l DIFFERENCES IN EXTENDING TERMINAL AND NONJERMINAL ENCOMPLETE LACTATIONS TO 305 DAYS Ram: {‘09 Hun Dam-cc a; M. S. MECHIGAN STAN W’Efifi-{TY Camilla C. Au-Eerich £965 ‘ LIBRARY Michlgan State Universny WWII/11H!!!”Ill/11111111) WWII!Ill/1111!!!!” 1W 3 1293 10454 0962 ABSTRACT DIFFERENCES IN EXTENDING TERMINAL AND NON-TERMINAL INCOMPLETE LACTATIONS TO 505 DAYS by Camilla C. Aulerich The purpose of this study was to establish character- istics of terminal lactations and to develop procedures for their utilization. Test day milk weights and ratios between consecutive test days of a lactation were employed in the analysis. The records of production utilized in this study were obtained from approximately 2,500,000 monthly production records of cows tested in Michigan D.H.I.A.—I.B.M. between January 1959 and October 1961. Over 58,000 records were classified as complete records, which were required to con- tain 10 test days in the first 505 days of lactation, while over 113,000 records were categorized as non-terminal. Non— terminal lactations included all records that were not marked by a disposal code within the first ten months of production; complete lactations, incomplete lactations and lactations with missing test days. Any record that was marked by a disposal code was classified as a terminal incomplete lac- tation, and more than 17,500 such records were present. Camilla C. Aulerich All records, both terminal and non—terminal, were cate- gorized into five breed groups (Ayrshire, Brown Swiss, Guernsey, Holstein, Jersey), two age groups (cows calving at less than 36 months of age and those freshening at 56 months of age or over), and two seasons of calving (cows freshening from April through July and those calving during the remain- ing months). Records were further separated according to milk yield on first test day. Three groups of equal numbers were formed to ascertain the influence of initial milk yield (high, medium, and low) on the characteristics of the lac- tation, Breed, age, and season affected the characteristics of the lactation curve and the relationship of the total lac- tation to its part. Rates of reduction in yield between test days varied for each breed-age-season group, indicating that a uniform reduction rate did not exist from one test day to the next. All terminal incomplete records were categorized ac- cording to a voluntary or an involuntary removal of the cow from the herd. A voluntary diSposal occurred when the dairy- man decided whether the cow should be retained or disposed, while an involuntary removal occurred when there was no possible choice. The distribution of involuntarily removed cows was constant for each test day during a lactation, when the tenth Camilla C. Aulerich 5 month was ignored. The rate of voluntary removal was most frequent during the later stages of the lactation for the cows calving at 56 months of age or over, whereas the ma- jority of the cows voluntarily culled were removed during the early part of the lactation for cows calving at less than 56 months of age. Cows voluntarily removed from the herd appeared to have a lower level of milk yield and a more rapid rate of decline during their lactation as compared to cows with completed records. Thus, a different relationship of the expected total milk yield to its part existed. Characteristics of involuntarily terminal records were similar to the complete records but the slight differences that existed could not be attributed to particular causes. Therefore, involuntarily terminal incomplete records should be projected to a 505- day basis by factors used for extending non-terminal lac- tations, whereas voluntarily terminal incomplete lactations should be extended by another set of projection factors, which were derived in this study. DIFFERENCES IN EXTENDING TERMINAL AND NON-TERMINAL INCOMPLETE LACTATIONS TO 305 DAYS BY Camilla C. Aulerich A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Dairy 1965 ACKNOWLEDGEMENTS I wish to express my sincere appreciation to Dr. Lon D. McGilliard for his suggestions, motivation and continual guidance throughout this study. Appreciation is also expressed to Mr. A. J. Thelen and his staff for their aid in the organization of the data, and to Mr. Marion Spohn of the Computer Laboratory for his assistance in programming the 5600 computer. Most of all I am grateful to my husband, Richard, for his encouragement, helpful suggestions and support throughout the writing of this thesis, without which the task would have been more difficult. ii TABLE OF CONTENTS Page INTRODUCTION . . . . . . . . . . o . . . . . . . . 1 REVIEW OF LITERATURE . . . . . . o . . . . . . . . 4 Variables Affecting the Characteristics of the Lactation . . . . . . . . . . . . . . . . . 4 Age . . . . . . . . . . . . . . . . . . . . 4 Season. . . . . . . . . . . . . . . . . . . 8 Breed . . . . . . . . . . . . . . . . . . . 10 Herd. . . . . . . . . . . . . . . . . . . . 12 Cows. . . . . . . . . . . . . . . . . . . . 15 Estimation of 505-Day Milk Production from Partial Lactations. . . . . . . . . . . . . 15 Correlations Between Parts of Lactations. . 15 Ratio Projection. . . . . . . . . . . . . . 18 Regression Projection . . . . . . . . . . . 18 Comparison of Methods for Developing Pro- jection Factors . . . . . . . . . . . . 19 Terminal Incomplete Lactations. . . . . . . . . 20 Distribution of Terminal Incomplete Lac- tations . . . . . . . . . . . . . . . . 21 Characteristics of Terminal Incomplete Lactations. . . . . o . . . . . . . . . 24 SOURCE OF DATA . o o u . o . . . . . . . o . . . . 26 METHODS AND RESULTS. . . . . . . . . . . . . . . . 28 Variables Affecting the Characteristics of the Lactation . . . . . . . o . . . . . . . . . 28 Age . . . . . . . . . . . . . . . . . . . . 28 Season. . . . . . . . . . . . . . . . . . . 28 Breed . . o . . . . . . . . . . . . o . . o 51 Cows. . . . . . . . . . . . . . . . . o . . 56 iii TABLE OF CONTENTS - Continued Page Estimation of 505-Day Milk Production from Partial Lactations . . . . . . . . . . . . . 45 Ratios for Projecting Incomplete Lactations to 505 Days . . . . . . . . . . . . . . . 46 Alternative Ratio Factors for Extending Incomplete Lactations . . . . . . . . . . 55 Terminal Incomplete Lactations . . . . . . . . . 56 Distribution of Terminal Incomplete Lac— tations . . . . . . . . . . . . . . . . . 56 Characteristics of Terminal Incomplete Lactations. . . . . . . . . . . . . . . . 68 Estimation of 505-Day Milk Yield from Terminal Incomplete Lactations. . . . . . 76 DISCUSSION. . . . . . . . . . . . . . . . . . . . . 88 Variables Affecting the Characteristics of the Lactation. . . . . . . . . . . . . . . . . . 88 Estimation of 505-Day Milk Production from Partial Lactations . . . . . . . . . . . . . 89 Ratios for Projecting Incomplete Lactations to 505 Days . . . . . . . . . . . . . . . 89 Alternative Ratio Factors for Extending Incomplete Lactations . . . . . . . . . . 90 Terminal Incomplete Lactations . . . . . . . . . 90 Distribution of Terminal Incomplete Lac- tations . . . . . . . . . . . . . . . . . 91 Characteristics of Terminal Incomplete Lactations. . . . . . . . . . . . . . . . 92 Estimation of 505-Day Milk Yield fro Terminal Incomplete Lactations. . . . . . 95 Application of Results . . . . . . . . . . . . . 97 Variables Affecting the Characteristics of the Lactation . . . . . . . . . . . . . . 97 Estimation of 505-Day Milk Production from Partial Lactations. . . . . . . . . . . . 99 Terminal Incomplete Lactations . . . . . . . 100 iv TABLE OF CONTENTS - Continued Page Future Investigations Required . . . . . . . . . 102 Variables Affecting the Characteristics of the Lactation . . . . . . . . . . . . . . 102 Estimation of 505-Day Milk Production from Partial Lactations. . . . . . . . . . . . 105 Terminal Incomplete Lactations . . . . . . . 105 SUMMARY . . . . . . . . . . . . . . . . . . . . . . 105 LITERATURE CITED. . . . . . . . . . . . . . . . . . 108 LIST OF TABLES Table 1. 10. 11. 12. 15. Distribution of complete records by breed, age, and season . . . . . . . . . . . . . . Distribution of non—terminal records by breed, age, and season . . . . . . . . . . . . . . Distribution of terminal records by breed, age, and season . . . . . . . . . . . . . . Grouping by milk yield on first test day within breed, age, and season . . . . . . . Milk yield and decline for each test day by age and season of calving (Ayrshire). . . . Milk yield and decline for each test day by age and season of calving (Brown Swiss) . . Milk yield and decline for each test day by age and season of calving (Guernsey). . . . . Milk yield and decline for each test day by age and season of calving (Holstein). . . . Milk yield and decline for each test day by age and season of calving (Jersey). . . . . Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Ayrshires . . . . . . . . . . . . . . . . . Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Brown Swiss . . . . . . . . . . . . . . . . . . . Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Guernseys . . . . . . . . . . . . . . . . Cumulative and non- -cumulative ratio factors for projecting 505- -day milk yield for Holsteins . . . . . . . . . . . . . . . vi Page 27 27 27 29 58 59 40 41 42 47 48 49 50 LIST OF TABLES - Continued Table 14. 15. 16. 17. 18. 19. 20. 21° 22. 25. 24. 25. Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Jerseys. Cumulative ratio factors for Holsteins develop- ed from average ratios and from the average pounds of milk produced on each test day . . Cumulative ratio factors based on initial level of milk yield for high, medium and low producing Holstein cows. . . . . . Removals by test days of Holsteins less than 56 months of age between July . . . . . . . . . . . . . . . Removals by test days of Holsteins less than 56 months of age between March. . . . . . . . . . . . . . . Removals by test days of Holsteins calving at April and calving at August and calving at 56 months of age or over between April and July . . . . . . . . . . . . . . . Removals by test days of Holsteins calving at 56 months of age or over between August and March. . . . . . . . . . . . . . . Removals by test days of Holsteins Frequency of removals of Holstein cows from each age-season group. . . . . . . Percentage of Holsteins culled from each age and season group . . . . . . . . . Percentage of cows removed by breed for each test day and age-season group. . . Cumulative and non-cumulative ratio factors for projecting 505-day milk yield from volun- tarily terminal incomplete records Holsteins. . . . . . . . . . . . . vii for Page 51 55 57 59 60 61 62 65 65 67 69 82 LIST OF TABLES - Continued Table Page 26. Cumulative and non—cumulative ratio factors for projecting 505-day milk yield from volun- tarily terminal incomplete records for Guernseys. . . . . . . . 85 27. Variations in estimating 505-day milk yields of Holstein voluntarily terminal incomplete lactations by terminal and non-terminal pro— jection factors. . . . . . 86 viii LIST OF FIGURES Figure 1. 2. 10. Lactation curves for age-season groups of HOlStéinS. O O O O O O O O O O O O O O O O O 0 Breed average lactation curves for cows fresh- ening at less than 56 months of age and calv- ing between April and July . . . . . . . . . . Breed average lactation curves for cows fresh— ening at less than 56 months of age and calv- ing between August and March . . . . . . . . . Breed average lactation curves for cows fresh- ening that are 56 months of age or over and calving between April and July . . . . . . . . Breed average lactation curves for cows fresh- ening that are 56 months of age or over and calving between August and March . . . . . . . Average lactation curves of Ayrshires, Brown Swiss, Guernseys, Holsteins, and Jerseys . . . Lactation curves based on first test day milk yield of Holstein cows freshening between April and July and calving at less than 56 months of age. . . . . . . . . . . . . . . . . Lactation curves based on first test day milk yield of Holstein cows freshening between August and March and calving at less than 56 months of age. . . . . . . . . . . . . . . . . Lactation curves based on first test day milk yield of Holstein cows freshening between April and July and calving at 56 months of age or over. . . . . . . . . . . . . . . . . . . . Lactation curves based on first test day milk yield of Holstein cows freshening between August and March and calving at 56 months of age or over. . . . . . . . . . . . . . . . . . ix Page 50 52 55 54 55 57 44 44 45 45 LIST OF FIGURES - Continued Figure 11. 12. 15. 14. 15. 16. 17. 18. 19. Voluntarily incomplete terminal and completed lactations of Holsteins freshening at less than 56 months of age and calving between April and July. . . . . . . . . . . . . . . . Voluntarily incomplete terminal and completed lactations of Holsteins freshening at less than 56 months of age and calving between August and March. . . . . . . . . . . . . . . Voluntarily incomplete terminal and completed lactations of Holsteins freshening at 56 months of age or over and calving between April and July. . . . . . . . . . . . . . . . Voluntarily incomplete terminal and completed lactations of Holsteins freshening at 56 months of age or over and calving between August and March. . . . . . . . . . . . . . . Voluntarily incomplete terminal and completed lactations of Holsteins showing low initial milk yield, freshening at 56 months of age or over and calving between August and March . . Involuntarily incomplete terminal and com- pleted lactations of Holsteins freshening at less than 56 months of age and calving be- tween April and July. . . . . . . . . . . . . Involuntarily incomplete terminal and com~ pleted lactations of Holsteins freshening at less than 56 months of age and calving between August and March. . . . . . . . . . . Involuntarily incomplete terminal and com- pleted lactations of Holsteins freshening at 56 months of age or over and calving between April and July. . . . . . . . . . . . . . . . Involuntarily incomplete terminal and com- pleted lactations of Holsteins freshening at 56 months of age or over and calving between August and March. . . . . . . . . . . . . . . Page 70 71 72 75 75 77 78 79 80 I NTRODUCTI ON Complete records, partial records in progress, and terminal incomplete records are present in a collection of Dairy Herd Improvement Association records. A complete lactation is a record that has 505 days of milk production recorded or that is ended in fewer days by a dry code. A partial or non—terminal incomplete lactation results prior to completion of the lactation. An incomplete terminal record is obtained when the cow is removed from the herd prior to completion of her lactation. Cows may be removed from the herd voluntarily or in- voluntarily. A voluntary diSposal occurs when an animal is culled for low production, old age, dairy purposes, or hard milking, while an involuntary disposal results when a cow is removed because of disease, death, etc., where the dairyman had no choice of retaining or disposing of the cow. Since more than one—fifth of all lactations initiated result in incomplete terminal records, the characteristics of voluntary and involuntary terminal lactations and methods for their utilization should be established. However, for comparison the characteristics of complete records must be ascertained and factors for predicting the total lactation from its parts developed. Establishing characteristics of I complete lactations would aid in predicting future lactations, in estimating missing test days, in projecting incomplete lactations to 505-day records, and in estimating the prob— able total milk yield from cows terminating their records. Comparison of the characteristics of terminal and complete records might indicate whether the slopes of the curves coincide and if separate extension factors would be required for estimating 505—day milk yields of terminal records. Terminal incomplete records should be extended and utilized in sire proofs because including terminal records with partial and completed lactations could allow for the evaluation of sires up to five months earlier than proofs based only on completed records (VanVleck, 1962; VanVleck and Henderson, 1961e,h). In addition, utilization of all available records leads to a more accurate ranking of bulls (VanVleck and Henderson, 1961h) and reduces the positive bias that is introduced into proofs when undesirable first calf heifers are culled before completing a record. The type of extension factors that would provide the best estimate of the potential 505—day milk yield of terminal lactations was not clear to VanVleck (1962). Accurate extension of terminal incomplete records would be especially important in evaluating bulls that have limited numbers of daughters. At present, terminal incomplete lactations that are extended for use in sire proofs are projected to a 505—day basis by factors for extending non-terminal lactations to completion. A more appropriate set of projection factors might be most beneficial. The objectives of this study were: (a) to establish the characteristics of completed lactations with which to compare terminal incomplete records; (b) to develop cumu— lative and non-cumulative ratio factors for extending non- terminal partial lactations to completion; (c) to establish characteristics of voluntary and involuntary terminal in- complete lactations; and (d) to develop procedures for utilizing terminal incomplete records. REVI EW OF LI TERATURE Variables Affecting the Characteristics of the Lactation The total milk yield of a lactation of standard length is determined by the initial milk yield and the rate of re- duction in yield during that lactation. These character- istics of the lactation may be affected by variables such as age at calving, season of calving, breed of cow, the in- dividuality of the cow, and management practices in the herd in which the lactation is produced. Age Age at calving influences the total milk yield of the cow for that lactation because the younger cows generally initiate their lactations at a lower level than the older animals. The younger cows have a smaller rate of decline during lactation, but due to the low starting level, less total milk is obtained than if the cow had been mature. Lush and Shrode (1950) noted that total milk production in- creased with age of the cow at a decreasing rate until the maximum production was reached at around six to eight years of age. Due to age effects on total milk yield, factors to correct for age at calving are employed in the comparison 5 of the complete records of young animals with those of mature cows (Kendrick, 1955; Searle, 1960; Mahadevan, 1951b; Lush and Shrode, 1950; Dickerson, 1940). However, these factors adjust only for the immaturity of the animal for that particular lactation. An effect of age on the rate of decline of the test day milk weights was observed from the results reported by Harvey (1956) and Madden §£_al. (1959). However, the results of the latter indicated larger differences in reduction rates due to age than those reported by Harvey (1956). The cows calving at less than 56 months of age had smaller reduction rates during their lactations than those cows calving at 56 months of age or over, indicating that the younger cows exhibit a more consistent lactation curve. Since total milk yield, consistency of lactation, and initial level of milk production differed with age, a con- stant relationship of the total lactation to its part would not be expected. Eldridge and Atkeson (1952) separated 2582 Holstein records into twelve age groups to measure the effect of age on the relationship of the partial lactation to its total. But when the records were regrouped into first and second lactations, they noted greater differences due to lactation number than to age. Thus, Eldridge and Atkeson (1952) found it advisable to form regression factors by lactation number rather than by age at calving to estimate total milk production and recommended two sets of factors, for first lactation and for subsequent lactations. To distinguish between the influences of age and lac- tation number on the relationship of the partial lactation to its total, Fritz (1958) categorized his data into eight age groups, cows calving at less than 24 months, 24 to 50, 50 to 56, . . . , 54 to 60, and 60 months or over, and into three lactation numbers, first, second, and third or more. Within each age and lactation number, linear regression equations were used to measure the relationship between the total milk production and its cumulative part. An analysis of variance, however, failed to indicate distinct differences in regression coefficients between various age groups and lactation numbers. Lamb (1959), employing ratios to detect differences between the influences of lactation number and age on the relationship of the total lactation to its part, grouped his data according to first, second, and third or more lac- tations and according to age at calving of less than 56 months, 56 to 48, 48 to 60, and 60 months or over. Although lactation number accounted for more variability in ratios of the total lactation to partial production than did age, he suggested the use of factors which adjust for age. Factors based on parity overestimate the total milk yield of cows having their first lactation initiated after 56 months of age, but underestimate total milk production of cows freshening for a second record at less than 56 months of age. In 90% of the cases, factors for various ages and lactation numbers were equally applicable, and in 10% of the cases, factors divided by ages were preferred. There- fore, Lamb (1959) recommended the use of different adjustment factors for two or three ages for extending incomplete lac- tations. Two sets of adjustment factors appeared necessary for extending partial milk production to 505 days since similarities existed among the factors for cows calving at various ages 56 months of age or over and among the factors for those freshening at less than 56 months of age, but factors for the two groups were distinctly different. This was verified in later work (Lamb, 1962). Investigating age as an important factor affecting the relationship of milk production from month to month, Madden et al. (1955, 1956) found that the lactation curves for records initiated by cows less than three years of age dif- fered distinctly from those of records started by cows three years or over. Therefore, to obtain the best estimate of the 505—day milk yield in projecting a partial lactation to completion, two sets of factors were proposed; one set for cows calving at less than 56 months of age and the other set for those animals freshening at 56 months of age or over. The older cows began their lactations with larger amounts of milk, but decreased in yield from month to month more rapidly than the younger cows until both groups were producing nearly the same amounts at the end of the lactation. Harvey (1956) developed ratio factors for extending partial lactations to 505-day records for three age groups of cows; those less than 52 months of age, those between 52 and 46, and those 47 months or over. Lamb (1962) also utilized three groups, cows calving at less than 56 months of age, between 56 and 47, and those freshening at 48 months of age or over, but noted that this grouping was required only for extending partial fat production to 505 days. VanVleck and Henderson (1961c) separated 177,575 test day records into 60 age groups to establish the effect of age on the ratios derived from the monthly mean milk proé duction and used for extending incomplete lactations to 505 days. Their results indicated the importance of adjust- ing for age in utilizing ratio factors. Season Season of calving influences milk yield, but less than does age. Cows calving in the fall and winter months produce more total milk than do cows freshening in the spring and summer months (Bereskin and Freeman, 1961; Bereskin §£_al., 1962; Brown §t_al,, 1961; Branton §E_gl., 1961; Searle, 1961; Johansson, 1961; Sundaresan and Freeman, 1961; Mahadevan, 1951a,b; Frick et_al., 1947; Cannon, 1955; Sanders, 1929; Hammond and Sanders, 1925; Turner, 1925). Frick §£_§l, (1947) and Mahadevan (1951b) reported 15.7 and 10% increases, respectively, in milk production for cows calving in the winter months as compared to those freshen- ing in the spring. The cows freshening in the fall exhibited a more consistent lactation curve than those calving in the other seasons (Rakes et al., 1965; Branton and Miller, 1959; Turner, 1925). However, Bereskin and Freeman (1961) noted that the high and low seasons of calving differed among areas in the United States. After separating herds into three groups of equal numbers based on average milk production of each herd, Bereskin and Freeman (1961) showed that the peak of milk production was reached in high—level herds a month earlier than in low-level herds. In addition, a significant dif— ference existed in the number of cows calving in the spring and summer seasons in the low and high herds, indicating that the low producing herds were not being managed to take full advantage of the increase in total milk yield due to winter calving. The existence of a true seasonal effect was supported by the data, and the following factors that Bereskin and Freeman (1961) believed to be of importance were recorded: "(1) climatic effects, such as temperature and humidity; (2) physiological factors, such as stage of lactation at dif— ferent seasons; (5) management practices, such as more adequate winter care; and (4) availability of suitable roughage supplies in different seasons." Mahadevan (1951b), in agreement with Sanders (1929), stated that the variation 10 in rate of decline during the lactation could be reduced by improving feeding and management because the differences in milk production due to month of calving were of a nutri- tional nature. However, Dickerson (1940) found month of calving to be a relatively unimportant source of variation in total milk production. The effect of season on the relationship of the partial lactation to its total accounted for almost as much variation as did age (Lamb, 1959; Lamb and McGilliard, 1960). Lamb (1959) also found that the differences between seasons in- creased as the stage of lactation progressed. Two seasonal groups, November through April and May through October, were used to develop ratio factors. Later work by Lamb (1962), however, showed that the adjustment for the season of calv- ing did not appear as important as the correction for age. He rearranged the two seasons to include April through July and August through March because differences were larger between the factors of these groups than between factors of the previous groups. In opposition to the above views, Fritz et al. (1960) and Eldridge and Atkeson (1952) reported seasonal differences to be insignificant in the prediction of total lactation from its part by regression. Breed Although cows within a breed have varying shapes of lactation curves due to environmental and inherited factors, 11 Cannon et al. (1942) reported that an average lactation curve could be formed for each breed because the shapes of the lactation curves for cows of the same breed have much in common. However, the Guernseys, Holsteins, and Jerseys had similar lactation curves. In spite of the likeness of the lactation curves, each breed probably exhibited a dif- ferent total milk yield due to the level at which they started their lactation. The results of studies by Turner (1925) and Fritz §£_§l. (1960) showed that breed affected the rate of decline during lactation. The Holstein and Brown Swiss had similar rates of reduction, and the Guernseys resembled the Jerseys. Compared with Guenseys and Jerseys, the rate of decline for the Holsteins and Brown Swiss was slower at the beginning of the lactation, whereas later in the lactation faster reduction occurred. A different relationship of the total to part lac- tation would be expected for each breed since lactation curves were similar in shape but not in initial level of milk production. Breed effects were present in the extension factors developed by Fritz (1958) although they were not mentioned. Even with large differences in the numbers of observations, Lamb (1959) reported significant differences between breeds in the relationship of the partial lactation to the completed (505-day) record. This effect was indi- cated by differences in cumulative and non—cumulative ratio 12 factors. Lamb (1959) reported that Guernsey and Jersey extension factors were similar, whereas the Holstein factors resembled the Brown Swiss factors. The Holstein and Brown Swiss factors were larger at the beginning of the lactation and smaller for the remainder of the lactation as compared with those of the Jerseys and Guernseys. fists Environmental factors such as management and nutrition account for the major portion of the differences in milk yield between herds (Sundaresan and Freeman, 1961; Pirchner and Lush, 1959). These herd differences account for approxi- mately 50% of the variation among records in the population (Bereskin and Freeman, 1961; Pirchner and Lush, 1959). Thus, the amount of milk produced by a cow during a lactation is affected by the herd in which the record was made. Average cows calving in herds with a high level of milk yield initiate their lactations at a higher level than do average cows calving in low producing herds, but the rate of decline is greater for the cows with high initial production. Hickman and Henderson (1955) reported that the level of herd production influenced successive lactations of a cow. Since successive lactations of a cow are influenced by the level of herd production, several workers (Searle and Henderson, 1959; Searle, 1961, 1960; Hickman, 1962) have 15 advocated the use of age correction factors based on herd level for adjusting the total milk yield for age at calving. Cows in herds of high level production should receive a larger correction than those of the same age in herds of low level production. Searle and Henderson (1959) proposed herd additive correction factors for age. However, they found a close association between multiplicative age adjust- ment factors and additive factors. Herd effects were unimportant in the relationship of the part lactation to its total (Fritz, 1958). Utilizing regression analysis ignoring herds, Fritz (1958) noted a significant herd effect only in the first month of production. Separate extension factors are not required for each herd since the component of variance among herds for the ratio of total lactation to its part was negligible in studies by Lamb (1959) and by Lamb and McGilliard (1960). Ignoring herd differences is more practical than con- sidering them in predicting the 505-day lactation from a part. VanVleck and Henderson (1961f) state, "For most combinations of records, regression ignoring herd effects is less than 20% less efficient and in many cases less than 10% less efficient than regression considering herd effects." Cows Lactation curves of several records of a cow are similar (Bonnier, 1955; Sanders, 1950; Ludwick gt al., 1945), 14 and Sanders (1950) noted consistency of lactation curve among lactations when corrections were made for external factors. The similarities between lactations could be genetically determined (Bonnier, 1955). Ludwick et al. (1945) postulated that "a major portion of the variation in persistency is probably the result of the inheritance of factors or genes which govern the development and rate function of various endocrine glands, and the interaction and interdependence of such glands, or the inherited or acquired ability of various tissues to respond to various secretions. The mode of inheritance is undoubtedly complex.“ The shape of the lactation curve varies among cows (Bonnier, 1955; Ludwick §t_al., 1945) because of variation in the rate of reduction of milk yields and in the level at which the records were initiated. However, the consist- ency of lactation is correlated (0.52) with total milk yield (Lennon and Mixner, 1958). The rate of decline from one test day to the succeed- ing one (50.5 days later) during a lactation varied among reports (VanVleck and Henderson, 1961g; Fritz §t_al., 1960; Madden et al., 1959; Lennon and Mixner, 1958; Kendrick, 1956; Harvey, 1956; Cannon §t_al., 1942; Turner, 1925; Brody et al., 1925). However, the constant rate of reduction of 10% per month (Turner, 1926) appeared to be in error in all cases. 15 Estimation of 505-Day Milk Production from Partial Lactations Although other variables affect the lactation, in projecting an incomplete lactation, adjustment for only breed, age, and season was necessary (Lamb, 1959, 1962). Cumulative or non-cumulative ratio or regression projection factors within breed, age, and season categories generally are employed to estimate 505-day milk yields. The cumu— lative projection factors employ the total amount of milk produced by the cow to date, whereas the non—cumulative factors utilize only a single month's milk yield. Correlations Between Parts of Lactations Correlations between parts of lactations indicate the probable accuracy with which a 505-day record can be pre- dicted from its part. The larger the correlation, the greater the expected accuracy of the predicted total milk yield. As cows mature, they initiate their lactations at a higher level of milk yield, but exhibit a greater reduction rate during their lactation (Rakes e£_§l,, 1965; Madden et al., 1959; Lennon and Mixner, 1958; Lush and Shrode, 1950; Sikka, 1950). In spite of the high rate of decline for cows initiating their lactation at a high milk yield, initial milk yield was highly correlated with total milk production (Sikka, 1950 (0.70); Lennon and Mixner, 1958 (0.81))° 16 This high correlation indicates that the initial level of milk yield is a good indicator of 505~day milk production. Thus, initial milk production could serve as an index of an animal's potential worth (Gooch, 1955). The number of days required to obtain maximum initial yield is relatively constant (55 days i 1) regardless of season of calving (Rakes e£_§l,, 1965). Rakes et_al, (1965) also observed that the correlations between the first few days of pro- duction and peak production were extremely high, finding, for example, a correlation of 0.96 between the 20§h day and the peak milk production. This would imply that the milk yield on first test day also would be highly correlated with the peak milk production. Madden §t_al. (1959) reported that the first test interval after calving averaged 55.5 days and from this Lamb (1959) deduced that on the average the first test day falls around the 17—18 countable day of production. Lamb (1962) noted larger product-moment correlations between cumulative monthly and total milk production than between monthly and total milk yield. When total milk production is estimated by non-cumulative factors, the fourth, fifth, and sixth months of lactation are the best months of lactation for estimating 505—day milk production from a single test period (Lamb, 1962; VanVleck and Henderson, 1961a,b,d; Madden g;_al., 1959; Voelker, 1957; Gaines, 1927). Correlations between total production and the fourth, fifth and sixth months of lactation were 0.87, 0 92, 0.80 (VanVleck and Henderson, 1961a) while Lamb (1962) noted 17 correlations of 0.86, 0.86, 0.85 for the first lactation, 0.85, 0.85, 0.85 for the second lactation, and 0.81, 0.84, 0.85 for later lactations. The cumulative milk yield of the first 70 days of lactation was an excellent guide to total yield in a study by Rendel §t_al. (1957), and Kennedy and Seath (1942) stated that production during the first four months of lactation was a good index of the lactational milk yield. When cumulative milk yield of the first four months was used to project the 505-day milk production without regard for age and seasonal effects, correlations were 0.92, 0.85 and 0.88 between the actual and estimated total milk production (Fritz §t_al,, 1960, Voelker, 1957; VanVleck and Henderson, 1961a,b, respectively). Madden, §£_al. (1959) noted a correlation of 0.95 for cows calving under 56 months of age and a correlation of 0.90 for those animals freshening at 56 months or over. However, Lamb (1962) reported corre- lations of 0.91 for Holsteins in their first lactation, 0.87 for those in their second lactation, and 0.84 for those in later lactations. Miller (1965) employed the non-cumulative ratio ex- tension factors formulated by Lamb (1962) in predicting 505-day milk yields. Utilizing 19,000 Michigan D.H.I.A. cows in the study, Miller extended all records for a single test day in each herd. He reported a correlation of 0.80 between the total milk yields and the estimated total pro- duction for records projected from all stage of lactation. 18 In addition, the correlation was 0.92 between the actual herd average and the average herd production estimated by non-cumulative ratio factors (Miller, 1965). Ratio Projection The ratio is a direct measure of the relationship of milk yield for 505 days to the part lactation (Lamb, 1959) since it does not include the incomplete repeatabilities of various portions of the lactation. The projection equation employing a ratio is Y = cX where Y is the estimated 505-day milk production; 2, the ratio of the completed lactation to its part; and X, the pounds of milk produced during the part lactation (Lamb, 1959; Madden §t_al., 1959,1955; Fritz, 1958). With this method, the variability of the 505-day estimated milk production approaches the normal variation in the completed records of milk production (Lamb, 1959; Madden et al., 1959; Fritz, 1958; Harvey, 1956). However, Lamb (1959), Madden et_al. (1959), Fritz (1958), and Harvey (1956) also reported that this procedure generally over- estimates the high producing cows and underestimates the low producing cows. Regression Projection The curvilinear characteristics of the regression of the total lactation on its cumulative part are of little significance when averaged over all herds (Madden et al,, 19 1959; Harvey, 1956), indicating that the total milk yield may be projected from a partial record by means of linear regression. The projection equation.Y = a + bX is employed in estimating the total milk production, where Y is the estimated 505-day milk yield; a, the y—intercept for a particular month of lactation; b, the regression coefficient measuring the average change in Y for each unit change in X; and X, the pounds of cumulative partial milk production (VanVleck and Henderson, 1961b; Fritz, 1958; Madden et al., 1959; Lamb, 1959). The regression analysis (least squares procedure) corrects for the incomplete repeatability of parts of the lactation as well as for the incompleteness of the lactation. Comparison of Methods for Developing Projection Factors The two most common procedures, ratio and regression, produce reasonable corrections for the incompleteness of the lactation in estimating 505-day milk yields (Fritz,1958; Lamb, 1959). Thus, the choice of methods depends on the purpose for which the records are being extended. The value of the regression procedure is in its ability to correct for the incomplete repeatability of various portions of the lactation, whereas the advantages of the ratio procedure are its direct measure of the relationship of the partial lactation to its total, its simplicity and ease of calcu- lation, and its availability from a single lactation (Lamb, 1959). 20 Separate equations are required for each stage of lactation when the regression procedure is employed because of the changing a_and b_values (Harvey, 1956). With this method, Harvey (1956) noted that the constants (a) ap- proached zero as the length of lactation increased causing similarities to exist between the ratios and regression co- efficients. The difference between the two methods (ratio and regression) can be expressed as (b-c)(X?§) where b.is the linear regression of the total lactation on its part; 9, the ratio of the total to part production; X, the actual partial milk production; and R, the mean of the partial milk production for the appropriate breed-age-season group (Fritz, 1958; Madden §t_§l., 1959; Lamb, 1959). g_is larger than b_for the first through third months of lactation; c > b_for the fourth through sixth month, gg< b_for the seventh, eighth, and ninth month of lactation. Terminal Incomplete Lactations According to D.H.I.A. records compiled by Johnson and Thelen (1960), 27% of the cows in Michigan are removed from their respective herds before completing their current lactations. These terminal incomplete lactations probably do not exhibit the same characteristics as the partial lactations still in progress. The shape of their lactation curves may be related to the reasons for removal of the COW . 21 Distribution of Terminal Incomplete Lactations The average productive life of a cow is approximately three and one-half years from the date of first calving (Lamb and KOpland, 1965; Parker et al., 1960; Lush and Lacy, 1952). O'Connor and Hodges (1965) found a similar average productive life (three and one-half to four and one—half years) for cattle in England. Johansson (1961) reported that the average reproductive life of dairy cattle has been declining in the last 50 years. As a result, a cow's actual number of milking years is extremely short compared to her potential productive life; however, the decreasing gener- ation interval should allow for an increased rate of genetic improvement. Utilizing records of Holstein cattle that calved more than once,Lamb and Kopland (1965) reported that the fewest number of lactations (5.0) initiated were for the cows initiating their first records at less than 24 months of age and for those starting their first lactation at 54 months of age or over. Cows calving near 27 months of age had the largest number of lactations (5.6) initiated prior to removal. However, as the cows increased in age prior to starting their first lactation, the pounds of milk per day from two years of age to the time of removal decreased. Cows producing at a high level during their first lactation completed more records and produced at a higher 22 level in successive lactations than those cows having a low first lactation record (VanVleck, 1964). As a result, the high producing cows have a longer productive life than their low producing first lactation herd-mates. In England, O'Connor and Hodges (1965) noted seasonal effects in the rate of culling. This they attributed partly to economic factors such as the price of cows. The peak heifer disposal was in the summer months, whereas the larg- est number of cows were removed in the winter. Asdell (1951) also noted that economic influences could be detected by the variation in the number culled from year to year. This was expressed by the number of cows removed for low production. The percentage of animals voluntarily and in- voluntarily removed was influenced by economic conditions, and the effect was present in the Michigan D.H.I.A. annual summaries (Johnson and Thelen, 1959, 1960, 1961, 1962). Of the cows on test in Michigan D.H.I.A.. 29% were removed from their respective herds in 1959. Voluntary disposal accounted for 57% of those removed, whereas only 45% of the removals were involuntary. Cows voluntarily culled accounted for 55% of the total number of animals eliminated in 1960 while those involuntarily removed ac- counted for 45% of the 27.6% of the cows removed from the population. In 1961, of the 26.6% eliminated, 57% were voluntarily disposed While 45% were involuntarily removed. 25 O‘Bleness and VanVleck (1962) noted the presence of breed and age effects in the percentage of terminal records. They found that, of the two year old cows removed, 67.9% were culled voluntarily while only 52.1% were terminated involuntarily. But as the cows increasedin age, the per- centage of cows voluntarily removed decreased to 56.6% for cows seven years or over, and the percentage of involun- tarily disposals increased to 65.4% for cows seven years or over. The average voluntary disposals for cows three years or over were 49.5% while the average involuntary removals were 50.5%. Studying the relation of sires to rate of culling, Dayton (1964) noted that Holstein bulls' daughters that calved at less than 56 months of age were removed at rates of 25.2% for those bulls having 11 to 20 daughters that might have completed their lactations, 15.4% for those having 21 to 49 daughters, and 16.5% for bulls having 50 daughters or more. This high frequency of disposal indi- cates that biases will be present in bull proofs based on the completed records of first lactations if incomplete terminal records are excluded. However, the effect of the omission of terminal incomplete lactations from sire proofs may become negligible as the number of animals included in the proof increases. For cows calving at 56 months of age or over, Holstein bulls! daughters were removed at a rate of 24.1% for those bulls having 11 to 20 daughters that might 24 have completed their lactations, 24.8% were removed for those having 21 to 49 daughters, and 20.6% were removed for bulls having 50 daughters or more. In the South Dakota State University herd, where the rate of culling was approximately 16% annually, Voelker (1957) reported that 5% of the cows were removed during their first month of lactation, 11% during the second, 9% during the third, 11% during the fourth, 15% during the fifth, 15% during the sixth, 18% during the seventh, 12% during the eighth, and 6% during the ninth month of lactation. He found that there were no significant differences in the rate of culling during the lactation even though the first and ninth months of lactation contained the lowest percent- ages of removal. Voelker (1957) also reported that the frequency of test day removal was approximately the same for each breed. - Characteristics of Terminal Incomplete Lactations Characteristics of the terminal incomplete records are unknown, but many questions have been raised as to their usefulness, methods of utilization, and similarities and differences compared to the completed lactations. The terminal records are initiated at a significantly lower level of milk yield and average considerably lower during the terminal record as compared to previously com— pleted lactations of the same cows (Voelker and Eastwood, 25 1960; VanVleck, 1964). Thus, the terminal records are dif- ferent, but whether the difference is due to genetic or non-genetic factors is unknown. Voelker and Eastwood (1960) reported that there were no significant differences between the slopes of the terminal records as compared to the cow's previously com- pleted lactations. But they further stated that the ratio projection factors were inadequate in estimating what the 505-day milk yield would have been if the cow had remained in the herd to complete her lactation. It appeared to them that the factors overestimated the total production. SOURCE OF DATA The records of milk production were obtained from approximately 2,500,000 monthly reports of cows tested in Michigan D.H.I.A. between January, 1959, and October, 1961. Only lactations initiated after January 1, 1959, and identi- fied by herd number, cow number, date of freshening (month and year), age at calving, and breed were included in the analysis. Each test day milk weight was recorded in tenths of pounds, and the records in which the first test occurred more than 50 days after calving were excluded. Complete lactations (Table 1) were required to have 10 test days in the first 505-days of lactation, whereas non-terminal lactations (Table 2) were not required to meet this restriction. The non—terminal records included all records that were not marked by a disposal code within the first ten months of production. This group was com- posed of all completed lactations, incomplete lactations and lactations with missing test days. Any record that was marked by a disposal code within the first ten months of production was considered as a terminal incomplete lactation (Table 5). 26 27 Table 1. Distribution of complete records by breed, age, and season. Age and season of calving Total Breed <56 Months <56 Months 256 Months 256 Months No. of Apr.-July Aug.—Mar. Apr.—July Aug.-Mar. records Ayrshire 28 46 64 120 258 Brown Swiss 67 218 186 575 1044 Guernsey 524 1202 985 2825 5554 Holstein 5486 11844 8271 24715 48516 Jersey 206 861 507 1702 5276 Table 2. Distribution of non-terminal records by breed, age, and season. Age and season of calving Total Breed <56 Months <56 Months 256 Months 256 Months No. of Apr.-July Aug.—Mar. Apr.-July Aug.-Mar. records Ayrshire 41 74 120 225 460 Brown Swiss 122 577 428 1129 2056 Guernsey 612 1906 2069 5255 9842 Holstein 7255 20706 19219 47555 94715 Jersey 597 1474 1129 5086 6086 Table 5. Distribution of terminal records by breed, age, and season. Age and season of calving Total Breed <56 Months <56 Months 256 Months 256‘Months No. of Apr.-July Aug.-Mar. Apr.-July Aug.-Mar. records Ayrshire 7 7 24 65 101 Brown Swiss 12 67 75 197 551 Guernsey 125 551 458 1174 2086 Holstein 794 2547 5097 7715 15955 Jersey 60 209 209 592 1070 METHODS AND RESULTS Variables Affecting the Characteristics of the Lactation All records were categorized, according to the re- sults reported by Lamb (1959, 1962), into five breeds (Ayrshire, Brown Swiss, Guernsey, Holstein, and Jersey), two age groups (cows calving at less than 56 months of age and those freshening at 56 months or over), and two seasons of calving (cows freshening from April through July and those calving during the remaining months). Records were further separated (Table 4) according to yield of milk on first test day into three groups of equal numbers of records (high, medium, low). Age Cows calving at less than 56 months of age started their lactations at a lower yield than those freshening at 56 months of age or over. However, the younger cows ex- hibited a more consistent lactation curve which caused the curves to meet near the end of the lactation (Fig. 1). Season Fig. 1 also illustrates the lactation curves of Hol- steins calving within each age-season group. Cows calving 28 29 Table 4. Grouping by milk yield on first test day within breed, and season. Age at Season Breed calving of fresh- Pounds of milk produced (months) ening Low Medium High Ayrshire <56 Apr.-July <55.0 55.0—59.9 240.0 <56 Aug.-Mar. <50.0 50.0-57.9 258.0 256 Apr.-July <44.0 44.0-51.9 252.0 256 Aug.-Mar. <45.0 45.0-52.9 255.0 Brown Swiss <56 Apr.-July <50.0 50.0—56.9 2257.0 <56 Aug.-Mar. <50.0 50.0-56.9 257.0 256 Apr.-July <45.0 45.0-51.9 .252.0 256 Aug.—Mar. <40.0 40.0-48.9 249.0 Guernsey <56 Apr.-July <50.0 50.0-55.9 256.0 <56 Aug.—Mar. <28.0 28.0-55.9 254.0 .256 Apr.-July <57.0 57.0-45.9 246.0 256 Aug.-Mar. <55.0 55.0—42.9 245.0 Holstein <56 Apr.-July <58.0 58.0-46.9 .247-0 <56 Aug.-Mar. <56.0 56.0-45.9 ‘244.0 256 Apr -July <50.0 50.0-59.9 260.0 ‘256 Aug.—Mar. <50.0 50.0-59.9 260.0 Jersey <56 Apr.-July <26.0 26.0-51.9 252.0 <56 Aug.-Mar. <25.0 25.0-50.9 251.0 256 Apr.—July <55.0 55.0-59.9 240.0 _256 Aug.—Mar. <52.0 52.0-58.9 259.0 Milk Yield in Pounds 50 Calving at 56 months of age 60? or over and freshening ++”++' between April and July. 0++++_ Calving at 56 months of age 3 --—- or over and freshening 2' between August and March. .. o—..,,_~~ 55 ’\ X- Calving at less than 56 months \\§* -+F++- of age and freshening \§* between April and July. \ \fi Calving at less than 56 \f -————— months of age and freshening 50“ Q; between August and March. 45” 40” \ 55” 504 25” 20" 0 1 2 5 4 5 6 7 8 9 10 Test Days Fig. 1. Lactation curves for age—season groups of Holsteins. 51 between August and March tended to initiate their lac- tations at a lower milk yield and exhibited a more con— sistent lactation curve than those animals freshening between April and July. Due to the greater consistency of curves of the cows yielding less initially, the two lactation curves crossed at three months of lactation for those ani- mals freshening at less than 56 months of age while for the cows calving at 56 months of age or over, coincidence occurred at three and one—half months of lactation. After the curves met within each age group, the milk yield was larger for each of the succeeding test days for those animals that freshened between August and March. However, for cows calving at less than 56 months of age, the lac- tation curves crossed again after approximately nine and one-half months of lactation. The cows initiating their lactation at a lower level also exhibited a lower test day milk yield on the tenth month of lactation as compared with that of cows calving between August and March. Breed The lactation curves of the breeds within each age— season group were similar (Figs. 2, 5, 4, and 5). The rates of decline of the lactation curves of the Jerseys and Guernseys coincided, but were less than the slopes of the curves for the Holsteins and Ayrshires, which were similar. The lactation curve of Brown Swiss was comparable Milk Yield in Pounds 52 45w «sass Holstein Ayrshire 40“ ““—‘ Brown Swiss +”*++' Guernsey Jersey 35.. 50‘L 25.1- 20‘" 15‘t # : i ; .L 4. t ‘r t s 0 1 2 5 4 5 6 7 8 9 10 Test Days Fig. 2. Breed average lactation curves for cows freshening at less than 56 months of age and calving between April and July. Milk Yield in Pounds 55 451? -+HH+— Holstein Ayrshire 40 “ -"—“' Brown Swiss +*“*+ Guernsey Jersey 55 t 50 T 25 “ 20 U 15 d— 4. 4. s ‘r ; # s : 1 1 0 1 2 5 4 5 6 7 8 9 10 Test Days Fig. 5. Breed average lactation curves for cows freshening at less than 56 months of age and calving between August and March. Milk Yield in Pounds 55 50 45‘ 40 55 50 25 20 15 " '9*F9- Holstein Ayrshire --“-- Brown Swiss T. 't+"t+ Guernsey O \\ ‘x ' fiF**— Jersey \ a 1 : % 4 : s7 t 4 e . i 0 1 2 5 4 5 7 8 9 10 Test Days Fig. 4. Breed average lactation curves for cows freshening that are 56 months of age or over and calving between April and July. Milk Yield in Pounds 55 50 45 40 55 50 25 20 15 55 -GiFO- Holstein Ayrshire ----H- Brown Swiss ++++ Guernsey Jersey .41- 1 I V 1 o 1 z 5 4. 5 ‘- db @1- q d) «3+ H C) Test Days Fig. 5. Breed average lactation curves for cows freshening that are 56 months of age or over and calving between August and March. 56 to that of the Holsteins in Fig. 2, but in Fig. 5 it more nearly followed the shape of the Guernsey lactation curve. However, as shown in Figs. 4 and 5, the Brown Swiss lactation curve appeared to be unlike that of the other breeds. The average lactation curves for each of the breeds (Fig. 6) reflected the relationship found in each age-season group (Figs. 2, 5, 4, and 5). Cows The average milk yields and the standard deviations on each test day for each breed—agewseason group are shown in Tables 5, 6, 7, 8, and 9. Each breed and age group dif— fered in average milk yields, but seasonal differences were small. Reductions in milk yield from one test day to the adjacent test day are also shown in Tables 5, 6, 7, 8, and 9. The rate of change within each breed-age—season group was not uniform. The average rate of decline for all breeds of cows freshening at less than 56 months of age was 5.9%, whereas the average percentage of reduction for those animals calving at 56 months or over was 9.4. Seasonal effects on the rate of reduction were negligible as compared with age differences. However, the cows calving between April and July declined in milk yield more rapidly between the second and third and between the third and fourth months of lactation as compared with the reduction rates for cows Milk Yield in Pounds 57 50" 'fi*°**' Holstein Ayrshire 45“ —--- Brown Swiss +++ + Guernsey .\ ‘~.\ Jersey 40*— ' 55‘" 50‘- 25" 20" 15" } i i % a: i : l t i 0 1 2 5 4 5 6 7 8 9 10 Test Days Fig. 6. Average lactation curves of Ayrshires, Brown Swiss, Guernseys, Holsteins, and Jerseys. 58 Table 5. Milk yield and decline for each test day by age and season of calving (Ayrshire). Age at Season Average Rate of calving of fresh- Test lb. of Standard decline (months) ening day milk deviation (%) <56 Apr.-July 1 57.6 5.71 ---- 2 57.1 5.80 1.6 5 55.5 4.90 4.2 4 52.5 5.27 8.9 5 29.9 4.75 7.6 6 28.6 4.82 4.5 7 27.2 4.99 4.9 8 25.6 6.05 5.8 9 24.7 6.22 5.6 10 22.5 6.71 8.6 <56 Aug.-Mar. 1 57.1 6.84 ---- 2 57.1 7.56 0.0 5 55.7 6.95 5.9 4. 52.6 7.54 8.5 5 51.1 6.06 4.5 6 29.5 6.45 5.2 7 28.0 6.24 5.1 8 26.5 6.20 5.9 9 25.7 7.17 10.1 10 20.0 6.47 15.8 256 Apr.-July 1 51.5 9.22 ---- 2 50.8 10.56 1.4 5 45.8 9.71 9.7 4 41.4 9.40 9.8 5 56.5 8.05 11.7 6 52.0 6.49 12.2 7 28.4 6.76 11.5 8 25.6 6.29 10.0 9 22.0 6.85 15.9 10 17.8 7.97 19.4 .256 Aug.-Mar. 1 49.9 9.67 --—- 2 50.2 10.27 +0.6 5 46.8 10.16 6.8 4 42.2 9.55 9.8 5 59.0 9.40 7.6 6 56.5 8.90 6.9 7 52.8 8.74 9.5 8 29.0 8.85 11.6 9 25.9 9.00 17.5 10 18.2 8.56 24.0 59 Table 6. Milk yield and decline for each test day by age and season of calving (Brown Swiss). Age at Season Average Rate of calving of fresh- Test lb. of Standard decline (months) ening day milk deviation (%) <56 Apr.—July 1 56.0 7.61 -—-- 2 55.5 7.52 1.9 5 55.4 7.10 5.5 4 29.1 6.59 15.0 5 27.1 6.48 6.7 6 26.5 5.58 5.2 7 25.4 5.55 5.1 8 25.9 5.55 5.9 9 22.8 5.98 4.8 10 21.0 6.68 8.1 <56 Aug.-Mar. 1 54.9 6.60 ---- 2 55.7 7.17 5.4 5 52.0 7.12 5.1 4 50.5 7.10 5.5 5 29.5 7.02 5.2 6 28.5 6.88 5.6 7 27.4 6.60 5.0 8 26.5 6.55 5.4 9 25.5 6.26 4.7 10 22.9 6.68 9.4 .256 Apr.-July 1 48.2 10.44 —-—- 2 47.1 10.56 2.4 5 45.2 9.64 8.5 4 58.7 9.06 10.4 5 54.9 8.55 9.8 6 51.8 8.00 8.9 7 28.8 7.20 9.5 8 26.0 7.15 9.5 9 25.4 7.62 10.1 10 21.2 8.05 9.4 256 Aug.—Mar. 1 47.1 10.25 ---- 2 45.4 10.55 5.5 5 42.5 10.15 6.8 4 59.6 9.87 6.4 5 57.5 9.20 5.9 6 55.5 8.70 4.7 7 55.4 8.52 5.9 8 50.7 8.19 8.2 9 26.7 8.15 15.0 10 22.5 8.56 16.4 40 Table 7. Milk yield and decline for each test day by age and season of calving (Guernsey). Age at Season Average Rate of calving of fresh- Test lb. of Standard decline (months) ening day milk deviation (%) <56 Apr.-July 1 54.6 7.19 ---- 2 52.8 7.09 5.1 5 29.6 7.00 9.9 4 26.2 6.57 11.4 5 24.0 5.78 8.2 6 22.5 5.62 6.5 7 21.5 5.26 5.5 8 20.5 5.10 5.8 9 19.6 5.15 4.2 10 18.8 5.62 4.0 <56 Aug.-Mar. 1 52.5 6.29 ---- 2 50.9 6.41 4.4 5 28.6 6.24 7.4 4 26.8 6.04 6.5 5 25.6 5.81 4.4 6 24.6 5.65 5.9 7 25.7 5.60 5.8 8 22.5 5.56 5.1 9 20.7 5.89 8.0 10 18.5 6.01 10.5 .256 Apr.-July 1 45.6 8.98 ---- 2 41.9 8.99 5.8 5 57.1 8.45 11.5 4 52.4 7.94 12.6 5 28.2 7.20 15.2 6 24.9 6.41 11.5 7 22.2 5.92 11.0 8 20.5 5.78 8.5 9 18.4 5.90 9.7 10 16.6 6.15 9.8 256 Aug.-Mar. 1 41.2 8.54 ---- 2 59.5 8.62 4.2 5 55.7 8.11 9.5 4 52.7 7.57 8.5 5 50.5 7.55 6.9 6 28.5 7.14 6.4 7 26.4 6.81 7.5 8 25.9 6.69 9.7 9 20.4 6.88 14.5 10 17.1 6.78 16.5 41 Table 8. Milk yield and decline for each test day by age and season of calving (Holstein). . Age at Season Average Rate of calving of fresh- Test lb. of Standard decline (months) ening day milk deviation (%) <56 Apr.—July 1 45.5 8.61 “" 2 42.8 8.95 1.1 5 59.1 8.59 8.6 4 55.8 7.84 8.5 5 55.4 7.50 6.7 6 52.0 7.17 4.4 7 50.6 6.98 4.2 8 29.5 7.01 4.2 9 27.2 7.25 7.2 10 25.0 7.91 8.1 <56 Aug.—Mar. 1 41.5 8.56 ---- 2 41.5 8.74 +0.5 5 59.0 8.45 5.9 4 57.1 8.09 4.9 5 55.6 7.86 4.0 6 54.2 7.61 4.0 7 52.7 7.46 4.5 8 51.1 7.48 5.0 9 28.5 7.82 8.2 10 24.9 8.12 12.6 256 Apr.—July 1 57.6 11.72 ---- 2 57.0 12.08 1.0 5 51.1 11.15 10.5 4 45.6 10.45 10.8 5 41.0 9.56 9.9 6 57.5 8.95 9.0 7 54.0 8.55 8.9 8 50.9 8.28 9.1 9 26.9 8.66 15.0 10 25.1 9.07 14.0 .256 Aug.-Mar. 1 55.1 11.41 ---- 2 54.6 11.90 0.8 5 50.5 11.55 7.9 4 46.5 10.74 7.6 5 45.5 10.19 6.4 6 40.6 9.75 6.6 7 57.7 9.42 7.2 8 54.0 9.26 9.8 9 28.8 9.58 15.5 10 25.6 9.45 18.0 42 Table 9. Milk yield and decline for each test day by age and season of calving (Jersey). Age at Season Average Rate of calving of fresh— Test lb. of Standard decline (months) ening day milk deviation (%) <56 Apr.-July 1 29.8 6.75 ---- 2 28.7 6.65 5.7 5 25.5 5.75 12.0 4 22.4 5.16 11.5 5 20.5 4.84 9.4 6 18.9 4.47 6.6 7 18.0 4.49 5.1 8 17.0 4.26 5.5 9 16.5 4.45 4.1 10 15.4 4.82 5.5 <56 Aug.-Mar. 1 28.8 6.49 ---- 2 27.9 6.40 5.5 5 25.6 6.07 8.4 4 25.7 5.81 7.5 5 22.4 5.62 5.5 6 21.5 5.51 5.8. 7 20.6 5.42 4.1 8 19.7 5.44 4.5 9 18.4 5.65 6.5 10 16.5 5.51 10.4 256 Apr.-July 1 58.5 7.67 ---- 2 57.6 7.72 1.8 5 55.2 7.26 11.7 4 29.1 6.95 12.5 5 25.6 6.65 11.9 6 22.6 5.85 11.7 7 20.5 5.58 10.4 8 18.2 5.40 10.2 9 16.5 5.56 10.6 10 14.8 5.82 9.1 256 Aug.—Mar. 1 56.8 7.52 ---— 2 55.8 7.78 2.8 5 52.2 7.61 9.9 4 29.4 7.26 8.8 5 27.5 6.88 6.6 6 25.8 6.69 6.1 7 24.1 6.54 6.6 8 22.1 6.48 8.5 9 19.2 6.67 15.5 10 16.5 6.69 15.1 45 calving between August and March. Cows calving in the fall and winter seasons tended to decline in production faster between the ninth and tenth months of lactation as compared with the other seasonal group. The differences in the declination rate between the two seasonal groups was one percent, with the more consistent lactations starting between August and March (Tables 5, 6, 7, 8, and 9). Figs. 7, 8, 9, and 10 show the shapes of the lac- tation curves for cows with high, medium and low initial yields. Cows initiating their lactations at a low level exhibited a more consistent lactation curve than the cows with a high initial level of milk yield. Shapes of the lac- tation curves, based on initial level of milk yield, were dissimilar because of their tendency to converge as the stage of lactation progressed. Even when cows calving at 56 months of age or over and cows calving at less than 56 months of age initiated their lactations at identical levels, the older cows still exhibited a greater reduction rate dur— ing their lactation than did the younger animals. 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Om EDHUOE // .vow / x :3 53m III- «x ..mm / 1'. :0s 20s spunoa UT pIeIA HITW 46 Ratios for Projecting Incomplete Lactations to 505 Days Cumulative and non-cumulative ratios extension factors were developed from the average of the ratios between con- secutive test days of a lactation within each breed-age- season group. Although a ratio occasionally was missing from a lactation, the other ratios calculated from the record were included in the analysis of non—terminal records. Ratios between consecutive test days of a lactation were formulated as follows: R1 = x1+1 whe W m Xi X- is the milk weight on the ith test day for i = 1,...,9. R- represents the ratio of milk produced on two consecutive test days. The average ratios between consecutive test days of a lactation for each breedeage-season group were utilized in forming non-cumulative extension factors for estimating the 505-day milk yield from a single month's production (Tables 10, 11, 12, 15, and 14). The ratios between consecutive test days were multiplied successively, and all intermediate products were recorded. The total of the intermediate products was divided by each intermediate product to obtain each non-cumulative ratio extension factor. The procedure may be represented as follows: 47 H Table 10. Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Ayrshires. Age at Season calving of fresh- Test Cumulative Non-cumulative (months) ening day factor factor <56 Apr.-July 1 7.86 7.86 2 5.97 8.02 5 2.71 8.56 4 2.10 9.25 5 1.75 9.99 6 1.49 10.49 7 1.51 11.09 8 1.18 11.90 9 1.08 12.45 10 ---- 15.75 <56 Aug.-Mar. 1 8.27 8.27 2 4.08 8.07 5 2.75 8.45 4 2.12 9.15 5 1.75 9.59 6 1.47 9.94 7 1.29 10.64 8 1.16 11.69 9 1.07 15.55 10 ---- 15.20 .256 Apr.~July 1 6.76 6.76 2 5.58 6.75 5 2.54 7.60 4 1.85 8.52 5 1.54 9.72 6 1.55 11.06 7 1.22 12.47 8 1.12 15.99 9 1.05 16.52 10 ---- 20.54 256 Aug.-Mar. 1 7.15 7.15 2 5.59 7.20 5 2.45 7.71 4 1.90 8.45 5 1.57 9.20 6 1.56 10.08 7 1.22 11.55 8 1.12 15.57 9 1.05 16.82 0 21.95 48 Table 11. Cumulative and non~cumulative ratio factors for projecting 505-day milk yield for Brown Swiss. Age at Season calving of fresh- Test Cumulative Non-cumulative (months) ening day factor factor <56 Apr.-July 1 7.75 7.75 2 5.89 7.85 5 2.66 8.41 4 2.07 9.56 5 1.72 10.14 6 1.48 10.69 7 1.51 11.20 8 1.18 11.95 9 1.08 12.61 10 —--- 15.75 <56 Aug.-Mar. 1 8.47 8.47 2 4.28 8.67 5 2.91 9.12 4 2.25 9.45 5 1.81 9.77 6 1.54 10.14 7 1.54 10.45 8 1.20 11.05 9 1.08 11.65 10 -—-- 12.85 i256 Apr.-July 1 7.10 7.10 2 5.57 7.18 5 2.45 7.81 4 1.91 8.70 5 1.60 9.67 6 1.59 10.78 7 1.25 12.10 8 1.14 15.46 9 1.06 15.55 10 --—— 17.08 256 Aug._Mar. 1 7.71 7.71 2 5.91 7.94 5 2.67 8.46 4 2.06 8.98 5 1.69 9.40 6 1.44 9.94 7 1.27 10.74 8 1.15 12.00 9 1.06 15.97 10 ~--- 16.75 49 Table 12. Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Guernseys. Age at Season calving of fresh- Test Cumulative Non-cumulative (months) ening day factor factor <56 Apr.-July 1 7.25 7.25 2 5.69 7.55 5 2.57 8.40 4 2.02 9.44 5 1.69 10.55 6 1.47 11.18 7 1.51 11.84 8 1.18 12.26 9 1.08 12.85 10 -—-- 15.44 <56 Aug.—Mar. 1 7.98 7.98 2 4.06 8.27 5 2.79 8.91 4 2.15 9.44 5 1.77 9.82 6 1.51 10.25 7 1.52 10.68 8 1.18 11.54 9 1.08 12.52 10 ---- 15.69 256 Apr.-July 1 6.52 6.52 2 5.51 6.71 5 2.51 7.62 4 1.82 8.68 5 1.54 9.98 6 1.56 11.58 7 1.25 15.01 8 1.15 14.46 9 1.06 16.22 10 ---- 18.01 256 Aug.-Mar. 1 7.15 7.15 2 5.64 7.44 5 2.52 8.15 4 1.96 8.82 5 1.62 9.49 6 1.40 10.25 7 1.25 11.51 8 1.14 12.92 9 1.06 15.28 10 —--- 18.25 50 Table 15. Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Holsteins. Age at Season calving of fresh— Test Cumulative Non-cumulative (months) ening day factor factor <56 Apr.-July 1 7.94 7.94 2 5.98 7.97 5 2.75 8.67 4 2.11 9.40 5 1.75 10.04 6 1.50 10.52 7 1.52 10.98 8 1.18 11.49 9 1.08 12.45 10 ---- 15.55 <56 Aug.-Mar. 1 8.47 8.47 2 4.22 8.59 5 2.86 8.86 4 2.18 9.27 5 1.78 9.62 6 1.51 10.06 7 1.52 10.52 8 1.18 11.16 9 1.08 12.20 10 ---- 15.88 256 Apr.-July 1 7.06 7.06 2 5.54 7.09 5 2.44 7.85 4 1.91 8.76 5 1.59 9.68 6 1.59 10.64 7 1.24 11.86 8 1.14 15.54 9 1.06 15.61 10 ---- 18.19 256 Aug.-Mar. 1 7.51 7.51 2 5.77 7.56 5 2.58 8.15 4 1.99 8.75 5 1.64 9.55 6 1.41 10.10 7 1.25 11.05 8 1.14 12.58 9 1.06 15.02 10 —--— 18.25 51 Table 14. Cumulative and non-cumulative ratio factors for projecting 505-day milk yield for Jerseys. Age at Season calving of fresh— Test Cumulative Nonécumulative (months) ening, day factor factor <56 Apr.-July 1 7.20 7.20 2 5.65 7.58 5 2.55 8.50 4 1.99 9.27 5 1.67 10.29 6 1.45 11.02 7 1.29 11.87 8 1.17 12.68 9 1.08 15.29 10 ---- 14.07 <56 Aug.-Mar. 1 7.77 7.77 2 5.96 8.05 5 2.75 8.76 4 2.11 9.59 5 1.74 9.90 6 1.49 10.41 7 1.51 10.96 8 1.18 11.62 9 1.08 12.50 10 -——— 15.86 .256 Apr.-July 1 6.61 6.61 2 5.55 6.72 5 2.51 7.58 4 1.85 8.67 5 1.54 9.94 6 1.56 11.50 7 1.25 12.79 8 1.15 14.46 9 1.06 16.56 10 ——-- 18.16 256 Aug.-Mar. 1 7.22 7.22 2 5.67 7.45 5 2.54 8.24 4 1.98 8.98 5 1.64 9.65 6 1.42 10.55 7 1.26 11.27 8 1.14 12.60 9 1.06 14.68 10 --—— 17.28 52 - l—' where Zk Fk represents the 5th non-cumulative ratio factor for test periods k = 1,...,10. 21: 1 k—1 2k: TTRi for i = 1,...,9 and 2 g_k g_10. i=1 Ri represents the average ratio between consecutive test days for each breed— age—season group. 10 T = Z Zk k=1 To obtain an estimate or the total milk yield, the 3th factor is multiplied by the milk yield of the 2th month of lactation. Cumulative ratio factors (Tables 10, 11, 12, 15, and 14) were formed also from the average ratios between con— secutive test days for each breed-age-season group. The ratios between consecutive test days were multiplied succes- sively, and all intermediate products were recorded. The intermediate products were summed to obtain a total, with all progressive totals recorded. The total was divided by each progressive total to obtain each cumulative ratio extension factor. This procedure may be represented as follows: F- = . where 55 F- represents the 3th cumulative ratio factor for ;_months of cumulative milk yield for i = 1,...,9. i represents the cumulative sum of Z Zk products of ratios for k = 1,...,10. k=1 2; = .1. k~1 Zk = FRI for 2: k :10. i=1 R1 represents the average ratio between consecutive test days for each breed- age-season group. 10 T = Z Zk k=1 To obtain an estimate of the 505-day milk yield, the 2th factor is multiplied by the sum of milk yield for ;_months of lactation. An estimate based on cumulative milk yield provides a closer estimate of the total production than an estimate obtained from the non-cumulative milk yield because more information is included. In Tables 10, 11, 12, 15, and 14 the ratios developed for Holsteins and Brown Swiss were similar, and the factors for the Guernseys closely resembled those for the Jerseys. The ratio factors for Ayrshires resembled the factors com- puted for the Guernseys and Jerseys. Alternative Ratio Factors for Extending Incomplete Lactations Although cumulative and non-cumulative ratio extension factors were calculated from average ratios formed between 54 consecutive test days of a lactation, an alternative pro- cedure is to form ratios of the average milk yields within each breed—age-season group. Differences between factors formed by the two methods might be expected since the cows more variable in milk yield between test days would influ- ence the average of the ratios more than they would the ratios of the average milk yields. In addition, herd effects might be present in the ratios of the average milk yields. However, the resulting factors from each procedure of forming cumulative ratio factors appeared similar (Table 15) . The differences between the cumulative ratio factors formed by the two procedures were negligible for cows calv- ing at 56 months of age or over and freshening between August and March. This might have been caused by the large number of observations which probably reduced the influence of herd effects and of the cows that varied in milk yield between test days. The differences between the cumulative ratio factors formed for cows calving at less than 56 months of age and between April and July were larger than between the factors formed for the other age-season groups. This was probably due to the fewer number of records in the group. Because cows high in initial yield decline at a faster rate during their lactations than do cows starting their lactations at a lower level, cumulative and non—cumulative 55 Table 15. Cumulative ratio factors for Holsteins developed from average ratios and from the average pounds of milk produced on each test day. Age at Season Cumulative fact- Cumulative fact:—— calving of fresh- Test Ors formed from ors formed from (months) ening day average ratios average milk yield <56 Apr.-July 1 7.94 7.82 2 5.98 5.95 5 2.75 2.70 4 2.11 2.10 5 1.75 1.74 6 1.50 1.50 7 1.52 1.52 8 1.18 1.18 9 1.08 1.08 <56 Aug.-Mar. 1 8.47 8.58 2 4.22 4.18 5 2.86 2.84 4 2.18 2.18 5 1.78 1.78 6 1.51 1.51 7 1.52 1.52 8 1.18 1.18 9 1.08 1.08 256 Apr.-July 1 7.06 7.05 2 5.54 5.55 5 2.44 2.44 4 1.91 1.92 5 1.59 1.60 6 1.59 1.40 7 1.24 1.25 8 1.14 1.14 9 1.06 1.06 256 Aug.-Mar. 1 7.51 7.55 2 5.77 5.78 5 2.58 2.59 4 1.99 2.01 5 1.64 1.66 6 1.41 1.45 7 1.25 1.26 8 1.14 1.14 9 1.06 1.06 56 ratio factors were derived for three initial levels (high, medium, low) of milk yield to ascertain if different ratio factors were required for different levels of production. Even though slight differences existed between the cumula- tive ratio extension factors for the three groups (Table 16), projection factors based on initial level of milk yield are not recommended since regression analysis could be employed if a more accurate projection of the 505-day milk yield is desired. Terminal Incomplete Lactations Terminal incomplete records for Holsteins were cate- gorized according to either a voluntary or an involuntary reason for removal from the herd. In addition, each group was subdivided into classes that were dependent upon the number of months completed in the lactation when the cow was removed. Hence, the groups of terminal records were dis- tinguished by breed, age of cow at calving, season of freshening, level of first test day milk yield, reason for removal, and time of removal. Distribution of Terminal Incomplete Lactations The distribution of 15,955 Holstein terminal records is recorded in Tables 17, 18, 19, and 20. Each of these tables contains a particular age and seasonal group and shows the number and proportion of cows removed on each test 57 Table 16. Cumulative ratio factors based on initial level of milk yield for high, medium and low producing Holstein cows. Age at Season calving of fresh- Test Cumulative factor for (months) ening day low level medium level high level <56 Apr.-July 1 8.55 7.96 7.58 2 4.15 4.00 5.79 5 2.81 2.74 2.65 4 2.16 2.15 2.05 5 1.77 1.76 1.71 6 1.52 1.50 1.47 7 1.55 1.52 1.50 8 1.19 1.18 1.17 9 1.08 1.08 1.07 <56 Aug.-Mar. 1 9.25 8.45 7.89 2 4.47 4.22 4.01 5 2.99 2.86 2.75 4 2.26 2.19 2.12 5 1.85 1.79 1.74 6 1.54 1.52 1.48 7 1.54 1.55 1.50 8 1.19 1.18 1.17 9 1.08 1.08 1.07 1256 Apr.-July 1 7.68 7.06 6.64 2 5.75 5.54 5.41 5 2.55 2.44 2.57 4 1.97 1.91 1.86 5 1.65 1.60 1.56 6 1.41 1.59 1.57 7 1.26 1.24 1.25 8 1.15 1.14 1.15 9 1.06 1.06 1.06 256 Aug.-Mar. 1 8.09 7.45 7.05 2 5.97 5.74 5.60 5 2.69 2.56 2.49 4 2.06 1.98 1.95 5 1.69 1.64 1.60 6 1.44 1.41 1.59 7 1.27 1.25 1.24 8 1.15 1.14 1.15 9 1.06 1.06 1.05 58 day for voluntary and involuntary reasons. Table 21 com- bines the removals over all ages and seasons. Of the total number of cows removed,the proportion eliminated on each test day appears relatively constant, excluding the tenth month of lactation. However, after sub- division of the cows removed from the herd into voluntary and involuntary disposal groups (Tables 17, 18, 19, 20, 21). the rate of involuntary removal was approximately equal for all test days, whereas the cows voluntarily culled were generally removed (Table 21) on the fifth, sixth, seventh or eighth test day. For cows calving at less than 56 months of age (Tables 17 and 18), the majority of the voluntary removals occurred during the first few test days, whereas those freshening at 56 months of age or over (Tables 19 and 20) were voluntarily culled during the later stages of lactation. Seasonal effects were negligible on the pro- portion removed on each test day during the lactation. Cows removed from the herd during their lactation were divided according to the level at which they started their record. The rate of involuntary removal during the lac- tations of cows starting at various levels was approximately equal for all age-season groups, whereas age affected the proportion of cows removed voluntarily during the lactation within each level of production. The cows calving at less than 56 months of age and initiating their lactations at a low level were voluntarily removed at a greater rate early 59 Table 17. Removals by test days of Holsteins calving at less than 56 months of age between April and July. Cows removed from each initial level of milk production Total cows Test Type of Low Medium High removed day removal (No.) (%WL (No.) (%f‘ (No.) (%f‘(No.) (%N’ 2 Voluntary 45 14 14 8 5 4 62 11 Involuntary 18 21 12 15 7 15 57 17 (Total) 65 16 26 10 10 7 99 12 5 Voluntary 57 18 21 12 6 7 84 15 Involuntary 14 16 14 18 1 2 29 15 (Total) 71 18 55 14 7 5 115 14 4 Voluntary 45 14 19 11 12 14 74 15 Involuntary 15 17 8 10 9 17 52 15 (Total) 58 14 '27 11 21 15 106 15 5 Voluntary 46 15 25 14 18 21 89 15 Involuntary 4 5 8 10 4 8 16 7 (Total) 50 12 55 15 22 16 105 15 6 Voluntary 57 12 25 15 19 22 79 14 Involuntary 15 15 9 11 5 9 27 12 (Total) 50 12 52 15 24 17 106 15 7 Voluntary 55 11 25 15 11 15 69 12 Involuntary 8 9 6 8 11 21 25 11 (Total) 45 11 29 12 22 16 94 12 8 Voluntary 54 11 29 17 11 15 74 15 Involuntary 4 5 7 9 7 15 18 8 (Total) 58 9 56 14 18 15 92 12 9 Voluntary 15 5 15 9 4 5 54 6 Involuntary 10 11 10 15 7 15 27 12 (Total) 25 6 25 10 11 8 61 8 10 Voluntary 5 2 4 2 1 1 10 2 Involuntary 1 1 5 6 2 4 8 4 (Total) 6 1 9 4 5 2 18 2 Total Voluntary 517 55 175 50 85 15 575 cows Involuntary 87 40 79 56 55 24 219 re- (Total) 404 51 252 52 158 17 794 moved lPercentage (%) of cows removed from the total cows disposed of in that group. 60 Table 18. Removals by test days of Holsteins calving at less than 56 months of age between August and March. Cows removed from each initial level of milk production Total cows Test Type of Low Medium High removed ’ day removal (No.) (%)l (No.) (%)J- (No.) (%)1(No.) (%)1 2 Voluntary 162 17 50 11 55 15 245 15 Involuntary 40 16 25 12 28 14 95 14 (Total) 202 17 75 11 61 15 558 14 5 Voluntary 151 14 55 12 28 11 212 15 Involuntary 22 9 15 7 26 15 65 9 (Total) 155 15 68 10 54 12 275 12 4 Voluntary 141 15 58 15 27 10 226 15 Involuntary 26 10 29 15 20 10 75 11 (Total) 167 14 87 15 47 10 501 15 5 Voluntary 149 15 76 17 52 12 257 15 Involuntary 54 15 24 11 19 10 77 11 (Total) 185 15 100 15 51 11 554 14 6 Voluntary 109 11 70 16 29 11 208 12 Involuntary 25 9 25 12 25 12 71 11 (Total) 152 11 95 14 52 11 279 12 7 Voluntary 107 11 50 11 56 14 195 12 Involuntary 56 14 59 18 25 12 98 15 (Total) 145 12 89 15 59 15 291 12 8 Voluntary 90 9 52 12 50 12 172 10 Involuntary 28 11 21 10 52 16 81 12 (Total) 118 10 75 11 62 14 255 11 9 Voluntary 65 7 54 8 55 14 154 8 Involuntary 55 14 55 15 25 12 91 14 (Total) 100 8 67 10 58 15 225 10 10 Voluntary 15 2 7 2 8 5 50 2 Involuntary 9 4 6 5 6 5 21 5 (Total) 24 2 15 2 14 5 51 2 Total Voluntary 969 58 450 27 258 15 1677 cows Involuntary 255 58 217 52 200 50 670 re- (Total) 1222 52 667 28 458 20 2547 moved lPercentage (%) of cows removed from the total cows diSposed of in that group. 61 Table 19. Removals by test days of Holsteins calving at 56 months of age or over between April and July. Cows removed from each initial level of milk production Total cows Test Type of Low Medium High removed day_g removal (No.) (%)l (No.) (%)l (No.) (%)1 (No.) (%)l 2 Voluntary 75 8 50 6 18 5 125 7 Involuntary 82 19 57 15 58 9 177 14 (Total) 157 12 87 9 56 7 500 10 5 Voluntary 94 10 51 6 26 7 151 8 Involuntary 65 14 58 15 51 12 172 15 (Total) 157 12 89 9 77 10 525 10 4 Voluntary 110 12 49 10 41 11 200 11 Involuntary 54 12 45 10 58 14 155 12 (Total) 164 12 92 10 99 12 555 11 5 Voluntary 154 15 70 14 59 10 245 14 Involuntary 46 10 40 9 46 11 152 10 (Total) 180 15 110 12 85 11 575 12 6 Voluntary 146 16 81 16 45 12 272 15 Involuntary 56 15 65 15 41 10 162 12 (Total) 202 15 146 15 86 11 454 14 7 Voluntary 147 16 94 18 87 25 528 18 Involuntary 55 12 47 11 62 15 162 12 (Total) 200 15 141 15 149 19 490 16 8 Voluntary 102 11 80 16 67 18 249 14 Involuntary 45 10 71 16 65 15 181 14 (Total) 147 11 151 16 152 16 450 14 9 Voluntary 79 9 69 15 49 15 197 11 Involuntary 52 49 11 52 12 155 10 (Total) 111 118 12 101 15 550 11 7 8 10 Voluntary 17 2 9 2 9 2 55 2 Involuntary 8 2 7 2 10 2 25 2 (Total) 25 2 16 2 19 2 60 2 Total Voluntary 904 50 515 29 581 21 1798 cows Involuntary 459 54 457 54 425 55 1299 re- (Total) 1545 45 950 51 804 26 5097 moved lPercentage (%) of cows removed from the total cows disposed of in that group. 62 Table 20. Removals by test days of Holsteins calving at 56 months of age or over between August and March. Cows removed from each initial level of milk production Total COWS Test Type of Low Medium High removed day removal (No.) (%)l (No.) (%)J. (No.) (%)J. (No.) (%)l 2 Voluntary 216 8 64 5 55 5 515 7 Involuntary 195 14 94 9 76 9 565 11 (Total) 411 10 158 7 111 7 680 9 5 Voluntary 274 11 100 8 48 7 422 9 Involuntary 191 14 106 10 79 9 576 11 (Total) 465 12 206 9 127 8 798 10 4 Voluntary 291 11 105 9 45 7 459 10 Involuntary 150 11 105 10 99 11 554 11 (Total) 441 11 208 9 144 9 795 10 5 Voluntary 564 14 159 12 76 11 579 15 Involuntary 152 11 106 10 99 11 557 11 (Total) 516 15 245 11 175 11 956 12 6 Voluntary 558 14 185 15 86 15 629 14 Involuntary 166 12 121 12 119 15 406 12 (Total) 524 15 506 14 205 15 1055 15 7 Voluntary 567 14 195 16 110 17 672 15 Involuntary 182 15 156 15 152 15 470 14 (Total) 549 14 551 18 242 18 1142 15 8 Voluntary 565 14 210 18 126 19 699 16 Involuntary 145 10 148 15 128 14 419 15 (Total) 506 15 558 16 254 16 1118 14 9 Voluntary 291 11 164 14 114 17 569 15 Involuntary 154 11 144 14 116 15 414 15 (Total) 445 11 508 14 250 15 985 15 10 Voluntary 55 2 58 5 26 4 119 5 Involuntary 55 5 58 4 58 4 111 5 (Total) 90 2 76 5 64 4 250 5 Total Voluntary 2579 58 1198 27 666 15 4445 cows Involuntary 1568 42 1018 51 886 27 5272 re- (Total) 5947 51 2216 29 1552 20 7715 moved lPercentage (%) of cows removed from the total cows disposed of in that group. 65 Table 21. Removals by test days of Holsteins. Cows removed from each initial level of milk production Total cows Test Type of Low Medium High removed day removal (No.) (%)1 (No.) (70)1 (No.) (%)1(No.) (%)1 2 Voluntary 498 10 158 7 89 6 745 9 Involuntary 555 16 188 11 149 10 672 12 (Total) 855 12 546 8 258 8 1417 10 5 Voluntary 556 12 205 9 108 8 869 10 Involuntary 290 14 195 11 157 10 640 12 (Total) 846 12 598 10 265 9 1509 11 4 Voluntary 585 12 229 10 125 9 959 11 Involuntary 245 11 185 11 186 12 616 11 (Total) 850 12 414 10 511 11 1555 11 5 Voluntary 695 15 510 15 165 12 1168 14 Involuntary 256 11 178 10 168 11 582 11 (Total) 929 15 488 12 555 11 1750 15 6 Voluntary 650 14 559 15 179 15 1188 14 Involuntary 258 12 220 15 188 12 666 12 (Total) 908 15 579 14 567 12 1854 15 7 Voluntary 656 14 562 16 244 18 1262 15 Involuntary 279 15 248 14 228 15 755 14 (Total) 955 14 610 15 472 16 2017 14 8 Voluntary 589 12 571 16 254 17 1194 14 Involuntary 220 10 247 14 252 15 699 15 (Total) 809 12 618 15 466 16 1895 14 9 Voluntary 450 9 282 12 202 15 954 11 Involuntary 251 11 256 15 198 15 665 12 (Total) 681 10 518 15 400 14 1599 11 10 Voluntary 92 2 58 2 44 5 194 2 Involuntary 55 2 56 5 56 4 165 5 (Total) 145 2 114 5 100 5 559 5 Total Voluntary 4769 56 2554 27 1590 16 8495 cows Involuntary 2147 59 1751 52 1562 29 5460 re- (Total) 6916 50 4085 29 2952 21 15955 moved lPercentage (%) of cows removed from the total cows disposed of in that group. 64 in lactation as compared to those starting their records at a high level. The rate of voluntary removal for cows calving at 56 months of age or over was approximately equal on each day of test for each of the three initial levels of milk yield. Of the total number of cows removed within each initial level of production (Tables 17, 18, 19, 20, and 21), the rate of involuntary removal was approximately equal among all levels of production, whereas approximately half of the cows removed voluntarily were from the group low in initial yield. The proportion of cows removed was the same for each initial level of production within each age—season group (Table 22). This indicates that there were no differential age-season effects on the proportions removed from the low, medium and high initial yielding groups. Approximately two and one-half times as many cows calving at less than 56 months of age were removed volun- tarily as involuntarily, whereas rates of voluntary and in- voluntary removal were approximately equal for cows calving at 56 months of age or over (Table 22). Sixty-one percent of the total number of animals removed were voluntarily culled from the herd while only 59% were removed involuntarily. The cows calving at less than 56 months of age contributed a larger portion to the total cows removed voluntarily than to those removed involuntarily, whereas for cows calving at 56 months or over, a larger portion was contributed to the involuntary removals than to the voluntary disposals. m.mm N.NN $.05 >.m R mmmma mash wmom 55mm 5mm .02 HMpOB m.mm m.mm m.ma 0.5 R H.0m 005m mmmm mama ohm mam .oz xumussfio>cH m.mm N.Hm >.ma m.© R m.ow mm5m M555 mama ssmfi mum .oz RMMDCSHO> m.mm m.>m m.ma >.5 R N.dm Nmmm Nmma 50m mm5 and .02 Lmflm m.5m m.mm m.ma m.w R m.mm mmO5 mamm 0mm mmm mmm .oz ESHUTS 5.>m 5.m5 >.>H m.m R m.m5 mfimo 55mm m5m5 Nmma 505 .oz 304 ARV A.ozv .HMZI.mS< >H5h|.uQ¢ .umZI.594 >HSbI.Hmm EmuH Hm>oEmH sofluospoum 69658 $3.62 SM 2362 mmN mficos mmv Ethos mmv Mom .633 is: 50 m3oo Hmuoe msH>HMU mo semmmm Usm mam Hm>ma HmawHCH .Qsoum commmmlmmm zomm Eoum mzou sampmaom mo mam>OEmn mo mocmsqmum .NN maflme 66 The total number of cows removed was separated according to age at calving (Table 25). Approximately 25% of the cows removed were from cows calving at less than 56 months of age, whereas the remaining 77% were from cows calving at 56 months of age or over. When adjustment was made for the number of months in each season, no seasonal effects were present, but of the total number of cows culled, approximately 28% were removed from cows calving between April and July, whereas 72% of the total were obtained from those freshening between August and March. Only an estimate of the percentage of cows removed from the population could be obtained because all the cows that calved between January 1959 and October 1961 were accepted in this study. Since the cows calving in the last month of the project were accepted, there was no way to determine what portion of these would be removed from the herd prior to completion of their records. In addition, cows that terminated their records prior to October 1961 were accepted for the terminal group; thus, some of these cows would not have had a chance to complete their lactations even if they had remained in the herd. An estimate obtained from the second test day group would underestimate the per- centage of animals removed from the population, whereas an overestimation would result from the completed group. However, of the total number of cows calving at less than 56 months of age, approximately 16% of them were removed, 67 Table 25. Percentage of Holsteins culled from each age and season group. Age at Season Percentage removed from_pqpulation calving of fresh- Number Test day 2 Completed Total cows, (months) ening culled lactation removed (108888)l (82289)1 (15955)1 <56 5141 2.9 5.0 22.5 256 10812 9.9 17.4 77.5 Apr.-July 5891 5.6 6.2 27.9 Aug.-Mar. 10062 9.5 16.2 72.1 1Number of observations. 68 whereas approximately 25% of the cows calving at 56 months of age or over were eliminated from the herd. Table 24 indicates that the proportion of records terminated on each test day was the same among breeds. However, Ayrshires differed from the other breeds in the proportion removed from each age-season group. The diverg- ence of the Ayrshires from the other breeds is probably the result of the limited number of herds and the small number of Ayrshire cattle in Michigan. Holsteins contributed the largest portion of the animals removed from Michigan D.H.I.A., whereas Ayrshires contributed the fewest. However, breed differences appeared evident in the portion of animals removed from each breed. Of the Holstein population, only 15% were culled, whereas 18% were removed from the Ayrshire population. These percentages are only an indication of the difference between culling rates of each breed, since an accurate percentage could not be determined from this study. Characteristics of Terminal Incomplete Lactations Distinct characteristics of the shape of the lactation curve and the level of milk yield of the terminal incomplete lactations resulted when the terminal records were separated into voluntary and involuntary removals from the herd. Cows voluntarily removed from the herd initiated their lactations at a lower milk yield (Figs. 11, 12, 15, and 14) and declined .msoum >mp ummp Ucoomm mflu mom m5nmummuom mpuoomu mo HTQESQ mnp so Ummmfl mommucmoumma II M as N5 N 5 555550 5mpou mo unmoumm M5 M5 M5 >5 M5 M5 5585550 Ummun mo ucmoumm mm mm mm om om mo .aozI.ma< onw NN ON NN NN 5N 5N >555I.um< MMA 65 55 ON >5 M5 m5 5 um:u.ms¢ MMV .8 o o o o m s saaou.um¢ omv M M M N M N 05 N5 55 55 N5 N5 55 m 55 55 55 55 55 M5 w 55 N5 55 55 55 M5 5 M5 55 M5 55 N5 55 M M5 M5 M5 M5 55 N5 M 55 55 55 N5 05 M5 5 55 N5 55 m 55 55 M 05 55 O5 O5 55 m N Uw>oEmu NWmHmb C5mum5om >mmcumsm mm53m s3oum mn5£mH>¢ mC5Cw£m®Hm Amnucofiv Nap m309.5muou mo “smoumm pwmum mo GOmmmm OS5>5mo umme um mmd .msoum commmmImmm 5cm >m© ummu Loom sow Ummufl >3 UT>OE®H mBOU mo mmMusmonm .5N $5988 Milk Yield in Pounds 45- 40 55 50 25‘ 20- 70 x ++u++ Completed lactation Terminal lactations qu— -L 4 5% I 5 4 5 6 7 8 9 10 Test Days -I- -()- db ‘- - qu- Fig. 11. Voluntarily incomplete terminal and completed lac— tations of Holsteins freshening at less than 56 months of age and calving between April and July. Milk Yield in Pounds 71 45.. + . r++4_+ox -++- + Completed lactation x x ._____ . . 401. x Terminal lactations 55+ 50-r 25“ 20‘r O 1 2 5 4: 5 6 7 8 9 10 Test Days Fig. 12. Voluntarily incomplete terminal and completed lac- tations of Holsteins freshening at less than 56 months of age and calving between August and March. Milk Yield in Pounds 60.. 55 1- 501* 45" 55‘t so 4.. 20 .I- 72 x +4~++- Completed lactation X ‘_——_ Terminal lactations 5 b l «I- 0 Fig. 15. PI)- 2 5 4 5 6 7 8 9 10 Test Days Voluntarily incomplete terminal and completed lactations of Holsteins freshening at 56 months of age or over and calving between April and July. Milk Yield in Pounds 60 ,_ 55*” 50" 45:- 55 <- 25 ._ 20 " 75 .++"++o ++"f+-Completed lactation x —————'Terminal lactations A l A —1 Fig. I. 14. l I l l r T _v I fl I 2 5 4 5 6 7 8 9 10 Test Days 1. Voluntarily incomplete terminal and completed lactations of Holsteins freshening at 56 months of age or over and calving between August and March. 74 at a faster rate than cows completing their records within the same age-season-group. Since the criteria for voluntary removals was based on low production, old age, hard milker or dairy purposes, these differences might be expected. The lactation curves of cows calving at less than 56 months of age and voluntarily removed from the herd showed greater divergence from the completed records within the same age group (Figs. 11 and 12) as compared with those of animals freshening at 56 months of age or over (Figs. 15 and 14). In both age groups, as the number of days on test increased prior to termination, the difference in milk yield between the terminal and completed lactations decreased. But, except for the first two months of lactation, the shapes of the lactation curves of the voluntarily terminal lactations were parallel. Since the majority of the voluntary removals were from the group with low initial milk yield, Fig. 15 was formed to show the differences between the voluntarily terminal records from the low producing group and the completed lac- tations of cows starting their records at a low level. The terminal lactations are parallel to each other, but the dif- ference in milk yield and rate of decline between the terminal and completed records is smaller than when level of milk yield was ignored. Cows involuntarily removed from the herd generally initiated their lactations at a slightly lower yield than the Milk Yield in Pounds 75 45 T x& X x . x x ++~++ Completed lactation x ox X Terminal lactations 40‘- 55" 50‘- it 25" p X x X X .X ’S 20 1. i I + f 41 I Jr fi‘ 5‘ fi‘ 0 1 2 5 4 5 6 7 8 9 10 Test Days Fig. 15. Voluntarily incomplete terminal and completed lactations of Holsteins showing low initial milk yield, freshening at 56 months of age or over and calving between August and March. 76 cows completing their records (Figs. 16, 17, 18, and 19). The lactation curves of cows involuntarily removed from the herd resemble the shape of the lactation curves for cows completing records. This might be expected since there was no choice involved in deciding whether the cow be re- tained or disposed. However, as the length of the terminal lactation increases, the two lactation curves diverge. The reason the lactation curves tended to diverge from the com— pleted records cannot be separated into genetic and non- genetic factors at this time. Thus, the lactation curves of cows removed involuntarily from the herd are considered to be similar to those of cows completing their records. For cows calving at 56 months of age or over (Figs. 18 and 19) similarities exist between the shape of terminal lactation curves within each seasonal group, whereas for cows calving at less than 56 months of age (Figs. 16 and 17) differences between the shapes of the terminal lactation curves were present. This may be due to the small number of involuntarily terminal records for cows calving at less than 56 months of age. Estimation of 505-Day Milk Yield from Terminal Incomplete Lactations The shapes of the involuntarily incomplete terminal lactation curves were similar to those of cows completing their records. The projection factors used for extending an incomplete non—terminal lactation can be employed in Milk Yield in Pounds 77 451’ -+++~+ Completed lactation Terminal lactations 40‘* X )r I x& 55 * xx x xx 0 fiXX (Ex ”x 50 “ ** X 'x x x x X x x X X x x 25 L N 20 1- 0 1 2 5 4 5 6 7 8 9 10 Test Days Fig. 16. Involuntarily incomplete terminal and completed lac- tations of Holsteins freshening at less than 56 months of age and calving between April and July. Milk Yield in Pounds 78 45V *“’*+'x ++++ Completed lactation 40" Terminal lactations \. 35“ 50+ 25" Ag 20~~ t 4 4 t f : e t # ~: 0 1 2 5 4 5 6 7 8 9 10 Test Days Fig. 17. Involuntarily incomplete terminal and completed lac— tations of Holsteins freshening at less than 56 months of age and calving between August and March. Milk Yield in Pounds 79 601- 55.. \\ +4~++- Completed lactation \‘\\\. -————' Terminal lactations 50~~ 451. 40-r 55 1t 50 1 25~r t 5 4 5 fit : 5 I c 1 0 1 5 4 5 6 7 8 9 10 Test Days Fig. 18. Involuntarily incomplete terminal and completed lac- tations of Holsteins freshening at 56 months of age or over and calving between April and July. Milk Yield in Pounds 80 60'" '+‘++.~ X Completed lactation 55+ Terminal lactations 501. 45.- xx x X 0 x x x X 40“ x O x x x x x 55+ x x X 0 k X x 50+ 5* & 25” 1 I ~55. ; : I I I i 4 0 2 5 4 5 6 7 8 9 10 Test Days Fig. 19. Involuntarily incomplete terminal and_completed lac- tations of Holsteins freshening at 56 months of age or over and calving between August and March. 81 estimating the 505-day milk yield of cows involuntarily removed from the herd during lactation. However, a slight underestimation of the 505-day milk yield may result for incomplete involuntarily terminal records due to the slight- ly faster decline of the lactations terminated involuntarily. In contrast, the shapes of the voluntarily incomplete terminal lactation curves were unlike those of the cows completing records. Cumulative ratio factors were formed (Table 25) for the voluntarily terminal records to ascertain the size of differences in the relationships of the expected total milk yield to its part. The ratios between consecutive test days for volun- tarily terminal incomplete records were employed in develop- ing cumulative ratio factors for voluntarily terminal records by the same procedure used in forming the ratio factors for the non—terminal lactations. The average ratio between the adjacent last two test days of each terminal group were multiplied and all intermediate products were recorded. However, the ratio between the ninth and tenth test day of cows terminating their record on the tenth test day was replaced by the ratio obtained from the completed records since the number of cows terminating their lactations in the tenth month was small. The intermediate products were summed, with all progressive totals recorded. The final total was divided by all progressive totals to obtain the cumulative ratio extension factors. This may be repre— sented as follows: 82 Table 25. Cumulative and non-cumulative ratio factors for projecting 505-day milk yield from voluntarily terminal incomplete records for Holsteins. Age at Season calving of fresh- Test Cumulative Non-cumulative (months) ening day factor factor <56 Apr.-July 1 6.74 6.74 2 5.49 7.25 5 2.46 8.55 4 1.95 9.44 5 1.64 10.55 6 1.45 11.25 7 1.28 12.05 8 1.16 12.91 9 1.07 15.58 10 --—- 14.81 <56 Aug.-Mar. 1 7.17 7.17 2 5.68 7.55 5 2.55 8.28 4 1.98 8.91 5 1.64 9.57 6 1.42 10.42 7 1.26 11.58 8 1.15 12.90 9 1.07 14.57 10 ---- 16.55 256 Apr.-July 1 5.95 5.95 2 5.09 6.45 5 2.19 7.54 4 1.75 8.74 5 1.49 10.06 6 1.52 11.55 7 1.20 15.44 8 1.12 15.64 9 1.05 17.96 10 -—-- 20.94 256 Aug.-Mar. 1 6.25 6.25 2 5.22 6.65 5 2.26 7.62 4 1.79 8.67 5 1.51 9.65 6 1.55 10.91 7 1.20 12.60 8 1.11 15.05 9 1.05 18.02 10 ---— 21.86 85 Qi =~ '—.—'—'— Where Qi represents the 2th cumulative ratio factor for ;_months of cumulative milk yield prior to disposal for i = 1,...,9. .sz:represents the cumulative sum of products k=1 of ratios for k = 1,...,10. 21: 1 k-1 Zk= TIRi for 23 k g 10. i=1 R- represents the average ratio between the consecutive last two test days of each terminal lactation for each breed-age- season group. 10 T = Z‘Zk k=1 The cumulative ratio factors derived from Holstein voluntarily terminal records (Table 25) were always smaller than the projection factors for non—terminal records (Table 15) . The level of milk yield and the shape of the lactation curve varied according to the number of test days recorded prior to the removal of the cow. Initial yield was smaller and the decline was faster, the earlier the removal. Due to these differences, total cumulative production should be utilized in estimating what the 505-day milk yield would have been if the cow had remained in the herd to complete her record. That is, if a record terminated after eight months of production is projected from the sum of the first 84 two months of lactation, the yield for 505-days will be underestimated. ' Since the Holstein and Brown Swiss ratio factors were similar for non-terminal lactations, the ratios of voluntarily terminal records for Holsteins are probably similar to those for Brown Swiss. If so, the voluntarily terminal incomplete lactations for Brown Swiss may be extended to 505 days by use of the Holstein factors. The Guernsey, Jersey, and Ayrshire non-terminal ratios also resembled each other. Since the Guernseys had the largest number of observations, ratio factors for extending volun- tarily terminal incomplete lactations to completion were computed fOD them (Table 26). All voluntarily terminal incomplete records of Guernseys, Ayrshires and Jerseys may be extended by the Guernsey factors. The variation in total milk yield estimated by terminal projection factors is small as compared to the variation from non-terminal projection factors (Table 27). Differ- ences among estimates from the non-terminal projection factors are large enough to prohibit using these factors to adjust records of cows removed voluntarily, especially for cows calving at less than 56 months of age, since they have no previous performance. The error in estimating the 505-day milk yield by the terminal factors (Table 27) varies more for cows ending their lactations after eight months of lactation than for 85 Table 26. Cumulative and non-cumulative ratio factors for projecting 505-day milk yield from voluntarily terminal incomplete records for Guernseys. Age at Season calving of fresh- Test Cumulative Non-cumulative (months) ening day factor factor <56 Apr.-July 1 6.16 6.16 2 5.54 7.51 5 2.42 8.74 4 1.95 10.08 5 1.66 11.54 6 1.46 11.87 7 1.51 15.25 8 1.18 11.87 9 1.08 12.62 10 ---- 15.19 <56 Aug.-Mar. 1 5.56 5.56 2 2.94 6.52 5 2.15 8.00 4 1.74 9.22 5 1.49 10.21 6 1.55 12.10 7 1.21 15.88 8 1.12 15.40 9 1.05 17.45 10 ---- 19.41 .256 Apr.-July 1 4.88 4.88 2 2.68 5.95 5 1.95 7.10 4 1.59 8.67 5 1.59 11.02 6 1.26 15.71 7 1.17 16.11 8 1.10 18.28 9 1.04 21.04 10 --—- 25.56 .256 Aug.-Mar. 1 5.95 5.95 2 5.15 6.71 5 2.19 7.21 4 1.75 8.25 5 1.47 9.55 6 1.29 10.99 7 1.18 15.61 8 1.10 16.66 9 1.04 19.70 10 -——- 25.51 86 8545» xaas smoumom .s05uospoum Hoqu Umpommxm ms» Usm map Mo s05uomnoum 05umn $55 cmm3umn mocmHmMM5U mnp m5 COHuM5>mQa MMMM MMMM M5MM M5MM 05 555 NM505 M5 MM005 NM >N>M 0 M5MM M 0MN MMN05 MN 55005 55N MMMM 0N MMMM M M05 5MM05 5 I 5MMM 5MM M>MM 0NI MNMM > 5>M NMM05 5M I 5MMM MM5 555M M5I >MMM M MN> M5>05 M55I M>MM >0> NMMM MNI >5MM M MMM M>M05 5M5I 50MM 0MM MMMM M 0MMM 5 MN05 55055 >5MI 5>MM 55N5 MMMM MM 5MMM M >M55 MM555 MM5I MMMM MMM5 50N05 0> M5>M N .l MMM5 5MM55 M5MI M>5m 5MM5 M>M05 5M5 MOMM 5 .Hmzl.0:¢ MMA 5MMM 5MMM MOM> MOM> 05 0M 5N5M M I MMMM MM 5MM> M I NOM> M 5M5 MM5M M MMMM M55 >NOM M I MOM> M 0MN 5NMM N5 M>MM 55N >55M 5 N5M> > 0MM 5M>M 05 5>MM MMM >MNM 0 MOM> M MMM 5MMM N I MMMM 5M5 N05M N5I MMM> M 0MM 5MMM 5M I >MNM MMM. 5MMM 5 I 50M> 5 >M> MMOM >M5I 50NM MMM >M>M 5N NMM> M 5MM MNNM 0>NI 5MoM MM55 5MOM M5 MMM> N >MM MMMM MM5I NNM> OM55 MMMM 55 NNM> 5 >5sbI.HQ¢ MMV a.>oo Houomm .>oQ Mowomm a.>oQ HOpomw a4>mo Monumm (Now 0:5sm Amzucoev c05uumflonm c05uomfloum c05uommoum s05uomnoum ummB Inmmum Mo ms5>5mo 5MC5Eumu 5ms5EumB 5MC5Eumu 56:5EHmB - GOmmmm um.mm¢ Icoz Isoz mnucoE M mausofi M "Hm5Mm Uwumc5Enmp >55Hmus95o> mUHoomm .muouomw c05uumfloum 5MC5EHmpIc0: Mam 5MC5Eumu >3 ms05uMHUM5 mum5mEoos5 5MC5EHmp >555muCS5o> C5mum5om mo m05m5% x55E >m©IM0M 0s5umE5um® :5 mco5pm5uo> .>N @5988 87 those voluntarily culled after five months of production. Thisincreased\muiation indicates the necessity of employ- ing the total cumulative milk production at the time of removal in estimating what the 505—day milk production would have been if the cow had remained in the herd to complete her present record. DI SCUSSI ON Variables Affecting the Characteristics of the Lactation The selection of the breeds, ages at calving and seasons of freshening in this study resulted from the con- clusions of Lamb (1959, 1962) concerning the variables that significantly influenced the relationship of the partial lactation to its complete 505-day record. These differences were verified. Initial level of milk yield and reduction rate during the lactation were related to the breed-age-season groupings suggested by Lamb (1959, 1962). In addition, the rate of re- duction varied according to the stage of lactation, which was contrary to the uniform reduction rate of 10%;per month of lactation suggested by Turner (1926). Lactation curves that were derived according to three levels of production within breed-age-season groups exhibit- ed different shapes from those represented in The Larro Graphmeters (1945). The Larro Graphmeters first increased and then decreased for all initial levels of production, whereas in this study only the cows with low initial yields exhibited this characteristic because the medium and high producing cows were continually decreasing in yield during 88 89 their lactations. This difference may be due to the shapes of The Larro Graphmeters having been formed from daily milk weights within a herd (Larro Dairy Guide, 1951), whereas in this study the shapes of the lactation curves were derived from average test day milk weights ignoring herds. Estimation of 505-Day Milk Production from Partial Lactations Ratio extension factors were developed by different procedures for extending partial lactations to completion from monthly or cumulative monthly milk production. Ratios for Projecting Incomplete Lactations to 505 Days The cumulative and non-cumulative ratio projection factors were formed from average ratios between consecutive test days of a lactation within each breed-age-season group. Slight differences existed between Lamb's (1962) factors and the ones reported in this study, the former being larger in all cases. These differences may be due to the types of records included in developing the extension factors. Lamb (1962) included only records with 10 con- secutive test days, whereas in this study all records that were not marked by a disposal code within the first ten test periods were utilized, including complete records, in- complete records, and records with missing test periods. 90 Alternative Ratio Factors for Extending Incomplete Lactations Cumulative and non-cumulative ratio factors were calculated from average ratios between consecutive test days of a lactation. An alternative procedure is to form ratios from the average milk yields within each breed-age-season group. Differences between the two procedures might be eXpected since cows more variable in milk yield between test days would influence the average of the ratios more than they would influence the ratios of the average milk yields. In addition, herd effects are present in the ratios of the average milk yields. Lamb (1963) found that the cumulative factors from the average ratios were always larger than those formed from the ratios of the average milk yields. However, in this study, only slight differ- ences existed between the cumulative ratio factors obtained from each procedure. Terminal Incomplete Lactations An incomplete terminal record results when a cow is removed voluntarily or involuntarily from the herd prior to completing the 505—day lactation in progress. The purpose of this study was to establish the characteristics of these terminal lactations and methods for their utilization. 91 Distribution of Terminal Incomplete Lactations More than one-fifth of the cows in a herd are re- moved annually for various reasons. Of these, the rates of removal on each test day were constant, excluding the tenth month of lactation. This observation was in agreement with Voelker (1957). The rate of involuntary removal was approximately equal for all test days, while the cows voluntarily culled were generally removed on the fifth, sixth, seventh or eighth test day. The equal distribution of cows involun- tarily removed from the herd might be expected, since dairymen had little control as to the time of death, in- fection, etc., of the cows removed. However, the dairymen had full control as to the time cows were voluntarily culled for low production, hard milking, old age or dairy purposes. For cows calving at less than 36 months of age, the majority of the voluntary removals occurred during the first few test days, whereas those freshening at 56 months of age or over were voluntarily culled during the later stages of lactation. Seasonal effects on the proportion removed on each test day were negligible. Although Holstein was the only breed considered in evaluating terminal lactations, the proportion removed on each test day was examined for each breed. Similarities existed among breeds in the frequency of removal on each test day, which was in agreement with Voelker (1957). 92 Of the total cows removed from the Michigan D.H.I.A. population, 61% were culled for voluntary reasons while 39% were disposed of involuntarily, which was in close agree- ment with the proportion obtained from the data of Johnson and Thelen (1959, 1960, 1961, 1962). However, for cows calving at less than 56 months of age, approximately two and one-half times as many cows were removed voluntarily as involuntarily, whereas cows freshening at 56 months of age or over were removed equally for voluntary and involun- tary reasons. These findings are in close agreement with the results reported by O”Bleness and VanVleck (1962). Among the total number of cows removed, 23 % were from cows calving at less than 56 months of age, whereas the remaining 77% were from cows calving at 56 months of age or over. However, of the total number of cows calving at less than 56 months of age, approximately 16% were removed, whereas approximately 25% of the cows calving at 36 months of age or over were eliminated from the herd. Characteristics of Terminal Incomplete Lactations Terminal incomplete lactations were initiated at a lower milk yield than lactations of cows completing their records within the same breed-age-season group. This agreed with the results obtained by VanVleck (1964) and Voelker and Eastwood (1960). Although means were less, the standard deviations of the test day milk weights of terminal 95 lactations were about three pounds larger than those for non-terminal records. This increase in the standard devi- ations may have been due to the high frequency of low producing cows in the terminal groups. Besides the termin- al lactations being initiated at lower yields, a greater rate of reduction from test day to test day existed during the terminal record. However, this was contrary to the report of Voelker and Eastwood (1960), where the slopes of the terminal records were similar to those of the cow's previously completed lactations. Cows voluntarily and involuntarily removed from the herd exhibited distinctly shaped lactation curves and dif- ferent initial levels of milk yield. Cows involuntarily removed from the herd initiated their lactations with slightly less milk than cows completing their records with- in the same breed-age-season group. This difference in milk yield was considered negligible in importance since causes of involuntary removal should affect cows at random. The lactation curves of cows involuntarily removed from the herd resembled the shape of the lactation curve for cows completing records. However, as the length of the terminal lactation increased, the two lactation curves diverged. The reason for this divergence could not be separated into genetic or non-genetic factors from data available in this study. 94 Cows voluntarily removed from the herd had a dis- tinctly different shape of lactation curve from that of cows completing their records within the same breed-age- season group. The cows voluntarily removed from the herd initiated their lactations at a lower milk yield and de- clined at a substantially faster rate during their lac- tations than cows completing 505 days. The cows that , started their lactations at an extremely low level of milk yield and exhibited a rapid rate of decline were removed immediately, whereas cows initiating their lactations at a slightly higher level, but still maintaining an increased rate of reduction, were removed at a later stage of lac- tation. This difference in level of milk production indi- cates that milk yield on first test day is an important factor in determining the number of test days recorded dur- ing the lactation of cows voluntarily removed from the herd. Except for the first two months of lactation, the shapes of the incomplete lactation curves voluntarily terminated after different test days were parallel. For cows calving at less than 36 months of age the voluntarily terminal incomplete lactation curves showed larger divergence from the completed records than in the case of cows calving at 36 months or over. However, in both age groups, as the number of days on test increased prior to removal, the difference in milk yield between the terminal and completed lactations decreased. The larger 95 differences-in milk yield between-the terminal and com- plete records of young cows may indicate that farmers were retaining their first-calf heifers producing below average for a second lactation and culling only the extremely low yielding two-year-old cows, whereas the animals producing slightly below average and calving at 56 months of age or over were removed during lactation. Estimation of SOS-Day Milk Yield from Terminal Incomplete Lactations Voelker and Eastwood (1960) reported that the terminal lactation was initiated at a lower level of milk yield, and that the slope of the terminal lactation curve was similar to that of the cow's previously completed records. But, they further stated that the ratio projection factors em- ployed on non-terminal records were inadequate for estimating what the 505-day milk yield would have been if the cow had remained in the herd to complete her lactation. It appeared to them that the factors overestimated the total production. Cows voluntarily and involuntarily removed from the herd exhibited distinctly shaped lactation curves and dif- ferent initial levels of milk production. The involuntarily removed cows had similar lactation curves to those of cows completing their records. Thus, the projection factors used for extending an incomplete non-terminal lactation should also be employed in estimating the 505—day milk yield of cows involuntarily removed from the herd during lactation. 96 However, an underestimation of the 505-day milk yield may result due to the slight divergence that exists between the shapes of the completed and involuntarily terminal lactation curves. In contrast, the shapes of the voluntarily incomplete terminal lactation curves were unlike those of the cows completing their records. Thus, cumulative ratio factors were formed for the voluntarily terminal incomplete records to ascertain if the relationship of the expected 505-day milk yield to its part was the same as that for cows com— pleting their records. Differences in the relationship of the total to its part existed since the ratio factors for voluntarily terminal records were always smaller than those for non-terminal records. The total cumulative production should be utilized in estimating what the 505-day milk yield would have been if the cow had remained in the herd to complete her record. A record that is terminated after eight months of pro- duction and is projected from the sum of the first two months of lactation will be underestimated because the earlier the removal, the lower the initial yield, and the faster the reduction rate. Since the Holstein and Brown Swiss ratio factors were similar for non-terminal lactations, the voluntarily termin- al ratio factors for Holsteins are probably similar to those for Brown Swiss. The non-terminal factors for Guernseys, 97 Jerseys,-and—Ayrshires also resembled each other. Ratio factors for voluntarily terminal records were formulated for the Guernseys because more observations were avail- able for that breed, but Guernsey ratios may be used for Jerseys and Ayrshires. The errors in the projected SOS-day milk yields are larger when projected by the non—terminal factors than when the projection is obtained from the voluntary terminal factors. Extension of voluntarily terminal incomplete lactations by the non-terminal projection factors for cows ending their records after two months of lactation results in an overestimation of approximately 1500 pounds whereas about a 1200 pound error is present in the expected total milk yield for those terminating their production at three months of lactation. Differences of this magnitude pro- hibit using the non-terminal projection factors to adjust records of cows removed voluntarily, especially for cows calving at less than 56 months of age, since they have no previous performance. Application of Results Variables Affecting the Character- istics of the Lactation The milk weights and the standard deviations that were recorded for each test day during a lactation within each breed-age—season group may be useful in designing experi- ments based on yield of milk. Cows may be separated into 98 groups of high or low yield, since the shape of the lac- tation curves vary according to level of milk yield. The reduction rate in milk yield between successive test days may be useful in estimating missing test periods of a cow's lactation. At present, D.H.I.A. testing is on a monthly basis. If, for some reason, a cow is unable to be tested on the same day as the rest of the herd, an esti- mate for that test period could be obtained from the last test day milk weight by utilizing declination rates. Utilization of these factors is accomplished by multiplying the appropriate reduction value by the last test day milk weight (50 days prior to the absent weight) and subtracting the product from the test day milk weight from which the estimate was made. This provides an estimate of the miss— ing test period. The procedure may also be valuable in nutritional and physiological studies, since an effect of the experiment may be noted at the first test period after the cows were placed on experiment. The reduction rates between successive test days may provide close estimates of succeeding or preceding test day milk weights to allow for bimmonthly or tri-monthly testing programs. If the monthly testing system was re- placed by a system requiring fewer official test days to obtain an accurate estimate of the 505-day milk yields, more herds could be tested and the cost per cow reduced. 99 Estimation of 505-Day Milk Production from Partial Lactations Total milk production may be estimated from the cumulative milk production during part of the lactation or from a single test day during the lactation. Since all testing programs record the total production to date from the time of calving,.utilization of the total cumulative milk production provides the best estimate of the total milk yield. A factor to extend the total cumulative pro- duction for any number of test days would be most applicable. These cumulative projection factors may be interpolated by the procedure reported by Lamb (1959). Meadows (1962) utilized Lamb's (1962) cumulative factors to develop a slide rule for projecting 505-day milk yields. This slide rule adjusts for the age and seasonal groups that Lamb (1962) reported to have a significant effect in projecting partial milk production. Since only the number of days in milk production and the total pro- duction to date are required, the slide rule is readily ap- plicable in estimating total milk production. In addition to providing an estimate of the SOS-day milk yield, factors (developed by Kendrick, 1955) to correct for age at calving were also incorporated into the slide rule so that dairy— men could extend partial production records and adjustiall milk yields of cows in the herd for age at calving. As a result, the cows may be ranked according to predicted milk 100 production on a mature equivalent basis allowing for the removal of the lowest producing animals prior to com- pletion of the lactation. Total milk production also may be estimated from a single test day during the lactation. This estimate is obtained by multiplying the appropriate non-cumulative ratio factor (based on month of lactation of the cow at the time of the test) by the product of the test day milk weight and 50.5 days. However, this procedure is not recommended when cumulative milk production is known, since it does not utilize all the available data. Terminal Incomplete Lactations Sire proofs should include records from all daughters that calved, whether the records are terminal, partial, or complete. The biases introduced into proofs by removing low producing cows prior to completion of the lactation would be less if all records were extended. Prior to estab- lishing new ratio factors for extending terminal incomplete lactations, characteristics of the lactation curves were examined to determine iftcompleted and terminal records were similar enough to permit use of the same factors for both. Cows involuntarily removed from the herd exhibited lactation curves similar in shape and level of milk yield to those of cows completing their lactations. Records of cows involuntarily removed from the herd may be extended 101 by use of the interpolation factors utilized for non- terminal lactations. However, the lactation curves of cows voluntarily removed from herds differed greatly in shape and level of milk production from those of animals complet- ing their records. Therefore, records of cows voluntarily removed from the herd must be extended by a different set of factors to provide more accurate estimates of the 305- day milk yields expected of the animals if they had re- mained in the herd to complete their lactations. The fact- ors derived for extending voluntarily terminal lactations were designed to utilize the cumulative milk production from the time of calving to the time of disposal. When terminal lactations cannot be identified by a voluntary or involuntary reason for removal from the herd, the voluntary terminal extension factors should be utilized since the majority of the cows removed from the herds each year are culled voluntarily. In addition to being useful in sire proofs, extended terminal lactations may also be of value in nutritional and physiological experiments in which the cow dies or is removed from the herd prior to completion of the experiment provided it was not a treatment effect that caused the re- moval. Thus, not all the information will be lost when the cow is removed from the experiment. Extended terminal lactations, particularly for cows removed during the first lactation, may be useful in 102 estimating the genetic value of a cow's daughter. A more accurate index might be formulated by utilizing extended terminal records rather than omitting them for ranking a cow's daughter within the herd. Future Investigations Required Variables Affecting the Character- istics of the Lactation The characteristics of a complete lactation were established so that they could be utilized for studying terminal records. While establishing the characteristics of a lactation, the study indicated other characteristics that should be considered: (1) Reduction rates between test days of a lactation should be formulated on another set of records. Stabilir zation of the reduction rates between test days would allow for a more accurate estimation of missing test day milk weights in D.H.I.A. testing programs. (2) Once reduction rates between test days of a lactation are known, an official testing system based on biwmonthly or tri-monthly tests may be adequate for testing cows. However, the added error compared with monthly test- ing must be established. If the error in estimating 505-day milk yields by a different testing system is small enough, more cows could be tested and the cost to the farmer slightly reduced, while the supervisor's salary would be maintained or increased. 105 Estimation of 505-Day Milk Production from Partial Lactations Several questions requiring further work arose in deriving ratio factors for estimating 505-day milk yields: (1) Repeatabilities of ratios between test days are needed to indicate whether the relationship of the total lactation to its part is similar between lactations. (2) The relationship of the total lactation to its part between paternal sibs or between daughters and dams would indicate whether the heritability of ratios between test days is similar. (5) The genetic and environmental correlations between test day ratios would indicate to what extend the same genes affect the ratios of different parts of the lactation or to what extend environment affects the shape of the lactation curve. Terminal Incomplete Lactations Additional problems with terminal incomplete records are: (1) The characteristics of the terminal incomplete lactations should be verified on another set of records. (2) The effects of voluntary and involuntary removal from the herd also should be verified on another set of records. Cows involuntarily removed from the herd prob- ably should be separated by cause of removal; groups removed for disease and for other reasons. 104 (5) The ratio factors for extending voluntary and in- voluntary incomplete terminal lactations should be verified and formulated for other breeds. (4) The genetic correlation between complete and terminal records would indicate whether the reason for re- moval was genetic or non-genetic, which would aid in determining the value of utilizing terminal lactations. (5) The importance of extending terminal records for utilization in sire proofs should be established. Once the value of terminal lactations in sire proofs is known, then the inclusion or omission of terminal records in sire proofs will be the same for all bulls. SUMMARY The purpose of this study was to establish character- istics of terminal lactations and to develop procedures for their utilization. Test day milk weights and ratios be- tween consecutive test days of a lactation were employed in the analysis. The records of production utilized in this study were obtained from approximately 2,500,000 monthly production records of cows tested in Michigan D.H.I.A.-I.B.M. between January 1959 and October 1961. Over 58,000 records were classified as complete records, which were required to con- tain 10 test days in the first 505 days of lactation, while over 115,000 records were categorized as non-terminal. Non-terminal lactations included all records that were not marked by a disposal code within the first ten months of production; complete lactations, incomplete lactations and lactations with missing test days. Any record that was marked by a disposal code was classified as a terminal in- complete lactation, and more than 17,500 such records were present. All records, both terminal and non-terminal, were cate— gorized into five breed groups (Ayrshire, Brown Swiss, Guernsey, Holstein, and Jersey), two age groups (cows calving 105 106 at less than 56 months of age and those freshening at 56 months of age or over), and two seasons of calving (cows freshening from April through July and those calving during the remaining months). Records were further separated ac- cording to milk yield on first test day. Three groups of equal numbers were formed to ascertain the influence of initial milk yield (high, medium, and low) on the character- istics of the lactation. Breed, age, and season affected the characteristics of the lactation curve and the relationship of the total lactation to its part. Rates of reduction in yield between test days varied for each breed-age-season group, indicat- ing that a uniform reduction rate did not exist from one test day to the next. All terminal incomplete records were categorized according to a voluntary or an involuntary removal of the cow from the herd. A voluntary disposal occurred when the dairyman decided whether the cow should be retained or dis- posed, while an involuntary removal occurred when there was no possible choice. The distribution of involuntarily removed cows was constant for each test day during a lactation, when the tenth month was ignored. The rate of voluntary removal was most frequent during the later stages of the lactation for the cows calving at 56 months of age or over, whereas 107 the majority of the cows voluntarily culled were removed during the early part of the lactation for cows calving at less than 56 months of age. Cows voluntarily removed from the herd appeared to have a lower level of milk yield and a more rapid rate of decline during their lactation as compared to cows with completed records. Thus, a different relationship of the expected total milk yield to its part existed. Character- istics of involuntarily terminal records were similar to the complete records but the slight differences that exist- ed could not be attributed to particular causes. Therefore, involuntarily terminal incomplete records should be pro- jected to a 505-day basis by factors used for extending non—terminal lactations, whereas voluntarily terminal incomplete lactations should be extended by another set of projection factors, which were derived in this study. LI TERATURE CI TED Asdell, S. A. 1951. Variations in Amount of Culling from D.H.I.A. Herds. J. Dairy Sci., 54:529. Bereskin, B., and Freeman, A. E. 1961. Effect of Month of Calving in Herds at Three Levels of Production. Mimeo. Amer. Dairy Sci. Assoc. Meeting, Madison, Wisconsin. (J. Dairy Sci., 44:1196, Abstract) Bereskin, B., Freeman, A. E., and Lush, J. L. 1962. Sources of Variation in D.H.I.A. Records as Related to Proving AI Sires. J. Dairy Sci., 45:677. (Abstract) Bonnier, G. 1955. Is the Shape of the Lactation Curve Genetically Determined? Hereditas, 20:199. Branton, C., Evans, D. L., and Waters, W. H. 1961. Some Genetic and Environmental ASpects of Certain Per- formance Traits in a Louisiana Holstein Herd. J. Dairy Sci., 44:1190. (Abstract) Branton, C., and Miller, G. D. 1959. Some Hereditary and Environmental Aspects of Persistency of Milk'Yield_of Holstein—Friesians in Louisiana. J. Dairy Sci., 42:925. (Abstract) Brody, S., Ragsdale, A. C., and Turner, C. W. 1925. The Rate of Decline of Milk Secretion with the Advance of the Period of Lactation. J. Gen. Physiol., 5:441. Brown, M. A., Vanderzant, C., Parker, B. A., and Rupel, I. W. 1961. Some Factors Affecting Milkfat'andj Protein Levels in Milk from Dairy Herds in Central Texas. J. Dairy Sci., 44:1196. (Abstract) Cannon, C. Y. 1955. Seasonal Effect on Yield of Dairy Cows. J. Dairy Sci., 16:11. Cannon, C. Y., Frye, J. B., Jr., and Sims, J. A. 1942. Predicting 505-Day Yields from Short-Time Records. J. Dairy Sci., 25:991. 108 109 Dayton, A. D. 1964. Unpublished data. Dairy Department, Michigan State University, East Lansing. 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Reasons for Disposal of Dairy Cows from New York Herds. J. Dairy Sci., 45:1087. 112 O'Connor, L. K., and Hodges, J. 1965. Wastage and Culling in Dairy Herds. Ani. Prod., 5(2):165. Parker, J. B., Bayley, N. D., Fohrman, M. H., and Plowman, R. D. 1960. Factors Influencing Dairy Cattle Longevity. J. Dairy Sci., 45:401. Pirchner, F., and Lush, J. L. 1959. Genetic and Environ- mental Portions of the Variation Among Herds in Butterfat Production. J. Dairy Sci., 42:115. Rakes, J. M., Stallcup, O. T., and Gifford, W. 1965. Persistency and the Lactation Curve of Dairy Cows. Agr. Exp. Station Bull., 678. University of Arkansas, Fayetteville. Rendel, J. M., Robertson, A., Asker, A. A.,Khishin, S. S., and Ragal, M. T. 1957. The Inheritance of Milk Production Characteristics. J. Agr. Sci., 48:426. Sanders, H. G. 1929. The Variations in Milk Yields Caused by Season of the Year, Service Age, Dry Period, and Their Elimination. Part IV. Dry Period, and Standardization of Yields. J. Agr. Sci., 18:209. Sanders, H. G. 1950. The Analysis of the Lactation Curve into Maximum Yield and Persistency. J. Agr. Sci., 20:145. Searle, S. R. 1960. Simplified Herd-Level Age Correction Factors. J. Dairy Sci., 45:821. Searle, S. R. 1961. Part Lactations I. Age-Correction Factors for Monthly Milk Fat Yields. J. Dairy Sci., 44:104. Searle, S. R., and Henderson, C. R. 1959. Establishing Age-Correction Factors Related to Level of Herd Production. J. Dairy Sci., 42:824. Sikka, L. C. 1950. A Study of Lactation as Affected by Heredity and Environment. J. Dairy Res., 17:251. Sundaresan, D., and Freeman, A. E. 1961. Variation in Milk Fat Production in State-Owned Herds in Iowa. J. Dairy Sci., 44:151. The Larro Graphmeter. 1945. General Mills, Inc. Turner, C. W. 1925. Seasonal Variations in Milk and Fat Production. J. Dairy Sci., 6:198. 115 Turner, C. W. 1926. A Quantitative Form of Expressing Persistency of Milk or Fat Secretion. J. Dairy Sci., 9:205. VanVleck, L. D. 1962. Effect of Incomplete Records on Sire Evaluation. J. Dairy Sci., 45:1511. VanVleck, L. D. 1964. First Lactation Performance and Herd Life. J. Dairy Sci., 47:1000. VanVleck, L. D., and Henderson, C. R. 1961a. Estimates of Genetic Parameters of Some Functions of Part Lactation Milk Records. J. Dairy Sci., 44:1075 VanVleck, L. D., and Henderson, C. R., 1961b. Regression Factors for Extending Part Lactation Milk Records. J. Dairy Sci., 44:1085. VanVleck, L. D., and Henderson, C. R. 1961c. Ratio Factors for Adjusting Monthly Test-Day Data for Age and Season of Calving and Ratio Factors for Extending Part Lactation Records. J. Dairy Sci., 44:1095. VanVleck, L. D., and Henderson, C. R. 1961d. Regression Factors for Predicting a Succeeding Complete Lac- tation Milk Record from Part Lactation Records. J. Dairy Sci., 44:1522. VanVleck, L. D., and Henderson, C. R. 1961e. Use of Part Lactation Records in Sire Evaluation. J. Dairy Sci., 44:1511. VanVleck, L. D., and Henderson, C. R. 1961f. Extending Part Lactation Milk Records by Regression Ignoring Herd Effects. J. Dairy Sci., 44:1519. VanVleck, L. D., and Henderson, C. R. 19619. Estimation of Missing Test—Day Records. J. Dairy Sci., 44:1865. VanVleck, L. D., and Henderson, C. R., 1961b. Utilizing both Part and Complete Daughter Records in Sire Evaluation. J. Dairy Sci., 44:2068. Voelker, H. H. 1957. Use of Extended Incomplete Lactation Records. J. Dairy Sci., 40:651. (Abstract) Voelker, H. H., and Eastwood, B. R. 1960. Covariance of Partial and Complete Lactations in Dairy Cattle. Proc. S. D. Acad. Sci., 59:167. (Abstract) HICHIGRN STRTE UNIV. LIBRQRIES MIN" 40 312931045 962