considered, but it tended to give an advantage to cows which left the herd during the first lactation even though some of these left because of breeding problems. To overcome this problem the measure was put in terms of opportunity to freshen after joining the herd. It took one freshening 36 to enter the herd. After entry, an opportunity to freshen comes once a year. This system discriminated against cows that left the herd before one year but not by as great a margin as freshening per year of herd life would have favored them. Also, the degree of discrimination was greatly reduced because any cow leaving the herd in the middle of any lactation was penalized for it. live freshenings = live freshenings - 1 per opportunity years of herd life Milking time Labor is a major cost on all farms. It has been the fastest increasing cost on most dairy farms for several years. Dairymen have turned to increased capital investment in mechanized equipment and facilities to combat rising labor costs (Hoglund, 1967). A major contributor to labor costs is milking. When most dairymen kept only a few cows, a hard milker who took extra long to milk was not too great an inconvenience. In modern milking systems such as the herringbone parlor, a slow milking cow holds up the entire string on her side of the parlor. Such a cow may increase labor costs even more than she would have in former years. Milking time is moderately heritable from .12 to .27 (Lamb, 1969a, b; Markos and Touchberry, 1970). Milking time is easily measured though it has not been common for most dairymen to do so. Not even in research herds have records been kept. No record of milk- ing times was available in the Michigan State University herd. A means of estimating milking times through consultation with the farm manager and herdsman was devised, as described previously, because of the ap- parent potential economic importance of this variable. 37 Each cow was assigned a milking time equivalent to the mean of the group in which the farm manager and herdsman placed her (Table 1). Body weight Body weight was the best available measure of body size. Some measurement of body capacity as a functional type characteristic might be preferable. Type classification score for body capacity might be used. There were two objections to this. First, type classification ratings are not as objective and accurate as actual measurements of body weight. Second, type classification scores were not available for all cows in the study. Most heifers that failed to complete a lactation were not scored for type. Since animals in the study were dead, it was not possible to develop an alternate means of scoring for type. Body weight is related to efficiency of feed utilization (Miller et al., 1971). This would indicate the probability of considerable eco- nomic importance since feed is the largest single cost of milk produc- tion. Body weight is also important economically in so far as it affects the size of calves available for sale and the salvage value of the cow. Body weight is highly heritable from .28 to .67 (Miller and McGilliard, 1959). Response to selection for body weight should be quite rapid. Body weights were available for all cows. These weights were scale weights taken a few days after freshening in each lactation. An average weight was obtained for each cow by summing the recorded weights (one per lactation) and dividing by the number of lactations. average weight at beginning weight at beginning + body = of lst lactation + of 2nd lactation ... eight number of lactations 38 Herd life Proponents of type classification often claim as one of its main benefits that it is a predictor of herd life. Cows should be of sound functional type to remain in the herd for a long time (Trimberger, 1958). Since type classification scores were not available for all cattle in this study, herd life was a variable with the assumption that herd life can be thought of as a complex geometric variable, according to the ideas advanced by Grafius (1965), some of whose components are P. various type characteristics. The main contribution of herd life will be related to the dif- ference in original cost of the cow and her salvage value when profit is measured per unit time. Thus, if all cows were purchased as spring- ing heifers at an average price considerably above the cost of rearing in this study and salvage values were the same, herd life would be more important. Similarly, its relationship to profit might change if more cows were sold for dairy purposes at substantially higher than salvage values. In any event, it seemed to be of considerable potential eco- nomic importance. Herd life is lowly heritable not significantly different from zero (Parker et al., 1960). It is not in any case the major factor in selection. Breeders do not want cows that simply live a long time. They want highly productive cows that will live a long time. Natural selection for long herd life is intense. Cattle that live longest leave the most offspring to reproduce their kind. Short lived cattle leave few offspring. This has been going on so long little genic variation is left. Herd life is easily and accurately measured as date of leaving 39 herd minus date of first freshening, expressed in years. It can be determined even in herds that maintain a minimum of records. Other possible index traits Many other traits could be considered as possible or desirable variables to include in an index of overall excellence. Some of these are mentioned briefly. A strong argument could be made for including type classifica- tions with division into categories as well as the overall score. These would have been included in this study had they been available. Certainly, in any herd where sale of cattle in consignment sales or through other outlets where selling price is based substantially or in part on type characteristics, the list of possible variables to be in- cluded in a selection index should include type scores and breakdowns. Another whole series of traits that should be investigated are the behavioral traits. Temperament, social dominance, tractability, symptoms of estrus, and aggressiveness at the feed bunk are only a few that would be of interest. Unfortunately, data are available in sign- ificant amounts for none of these traits. They have received little or no attention in the past. This dirth of knowledge is especially reprehensible at this time when the dairy industry is going through epic changes in the housing and handling of cows. New systems may be sold and put into operation with no idea of what effects they may have upon cows, men, or profits. In choice of variables in the index subjectivity enters into the adaptation of Grafiusi plant selection methods to construction of an index for selection of dairy cattle. Variables chosen here were necessarily limited by the data available. Within that limitation, - . .. 1 40 every attempt was made to select those variables that would most accu- rately reflect each cow's profitability. Determination of economic importance A least squares linear regression analysis determined the rel- ative economic importance of each trait in a primitive index as de- scribed by Grafius (1965). As right hand sides in his prediction equa- tion, Grafius used subjective ratings of barley varieties based on comparisons with a "standard." The same method could have been used here as indicated by positive results in a preliminary study. Since development of economic weights for known traits was a primary objec- tive, actual profit per year of herd life, as determined by items detailed in the income and expense sections, was used as dependent variable. The model was: Y=£lgixi+e, 1=0to7 where Y profit per year of herd life of an individual cow. Y0 = average profit per year of herd life. X1 = deviation of freshenings per opportunity from average. X2 = deviation of herd life from average. X3 = deviation of butterfat test from average. X4 = deviation of body weight from average. X5 = deviation of milking time from average. X6 = deviation of mastitis cases from average. X7 = deviation of milk production from average. e = deviation of Y from linear regression. The 31's are partial regression coefficients. Substituting A in the g determined for each variable along with the Xi's in devia- tion units for each cow will estimate her profit per year of herd life. 41 The prediction equation is: /\ ? =fp.x., 1:01:07 1 1 where Q'= estimated profit per year of herd life. The Xi's are de- .A fined as before;the‘?i's are estimates of the partial regression co- efficients. These estimates with their standard errors are in Table 6. Table 6. Partial regression coefficients and their standard errors. Partial Regression Standard Errors Variable Coefficients of Coefficients "“' Freshenings 70.00 22.58 Herd Life 7.74 5.73 Butterfat Test 75.80 15.42 Body weight .08 .06 Milking time 3.74 6.76 Mastitis - 13.16 1.96 Milk production .026 .0027 For direct comparison of the importance of each trait relative to others in the primitive index, standard partial regression co- efficients were needed. These are the éi's converted to standard units by multiplication of each Xi by the ratio of the standard deviation of Y and the standard deviation of the particular Xi’ so that the multiple regression equation becomes, Y=ffli’ (ay/oimi, i=0to7 where pii's are standard partial regression coefficients;the (W/Op's are the ratios of standard deviations; and the Xi's are defined as be- fore. The standard partials with their standard errors and signif- icance (probability of a type I error) are in Table 7. 42 Table 7. Standard partial regression coefficients with their standard errors. Standard Partial Standard Errors Type I Error Variable Regression Coefficient of Coefficients p,‘ Freshenings .22 .07 .002 Herd life .10 .08 .179 Butterfat Test .31 .06 .0005 Body Weight .09 .07 .190 ! Milking Time .03 .06 .581 -‘ Mastitis '- .38 .06 .0005 Milk Production .64 .07 .0005 Q from the prediction equation is only an estimate of Y, actual profit per year of herd life from income minus expense. Since the utility of the method depends upon how accurately Q‘predicts Y, rankings by actual profit and predicted profit were compared (Table 8). The final step in a usable selection index is to put in herit- abilities for each trait (Grafius, 1965). The final index then becomes, $=ffii hizxi, i=0 to7 where'? is an estimate of the breeding value of the individual for profit per year of herd life. This model treats genetic correlations as if they were zero. If heritability is zero or economic importance is insignificant, the trait will drop out of the index. "It is dif- ficult to ignore an important trait, but if the heritability approaches zero, there is little hope of progress through selection." (Grafius, 1965). Multiple correlation coefficients, partial correlation co- efficients, R2 deletes, and simple correlations are in Tables 9, 11, and 12. 43 Comparisons of rankings The primitive index as a starting point may not be the final index for a culling or selection guide. Some traits may not be signif- icant determinants of profit. Some traits may not be sufficiently heritable to be considered in selecting parents of future offspring. Rankings from four different measures in addition to the primitive index, 1) index of 4 economically significant traits, 2) final index, 3) milk production per day of herd life, and 4) mature equivalent milk production per day of herd life are compared in Table 13. Comparisons of means and effects on profit Means of traits for the primitive index were compared under various selection (Table 14) and culling (Table 15) schemes. Multiple correlation coefficients were obtained for each of the indexes (Table 9% RESULTS AND DISCUSSION The value of any application of this method of index construc- tion depends upon the accuracy of the prediction equation in estimat- ing the dependent variable. Independent variables should account for a reasonable amount of variation in the dependent variable; the more, the better. Since selection of cows is essentially a ranking process, it is important that deviations from the true ranking not be violent. Since this index was for overall excellence defined as profit per year of herd life, the economic importance of each trait in the primitive index, relative to others and as a portion of the total variation in profit, was sought. Comparison of profit and ranking The prediction equation was useful for estimating profit amassed by individual cows. Predicted profit tended to approximate actual profit closely, and rankingstended to be near each other (Table 8). The equation was capable of predicting profit or loss. Only 19 of 111 cows were misjudged, and most of them were near the middle of the scale. Thirteen of these were within 20 cows either side of the point where profit changed from positive to negative. 44 Table 8. 45 Comparison of estimated profit, profit, and rank accord- ing to each. Estimated Pr fit Profit Cow 6 Rank Y Rank 702 318.98 1 195.36 12 718 264.96 2 224.00 7 766 258.07 3 211.61 8 740 237.65 4 285.78 2 685 231.83 5 490.18 1 716 230.44 6 245.38 4 644 219.64 7 149.27 24 765 218.38 8 200.05 9 709 215.34 9 196.98 11 707 205.98 10 230.70 5 714 204.33 11 186.86 14 643 200.43 12 179.21 19 753 200.24 13 176.09 21 650 193.75 14 181.40 16 688 189.47 15 199.63 10 679 187.43 16 —-1.02 82 668 186.09 17 188.29 13 638 183.48 18 125.10 32 630 166.34 19 257.81 3 701 163.67 20 180.91 17 713 157.55 21 160.06 23 741 151.04 22 34.86 65 742 150.76 23 229.23 6 725 150.34 24 124.28 34 677 137.82 25 114.36 40 763 134.33 26 183.36 15 694 131.29 27 -lO.54 85 686 128.68 28 117.90 39 673 126.85 29 108.06 43 769 124.35 30 172.88 22 680 119.55 31 132.19 29 665 119.09 32 125.98 31 626 119.05 33 113.66 41 649 117.09 34 120.62 38 762 116.92 35 122.34 35 746 114.26 36 132.60 28 642 110.99 37 82.58 51 738 108.92 38 177.61 20 758 107.55 39 180.30 18 46 Table 8. Continued Estimated Profit Profit C ow ? Rank Y Rank 662 106.71 40 95.98 45 755 106.61 41 121.44 37 754 101.50 42 60.36 58 690 101.42 43 124.74 33 641 98.85 44 96.00 44 683 91.79 45 113.45 42 768 91.06 46 3.65 78 708 85.72 47 '- 96.98 101 761 81.54 48 -— 25.41 90 661 77.24 49 139.88 25 756 76.63 50 '— 86.26 100 625 75.47 51 61.88 57 697 74.86 52 135.71 27 667 56.30 53 93.51 47 712 61.13 54 29.25 69 687 59.15 55 27.19 70 653 58.29 56 93.84 46 627 58.19 57 73.47 54 704 56.60 58 122.05 36 743 51.83 59 81.28 53 767 50.81 60 13.59 72 635 50.01 61 63.59 56 666 45.90 62 81.97 52 645 45.62 63 131.55 30 663 39.52 64 46.83 63 693 38.56 65 52.16 60 728 33.62 66 3.55 79 676 25.48 67 50.46 62 721 23.31 68 8.60 74 717 19.94 69 26.84 71 648 19.25 70 70.79 55 651 18.79 71 ~— 21.82 88 646 14.50 72 91.27 49 670 10.94 73 - 62.38 98 658 8.85 74 57.22 59 678 3.87 75 9.72 73 691 3.80 76 137.78 26 735 1.51 77 7.05 76 682 - 4.06 78 33.37 67 640 '- 5.12 79 86.74 50 698 - 6.69 80 .72 81 727 -— 6.90 81 '— 23.22 89 Table 8. Continued Estimated Profit Profit Cow Rank Y Rank 675 - 8.85 82 - 34.25 94 652 — 10.49 83 5.18 77 737 — 13.13 84 — 25.85 92 719 - 16.76 85 -171.71 109 724 - 20.31 86 - 3.04 83 655 - 24.52 87 45.62 64 736 — 29.78 88 - 25.75 91 733 - 34.51 89 33.47 66 656 - 35.55 90 92.44 48 647 — 36.12 91 - 11.88 86 723 - 45.00 92 — 37.09 95 703 - 45.57 93 -- 29.44 93 748 - 48.64 94 3.31 80 654 - 50.16 95 -157.79 107 770 - 57.54 96 51.83 61 674 - 62.96 97 7.42 75 739 - 63.05 98 32.00 68 636 - 69.34 99 —124.71 105 664 - 70.19 100 - 16.95 87 639 - 73.78 101 -253.78 110 637 - 79.04 102 -116.18 104 672 - 80.75 103 4.43 84 671 - 85.78 104 —137.79 106 730 - 87.06 105 - 76.65 99 734 —105.50 106 - 58.08 97 657 —105.58 107 - 97.99 102 659 -108.30 108 - 47.94 96 759 -152.91 109 —103.87 103 722 -181.60 110 -160.65 108 747 -333.35 111 -658.19 111 48 Rankings were similar. The prediction equation ranked only 12 cows 30 or more positions from their true ranking. Accuracy of ranking was greatest at the extremes and least in the middle. Of 22 cows ranked in the bottom 20% by the prediction equation, eight would have been in a higher group on actual profit. Only three would have ranked more than six positions above the highest place in the bottom 20%, and only two would have ranked higher than the bottom 40%. Both of these would have been ranked in the middle 20% by actual profit. Only four of eleven cows estimated in the bottom 10% actually ranked higher. Only one of these ranked higher than the bottom 20% and was included in the lowest 25%. The cow receiving the greatest injustice by the prediction equation was one who ranked 26th on actual profit but only 76th on estimated profit. On the upper end of the scale, ranking was even more accurate. Only five of 22 cows ranked in the top 20% by estimated profit failed to rank in the top 20% on actual profit. Of these only two failed to rank in the top 40%. One was in the middle 20%, the other in the 4th 20%. Only two cows, ranked in the top 10% by the prediction equation, failed to rank high on actual profit. One ranked in the top 15%, the other in the top 25%. The most badly overrated COW'WaS predicted to rank 16th but actually ranked 82nd. The cow most highly overrated had an extremely low butterfat test while the cow most badly underrated consumed less concentrates than expected. Such conditions, while apparent in retrospect, are not likely to be noticed in practice. Ranking cattle in a herd for profit by the prediction equation postulated would produce occasional errors of large magnitude. However, agreement seems general enough 49 that the system might be useful, especially since mistakes are less likely, and also less likely to be serious, at the extremes. This would permit prediction of the least profitable cows for culling and the most profitable for special matings. Accuracy of prediction could be improved by finding other variables to account for a greater proportion of the total variation in profit. Of the variation in actual profit per year of herd life 67.6% was explained by the seven independent variables while 32.4% re- mained unaccounted for. Multiple correlation coefficients or R2 are in Table 9. Table 9. Proportion of profit explained by various selection indexes.a No. R2 Values Index Variables Actual Milk M. E. Milk primitive 7 .676 .526 economically significant 4 .656 .502 final index 3 .560 .432 aActual milk production and M.E. milk production were analyzed separately to determine accuracy of indexes with each. Relative economic importance of independent variables Four of the seven independent variables made highly significant contributions to profit. Freshenings per opportunity, butterfat test, mastitis cases, and milk production, had p (.002, p (.0005, p<.0005, and p (.0005 (Table 7). As expected, milk production made the largest contribution to profit by far. Mastitis, a costly ailment which can greatly reduce the profit potential of high producing cows and make moderate producers into financial liabilities, proved to be second in importance. 50 Butterfat test and freshenings per opportunity followed in that order as indicated by their standard partial regression coefficients. Table 7 gives a subdivision of the comparative importance of all seven independ- ent variables. Standard partial regression coefficients reflect the direct con- tribution of each variable to the variation separate from joint contri— butions. If milk production, the most important variable, is assigned an importance of 1.00, the importance of each other variable relative to milk production is the ratio of the standard partial regression co- efficients. These relative values are in Table 10. Correlated varia- tion is excluded from these comparisons. Table 10. Ratios of standard partial regression coefficients of each other variable to milk production. Variable Ratio Milk production 1.00 Mastitis .60 Butterfat Test .48 Freshenings per opportunity .34 Herd Life .16 Body Weight .14 Milking Time .05 Milk production was less than twice as important as mastitis, about twice as important as butterfat test, and nearly three times as important as freshenings per opportunity in determining profit. By contrast, it was more than six times as important as herd life, nearly seven times as important as body weight and more than 20 times as im- portant as milking time (Table 10). In their failure to show statistical significance, herd life, 51 body weight, and milking time had relatively large standard errors. That for milking time was larger than the estimates and those for body weight and herd life were almost as large as the estimates (Table 7). These facts seriously impaired the utility of these three variables as estimators of profit. When the partial correlation coefficients and R2 deletes in Table 11 were considered as well, herd life, body weight, and milking time were eliminated from the index. Table 11. Partial correlation coefficients and R2 deletes. Partial Correlation Variable Coefficients R2 deletes Milk Production .689 .383 Mastitis ‘- .551 .534 Butterfat Test .436 .600 Freshenings .292 .646 Herd Life .132 .670 Body Weight .129 .671 Milking Time .054 .675 If milk production is removed from the multiple regression equation, only 38.3% of the variation in profit is explained by the remaining six variables. By contrast, removing milking time still leaves 67.5% of the variation explained by the other six. Or, the partial correlation between milk production alone and profit is only .05 (Table 11). Simple correlations between all seven independent variables and the dependent variable and each other are in Table 12. Simple correlations explain the results already discussed. However, there are a few seeming inconsistencies to be explained and a few additional insights of interest. Milk production, herd life, freshenings per opportunity, and body weight were each moderately 52 II‘.‘ .mzou HHS m 000.H new. Nam.u. ANO. NHm. 0N0.:. 000. Has. bemoan 000.H 0H0. 000. 0N3. H00... N00. 000. couuos0oum x00: 000.0 0HH. 000. 000. 000;: 000... museumaz 000.H 0H0. 000. 00H.|. 0m0.|. mane 000x00: 000.H 000.1. 500. 000. 000003 >000 000.0 000.:. H0H.I. “map 000 000.0 000. 0000 060: ooo.H mwcwcocmwum uuuoum .0oum museummz 0509 0:000: same menu mwaaamzmmae 03000H0> x002 000x002 >000 000 0H0: m .maowumaouuoo oflazuoaonm oHaEHm .NH ofinme S3 correlated with profit. Mastitis was also moderately correlated with profit but negatively. Two of these factors, body weight and herd life were not significant contributors to profit in the multiple regression equation. Why should these factors be as highly correlated with profit as they were when they made no significant contribution to it? Why should butterfat test, which did make a significant positive contribu- tion to profit, be slightly negatively correlated with it? The answers lie in the contribution of milk production and mastitis (especially milk production) to profit and the correlations between these two variables and body weight, herd life, and butterfat test, and the correlations of the latter three with each other. Most of the correlation of body weight with profit was prob- ably an outcome of its correlation with milk production, freshenings, and herd life. Its correlation with milk production, though small, was important because of the relatively high correlation between milk production and profit. Milk production was not corrected for age nor were cows of larger body size charged for decreasing efficiency of feed utilization for maintenance. Had these been adjusted, it is likely that correlations between body weight and milk production, and body weight and profit would have been near zero. Body weight con- tributes directly to profit mainly by its effect upon salvage value of the individual cow. While this is a positive contribution, it is usually small relative to a cow's total profit per year of herd life, especially if she has been a profitable producer for an extended time. Body weight was moderately correlated with both freshenings and herd life which were themselves moderately correlated with milk production. Correlations of body weight with butterfat test, milking time, and 54 mastitis, factors which were negatively or only lowly correlated with profit, were small in absolute value. Herd life also contributes directly to profit in a positive manner. This contribution is mainly through spreading the difference between rearing cost and salvage value over a longer time. This is also a small contribution relative to milk production or cases of mast- itis. However, the fairly strong correlation between herd life and milk production apparently did a lot to increase the correlation be- tween herd life and profit. High producing cows and profitable cows are generally kept as long as possible. Herd life was also moderately correlated with freshenings, an important contributor to profit, and body weight. It was only lowly correlated with butterfat test, mast- itis, and milking time. Perhaps, the most surprising implication of the simple cor- relations, at first glance, was the negative correlation between but- terfat test and profit. This apparent inconsistency is explained by just two things. First, though negative, the correlation was small. Second, the relatively large negative correlation between butterfat test and milk production makes the result understandable. Even though butterfat test made a significant contribution to profit because of the price structure of the milk market, its effect upon profit was overwhelmed by the effect of milk production. Variables dropped from index Herd life, body weight, and milking time were dropped from the index because of their insignificant statistical contribution to profit and the large standard errors associated with their partial and standard partial regression coefficients. A few more observations 55 about the economic importance of each of these traits seem appropriate. Herd life Though not a significant contributor to profit in the multiple regression equation, herd life is important to profit. It is more highly correlated with profit than any other factor included in the index, with the exception of milk production. This stems from the only thing better than a highly profitable cow is a highly profitable cow for a long time. This is true in the commercial herd or the herd sell- ing breeding stock. In the former, longer herd life spreads capital outlay and permits larger selection differentials. In the latter, it is necessary to make more animals available for sale (Smith, 1931; Rendel and Robertson, 1950). Heritabilities for herd life have always been low, usually not significantly different from zero (Miller et a1., 1967). Herd life is not likely to improve by selection (Parker et al., 1960). Further- more, a long average herd life may not be desirable in a commercial herd if real genetic gains are being made. It may be desirable to supersede one generation with the next as rapidly as possible to shorten the generation interval especially if rearing cost can be held close to salvage value. Yet, it is necessary that a large reserve of fecundity be available to permit rapid expansion when needed and to maintain a reasonable flexibility in the industry. This reserve is manifest in the ability of cows to live and reproduce longer than they must live and reproduce. Many cattle are slaughtered that could live and re- produce for a considerable time. Reserve fecundity is protected by natural selection imposed by cows who live longest leaving the most descendants. Cows which are not physically sound cannot have long 56 herd life and cannot leave many of their kind. This is the most prob- able reason for low heritability of herd life. Natural selection has been operating so long, at such intensity, that there is little genic variation left. The ability for long herd life is apparently adequately pro- tected by natural biological processes. Therefore, herd life, as such, can be dropped from selection indexes without fear of reducing overall excellence. Body weight There has been considerable emphasis on selection for body size in recent years. Such selection has not necessarily been for body weight, but it has tended to increase body weight. Partly, it has been in the form of emphasis on upstandingness, stretchiness and power. Much of it has been contributed through the commercial sector by in- creased emphasis on early maturity, pricing of springing heifers by size (often weight), salvage value and the feeding of dairy steers. Body weight is highly heritable (Miller and McGilliard, 1959). Selec- tion for body weight can be and is effective. The important questions that must be answered are all inter- related. Should dairy cattle breeders be selecting for increased size? If so, how large should cows be? Should all breeds be the same size? Is there a magic size where returns are maximized? In the regression equation body weight did not make a statis- tically significant contribution to profit (Table 7). Yet, it did show a moderately high positive correlation with profit. Holding all other index factors constant while increasing body weight increased predicted profit. Since milk production records were not corrected 57 for age, this might partly reflect increased production due to in- creased maturity. Granted a maturity effect, the correlation seems strong enough to indicate that larger production records can continue to be obtained by breeding larger cows. At the same time, no allow- ance was made for decreased efficiency of feed utilization for main- tenance with increasing size. Since such a relationship exists, it I follows that there is a point of diminishing returns beyond which further increases in body weight will cause decreased rather than in- creased profit (Miller et a1., 1971). Even if there were no bounds on profit with increasing size, there would be a practical limit on the size cows should ultimately attain. This would be a size proportionate to the men who care for them and facilities used. There appears to be little justification for selection on body weight. In particular, increases or decreases in body weight without accompanying increases in production are not warranted. Selection for earlier maturity to reduce rearing costs and permit easier calving would seem to be more useful than increased size. Milking time Milking time did not make a statistically significant con- tribution to profit in the regression equation. In Spite of milking time being an expense item due to labor costs, it showed a small positive correlation with profit (Table 12). Increasing milking time while holding all other factors constant in the regression equation, increased profit slightly. This apparent inconsistency was due to the positive correlation between milk production and milking time and the narrow, high peaked distribution of milking time. The correlation with milk production, though low, (.06), is sufficient to override the 58 negative effect of increased cost with increased milking time because of the importance of milk production to profit. (Table 12). Milking time also showed a small positive correlation with butterfat test (.09), which would have a similar effect (Table 12). The distribution of milking time accounted in large measure for its failure to be statistically significant and for its correlations to be opposite in sign from what might have been expected. The distrib- ution was characterized by a high narrow, peak (Figure 2). Even though this peak is no doubt higher and narrower than curves for cattle in general, 95% of all cattle would be expected to have a milking time ranging between 3 and 8 min (Touchberry and Markos, 1970). Men never did like cows that were hard to milk or took a long time to milk. They like them even less in modern milking facilities than previously. Automatic selection for a reasonable milking time is strong. While milking time has high enough heritability to allow for improvement by selection, economic rewards available do not merit it being included in an index. It apparently receives sufficient attention already through automatic selection. Some caution in the selection of bulls or dams of bulls may be justified to avoid any tendency to increase milking time (Lamb, 1969a). Economically important traits Four of the chosen traits were economically important; milk production, mastitis cases, butterfat test, and live freshenings per opportunity. The nature and importance of the effect of each on profit was considered before construction of the final selection index. NUMBER OF COWS 59 80 ”— I40 1— 20 r- L l J l l 1 - L _ y 2 3 4 5 6 7 8 9 10 11 MILKING TIME IN MINUTES Figure 2. Distribution of milking time as remembered by farm manager and herdsman. 12 60 Milkyproduction The importance of milk production to profit would be difficult to overemphasize. Its standard partial regression coefficient was almost twice as large as that of the next most important variable (Table 7). It is moderately high in heritability (Wilcox et al., 1971). Selection for milk production has been effective. An increase of 454 g in milk production per year of herd life increased profit $.026. (Table 6). However, if profit is what is desired, then other factors should be considered as well. Mastitis Mastitis strikes at profit in at least five ways. (1) It reduces milk production by the cow being ill. (2) It reduces income from milk by causing it to be unsale- able. (3) It costs for antibiotics and veterinary services. (4) It costs the time of herdsman and milker. (5) It may shorten the life of an otherwise highly profitable cow. The standard partial regression coefficients showed mastitis just slightly more than half as important as milk production in its effect upon profit (Table 7). Reducing mastitis cases by one per year of herd life increased profit by $13.16 (Table 6). Heritability is relatively low to moderate (Schmidt and Van Vleck, 1965). Mastitis should be included in the index. Butterfat test Milk pricing patterns have not been changed as much as advocated. In Spite of calls for pricing on protein, total solids, minerals, or 61 some other factor, up to the present time variation in price of milk has been almost entirely on butterfat test. Price makes itself felt in profit by causing butterfat test to be a significant contributor. An increase of .1% in average butterfat test caused an increase of $75.80 in profit per year of herd life. (Table 6). Butterfat test was slightly negatively correlated with profit, freshenings, herd life, body weight, and milk production (Table 12). All the other negative correlations are probably due to the negative correlation with milk production. It might be argued that butterfat test should be replaced by some other variable more indicative of the modern usage of milk. Such might be used as soon as the pricing structure is based upon it and records make data available. However, all past pricing systems and most present pricing systems are most accurately represented by butter- fat test. Butterfat test is highly heritable and thus should be in- cluded in the index (Tabler and Touchberry, 1955). Live freshenings per opportunity Live freshenings per opportunity was statistically significant to profit. An increase of one live freshening per opportunity increased profit by $70 (Table 6). Reproductive traits have low heritability. The trait measured here is a conglomerate reflecting calving interval, length of lactation of cows not rebred, and livability of calves. Heritability cannot be significantly different from zero (Rennie, 1952). Thus, though eco- nomically important, it will drop out of the index when heritabilities are added. As observed by Grafius (1965), it is hard to leave a trait that is economically important out of the index. However, if "5 I 62 heritability is near zero, there is little chance of improving the trait by selection. We must either discover significant heritability, which may be a possibility for some facets of the trait in question, or we must find some other way to improve the trait. Fortunately, natural selection for reproductive traits is strong and automatic. As previously pointed out, cattle that do not reproduce do not leave descendants to carry their genes. Cows that reproduce less frequently than others leave fewer descendants to pass on their traits. Frequently, the easiest and most effective way to improve live freshenings per opportunity or to reduce calving interval is to im- prove management practices. More careful detection of heat, more skilled and timely insemination, and closer attention at calving time in particular are effective. To improve livability of calves,-inbreeding might be avoided. The possibility of cross breeding for increased vigor might well be considered for some herds. Certainly means should be sought of im- proving the quantity and quality of attention at calving time, espe- cially in the larger herds prevalent today. Another remedy particu- larly applicable to larger herds is improved care of calves after they have arrived safely. Calf livability decreases as herd size increases (Speicher, 1968). Comparison of different indexes The proposed primitive index explained a reasonably large amount of the variation in profit (Table 9). The prediction equa- tion based on the primitive index also did a reasonably good job of ranking individual cows for profitability (Table 8). Some of the 63 traits in the primitive index had no significant economic importance (Table 7). One trait which was of economic significance had herit- ability of zero (Rennie, 1952). The question which naturally follows is, how well do the reduced indexes explain the variation of profit and rank the cattle for profitability? Variation in profit accounted for dropped from .68 in the primitive index to .66 in the index of economically significant traits and .56 in the final index (Table 9). Rankings changed similarly. Of the top 22 cows, 17, 18, and 10 were correctly identified by the prim- itive index, the index of economically significant traits, and the final index. Of the bottom 22 cows, 14, 14, and 15 were correctly identified by the three indexes. Further comparisons of the number and gravity of errors in predicting profit showed the primitive index most accurate, the index of economically significant traits next most accurate and not greatly different from the primitive index in accuracy. The final index was least accurate (Table 13). Rankings on actual milk production alone and mature equivalent milk production alone were as expected. Actual milk production cor- rectly identified 16 of the 22 most profitable cows; mature equivalent milk production, 14. Eleven and nine of the 22 least profitable cows were correctly identified by the two measures. Actual milk production was less useful in ranking cows for profit than any of the indexes but more useful than mature equivalent milk production (Table 13). How- ever, perusal of Table 14 and Table 15 showed that selection on either actual or mature equivalent milk production would increase profit sub- stantially. Body weight might be increased, especially by selection on mature equivalent milk production. Butterfat test would likely be 64 Table 13. Comparison of rankings based on four different measures of worth. Index of Economically Actual Milk M. E. Milk Significant Final Per Year of Per Year of Cow No. Traits Index Herd Life Herd Life 625 58 53 97 94 626 37 35 71 69 627 60 61 91 101 630 22 3O 31 42 635 62 70 87 95 636 100 96 110 110 637 101 81 108 109 638 21 22 23 23 639 103 105 109 111 640 81 62 61 62 641 43 51 47 56 642 48 75 27 25 643 l4 14 33 52 644 16 16 21 15 645 54 63 89 97 646 65 66 10 11 647 93 90 101 72 648 78 50 93 87 649 42 46 55 63 650 18 6 53 60 651 63 77 106 100 652 76 42 100 103 653 61 56 79 76 654 92 104 105 58 655 88 102 81 73 656 90 60 92 96 657 105 99 107 108 658 72 82 85 91 659 108 ' 100 88 78 661 39 12 29 30 662 38 ll 45 28 663 69 79 73 67 664 95 91 57 44 665 27 10 20 26 666 55 38 103 107 667 50 54 84 92 668 19 4 39 32 670 79 68 83 33 671 107 95 111 99 672 104 94 63 55 673 35 13 86 79 674 96 58 65 83 675 94 21 46 68 65 Table 13. continued Index of Economically Actual Milk M. E. Milk Significant Final Per Year of Per Year of Cow No. Traits Index Herd Life Herd Life 676 66 44 59 81 677 36 1 82 80 678 71 49 75 75 679 5 36 5 7 680 33 17 44 36 682 80 89 102 39 683 57 67 3O 31 685 6 18 17 18 686 45 69 34 40 687 51 71 54 82 688 12 2 24 9 690 28 55 72 54 691 83 85 95 65 693 67 72 8O 64 694 23 37 36 19 697 56 39 40 71 698 86 74 67 77 701 20 27 35 50 702 2 3 2 2 703 84 98 104 59 704 53 80 42 13 707 13 32 19 34 708 44 9 51 53 709 10 45 6 8 712 52 24 64 37 713 24 25 26 41 714 8 29 13 14 716 7 28 8 22 717 68 84 76 48 718 1 5 7 1 719 75 107 37 21 721 73 97 58 45 722 110 106 98 106 723 98 109 94 49 724 87 87 77 89 725 15 31 43 102 727 77 108 48 43 728 59 4O 52 85 730 102 111 74 93 733 82 52 62 98 734 106 110 96 105 735 70 78 41 57 736 85 92 66 86 737 89 83 70 35 66 Table 13. continued Index of Economically Actual Milk M. E. Milk Significant Final Per Year of Per Year of Cow No. Traits Index Herd Life Herd Life 738 41 73 12 10 739 99 48 38 70 740 3 20 4 20 741 29 41 25 24 742 17 43 9 4 743 64 86 6O 51 746 26 19 69 74 747 111 103 99 104 748 91 59 68 84 753 9 7 15 27 754 31 8 16 66 755 40 57 56 61 756 47 23 50 88 758 34 63 18 12 759 109 93 59 46 761 46 65 l 3 762 30 47 28 38 763 25 26 11 6 765 11 33 14 16 766 4 34 3 5 767 74 101 90 17 768 49 88 32 29 769 32 15 22 47 770 97 76 78 90 67 lowered in either case. The latter may not be a bad effect, partic- ularly if milk marketing practices catch up to milk marketing rhetoric. Examples of index selection to illustrate expected changes are given in the next section. Effects of index selection on other traits What is likely to happen to other traits if selection is on the proposed index? Two separate approaches to this problem were ex- plored to provide possible answers. Table 14 shows what might have been expected if the index con- taining the four economically significant traits, the final index, actual milk production per year of herd life, and mature equivalent milk production per year of herd life had been used as culling guides. Mean values of the variables in the primitive index, after the bottom 20% of the herd had been culled on each of the four criteria, are com- pared with the original herd means. Table 14. Means of primitive index traits under various culling schemes. Remainder after Bottom 20% Culled Economically Original Significant Final Actual M.E. Trait Herd Index Traits Index Milk Milk Freshenings .45 .54 .48 .45 .46 Herd Life 2.37 2.62 2.53 2.47 2.57 Fat Test 3.58 3.56 3.65 3.52 3.52 Body Weight 1241 1254 1249 1240 1255 Milking Time 5.90 5.92 5.94 5.94 5.94 Mastitis 2.53 1.85 2.21 2.45 2.46 Milk Production 13468 14207 14195 14545 14347 Profit 59.23 95.35 97.81 88.42 83.26 68 As expected, culling on the final index improved total profit more than any other criterion. While the difference in gain is slight, heritability has been considered in the increase achieved by the final index. Gains achieved by the other schemes would be reduced when herit- ability is considered. Even though milk production is the most import- ant single factor affecting profit, milk production was improved least by the final index. Actual milk production was improved most by cull- ing on actual milk production and next most by culling on mature equiv- alent milk production. Culling on the final index reduced incidence of mastitis slightly more than either culling scheme based on milk production but less than the index based on economically significant traits. The final index gave butterfat test a sizable boost while all other schemes tended to reduce test slightly. Selection for higher test is a result which would find little favor in many dairy circles and perhaps should not be recommended. However, it does in- dicate that profit could have been increased more, during the past 10 or 11 years at least, by culling a bit more on low butterfat test even though intensity of culling on milk production had to be relaxed slightly. It lends credence to the recent controversial sire evalua- tion systems which give credit for butterfat test in arriving at a sire's dollar transmitting ability. Market forecasts of the future continue to stress the value of solids other than fat, but market prices continue to be based on percent butterfat. Only the scheme of culling on the economically important traits made a significant difference in live freshenings per opportunity. Any changes in this trait brought about by other culling schemes were 69 apparently due purely to chance. Improvement in this trait is non- heritable (Rennie, 1952). All culling schemes increased herd life. This is probably evidence only that better cows tend to remain in the herd longer than poorer cows. Automatic selection for herd life is strong. Culling on actual milk production did not tend to change body weight. All other culling schemes tended to increase body weight slightly. Substantial parts of such increases would be heritable. Milking time was increased slightly by all four culling schemes. However, it is likely that such small increases are merely indicative of the increased amount of milk that must be removed from the higher producing cows remaining in the herd and not a sign of a genetic in- crease in milking time. It does lead to speculation that milking time might increase rapidly if selection was not strong and automatic against it. Table 15 shows what might be expected if the top 20% of the herd were selected for special mating on the basis of the same four criteria for culling. Since the numbers are fewer by four times than the numbers in the culling guide data, results may be a bit more er- ratic and not as dependable. 70 Table 15. Means of primitive index traits under various selection schemes. Top 20% of Herd Economically Original Significant Final Actual M.E. Trait Herd Index Traits Index Milk Milk Freshenings .45 .75 .45 .60 .72 E Herd Life 2.37 4.09 2.85 3.30 3.28 3 Fat Test 3.58 3.52 3.71 3.24 3.14 : Body Weight 1241 1320 1204 1282 1303 Milking Time 5.90 5.90 5.86 6.18 6.30 Mastitis 2.53 1.06 1.08 2.22 2.59 ' Milk Production 13468 16978 15709 17976 17448 1 Profit 59.23 202.61 136.99 181.22 153.36 & At first glance Table 15 may seem to be in error when it shows least profit under selection by final index. Heritability has been considered in determining superiority of profit when selecting on the final index. Thus, expected profit under the other schemes would be reduced by the amount that is nonheritable. Each of the other schemes depend upon substantial increments from freshenings per opportunity and herd life, both nonheritable factors, for their larger profit margins. They also depend more on milk production, only part of which is heritable. In Table 15 the tendency of the final index to put considerable emphasis on butterfat test is reiterated. Selection for profit may reduce rather than increase body weight. In other respects, results of selecting the top 20% of cows in the herd were similar to removing the bottom 20%. The comparison between the two practices serves to emphasize the importance of re- productive rate and consequent percentage of animals required for re- placement upon the kinds and rates of change that can be effected. 71 Analysis based on M.E. milk production Since it is customary to calculate milk production records on a mature equivalent basis to compare cows of different ages, milk production was analyzed in those units. The resultant fraction of variation explained by the three indexes was reduced to .53, .50, and .43 (Table 9). The relative effects of other traits in the primitive F1 index were also changed considerably thereby. Milk production itself became less important because of the failure of mature equivalent milk to predict actual milk production exactly. Actual milk is what is E? sold. Mastitis was also reduced slightly in importance, as were but- terfat test, freshenings per opportunity, and body weight. Herd life and milking time were increased in importance (Table 16). Table 16. Standard partial regression coefficients with their standard errors and significance, mature equivalent milk production. Standard Partial Standard Regression Errors of Variable Coefficients Coefficients Significance Freshenings .18 .08 .039 Herd life .15 .09 .124 Butterfat Test .24 .08 .003 Body Weight .07 .09 .418 Milking Time .05 .07 .484 Mastitis '- .36 .07 .0005 Milk Production .48 .09 .0005 Significance changed slightly but the same traits were statistically significant as before. The significance of body weight went to .42 which indicated no effect on profit, other than what might be due purely to chance, when milk production is corrected for age (Table 16). 72 Partial regression coefficients with their standard errors are in Table 17. Standard partial regression coefficients with their stand- ard errors and significance are in Table 16 and partial correlation coefficients and R2 deletes are in Table 18. Table 17. Partial regression coefficients and their standard errors, mature equivalent milk production. Partial Regression Standard Errors Variable Coefficients of Coefficients Freshenings 57.14 27.34 Herd Life 10.91 7.04 Butterfat Test 56.65 18.69 Body Weight .06 .08 Milking Time 5.76 8.20 Mastitis — 12.23 2.37 Milk Production .017 .0031 Table 18. Partial correlation coefficients and R2 deletes,mature equivalent milk production. Partial Correlation Variable Coefficients R2 deletes Freshenings .202 .506 Herd Life .151 .515 Butterfat Test .286 .484 Body Weight .080 .523 Milking Time .069 .524 Mastitis - .453 .404 Milk Production .483 .382 The main effect of mature equivalent milk production records in the analysis was to reduce the overall ability of the indexes to explain variations in profit. If an index of this type is to be useful, production must be measured in actual production. Because of this, no further analyses were performed on mature equivalent milk production. SUMMARY AND CONCLUSIONS Lifetime milk production, feed consumption, and health records a of 111 cows were analyzed to determine the individual profitability of each cow. Total profit was converted to a unit time basis by dividing each cow's lifetime profit by her years of herd life. Profit per year of herd life varied from a high of $409.18 to a low of‘— $658.19 ' (Table 8). Average profit per year of herd life was $59.23. A selection index for overall excellence, defined as profit per year of herd life, was developed by methods of Grafius (1965) as a model. A primitive index was prepared by choosing traits known to influence income or expenses or both for which data were avail- able or could be obtained. Seven traits were chosen, live freshen- ings per opportunity, herd life, butterfat test, body weight, milking time, mastitis, and milk production. With actual calculated profit as right hand sides, the seven traits were analyzed by least squares linear multiple regression to determine individual effects on profit. The seven traits in the primitive index accounted for 67.6% of the total variation in profit (Table 9). Three of the traits, milking time, herd life, and body weight made no statistically sign- ificant contribution to profit. The remaining four traits accounted for 65.6% of the total variation in profit (Table 9). When herit- abilities from the literature were put with the four traits remaining in the reduced index, another trait, freshenings per opportunity, 73 74 was dropped because of zero heritability. The resultant final selec- tion index explained 56% of the variation in profit (Table 9). Ability of five criteria to rank cows accurately for profit- ability was in the order, primitive index, reduced index, final index, actual milk production, and mature equivalent milk production. In general, the primitive index was quite efficient in ranking cows accur- a ately, especially at the extremes. Seventeen of the top 22 and 14 of the bottom 22 cows were correctly identified. The reduced index was only slightly less accurate than the primitive index. The final index was less accurate still and the two measures of milk production even less accurate (Table 13). The possible effects on other traits in the primitive index if selection were by the reduced or final indexes or either of the measures of milk production were considered. Profit was improved con- siderably by selecting on any of the four criteria. Profit was im- proved $38.58 per cow per year by removing the bottom 20% of the herd by means of the final index. Heritability of traits was considered in the final index. The other criteria showed only slightly less improvement, reduced index $36.12, actual milk production $29.12, and mature equivalent milk production $24.03. While improvement shown by the other criteria would be reduced when heritability is considered, the final index had the disadvantage of putting considerable emphasis on butterfat test (Table 14). Milk production would also be improved considerably, incidence of mastitis reduced slightly, and herd life and milking time increased slightly by all four culling schemes (Table 14). Body weight tended to increase under every culling scheme 75 except actual milk production. Gains in body weight would tend to be passed on to offspring. Freshenings per opportunity were increased significantly only by culling on the reduced index. The other three criteria showed slight, probably random increases (Table 14). Butterfat test was increased substantially by culling on the final index but decreased by the other three schemes (Table 14). Variation in profit accounted for was reduced to 52.6, 50.2, and 43.2% by the primitive, reduced, and final indexes when milk production was measured as mature equivalent rather than actual pro- duction (Table 9). Measurement of milk production should preferably be on an actual rather than mature equivalent basis when it is used to estimate profitability. Comparison of cows of the same age only would be a useful approach in determining profitability. When production is adjusted for age, body weight is not an important determining factor in either production or profit. Cows should not be selected on size alone. Selection for profit under current market conditions would bring about an increase in butterfat test. This might not be desirable since butterfat is not now as useful as protein, calcium, or phos- phorous. However, if pricing remains on the basis of butterfat test, increased test should receive consideration along with milk production in realistic selection. Mastitis, one of the most serious diseases of the dairy in- dustry could have its incidence reduced by selection. Reproductive traits could be improved by management practices. Though already subjected to strong, automatic selection and not subject 76 to further improvement by breeding, reproductive performance could be improved by planned cross breeding and careful avoidance of in- breeding. Herd life and milking time are important factors affecting income. Nevertheless, selection for both of these traits is already automatic and so strong that further emphasis on them is not needed 5‘ at this time. Their relative importance, economically, is so low that they should not be included in a selection index for overall excellence because their inclusion would tend to reduce emphasis 3 L on more important traits. Selection indexes of the kind suggested by Grafius (1965) can be applied successfully to animal selection. The problems associated with their construction are many but not nearly so burden- some and time consuming as earlier approaches. Genetic correlations require many data and their standard errors are large relative to numbers analyzed. Data must come from relatives hard to obtain in sufficient numbers. In practice, the calculation of actual profit need not be done as in this study. The system of assigning animals to groups by comparison with a standard or "yardstick" as Grafius (1965) did with plants could be used. The "yardstick" for comparison in animals could be the herd mean or an area or breed mean. The researcher would compare each individual in the herd with the "yardstick", trait by trait, and give a numerical rating, say one to five. One could be superior, five inferior. The ratings thus assigned would be used as right hand sides in the least squares analysis. A trained animal scientist could vary the traits to be included and the emphasis on traits by his 77 knowledge of the economic conditions affecting the herd under study. For example: A herd receiving a substantial income from sale of animals for show purposes would want type classification score in- cluded in an index. The worker constructing the index could increase the emphasis on type by giving animals superior in type a higher rat- ing than animals superior in some other trait. If greater objectivity El was desired, more than one scientist could be called upon to rate animals. Studies should be initiated to investigate other traits such as; feed efficiency, age, physiological traits, udder characteristics and behavioral traits. Behavioral traits in particular should receive more emphasis. Facilities and management practices requiring drastic changes in behavior are being adopted almost daily without even a good guess as to effects on productivity or profit. Indexes constructed as suggested might not be as accurate as those utilizing adequate estimates of genetic correlations, but they could be applied to a much wider range of problems more easily and utilize much data not suitable to indexes requiring genetic correlations Where data are available to calculate right hand sides as in this study, Grafius' so called "backward" approach permits solution of economic weights much more accurate than those usually assigned arbi- trarily. 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