USEFULNEfiS OF PART RECORDS lN ESTIMATING THE QREEDING VALUES OF DAIRY CATTLE; Thesis for the Dogm of P11. D. MCHEGAN STATE UNIVERSITY Rainer? C. Lamb 1962 This is to certify that the thesis entitled USEFULNESS OF PART RECORDS IN ESTIMATING THE BREEDING VALUES OF DAIRY CATTLE presented by Robert C. Lamb has been accepted towards fulfillment of the requirements for Ph D degree mm aim 9 mcfifl.md, Major' professor Datelfl flail/(421 /7éZ 0-169 LIBRARY Michigan State University USEFULNESS OF PART RECORDS IN ESTIMATING THE BREEDING VALUES OF DAIRY CATTLE By \I‘ Robert C iamb AN ABSTRACT OF A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Dairy 1962 ABSTRACT USE FULNESS OF PART RECORDS IN ESTIMATING THE BREEDING VALUES OF DAIRY CATTLE by Robert C. Lamb Complete lat-ration records for 24, 602 Holsteins, 4, 309 Guernseys, 1, 878 Jerseys, and 892 Brown Swiss compiled in Michigan DHIA-IBM from June 1954 through December 1957 were analyzed to ascertain the effects of breed, age, and season of freshening on the relationship of total to part pro- duction and to develop factors which adequately take into account the effects of these variables in extending records to 305 days. The same data were used to measure heritabilities and repeatabilities of monthly, cumulative, and total production, to obtain genetic and phenotypic correlations between part and whole records, and to measure the relative genetic gain in whole records from selecting for genetic gain in part: records. Breed, age, and season of freshening influence the ratios between total and part production sufficiently to require adjustment in extending part records to completion. Separate factors should be used in extending milk and butterfat records. Repeatabilities of single months increase gradually up to the seventh month and then decline rapidly. Repeatability of cumulative production shows an upward trend until the eighth or ninth month of the lactation where it is as high as for total yield. The repeatabilities for milk are slightly larger than 2 Robert C . Lamb those for butterfat and repeatability is larger for adjacent than for non- adjacent records. Heritabilities of monthly production range between zero and . 29. Her- itabilities of cumulative production generally increase with each additional month. Heritabilities of total production range between zero and . 29 for milk and between zero and . 19 for butterfat. Heritability of butterfat production is lower and more erratic than for milk production. Lactations differ in heritability of monthly, cumulative, and total production of milk and butterfat. Phenotypic correlations between monthly and total production are largest for the fifth month and smallest for the first and last months of the lactation. Phenotypic correlations between cumulative and total production increase rapidly for the first six months and then more slowly to . 99 by the ninth month. The correlations are higher for milk than for butterfat, for first lactations than later lactations, and between a part and a total of the same record than between a part of one record and the total of a succeeding record. Genetic correlations between monthly and total production tend to be higher for the center months of the lactation, while between cumulative and total production they tend to increase as the lactation progresses. Except for one or two months during the lactation, selection based on a single monthly record will provide only 50 to 90 percent as much genetic progress per generation in the complete record as selecting on the complete record. The relative efficiency of selecting for a complete record using a 3 Robert C . Lamb cumulative part record as the basis for selection increases as each succeed- ing month is added to the cumulative total. The phenotypic correlations between part and whole records indicate that partial records can be extended with considerable accuracy, but the genetic parameters indicate that in general the genetic progress in complete records will not be as rapid if part records are used as the criterion for selection. However, genetic progress can still be made under this system and if the generation interval can be reduced markedly, if the selection pressure can be increased considerably, or if the economic conditions justify, it may be advantageous to use a part record as an aid in selection. USEFULNESS OF PART RECORDS IN ESTIMATING THE BREEDING VALUES OF DAIRY CATTLE By M Robert CI” Lamb A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Dairy 1962 - I \ ,1; / '7 ,/ . ACKNOWLEDGENE NTS I would like to express my appreciation to Dr. L. D. McGilliard for his patient and friendly guidance during the formulation and investigation of this problem, and especially for his assistance in suggesting improvements in the writing of the thesis. I am very grateful to have had the opportunity to study and work with the staff members and graduate students of the Department of Dairy, Michigan State University, and especially those whom I have worked so closely with in the dairy breeding section. Appreciation is also expressed to Dr. Neeti R. Bohidar for his assist- ance in working out parts of the statistical methods used in the analysis. Finally, I would like most of all to express sincere appreciation to my wife, Janice, for her enduring patience, her never ending encouragement, and for her moral support during these years of graduate study, without which this endeavor would have been much more difficult. ii TABLE OF CONTENTS INTRODUCTION . REVIEW OF LITERATURE . . . Predicting Complete Yield from Part Records . Phenotypic relationship between total and part production Factors for extending part records . Variables Affecting Relationship of Total to Part Production Age and parity Season of freshening Breed . . . . Herd O O I O O O 0 O O O O O O Level of production . . . . . . . . Frequency of milking . . . . . . . Genetic Parameters Repeatability . . . . . . . . . . . Heritability . . . . . . Genetic correlations . . . . . Relative Efficiency of Selection Based on Part Records SOURCE OF DATA . . . . . . . . . . . METHODS O O o O o O o O Q 0 o O Q 0 O O 0 0 Variables Affecting Relationship of Total to Part Production Genetic Parameters and Phenotypic Correlations . Repeatability and phenotypic correlations . . . . . Heritability . . . . . . . . . Genetic correlations Relative Efficiency of Selection . . . . . . iii Page 10 10 11 11 11 11 14 16 18 20 20 22 24 29 37 40 TABLE or CONTENTS (Continued) RESULTS AND DISCUSSION Variables Affecting Relationship of Total to Part Production Age and parity Season of freshening . . . . . . . . . Breed Phenotypic Correlations . Genetic Parameters . . . . . . . . . . . . Repeatability Heritability Genetic correlations Relative Efficiency of Selection Based on Part Records APPLICATION OF RESULTS SUMMARY . LITERATURE CITED iv Page 42 42 47 55 59 61 73 73 80 85 90 98 103 107 Table 10. 11. 12. 13. LIST OF TABLES Ratio factors for extending monthly production for Holsteins according to age and season of freshening . . . . Ratio factors for extending monthly production for Guernseys according to age and season of freshening . Ratio factors for extending monthly production for Jerseys according to age and season of freshening . . . . . Ratio factors for extending monthly production for Brown Swiss according to age and season of freshening . Ratio factors for extending cumulative production for Holsteins according to age and season of freshening Ratio factors for extending cumulative production for Guernseys according to age and season of freshening Ratio factors for extending cumulative production for Jerseys according to age and season of freshening . Ratio factors for extending cumulative production for Brown Swiss according to age and season of freshening . . . Phenotypic correlations between monthly production and total production for the same lactation for Holsteins . . . Phenotypic correlations between cumulative production and total production for the same lactation for Holsteins Phenotypic correlations between monthly production and total production for the succeeding adjacent lactation for Holsteins Phenotypic correlations between monthly production and total production for a succeeding non-adjacent lactation for Holsteins . . . . . . . . . . . . Phenotypic correlations between cumulative production and total production for the succeeding adjacent lactation for Holsteins . . . . . . . . . . . . . . . Page 43 44 45 46 48 49 50 51 63 64 68 69 7O Table 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. LIST or TABLES (Continued) Phenotypic correlations between cumulative production and total production for a succeeding non-adjacent lactation for Holsteins . . . . . . . . . . . Repeatability of single months of adjacent lactations for Holsteins . Repeatability of single months of non-adjacent lactations forHolsteins Repeatability of cumulative months of adjacent lactations forHolsteins Repeatability of cumulative months of non—adjacent lactations for Holsteins . . . . . . . . Heritability of monthly production for Holsteins . . . . Heritability of cumulative production for Holsteins . . Genetic correlations between monthly and total production for the lactation for Holsteins . . . . . Genetic correlations between cumulative and total production for the lactation for Holsteins . . . . . . . . Relative efficiency of selection for complete lactations for Holsteins using monthly records as the criterion for selection Relative efficiency of selection for complete lactations for Holsteins using cumulative records as the criterion for selection vi Page 71 75 76 77 78 81 82 87 88 92 93 INTRODUCTION A large portion of the current selection in dairy cattle utilizes lactation records still in progress at the time of selection. This is true for selection of both sires and individual females. An even more intensive use of part records may be a valuable tool for earlier evaluation of the genetic worth of dairy cows and bulls. This preliminary information could provide a basis for making decisions on culling cows after only a few months of their first or second lactations. Earlier evaluation of the daughters of bulls would shorten the time required to test bulls, thus reducing the cost of maintaining young sires until proven. Artificial insemination units could profit from this by in- creasing the number of sires which could be tested in a young sire program without materially increasing the cost of maintaining young unproven sires. Sires destined for potentially heavy service could be selected sooner to length- en their productive life. The use of part records should provide additional information in evalua- ting the probable merit of a sire by including information from a larger num- ber of daughters more quickly. The use of all records, complete and incom- plete, should eliminate some biases in evaluating bulls caused by the differ- ential culling among progeny of sires resulting from the removal of dispro- portionate numbers of potentially low producing daughters on the basis of early parts of the first lactation. Total yield estimated from production during an early portion of the lacta- tion could provide- a way to use individual cows as their own controls in phys- iology, nutrition, or management experiments. Deviations from the extended lactation curve or from estimated total yield might serve to estimate more precisely the treatment effects than the difference between paired individuals. Another use for part records may be to measure complete records with fewer tests. If a cow can be tested less frequently and each test weighted properly to estimate with sufficient accuracy actual production for 305 days, more herds could be tested without greatly increasing the cost or the labor involved. Before using part records to the extent indicated, more should be known concerning their use. Part records may be either incomplete records still in progress or incomplete terminal records, the latter being lactations pre- maturely terminated by death or sale of the animal. What, if any, distinction must be made between them in actual use has not been determined. However, work along this line is currently in progress (51). Incomplete terminal rec- ords and records still in progress need to be extended to be comparable to complete records. Factors used to extend part records to a 305-day basis need to compensate for the influence of environmental variables which affect the relationship of total to part production. Early parts of records are valuable for making wise decisions of selec- tion only if the early months of lactation provide a reliable estimate of a cow's ability to produce for a complete lactation of 305 days. A partial first record may be less valuable for estimating a cow's ability to produce during 3 a lactation, or for predicting a bull's probable transmitting ability than is an average of several completed records. The part record does become avail- able earlier and by shortening the generation interval and by providing infor- mation from a larger number of daughters may more than compensate in genetic gain for errors which may be introduced in selection based on early parts of a first record. Estimates of genetic parameters are necessary to evaluate whether part records are reliable enough to be used to evaluate the genetic worth of dairy cattle. These parameters can be used to determine the genetic progress in 305-day production from selection based on part records as compared to genetic progress from selection based on complete records. The objectives of this study are: (a) to ascertain more clearly whether age, breed, and season of freshening should be adjusted for in extending milk and butterfat records and whether the age and season groupings used in earlier studies adequately remove the effects of these variables; (b) to meas- ure the repeatability (correlations between the same period of different lacta— tions) of monthly, cumulative, and total production; (c) to obtain the correla- tions between individual and cumulative months of one lactation and complete yield of a succeeding lactation; (d) to measure the heritability of monthly, cumulative, and total lactation production; (e) to estimate the genetic correla— tions between monthly production and total yield and between cumulative and total lactation periods; and (f) to use the estimates of genetic parameters to measure the relative efficiency of selection for a 305—day record using a part record as the criterion for selection. REVIEW OF LITERATURE Predicting Complete Yield from Part Records Phenotypic relationship between total and part production The desirability of estimating a cow's complete lactation yield from only a few tests has led to several investigations of this possibility. Yapp (77) found in 1915 that a 7-day test early in lactation was not highly correlated with total yield for the lactation and concluded that this was not a satisfactory test. Gowen and Gowen (20) later reported a correlation of . 58 between 7—day and 365-day yield of milk. Gaines (14) concluded that the 7-day test was of most value when made during the fifth month of the lactation. Kartha (31) found that a shcrt~time test most accurately estimated 305-day production when the test was taken during the fourth month after calving. Estimation of lactation yield from one test during a lactation was reported by Cannon gt at. (5) to be most accurate when the test was made during the fifth or sixth month of the lactation. The correlations between production for these months and 305-day yield were . 91 for the Iowa State College herd and . 72 for Iowa DHIA herds. The work of Madden gt a_1_. (46) also showed the fifth month to be the most accurate if only one test is to be made. A single test in the sixth, fourth, or seventh month was almost as accurate as one in the fifth month for estimating total yield for the lactation. Working with New Zealand dairy records, Searle (62) found a test in the fifth month to be the most closely 4 5 correlated (r = . 76'; with 305-day yield of butterfat, followed in turn by a single test in the fourth and sixth months. VanVleck and Henderson (7 0) re- ported a correlation of . 85 between production on test day for each of the fourth, fifth, and sixth months and total production of milk for the lactation. Kennedy and Seath (36) found that cumulative production for the first four months was at least as valuable as any single month for predicting total pro- duction for the lactation. Rendel e_t a_l_. (59) found a correlation of . 80 between 70-day and 305-day yield and concluded that 70-day yield could be used as a guide to early selection. PerTuff (56) reported that the correlation between l80-day yield and complete yield was . 90. More recently O'Connor and Stewart (54) reported a correlation within herds of .92 between 180-,day and 305-day yield of milk. In a study of Ayrshire records by Harvey (23), the correlations between cumulative production and total production for both milk and butterfat increased rapidly to . 88 by the fourth month and . 94 by the sixth month and then increased more slowly until the correlation at the end of 9 months was 1. 00. The cor- relations found by Voelker (73) for two~year-old Holsteins were slightly lower, but followed the same pattern. Madden e_t a_l. (46) reported correla- tions for cumulative production with 305-day yield that reached . 90 by the fourth month for cows over 3 years and . 93 for cows under 3 years of age, and reached . 95 and . 97 by the sixth month for cows over and under 3 years of age, respectively. Using Michigan DHIA records for four breeds, Fritz gt a_l. (13) obtained correlations between cumulative production and total production for both milk and butterfat. The correlations for Holsteins and Brown Swiss 6 compared very closely and were at least . 91 by the fourth month and . 95 by the sixth month. The correlations for Guernseys and Jerseys were similar to each other and, although being lower in the initial stage of lactation, were . 91 by the fifth month and . 94 by the sixth month. Reece (58) correlated the average butterfat test for cumulative periods with the average butterfat test for the lactation and found a correlation of . 93 by the sixth cumulative month. Factors for extending part records Ratio and regression factors for estimating complete lactation yield from various portions of the lactation have been reported by several investi- gators. The question of which type of factors, ratio or regression, is most appropriate for extending part records has been reviewed by Harvey (24), Lamb (37), and Madden gt al. (46). Among the earliest reports of extrapolation factors for extending milk production were those of Pearl and Patterson (55), Gowen and Gowen (20), Gowen (19), Turner and Ragsdale (68), Kartha (31), and Kendrick and Bain (35). Later Cannon _e_t a1. (5) and Eldridge and Atkeson (8) developed factors for extending butterfat records. Some authors have presented multiple sets of factors. Harvey (23) and Kendrick (34) reported factors for three different age groups. Kendrick (34) also presented factors based on season of freshening and level of production. An extensive set of tables for each of three age groups for estimating total milk and butterfat production from any single test day during the lactation was developed by Erb _e_t_ a_l_. (9) from DHIA data. Madden g a_l_. (44, 45, 46) 7 presented both ratio and regression factors for extending monthly and cumula- tive production of milk and butterfat to 305 days. Separate factors were given for each of the two age groups, and in the latter two papers factors were pre- sented which would adjust for age and frequency of milking. Extension factors which would adjust for season of freshening for Jersey and Sindhi-Jersey crossbreds were presented by Fletcher e_tal. (11). Lamb and McGilliard (38, 39) developed ratio factors that would adjust for age and season of freshening in extending cumulative production of milk and butterfat for four breeds. Regression factors for extending cumulative test-day production of milk and butterfat to a 305-day basis for four breeds were developed by Fritz _et a. (13). VanVleck and Henderson (70, 71, 72) used Holstein records from New York DHIA to develop factors for predicting 305-day production of milk from a single monthly test, from sequential test- day data, from cumulative monthly tests, and from sequential bimonthly and trimonthly test-day information. Variables AffectingRelationship of Total to Part Production Production records of dairy cows are influenced by many environmental factors. The effects of these same variables on the relationship of total pro- duction during a lactation to production during various portions of the lactation are of primary concern in developing factors for estimating total yield for the lactation from short-time records. Age and parity Eldridge and Atkeson (8) developed regression factors for estimating total yield of butterfat from one day's test for 12 different age groups. Sep- arate factors appeared necessary, especially for younger cows. By regroup- ing the early ages into first and second lactations, they found that factors based on parity more accurately extended the part record to a complete lacta- tion. Erb _e_t_ e_t. (9) found a very marked difference between young and old cows with respect to the shape of the lactation curve. They divided records into three age groups ($30 mo. , 31-42 mo. , and 2 43 mo. ) to develop factors for predicting 305—day production of milk and butterfat from a single test. Madden and co-workers (44, 45, 46) also showed a difference in the shape of the lactation curve for first-calf heifers as compared to older cows. They concluded that separate factors are needed for records initiated at less than 3 years and for those started at 3 years and older. Kendrick (34) and Harvey (23) separated records into three age groups, roughly corresponding to first, second, and all later lactations, respectively. Differences between factors for different age groups indicated a need for sep- arate factors for each age group. Fritz e_t al. (13) studied the influence of age and parity, but failed to show any influence on regression factors attrib- utable to either of them. Lamb and McGilliard (38, 39) studied simultaneously the influence of age and parity on the ratio of total production in 305 days to monthly production of milk and butterfat. Both were found to be important. Analysis of components of variance indicated that parity had a larger influence on the total to part relationship than did age at freshening. However, the ratio 9 factors themselves indicated no practical differences between the factors for age and parity. The conclusion of these workers was that in actual practice extension factors based on age are more desirable. Working with New Zealand records, Searle (61) found that monthly butter- fat records needed to be corrected for age. Separate factors were developed for two-, three-, and four-year-old cows. VanVleck and Henderson (71) divided New York Holstein data into 60 age groups and found a significant effect of age on ratio factors for extending individual and cumulative monthly tests to a complete lactation basis. Season of freshening Eldridge and Atkeson (8) and Fritz e_t a_l. (13), using methods of regres- sion, considered the effect of season of freshening on the relationship of total to part production, but found it insignificant. On the other hand, Kendrick (34) concluded that season of freshening should be considered for at least the first six months in extending cumulative short-time Ayrshire records. Fletcher e_t a1. (10, 11) reported a need for adjustment for season of calving in extending part lactations for Jersey and Sindhi-Jersey cows. Lamb and McGilliard (38, 39) found that differences due to season of freshening con- tributed only slightly less to the variance than did parity or age. Searle (61) and VanVleck and Henderson (71) concluded that age and season of freshening should be adjusted for simultaneously in extending part-time milk and butter- fat records . 10 222st Cannon e_t gt. (5), using data from five breeds, concluded that the shapes of the lactation curves were so similar that breeds do not need to be consid- ered separately in calculating factors for extending incomplete records. Erb gt g_l_. (9) reported that analysis of records from Jerseys, Guernseys, and Holsteins showed that breed had little effect on the shape of the lactation curve; therefore, they did not consider breeds separately in the extension factors which they developed. Fletcher gt gt. (11) found only a slight differ- ence between extension factors for Jerseys and those for Sindhi-Jersey cross- breds. Although Fritz gt gt. (13) studied breeds separately, no conclusions were drawn as to possible breed differences. However, a visual comparison of the extension factors which they present for four breeds indicates definite breed differences in the relationship of total to part production. In studies by Lamb and McGilliard (38, 39) the ratio factors for cumulative production differed between breeds. Holstein and Brown Swiss factors tended to be alike for milk but differed widely for butterfat. Guernsey and Jersey factors were very similar to each other but differed from the Holstein and Brown Swiss factors for both milk and butterfat. Herd Michigan data (13, 38) indicated that herd differences were not important in the relationship of total to part production; therefore, separate factors are not needed for each herd for extending records. 11 Level ofJJroduction Kendrick (34) found a significant difference between extension factors for low-producing and high-producing cows freshening between 31 and 44 months of age, while for more mature cows there was only a slight difference due to level of production. Harvey (23) found a slight tendency for higher producing cows to decline more rapidly in production than did the lower producing cows, while Madden _e_t_a_l. (46) concluded that the relationship between total and part production was similar for low-producing and high-producing cows. Fregency o_f milking The study by Madden gt 91. (46) indicated that milking frequency is not important in extending part-time records. Genetic Parameters Repeatability Early reports (16, 17, 18, 19, 20, 64) on the repeatability of complete milk and butterfat records were of the order of . 55 to . 80. Estimates of re- peatability were high in these studies because herd differences were not removed. Gifford (16) estimated intra-herd repeatability of cumulative monthly production from correlations between two- and three-year-old rec- ords, three- and four-year-old records, and four- and five-year-old records. The magnitude of the correlations increased up to eight months where they were . 57, . 51, and . 61, respectively, for milk and . 54, . 45, and . 59, re- spectively, for butterfat. Berry (3) reported an intra-herd repeatability of 12 . 29 for butterfat yield for cows with at least six records. The correlation between records by the same cow decreased as the number of intervening records increased. Sikka (64), Rendel gt gt. (59), Gowen (18), and Mahadevan (50) have also reported that the repeatability of adjacent records was higher than that of non-adjacent records. During recent years repeatability has been calculated on an intra-herd basis, resulting in estimates ranging from approximately . 3 to . 5. Hartmann (21) estimated repeatabilities of . 34 and . 37 for milk and butterfat yield, re- spectively. Working with Swedish cattle, Johansson (26, 27) reported repeat- abilities of . 38 to . 42 for milk yield and . 32 to . 45 for butterfat yield. Plum e_t _a_l_. (57) reported a repeatability of . 32, while Carneiro (6), Berousek e_t a_l. (2), and Thompson gt gt. (66) found repeatabilities of approximately . 40 for milk and butterfat yield. Slightly higher estimates were found by Specht and McGilliard (65) (r = . 40 for butterfat, .46 for milk), Madden e_t _a_l_. (44) (r = . 43 for butterfat, . 51 for milk), Johnson and Corley (30) (r = . 45 for butterfat, .47 for milk), Wadell e_t g_l_. (74) (r = . 47 for butterfat, .50 for milk), Rendel gt a_l. (59) (r = . 55 for butterfat, . 48 for milk), VanVleck-and Henderson (69) (r = . 50 for butterfat, . 53 for milk), and Mahadevan (48, 50) who found repeatabilities for milk yield of . 46 and . 53 with two different groups of cattle. When year effects were neglected, Castle and Searle (7) obtained a repeatability of . 49, but when a correction was made for year effects the estimate was . 61. In a separate study, Searle (62) obtained a repeatability estimate of . 60 for lactation yield of butterfat. 13 Several investigators have reported correlations between a part of one lactation and the same part of a succeeding lactation. Gaines (15) measured the correlations between cumulative months in a current and the subsequent lactation. The resulting correlations for milk and butterfat increased from approximately . 50 for the first month to . 65 by the tenth month. In studies by Gifford (16, 17), gross and intra-herd correlations between cumulative months of succeeding lactations increased rapidly during the first four months and then increased more slowly with each additional month of production. Estimates of repeatability for monthly and cumulative production of milk and butterfat were computed from intra-class correlations by Madden e_t a_l. (44) who found that repeatability increased to the second month for monthly records and the third month for cumulative records and then decreased with each succeeding month in the lactation. Searle (62) found that repeatability of monthly records increased as lactation progressed, leveling off at the fourth or fifth month. A still different trend was found by VanVleck and Henderson (69). Repeatability of single test-day records increased with stage of lactation until the sixth month and then declined rapidly. First, sixth, and tenth month repeatability estimates were . 38, . 50, . 25 for milk and . 30, .44, and .26 for butterfat, respectively. Repeatability'estimates for cumulative production showed an upward trend until the eighth or ninth month of the lacta- tion. Correlations between 180—day production (. 52 for milk, . 48 for butter- fat) were almost as high as between 305-day yield (. 53 for milk, . 50 for butterfat). Mahadevan (49) found a slightly higher repeatability for 180—day records (r .-. . 52) than for 305-day records (r z .49). Rendel gt gt. (59) 14 reported repeatability of 70-day records (r ; .40) to be lower than repeat- ability of 305-day records (r = . 50). The only reported work dealing with correlations between a part of one lactation and a complete succeeding lactation is that of Gowen and Gowen (20) who reported that correlations between a 7-day test in one lactation and a 365-day record for a later lactation were .48 for milk yield and .42 for butter- fat percentage. Heritability Early workers reported heritability estimates from daughter-dam cor- relations of . 36 to . 50 for milk and . 24 to . 40 for butterfat. These estimates were not made on an intra-herd or intra-sire basis and, therefore, appear high because of the inclusion of environmental correlations between relatives within a herd or sire line. Shrode and Lush (63) reviewed earlier studies and reported that estimates of heritability of intra-herd differences in milk and butterfat production were of the order of . 20 to . 30. Reports since then have substantiated these figures. These reports include: Beardsley gt gl_. (1), Berousek gt gl_. (2), Harvey and Lush (25), Johnson (29), Kempthorne and Tandon (32), Legates (41), Legates and Lush (42), Mitchell e_t gl_. (53), Touchberry (67), VanVleck and Henderson (69), and Yao gt a_l. (75, 76). Heritability estimates from other countries by Carneiro (6) in Brazil, Hartmann (21) in Germany, Mahadevan (50) in Great Britain, and Searle (62) in New Zealand have been in close agreement with American estimates. On the other hand, estimates of heritability by Hartmann (22), Johansson (27), 15 and Sikka (64) have been somewhat higher. Estimates of heritability of individual lactations (12, 21, 28, 30, 40, 48, 59) have indicated a higher value for first records than for later records, suggesting that first lactations are influenced less by environment and more by heredity. In a study by Freeman (12), heritability estimates for first, second, and third lactations were . 36, . 24, and . 26 for milk, and .43, . 35, and . 26 for butterfat, respectively. Several reports of heritability of part records are available. Mahadevan (48) obtained a heritability of . 31 for first ISO-day production of milk. Rendel _e_t_ gl_. (59) reported a heritability for the first lactation of . 36 for 7 0-day yield of milk as compared to . 43 for 305-day yield of milk. Heritability for the second lactation was . 09 and . 24 for 70-day and 305-day yield of milk, respectively. Heritability estimates were of the order of . 30 for loo-day milk and butterfat records and . 34 for ZOO-day milk and butterfat production 7 in a study by Johnson (30). The differences between the 100-, 200-, and 305- day regressions were not significant. Madden gt gt. (44) estimated heritabil- ity of monthly and cumulative records and found the later months of the lacta- tion influenced less by genetic effects than the earlier months. Estimates for the first eight months ranged between . 31 and . 41 for milk and . 14 and . 32 for butterfat. Estimates for cumulative records were relatively higher, ranging from . 35 to . 63 for milk and . 30 to . 47 for butterfat. Searle (62) estimated the heritability of monthly yield of butterfat from New Zealand data using both the regressiOn of daughter-on—dam and the half-sib analysis of variance components. The dam-daughter estimates were lower than those obtained 16 by Madden gt gt. (44), but they appeared to follow the same downward trend toward the end of the lactation. The estimates from the analysis of paternal half-sibs were larger than those from the dam-daughter analysis, particular- ly in the later months of the lactation. A paternal half-Sib analysis was used by VanVleck and Henderson (69) to estimate heritability of monthly and cumu- lative monthly records for milk and butterfat production. The heritability estimates for monthly production were low in the first and last months of the lactation, but reached approximately . 20 in the third through the fifth months. The heritability estimates for cumulative production of milk followed an up- ward trend for the first four months and then leveled off at . 22, while the estimates for cumulative production of butterfat remained fairly constant around . 17. Genetic correlations Freeman (12) reported that genetic correlations between firstand second records were . 68 for milk and . 80 for butterfat; the values for first with third lactation and second with third were of the order of . 40 for both milk and butterfat. He concluded that, to some extent, different sets of genes in- fluence milk and butterfat production in different lactations. Madden gt g_l_. (44) estimated genetic correlations between cumulative and total production and found them near unity for all months, suggesting that genes affecting production early in lactation also affect other parts of the same lactation. Robertson (60) obtained a genetic correlation of . 74 be- tween 70-day and 305-day yield. 17 Searle (62) estimated genetic correlations between monthly records and between monthly and total production of butterfat for the lactation. Estimates of genetic correlations between monthly and total production from a daughter- dam analysis, although lower than those of Madden gt gt. (44),, showed an in- crease up to the third month and then a general decline. The estimates from correlations between paternal half—sibs approached unity for the middle months correlated with total yield. The genetic correlations between monthly records tended to be higher among the early months than among later months and also higher than the correlations between early and later months. VanVleck and Henderson (69) found the middle months of the lactation highly correlated genetically with total yield. The correlation estimates ranged from a high of 1. 01 in the fifth month down to . 79 in the second month and .71 in the tenth month. The genetic correlations between cumulative records and total yield increased with an advance in the stage of lactation, reaching .94 by the fifth month and 1. 00 by the ninth month. The genetic correlations among monthly records were near unity for adjacent months and decreased with an increase in the time between tests. Lerner and Cruden (43) found that the genetic correlation between cumu- lative and annual production of eggs increased steadily with each succeeding month of production, reaching . 93 by the seventh month and unity by the tenth month. Blow gt gl_. (4) found a genetic correlation of . 89 between part and complete egg records in turkeys. Maddison (47) obtained genetic correlations of . 69 and . 72, respectively, between cumulative 4 and 5 month egg produc- tion and annual yield of eggs. 18 Relative Efficiency of Selection Based on Part Records Few investigators have studied the relative efficiency of selection for a whole record using a part record as the criterion for selection. Madden gt_ gt. (44) found that "selection on the basis of first 60-day production best ap- proaches the gain expected in the whole record until the part record is six months or more in length. " In a study by VanVleck and Henderson (69) it was found that a single third or fifth month would provide 92 percent as much progress as selection on total yield. Cumulative production for 6 months was 95 percent as effective as 10-month yield, and 9 months production was 100 percent as efficient as production for 10 months. Lerner and Cruden (43) found genetic progress was 95 percent as efficient with selection based on cumulative production for 9 months as with selection based on egg records 12 months in length. SOURCE OF DATA The data were 31, 681 complete lactation records initiated during the period June 1954 through December 1957. These records were obtained from the Michigan DHIA-IBM program and represented four dairy breeds. Included were 24,602 Holstein, 4,309 Guernsey, 1,878 Jersey, and 892 Brown Swiss lactations. Each of these records conformed to the following specifications: (a) 2X milking, (b) production for less than 50 days calculated from a single test day, (0) first test day within 34 days of freshening, and (d) 10 consecutive monthly tests. Only the first 10 months of each record were used. Each record identified the cow, the herd in which the record was made, and contained information on the month and year of freshening, breed, age at freshening (in months), lactation number, identification of sire and dam, and production of milk and butterfat on test day. Milk production was re- corded to nearest one-tenth pound, and butterfat production was recorded to the nearest one-hundredth pound. 19 METHODS Variables Affecting Relationship of Total to Part Production Previous investigations by Lamb (37) and Lamb and McGilliard (38, 39) used components of variance to study the effects of breed, herd, age, parity, and season of freshening on the relationship between monthly and total produc- tion. The results indicated that breed and age or parity should be considered in extending incomplete records of both milk and butterfat. The effect of season of freshening appeared important for milk, but not as important for butterfat. Differences among herds were not important. The present study combined new data with the earlier data to increase the volume and reduce sampling errors. The availability of additional rec- ords made possible the verification of earlier results and allowed a more complete evaluation of the influence of season of freshening by providing a larger number of groupings. Factors for extending milk and butterfat records from each of 10 monthly tests were computed separately for sub-groups of various combinations of breeds, ages, parities, and seasons of freshening. Ratios of total production from ten test days to production on each test day were averaged for all rec- ords in each sub-group. Ratio factors for cumulative test days were obtained from factors for individual test days in the following manner. The recipro- cals of the factors for monthly production for the first 2 months were added 20 21 and the reciprocal of the sum was the factor for extending production for the first 2 cumulative months. The reciprocal of the factor for the third month was added to the sum of the reciprocals for the first 2 months and then re- ciprocated to obtain the factor for 3 cumulative months. Factors for succeed- ing months were obtained in a similar manner. Ratio factors for ages of freshening were computed for each of these 42 age groups: less than 20 months, 1 month intervals from 20 months through 59 months, and 60 months and over. Factors were obtained for the first, second, and a combination of all later lactations. Sets of ratio factors for each of the 12 calendar months were used to study the influence of season of freshening. The factors were grouped to- gether in all possible combinations of 3, 4, and 6 adjacent months to find the seasons of freshening with the largest difference between their respective ratio factors. Adjustment for season on the basis of this grouping should remove more of the variance due to season of freshening than adjustment for any other choice of grouping. Ratio factors were computed from 16, 272 lactation records used in ear- lier studies (37, 38, 39), and a separate set of factors was computed from an additional 15, 409 records. The ratio factors from the two sets of data were almost identical for Holsteins and agreed very closely for the other three breeds. Any differences between the two sets of factors for Guernseys, Jerseys, and Brown Swiss could be attributed largely to sampling due to the relatively small numbers of observations. Since the conclusions concerning the environmental influences were similar for the two sets of data and since 22 there were no practical differences between the ratio factors derived from each set, the two sets were combined in the final analysis. Genetic Parameters and Phenotypic Correlations The parameters needed to study the genetic relationships between total and part production are: (a) the repeatability and heritability of production for individual months, for cumulative months, and for the complete lactation; and (b) the genetic correlations between total and part records. Actual pro- duction of milk and butterfat on test day was used as the measure of produc- tion for this part of the analysis. In. order to study the genetic relationship between total and part produc- tion, the influence of environment must be removed as completely as possible. One way to do this is to standardize the environment in which all cows are placed so that any differences between animals are caused entirely by genetic differences. A second approach is to remove statistically the environmental differences. Statistical control is less expensive than physical control, but its effectiveness is limited by an incomplete knowledge of just what environ- ment prevailed or in estimating how much effect the particular environment had on each phenotype. Unfortunately, the first approach is practically im- possible, both physically and economically; therefore, statistical control is the only practical method available for use in studying large populations of dairy cattle. Failure to remove differences between herds generally causes estimates of genetic parameters for complete records to be too large. Presumably the 23 same is true for part lactations. Since breed, age, and season of freshening influence the amount of milk and butterfat produced, it becomes desirable to determine whether the influence of these three variables should also be re- moved when estimating genetic parameters of part records. Differences in part records due to age or season of freshening can be re- moved either by the use of appropriate correction factors or by performing the analysis within herds, ages, and seasons. Madden _e_t a_l_. (46) adjusted part records for age by using age correction factors which had been derived from 305-day lactation totals. They found that these factors were fairly suit- able for correcting the center months of the lactation, but were less applicable for the first and last months of the lactation. At the time the study being re- ported here was undertaken, factors were not available for adjusting either individual or cumulative months of a lactation for age or season of freshening. Since then, Searle (61) in New Zealand has reported multiplicative factors to correct monthly butterfat yields for age and first month on test. However, since dairying is seasonal in New Zealand, only three months were considered for first month on test, and ages were recorded to the nearest year only. This restricts the application of these factors almost entirely to data from New Zealand. With no appropriate correction factors for age or season of freshening available, two alternatives were possible: (a) derive correction factors for age and season of freshening from all the available data and then reapply them to the same data in order to make the correction as exact as possible, or (b) perform the analysis on a within-herd-age-season basis. The analysis within 24 classifications sets aside the variation due to differences between units, such as ages or herds, by including in the analysis only those differences that exist within the unit. This method should be even more exact in removing differ- ences since it sets them aside rather than trying to correct for them. The use of correction factors does have the advantage that all of the data are usable, whereas with the within—classification method there must be a mini- mum of two observations within each classification in order to measure differ- ences. Thus, some of the data may be lost in this method. Considerable extra time, effort, and cost are involved in developing and applying correc- tion factors in addition to their providing a less exact removal of differences; therefore, the within-classification method was used in this study. The vari- ation due to differences between herds, between ages, between seasons, and possible interactions between them was eliminated by analyzing only the differences which occur within an age-season-herd group. Because of the relatively small number of records for Guernseys, Jerseys, and Brown Swiss, only the Holstein records were used to estimate the genetic parameters and the phenotypic correlations. Repeatability and phenotypic correlations Repeatability is herein defined as the coefficient of correlation between the same part of different lactations by the same cow. The coefficient of correlation between different parts of the same lactation or between a part of one lactation and the total of a succeeding lactation is designated simply as a phenotypic correlation to distinguish this from repeatability and from a 25 genetic correlation which will be defined later. The same data were used to calculate both repeatability and phenotypic correlations; hence, the methods used are included in the same section. Estimates of repeatability for parts of first and second lactations sep- arate from later lactations are needed because so relatively little is known about the producing ability of the cow at these early ages. Several workers (3, 18, 50, 59, 64) have reported that the repeatability of adjacent records was higher than that of non—adjacent records. For these reasons estimates of repeatability were obtained from correlations between first and second lactations, between second and third lactations, between all later adjacent records; and separate estimates were obtained by correlating first and third or later lactations, second and fourth or later lactations, and all non-adjacent third or later records. Repeatabilities were computed as product-moment correlations between total production for a first recorded lactation and the succeeding adjacent record, between total production for a first recorded lactation and a suc- ceeding non-adjacent record, between individual months of a first recorded lactation and the succeeding adjacent record, between individual months of a first recorded lactation and a succeeding non-adjacent lactation, between cumulative months for an early record and the succeeding adjacent record, and between cumulative months for a first recorded lactation and a succeeding non-adjacent lactation. Phenotypic correlations were computed as product- moment correlations between monthly and total production for the same lacta- tion, between cumulative and total production for the same lactation, between 26 monthly production for an early record and total production for the succeeding adjacent record, between monthly production for a first recorded lactation and total production for a succeeding non—adjacent record, between cumula- tive production for a first recorded lactation and total production for the succeeding adjacent record, and between cumulative production for an early record and total production for a succeeding non-adjacent record. When a cow had three or more complete records during the period studied. all combinations of pairing a given record with a later record were used. Re- peating records is not entirely correct, particularly when a record is used more than once in the same estimate. On the other hand, using each record only once eliminates part of the data when an odd number of records is in- volved and, in any case, requires setting up a system for selecting the pairs of records to be used. Some procedure between these two alternatives is optimum; however, since it is much easier mechanically to handle all combi- nations of pairs of records, records were repeated when more than two rec- ords for the same cow were available. Repeatabilities and phenotypic correlations were estimated from 10, 898 records from 4, 962 Holstein cows having two or more complete records in 2, 115 herds. Of this number, 4, 032 cows had two records, 886 had three records, and 44 cows had four complete records. Let x and y represent the two variables being correlated and x and jklm th yjklm denote the production for the 111 record made during the 1th season in h the kth age group of the jt herd. Then: 27 Z Z Z Z (xjklm) 2 = uncorrected total sum of squares, j k l m i5 WM 2: Z é‘jklm) (yjklm) = uncorrected total sum of products, 1 m HM wM Z 2 Z (X'kl. : uncorrected sum of squares among age-herd- l njkl. season groups, Z Z (21k— ) 2 : uncorrected sum of squares among age-herd groups, 3' k njk.. X. n. 2 2: i j. . . i : uncorrected sum of squares among herds. j J. . . The same notation applies for calculating the-sum of squares for y and for the within-classification sum of products. The dot notation signifies summa- tion over a subscript, and “jkl. is the number of observations in the 1th kth age group in the jth herd. season for the The effects of herd, herd and age, and herd, age and season of fresh- ening were removed separately by subtracting first the uncorrected sum of squares and products among herds from the uncorrected total sums of squares and products, and then in each of two completely separate operations sub- tracting from the uncorrected total sums of squares and products the uncor- rected sums of squares and products among age—herd groups and among age- herd—season groups. In each case the remaining sums of squares and prod- ucts were used to calculate the product—moment correlations. Thus, 28 E r = xy 1ft! : product-moment correlation, where (Exx 37y) Exy -.- residual sum of products = uncorrected total sum of products minus uncorrected sum of products within classifications, Exx and By = residual sum of squares = uncorrected total sum of squares minus uncorrected sum of squares within classifications. Separate removal of the effects of herd, herd and age, and herd, age and season allows a comparison of the variation removed by each. Removing only the effects of herds will leave the largest number of degrees of freedom for the correlations; however, if age and season differences do influence re- peatability, removal of variation of herds, ages, and seasons should be more useful wherever this leaves enough degrees of freedom to give a stable estimate. In an analysis within classifications, multiple groupings may rapidly de- plete the number of degrees of freedom. On the other hand, broad groupings may not adequately remove the effects of the important environmental vari— ables. A balance is sought between stability with larger numbers and ade- quate removal of environmental correlations. The following reasoning was used to decide upon the age grouping to use. Conversion factors commonly used to adjust complete records for the effect of age at calving differ for monthly groups up to about 50 months of age, after which the groupings include more months per group. From a stand— point of adequate adjustment for age of f rcshening, monthly groupings would seem to be desirable, especially at younger ages. However, a preliminary 29 survey of the data showed that the many groups would use up more degrees of freedom than were available. Therefore, first lactations were grouped ac- cording to age at freshening as less than 24 months, 24 to 29 months, 30 to 35 months, and 36 months and more. Second lactations were grouped as less than 42 months and 42 months and more. Third and later lactations were not differentiated by age. Such grouping for ages, which narrows the limits for younger ages but leaves a broad limit for older ages, should facilitate remov- al of the effects due to age from the younger ages where the effects are apt to be larger and where interest in obtaining estimates of repeatability is great- est. Such a system of grouping should not seriously deplete the degrees of freedom. To facilitate removal of the effects of season of freshening, the records were grouped into the seasons defined in the section on environmental var- iables (April to July and August to March for milk, March to June and July to February for butterfat). Heritability Heritability is the fraction of the observed phenotypic variance caused by differences between the genotypes of the individuals. It is used in both a narrow and a broad sense. Used in the broad sense it refers to the whole genotype functioning as a unit and contrasts heredity with environment. But the genotype is not transmitted as a unit, instead its constituent genes segre- gate and recombine in new combinations. The genes may interact with each other in nonadditive ways, resulting in deviations due to dominance or to 3O epistasis. Heritability in the narrow sense includes only the average effects of the genes, i. e. , only the genie or additively genetic variance. The narrow definition is used to describe the fraction of differences between parents which are recovered in their offspring. Because of the methods used to estimate heritability, the values obtained are generally somewhere between the broad and narrow definitions. In statistical terms the definition of heritability in the broad sense is: 2 2 + 2 * 2 “I; ~ 9i “2 «.2 2 2 6P 6gIJd+Ji+Je+reh and in the narrow sense is: iii 6; h2=€::6:+0’:46i2+6': +031. where 6: = additively genetic or agenic variance, 6 (21 = variance due to dominance, 0'? = epistatic variance, 6 ‘23 = environmental variance, 63h .-. variance due to heredity-environment interaction. Estimates of heritability apply to a particular characteristic and to a particular population in a specific environment. Methods for estimating heritability are based on resemblances between relatives and depend upon 31 being able to measure the extent to which related individuals are more like each other than unrelated ones. The two methods which are most frequently used on dairy cattle populations are the intra-sire regression of daughter on dam and the correlation between paternal half-sibs. The resemblance between dams and their daughters is generally more useful because (a) sampling errors are less important in correlations be- tween closely related individuals than between more distantly related ones. Heritability is equal to twice the daughter-dam regression but four times the correlation between paternal half-sibs; therefore, sampling errors are multi- plied by two in the first case and by four in the second case. (b) Less en- vironmental correlation is likely to be included in daughter-dam regressions than in correlations between contemporaries. (c) In most non-experimental data the daughter-dam regression dodges correction for system of mating since the differences being investigated are only between females mated to the same sire. The half-sib correlation method is useful in that (a) half-sib populations are more likely to be unselected than are parents. (b) In data limited to only a few years there may be more data available for a half-sib analysis than for a daughter-dam regression. The regression of daughter on dam was used in this study. A total of 3, 555 Holstein daughter-dam pairs was used for this analysis. The same data were also used to estimate genetic correlations. 32 Heritability (h2) can be expressed as: 112 3 2b, where E b : “if z; intra—herd-«SIre regressmn of daughter on dam. xx Let x represent production for dams and y represent production for the 1th daughters. Th en xjkl denotes production for the record made by the dam kth -th h sire in the j of a daughter of the erd and yjkl denotes production for the 1th record made by a. daughter of the kth sire in the jth herd. Then, 0 Z Z Z: (xjkly : uncorrected total sum of squares for ' 1 production of dams, Z X Z (xjk1)(yjkl) : uncorrected total sum of products, j k l (x 2 ' Z Z '.k z uncorrected sum of squares for production of dams j k njkL among herd-sire groups, :2: (xjk 2 j(yj k.) : uncorrected sum of products among herd- j sire groups. The influence of sire and herd was removed by analyzing on a within-herd- sire basis. The uncorrected sums of squares and products among herd-sire groups were subtracted from the uncorrected total sums of squares and prod- ucts to obtain the intra—herd-sire sums of squares and products. Hence, Exy intramherde-Sire sum of products, E xx intra-herd-sire sum of squares for production of dams. 33 The daughter-dam pairs were separated into the following six groups to remove the effect of age from the heritability of part records: first lactation for both daughter and dam; first lactation for daughter, second lactation for dam; first lactation for daughter, third or later lactation for dam; second lactation for both daughter and dam; second lactation for daughter, third or later'lactation for dam; and third or later lactation for both daughter and dam. Within each of these groups heritability was estimated on the within-herd-sire basis for monthly production, cumulative production, and total production. Inclusion of season of freshening as one of the variables in this portion of the study reduced the number of degrees of freedom to almost zero, neces- sitating omission of season of freshening from the analysis. The restrictions placed upon the data by analyzing on a within-herd—sire basis combined with dividing the dam-daughter pairs into groups according to the lactation number of both the daughter and the dam reduced the number of degrees of freedom to the point where sampling caused the resulting estimates to be quite erratic. To overcome this, the within-herd-sire sums of squares and products were pooled over parity groups to reduce the number of separate estimates and to accumulate more degrees of freedom to increase the stability of the re- sults. Separate estimates were pooled by summing the sums of squares and products over the parity groups being pooled. Pooled estimates were obtained for first lactation for the daughter irrespective of the parity of the dam, for second lactation for the daughter and second or later lactation for the dam, for second or later lactations for both daughter and dam, and then all the data were pooled to give one over-all estimate. 34 The pooled estimate of heritability was: n 2 Z Exyi 2bC : l = 1 ’ where n E Z “i i n 1 be -_- pooled estimate of regression of daughter on dam, n Z Exy1 -, pooled intra—herdusire sum of products, i = l n Exxi = pooled intra-herd-sire sum of squares for dam's production, i denotes the parity groups over which the data were pooled, n = number of intra—sire-herd regressions of daughter on dam. In the above method of pooling, the regressions to be pooled are assumed to be independent, equal, and have homogeneous variances. Except for the situation to be described more fully later in which a dam's record may be re- peated, the regressions to be pooled were independent. The slopes of the lines were similar and appeared to be from the same population of regres- sions . The assumption of homogeneity of variances was checked by comparing the standard error of estimate for the regressions which were pooled. The standard error of estimate can be expressed mathematically as: 2 1/2 S 3 F3“ Eyy (Exy) , where yox _ (N 2) Exx 35 Sy . x :2 the standard error of estimate, Exx z intra-—herd~sire sum of squares for production of dams, Eyy : intra-herd-sire sum of squares for production of daughters, Exy = intra-aherd-sire sum of products, N = number of dam—daughter pairs. The standard errors of estimate fell within narrow ranges for both milk and butterfat for all estimates of regression which were pooled. The narrow range of these standard errors indicate that the deviations of sample points from the regression lines are small for all regressions and that the variances, which are the squares of the standard errors, are essentially equal. Thus the regressions being combined appear to be homogeneous and the method of pooling should be valid. Occasionally a dam had more than one daughter, and in many cases there was a different number of complete records available for the dam from that for the daughter (or daughters). When a dam had more than one record but only one daughter with a single lactation, the record made by the dam at the nearest age comparable to that of the daughter was used. When a dam had only a single record but had one daughter with multiple records or more than one daughter with one or more records each, the dam's record was repeated with each record by a daughter. In most cases each repetition of the dam's record fell in a different parity grouping, making duplication of the records by the dam a valid procedure since it introduces no systematic bias into the resulting estimates. Even when the parity groups 36 were combined the main effect of repeating retords for the dam was that the actual number of degrees of freedom became smaller than it appeared. Kempthorne and Tandon (32) considered three methods of weighting the records in a situation where some of the dams had more than one offspring. The three methods used to estimate heritability were: (a) repeat the dam's record with each daughter's record, (1)) average the production for all of the daughters of the dam and regress each unweighted average on the dam's rec- ord, and (c) weight the average production for the daughters of a dam and regress each weighted average on the dam's record. The authors pointed out that (a) would be valid if the correlation among the offspring of a dam were zero, while (b) would be valid if the correlation among members of each progeny group were one. The real situation in most animal material is intermediate to these two extreme conditions, although usually nearer to the former. The weighted regression method (c) should fall somewhere be— tween the other two estimates. From an actual sample of data the authors concluded that there was little difference between the three methods. They did note, however, that the estimate obtained from the weighted regression method was closest to the estimate resulting from repeating the record for a dam with each record by a daughter. The authors suggested that the small- ness of the difference between the estimates arose because a large proportion (71 percent) of the dams had only one daughter. In the study reported here approximately 78 percent of the dams had only one daughter. If single daughters with multiple records are counted as multiple daughters then 66 percent of the dams had only one daughter. :37 When both the dam and daughter had multiple records, the records made at the nearest comparable ages Were paired. Any excess records for a dam were discarded, while if the daughter had more records than the dam then the dam's record at the closest comparable age was repeated as above. The 3,555 dam—daughter pairs included 1,429 pairs with single observa- tions for dam and daughter, 468 dams with more than one daughter, each with one or more records for a total of 1,005) daughters with l, 526 records, and 259 dams with single daughters with multiple records for a total of 600 records. Thus 2, 156 dams had 2,753 daughters with 3,555 completed lacta- tions. Genetic correlations Observed phenotypic correlations bett‘vecn two characteristics x and y in the same individual may result from two kinds of causes: (a) the same or associated genes affect both traits (correlated genic effects), and/or (b) common environmental factors affect both traits. Genie values are the aver— age effects of the genes. Thus a genetic correlation is the correlation be— tween the genic values for two traits x and y measured in the same individual. In terms of the present study, the genetic correlations measure the extent to which the same genes affect produtirtion in the same individual during various parts of the lactation. The formula used for estimating genetic correlations between part and whole records was: 3b where x and y refer to production for dam and offspring, respectively, p and w refer to part and whole records, respectively, and Exy denotes the sum of products within herd and sire. The same data were used to estimate genetic correlations as were used to estimate heritabilities. Estimates of genetic correlations were made for the same six parity groups defined for estimating heritability. Genetic cor- relations were computed between monthly and total production and between cumulative and total production. The small numbers of degrees of freedom associated with each parity group resulted in erratic estimates of the genetic correlations. The sep— arate estimates were then pooled by summing the sums of products over the parity groups as described previously for heritabilities. The pooled estimate of a genetic correlation was: rec C .-. E1 6:ng 1;: (Bambi () 1p ,w n n : a . 12::1 (R5591 12:1 (”THY“) : pooled estimate of genetic correlation, 1/2 where rc 'xy)° : 1ntra-herd-31re sum of products for the 1 group, 1 n -.- number of intra~herd~sire Bllln of products, 1 denotes parity groups over which the data were pooled. 39 Pooled estimates of genetic correlations were obtained for first lactation for daughter irrespective of the parity of the dam, for second lactation for the daughter and second or later lactation for the dam, for second or later lactations for both daughter and dam, and then all the data were pooled to give one overs-all estimate. The same assumptions of independence and homogeneity of the estimates were made for pooling of genetic correlations as for pooling heritabilities. Even after the data were pooled, part of the sums of products were neg- ative. Both positive and negative sums of products can be expected in the numerator of (a) but are not normally expected in the denominator. When- ever the sums of products in the numerator were of opposite sign, the arith— metic mean of the numerator was used. The formula for calculating the pooled estimate of a genetic correlation then became: in: (EWW)i " ,2: (Exwyp)i r poGW 3 l t: 1 1 2 i1 (Expyp)i 1231 (Exwyw)i i=1 all In a few cases the sums of products were of opposite sign in both the numerator and denominator, in which case formula (a) was used. Whenever the sums of products were of opposite sign in the denominator but not in the numerator, the arithmetic mean was used for both. Then the formula for the pooled estimate of a genetic correlation became: 40 r . C0'pr ’3 (c). 31% 3.3% Relative Efficiency of Selection According to Lerner and Cruden (43), the relative efficiency of selection for a whole record by using a part record as the selection criterion is indi- cated by the ratio: —‘2Argw3T—, where the numerator represents genetic progress per generation in the whole record when selection is based on a part record and the denominator represents genetic progress when selection is based on the whole record. This ratio can be expressed mathematically as: [3G1 = 1G pr hW 6E)“, z/v (a) 2 6— ’ A Gw hw PW z/v where G and P represent genotype and phenotype, respectively, w and p refer to whole and part records, respectively, hW2 is the heritability for whole records and 6.1-3“, z/v is the selection differential. The same selec- tion differential is assumed for both methods of selection to compare their r G relative progress; hence, equation (a) becomes _‘l_2_. Since the pheno- typic expression of part records P is a function of the genotype G plus an P P environmental contribution Ep, 41 rG P Cov ()pr _ Cov GwGp + Cov Gpr W p” z: a f: (b)' mw cap (cw nap But the expected Cov (3pr is zero and drops out of the numerator. Since the phenotypic va mam-e of part, records ( Pp ) times the herltability of part r. - 2‘ -,.~- ‘ 4‘. - °. v 14”“ was. "4" '4‘ . 3 r 2 records (hp ,1. r qua: t; the genetic \-a,.z.....tan,t par 1. .r ecords ( Gp ), (b) can be written as c h Cov (3ng hp Cov GW ‘p *p .. y I: (Tow G'rp h. (ow C'Gp P The ratio (a) then becomes 1‘ h ) G .G + (0). Formula (3) v as used to compare progress in genetic merit for complete lactations when sel.or.‘-tion was on the basis of part records .rith progress when selection was based on complete records. When the estimated genetic correla- tions were greater than one, the value one rather than the actual estimated value was used in calculating the relative effiwzviencics of; selection. RESULTS AND DISCUSSION Variables Affecting Relationship of Total to Part Production Production records of dairy cows are influenced by many environmental factors. The effects of these same variables on the relationship between total production for the lactation and production during various portions of the lactation is of primary concern in developing factors for estimating total yield for the lactation from short—time records. This part of the study was under- taken to ascertain more clearly whether age, parity, breed, and season of freshening should be taken into account in extending both milk and butterfat records, and secondly, whether the age and season groupings used in earlier studies adequately remove the effects of these variables. Tables 1-4 present factors for four breeds for extending individual month- ly tests to 305 days. Separate factors are given for extending milk and butter- fat records. Each table contains factors which will adjust for age and season of freshening simultaneously and factors which will adjust for age alone. Fac- tors which will adjust only for season of freshening can be obtained from the tables by combining the factors for a season over all ages, each one weighted according to the proportion of records in that group. The last column in each table gives the factors to be used if adjustments are not made for either age or season of freshening. 42 43 Table 1. Ratio factors for extending monthly production for Holsteins according to age and season of freshening Milk 4 36 236 < 36 336 Over-all Test April Aug. - April Aug. - day -July March -July March (1, 409? (6,102) (3, 764) (13, 327) (7, 511L Q7, 091) (24, 602) 1 7.81 8.51 7.14 7.67 8.38 7.55 7.81 2 7.90 8.50 7.13 7.78 8.39 7.64 7.87 3 8.73 9.03 8.01 8.45 8.97 8.35 8.54 4 9.59 9.53 9.01 9. 18 9.54 9. 14 9.26 5 10. 32 9. 96 10. 06 9. 83 10. 03 9. 88 9. 93 6 10. 87 10. 35 11. 11 10. 48 10. 45 10. 62 10. 57 7 11. 38 10. 67 12. 28 11. 16 10. 80 11. 41 11. 22 8 11. 91 11. 17 13. 56 12. 25 11. 31 12. 54 12. 16 9 12. 90 12. 22 15. 69 14. 58 12. 35 14. 82 14. 07 10 15. 04 14. 96 21. 14 21. 26 14. 98 21. 23 19. 32 Butterfat <36 36-47 2 48 436 36-47 248 Over-all Test March July- March July— March July- day -June Feb. ~June Feb. -June Feb. (1, 060) (6, 451) ( 913) (4, 400) (2 , 635) (9, 143) (7, 511) (5, 313)Q1, 778)(24, 602) H 7. 78 8. 22 6. 94 7. 32 6. 77 7. 02 8. 16 7. 25 6. 97 7. 39 8.38 8.79 7.80 8.18 7.52 7.84 8.73 .12 .77 .14 3 9.04 9.35 8.68 8.94 8. 37 8.70 9.31 8.90 8.63 8.90 N) co q 00 4 9.80 9.83 9.55 9.58 9.23 9.42 9.82 9.57 9.38 9.57 5 10. 43 10. 19 10. 33 10. 11 10. 09 10. 13 10. 22 10. 15 10. 12 10. 16 6 10. 80 10. 51 10. 93 10. 64 10. 97 10. 80 10. 55 10. 69 10. 84 10. 72 7 11. 14 10. 74 11. 73 11. 17 12. 12 11. 48 10. 80 11. 27 11. 62 11. 30 8 11. 60 11. 08 12. 90 11. 95 13. 59 12. 48 11. 15 12. 11 12. 73 12. 11 9 12. 43 11. 89 14. 25 13. 54 15. 74 14. 64 11. 96 13. 66 14. 87 13. 74 10 14.38 14.05 18.30 17.78 21.40 20.56 14.09 17.87 20.75 18.09 aNumbers of records averaged to obtain the ratio factors. 44 Table 2. Ratio 13371018 for extending monti‘ly production for Guernseys according to age and season of freshening its; 436 2 36 _< 36 1?. 36 Over-all Test April Aug. - April Aug. -- day -July a Martin ~Ju1y Marc-h L 213} _ (1. 0361: ( 640) (2 42 0) (1, 249) (3, 060) (4, 309) 1 7.43 8.09 6.64 7.29 7.98 7.15 7.39 2 7.55 .8. 33 6.79 7.37 8.20 7.41 7.64 3 8. 57 9. 00 7.70 8, 45 8. 93 8. 29 8.48 4 9.57 9.64 8.96 9.36 9.63 9.28 9.38 5 10. 38. 10.20 10. 38 10. 2 10. 23 10.10 10. 14 6 11.52 10.54 11.82 10. 74 10.71 10.97 10.89 7 12.08 11. 10 13.25 11.44 11.27 11.82 11.66 8 12.56 11.41 14.89 12.69 11.61 13. 15 12.70 9 13.24 12.46 16.70 15.17 12.59 15.49 14.65 10 14. 62 15. 16 20. 51 21. 53 15. 07 21. 32 19. 51 _I}utterfat < 36 3647 e_- 48 < 36 36-47 248 Over-all Test March July- March July— March July- day -June Feb. -June Feb. -June Feb. L 206) (1., 043}( 169)( 708) L 4811(1, 702} (1, 249) L877)_(2,183)(4, 309) 1 8.39 8.88 7.19 7.67 7.02 7.41 8.80 7.57 7.32 7.80 2 8. 2 9.06 8.13 8.21 7.33 7.93 8.94 8.20 7.80 8.21 3 9.00 9.51 8.32 9.22 8.15 8.73 9.43 9.05 8.60 8.93 4 9.57 9.87 9.20 9.70 8.93 9.48 9.82 9.60 9.36 9.54 5 10. 7 10.19 10.21 10.16 9.89 10.08 10.17 10.17 10.04 10.10 6 11.11 10.38 11.41 10.68 11.10 10.72 10.50 10.97 10.80 10.71 7 11.13 10.72 12.27 11.15 12.44 11.29 10.79 11.37 11.54 11.29 8 12.03 10.76 13.28 11.86 14.40 12.31 10.97 12.13 12.77 12.12 9 12.41 11.49 14.71 13.32 16.26 14.49 11.64 13.59 14.88 13.68 10 14.01 13.44 18.05 17.07 20.68 19.93 13.54 17.26 20.10 17.62 8‘Numbers of records averaged to obtain the ratio factors. Table 3. Ratio factors for extending monthly production for Jerseys 45 according to age and season of freshening Milk < 36 2:36 <36 2:36 Over-all Test April Aug. - April Aug. - day -July March ~July March ( 100) ( 488) ( 276) (11014L ( 588) (1,290) (1,878) 1 7.27 7.95 6.60 7.24 7.83 7.11 7.33 2 7.26 8.18 6.73 7.56 8.02 7.39 7.59 3 8.12 8.99 7.63 8.48 8.84 8.30 8.46 4 9.43 9.74 9.15 9.44 9.69 9. 38 9.48 5 10.60 10. 26 10.50 10. 31 10.32 10. 35 10. 34 6 11. 55 10. 87 11. 84 10. 88 10. 99 11. 08 11. 05 7 12. 52 11. 15 13.52 11. 44 11. 38 11. 88 11. 72 8 12. 94 11. 53 15. 04 12. 65 11. 77 13. 15 12. 72 9 14. 07 12.75 17. 07 14. 73 12. 97 15. 22 14. 52 10 15.51 15.62 19.90 21.23 15.60 20.95 19.28 Butterfat < 36 36-47 2. 48 < 36 36-47 2:48 Over-all Test March July- March July— March July— day -June Feb. -June Feb. —June Feb. ( 82) ( 506) ( 67) i 306)i184) ( 733) ( 588)( 373) ( 917) (1,878) 1 8.29 8.74 7.00 7.60 7.30 7.50 8.68 7.49 7.46 7.85 2 8.21 8.77 7.53 8.02 7.66 7.80 8.69 7.93 7.77 8.09 3 8.72 9.22 8.12 8.76 8.26 8.58 9.15 8.64 8.51 8.74 4 9.61 9.75 9.77 9.55 8.96 9.41 9.73 9.59 9.32 9.50 5 10. 06 10. 02 10. 45 10.18 9. 86 10. 23 10. 03 10. 23 10. 16 10. 13 6 10. 52 10. 51 10. 95 10. 73 11. 05 10. 83 10. 51 10. 77 10. 88 10. 74 7 11.39 10.78 12.42 11. 19 11.94 11.44 10.87 11.41 11.54 11.31 8 12.14 11. 10 13.43 12. 35 13.63 12.45 11.24 12. 55 12.69 12.21 9 12. 71 12. 03 15. 16 13.55 16. 06 14.44 12.13 13. 84 14. 77 13. 75 10 14.29 14.48 18.69 19.44 19. 32 19.64 14.45 19. 30 19.57 17.92 aNumbers of records averaged to obtain the ratio factors. 46 Table 4. Ratio factors for extending monthly production for Brown Swiss according to age and season of freshening _Milk <36 2 36 < 36 a. 36 Over-all Test April Aug. — April Aug. - day -Julya March -July March . ( 49) ( 160) ( 233) ( 450) ( 209) ( 683) ( 892L 1 8.59 8.65 7.55 8. 08 8.64 7.90 8.07 2 8.38 8.73 7.46 8.22 8.64 7.96 8.12 3 8.49 9.31 8.01 8.74 9.12 8.49 8.63 4 9.35 9.58 8.97 9.31 9.53 9.19 9.27 5 10.25 9. 81 9.81 9.92 9.91 9.88 9.89 6 11.21 10. 32 10.94 10.29 10.53 10.51 10.51 7 11. 82 10. 61 12. 14 10. 89 10. 89 11. 32 11. 22 8 12. 05 10. 97 13. 27 11. 78 11. 22 12. 29 12. 04 9 12.59 12. 05 15.28 13. 59 12.18 14. 16 13.70 10 16. 07 14. 27 19. 15 19.09 14. 69 19. 11 18. 07 Butterfat ' < 36 36-47 2 48 <36 36-47 >48 Over—all Test March July- March July- March July- day -June Feb. -June Feb. -June Feb. ( 43) ( 166) ( 44) ( 110) ( 192) ( 337) ( 209) ( 154) (529L( 892) 1 9.19 8.82 8.05 7.97 7.55 7.77 8.90 8.00 7.69 8.02 2 9.11 9.16 8.62 8.76 7.70 8.37 9.15 8.72 8.13 8.47 3 8. 92 9. 62 8. 66 9. 25 8. 33 8. 96 9.48 9. 08 8. 73 8. 97 4 9.72 9.79 9.61 9.58 9.30 9.46 9.78 9.59 9.40 9.52 5 10. 19 9. 85 10.21 10.28 9.94 9.97 9.92 10.26 9.96 10. 00 6 10. 72 10. 32 10. 55 10. 38 10. 72 10. 62 10. 40 10. 43 10. 65 10. 56 7 10. 89 10. 58 11. 21 10. 95 11. 76 10. 99 10. 64 11. 03 11. 27 11. 08 8 11. 44 10. 66 11. 96 11. 36 13. 09 11. 70 10.82 11. 53 12. 20 11. 76 9 12. 18 11. 47 13. 05 12. 53 14. 84 13. 31 11. 62 12. 68 13. 86 13.13 10 15. 18 12. 74 17.04 14. 97 18. 80 17.96 13. 24 15. 56 - 18. 26 16. 62 aNumbers of records averaged to obtain the ratio factors. 47 Ratio factors for extending cumulative test-day production based on breed, age, and season of freshening are presented in tables 5—8. Separate factors are given for extending milk and butterfat records. The factors differ from those in earlier tables only in that they are calculated so as to extend cumulative test—day production rather than production from a single test day. Age and parity The factors for monthly production were larger for young cows than for older cows during the early months of the lactation but smaller during the later months of the lactation. This indicates that first-calf heifers do not produce as large a proportion of their total production for the lactation during the early months as do older cows, nor do they decline in production as rap- idly during the last months of the lactation; i. e. , the lactation curve is flat- ter for young cows than for older cows. This observation is in agreement with other reports (8, 9, 13, 23, 34, 37, 38, 44, 45, 46, 61, 71). Although the change in the shape of the lactation curve from younger to older ages was in general quite gradual, a distinct change in the factors for cumulative pro— duction occurred between 35 and 36 months of age for both milk and butterfat, and between 47 and 49 months for butterfat only. These are the ages roughly coinciding with the break between first and second lactations and between second and third lactations, respectively (13, 46). The data were grouped into broader age classes and factors computed for ages less than 36 months, 36 to 47 months, 48 to 59 months, and 60 months and over. Factors for ages less than 36 months were distinctly 48 Table 5. Ratio factors for extending cumulative production for Holsteins according to age and season of freshening Milk < 36 P: 36 < 36 E: 36 Over-all Test April Aug. - April Aug. - day —July March -July March (1, 409) (6, 102) (3, 764) (13, 327) (7, 511) (17, 091) (24, 602) 1 7.81 8.51 7.14 7.67 8.38 7.55 7.81 2 3. 93 4. 25 3. 56 3. 86 4. 19 3. 79 3. 92 3 2.71 2.89 2.47 2.65 2.86 2.61 2.69 4 2.11 2.22 1.94 2.06 2.20 2.03 2.08 5 1. 75 1.81 1.62 1.70 1.80 1.68 1.72 6 1. 51 1. 54 1. 42 1.47 1. 53 1.46 1. 48 7 1. 33 1. 35 1. 27 1. 30 1. 35 1. 29 1. 31 8 1. 20 1. 20 1. 16 1. 17 1. 20 1. 17 1. 18 9 1. 10 1. 10 1. 08 1. 08 1. 10 1. 08 . 1. 09 Butterfat <36 36-47 2 48 <36 36-47 £48 Over-all Test March July- March July- March July- . day -June Feb. -June Feb. -June Feb. (1, 060)(6,451) ( 913) (4,400) (2,635) (9, 143) (7,511) (5, 313)(11, 778)(24,602) H .‘1 .3 m on . 22 6. 94 . 32 6. 77 . 02 .25 3.67 . 86 3. 56 .70 3 2.79 2.92 2.58 2.70 2.50 2.60 .q q . 16 7.26 6.97 7.39 . 22 3. 83 3. 67 3. 87 .90 2.68 2.58 2.70 to 2" 3 as e: co Nissan 4 2.17 2.25 2. 03 2.10 1.97 2.04 2.24 2.09 2. 02 2.10 .84 . 70 1.74 1.65 1.70 . 83 1.73 1.69 1. 74 6 1.54 1.57 1.47 1.50 1.43 1.47 . 57 1.49 1.46 1.49 U1 2" m C H H H H 7 1. 35 1. 37 1. 31 1. 32 1. 28 1. 30 1. 37 1. 32 1. 30 1. 32 . 22 . 19 . 19 1. 17 . 18 1. 22 1. 19 1. 18 1. 19 9 1. 10 1. 11 1. 09 1. 09 1. 09 1. 09 1. 11 1. 09 1. 09 1. 09 on H N H H H H H 3Numbers of records averaged to obtain the ratio factors. 49 Tat-1e 6. Ratio fatter-s for extending cumulative production for Guernseys according to age and season of freshening 91.1.13. 4 36 -1“ 2: 36 ”1‘36 3 36 Over-mall Test April Aug. m April Aug. _. day ~July a Marc h wJuly March (213) (1,036). (640) (2,420) (1,249) (3.060) (4,309) 1 7.43 8.09 6.64 7.29 7.98 7.15 7.39 2 3. 74 4.11 3. 36 3. 71 4. 05 3. 64 3. 75 3 2.61 2.82 2.34 2.58 2.78 2.53 2.60 4 2.05 2.1.8 1.86 2.02 2. 16 1.99 2.03 5 1.71 1.80 1.58 1.68 1.78 1.66 1.70 6 1.49 1.54 1.39 1.46 1.53 1.45 1.46 7 1.33 1.35 1.2 1.29 1. 35 1.28 1.30 8 1.20 1.21 1.16 1.17 1.21 1.17 1.18 9 1 10 1 10 1 08 1.09 1 10 1 09 1 09 Butterfat < 36 36--47 2 48 < 36 ‘ 36.947 _23 48 Over-mall Test March July- March July—a March July— day -June Feb. -June Feb. —June Feb. ( 206) (1,043) ( 169) ( 703) ( 4.81) (1,702) (1,249)( 877) (2,183)(4,309) 1 8.39 8.88 7.19 7.67 7.02 7.41. 8.80 7.58 7.32 7.81 2 4. 18 4.48 3.82 3.97 3.59 3.83 4.43 3.94 3.78 4. 00 3 2.85 3.05 2.62 2.98 2.49 2.66 3.02 2.91 2.62 2.76 4 2.20 2.33 2.04- 2.28 1.95 2.08 2.31 2.23 2.05 2.13 5 1.80 1.90 1.7 1.86 1.63 1.72 1.88 1.83 1.70 1.76 6 1.55 1.60 1.48 1.59 1.42 1.48 1. 59 1.57 1.47 1.51 7 1.36 1.39 1.32 1.39 1.27 1.31 1.39 1.38 l. 30 1.33 .22 .23 1.20 1.24 -19 1.23 1.24 .19 1.20 9 1.11 1.11 1.11 1.14 1. 09 1.10 1.11 1.14 1.10 1.11 CD H H H H q H H aNumbers of records averaged to obtain the ratio factors. 50 Table 7. Ratio factors for extending cumulative production for Jerseys according to age and season of freshening n—‘MJ < 36 a 36 < 36 z 36 Over—all Test April Aug.- April Aug. - day -Ju1y March -July March ( 100)a ( 433) ( 276) (1,014) ( 533) (1,290) (1,373) 1 7.27 7.95 6.60 7.24 7 83 7.11 7.33 2 3.63 4. 03 3. 33 3.70 3.96 3.62 3.73 3 2 51 2 78 2 31 2.58 2 73 2 52 2 59 4 1.98 2.16 1.85 2.02 2.13 1.98 2.03 5 1.67 1.79 1. 57 1.69 1.77 1.66 1.70 6 1.46 1.54 1. 39 1.46 1.53 1.44 1.47 7 1. 31 1. 35 1. 26 ' 1. 29 1. 34 1. 28 1. 30 8 1. 19 1. 21 1. 16 1. 17 1. 21 1. 17 1. 18 9 1. O9 1. 10 1. O9 1. 09 1. 10 1. 09 1. 09 Butterfat 4 36 36-47 a- 48 <36 36-47 >— 48 Over-all Test March July- March July- March July- day -June Feb. -June Feb. -June Feb. ( 82) ( 506) ( 67) ( 306) ( 184) ( 733) ( 588) ( 373) ( 917) (1,878) 1 8.29 8.74 7.00 7.60 7. 30 7.50 8.68 7.49 7.46 7.85 2 4. 13 4. 38 3. 63 3. 90 3. 74 3. 82 4. 34 3. 85 3. 80 3. 98 3 2.80 2.97 2.51 2.70 2.57 2.64 2.95 2.67 2.63 2.73 4 2.17 2.28 1.99 2.10 2.00 2.06 2.26 2.08 2.05 2.12 .78 . 85 1.68 1. 74 1.66 1. 72 .84 1.73 1. 71 1.75 6 1.53 1.58 1.45 1.50 1.44 1.48 1.57 1.49 1.47 1.50 01 H H H 7 1.34 1.38 1. 30 1.32 1.29 1.31 1. 37 1.32 1.31 1.32 8 1. 21 1. 22 1. 19 1. 19 1. 18 1. 19 1. 22 1. 19 1. 19 1. 19 9 1. 11 1. 11 1. 10 1. 10 1. 10 1. 10 1. 11 1. 10 1 10 1. 10 aNumbers of records averaged to obtain the ratio factors. Table 8. 51 according to age and season of freshening Ratio factors for extending cumulative production for Brown Swiss Milk 4 36 E: 36 < 36 2 36 Over-all Test April Aug. — April Aug. - day -July a March -Ju1y March ( 49) ( 160) ( 233) ( 450) ( 209) ( 683) ( 892) 1 8. 59 8. 65 7. 55 8. 08 8. 64 7. 90 8. O7 2 4. 24 4. 34 3. 75 4. O7 4. 32 3. 96 4. 05 3 2. 83 2.96 2. 55 2. 78 2. 93 2. 70 2. 76 4 2.17 2.26 1.99 2.14 2.24 2.09 2.12 5 1. 79 1. 84 1. 65 1. 76 1. 83 1. 72 ‘ 1. 75 6 1. 54 1.56 1.44 1.50 1.56 1.48 1.49 7 1. 37 1. 36 1. 29 1. 32 1. 36 1. 31 1. 32 8 1.23 1.21 1. 17 1.18 1. 21 1.18 1. 19 9 1. 12 1. 10 1. 09 1. 09 1. 10 1. 09 1. 09 Butterfat < 36 36-47 2 48 < 36 36—47 a: 48 Over-all Test March July- March July- March July- day -June Feb. -June Feb. -June Feb. ( 43) ( 166) ( 44) ( 110) ( 192) ( 337) ( 209) ( 154) ( 529) ( 892) 1 9. 19 2 4. 57 3 3. 02 4 2. 31 5 1. 88 6 1. 60 7 1. 40 8 1. 24 9 1. 13 oat-boo H H .82 .49 .06 .33 .89 .59 .39 .23 .11 . 05 . 16 2. 81 ##G) 2. 17 1. 79 1. 53 1. 35 . 21 1. 11 H the H .97 .17 .88 .21 .82 .55 .36 .21 .11 00 H .55 .81 .62 .04 .69 .46 .30 .18 .10 4541 H .77 .03 .73 .15 .77 .52 .33 .20 .10 8. 90 . 51 3. 05 a; 2. 33 1. 89 1. 59 1. 39 . 23 1. 11 H [0.54] H H .99 .17 .86 .20 .81 .54 .36 .21 .11 (.04 .69 .95 .72 .11 .74 .50 .32 .19 .10 .02 . 11 2. 82 QC» 2. 17 1. 79 1. 53 1. 34 1. 20 1. 10 2:Numbers of records averaged to obtain the ratio factors. 52 different from all older ages for both milk and butterfat. Factors for ages 36 to 47 months differed from those for older ages for butterfat but not for milk; while for both milk and butterfat all ages above 47 months were similar enough to be combined into one age grouping. Thus, it appears that only two age groupings are necessary in extending milk records, whereas three age groupings appear useful for butterfat. Whether the use of a different number of age groupings for butterfat and milk is justified will depend somewhat on personal preference, on the mechanics of handling the extension of the records, and on the degree of pre- cision desired. Three age groupings for butterfat are expected to give more precise estimates of extended production than are two, but extra time and effort are involved in computing them. However, the rapid advances now being made in machine processing of records makes it appear probable that this problem will largely be eliminated and three age groupings for butterfat will be justified. The factors for the first lactation were distinctly different from those for the second or later lactations for both milk and butterfat for all four breeds. Those for second lactations for both milk and butterfat were so sim— ilar to to those for lactations three and above that the data for second lacta- tions were incorporated with data for later records and one set of combined factors obtained. The ratio factors for all four breeds indicate that. the shape of the lacta- tion curve for milk does not change much after 36 months of age, while the lactation curve for butterfat is flatter for cows 36~47 months of age than for 53 older cows. Although 366-47 months is th: approxrmate age for second lacta- tions. the factors did not indicate any apprecmhle difference in the shape of the lactation curve tetween second and later lactations. This suggests that the difference in the shape of the tutterf‘at curve for cows 36-47 months of age as compared to oldtfi-r LW') is strictly an age effect and not due to parity; whereas, the (11116:! ence in the shape of the lactation curve for cows less than 36 months as compared to that for older cows appears to be an effect of both age and parity. Since ages and parities almost coincide within the limits used here and, in general, have tr. e same effect it seems necessary for only one of these variables to be taken into account in extending records. The choice of which to use is the same for both. milk and butterfat and is similar to that reported for milk in an earlier study (38). From a pratgrtical standpoint, extension factors based on age should be used to extend first lactation records initiated after 36 months of CF. since factors based on parity will overestimate pro—- duction and favor an undesirable managemental situation. Factors for ages should also be used to ext end second lactation records started prior to 36 months, since using factors for parity in this case will underestimate produc» tion and penalize a desirable breeding practice. The remaining 90 percent of the time either age or parity factors will work equally well. However, parity is less frequently reported than is age, and all incomplete records can be ex- tended by factors for age irrespective of lactation number while factors for parity also should consider age 10 percent. of the time. In addition, if three sets of factors are deemed preferable for extending butterfat records, then thes fion: tend intl fact tors COW adjt und the t8!) the fer 01d eSt 54 these must be based upon age rather than parity. In view of these considera— tions, factors based on age are preferable to factors based on parity for ex— tending incomplete records, and factors based on parity have not been included in the tables. If the age of a cow is not known but the lactation number is, the age factors for less than 36 months should be used for first lactations, the fac- tors for 36-47 months used for second lactations for butterfat, and the re- maining factors used for all later lactations. The difference between the ratio factors for cumulative production for cows under 36 months and those for older cows indicates the importance of adjusting for age in extending part records. The factors for older cows underestimate the production for young cows. Based on what the total esti- mate should be for cows under 36 months, this underestimate for milk pro- duction amounts to approximately 10 percent for the first three cumulative months, gradually declining to 1 to 2 percent for 9 cumulative months. The difference is even larger for butterfat production, being about 10 percent for the first 3 cumulative months if the factors for 36-47 months are used to ex- tend records for cows under 36 months of age and as high as 17 percent for the first month and remaining over 10 percent for the first four cumulative months if the factors for ages 48 months and older are used. Again the dif- ference gradually declines to 1 to 2 percent by the end of 9 cumulative months. If the over-all factors are used to extend part records, records for older cows will be overestimated while those for younger cows will be under- estimated. Based on what the total estimate should be for cows under 36 months, I two-year- much as months. is smallt more the nearly ti Th are almt: and MCG for age 1 ilar to 12 W Th together to find I} reSpecti 55 months, the use of over-all factors will underestimate milk production for two-year-old cows as much as 6 to 7 percent and butterfat production as much as 9 to 11 percent when estimated from only one or two cumulative months. The error introduced by estimating with one over-all set of factors is smaller for older cows since the number of cows over 36 months of age is more than double that of the younger cows and the over-all factors are more nearly the same as those for older cows. The factors adjusting for age in extending cumulative production of milk are almost identical to the factors reported earlier by Lamb (37) and Lamb and McGilliard (38) from a smaller sample of data. The factors adjusting for age in extending cumulative production for Holsteins are also very sim- ilar to factors obtained by Madden 91 a_l. (46) from Holstein HIR data. Season of f reshening The calender months in which the lactations were initiated were grouped together in all possible combinations of three, four, or six adjacent months to find the seasons of freshening with the largest differences between their respective ratio factors. Adjustment for season of freshening on the basis of this grouping should remove more of the variation in factors due to season of freshening than adjustment based on any other grouping. A four and eight month system of grouping showed a larger difference for both milk and butter- fat for all breeds than did any combination of two six-month groupings, three four—month groupings, or four three-month groupings. However, the best season grouping for the two measures of production differed, with April to July a and JL by 0th ember sons 2 havet beret Vary fresh indie: 1‘9001 table: 56 July and August to March being the best grouping for milk and March to June and July to February being optimum for butterfat. This system of grouping for month of freshening differs from that used by other workers inasmuch as in most of the earlier studies months were either arbitrarily grouped into quarters according to the calendar, into sea- sons according to feeding practices, or into season which had been shown to have the most influence on total production. However, the conclusion reached here that season of freshening does influence the relationship of total to part production as shown by the large differences between factors for the different seasons and that adjustment should be made for season of freshening in ex- tending part records is in agreement with other studies (10, 11, 34, 37, 38, 39, 61, 71). Groupings for season of freshening found to be optimum in this study may not be optimum for all areas of the nation. Since climatic seasons do vary from one part of the country to another, factors adjusting for season of freshening may be needed for each different area of the country. These data indicate that season of freshening should be considered in extending part records under conditions prevalent in Michigan. The factors presented in tables 1—8 take these conditions into account. As far as can be ascertained, there are no other reports indicating that the season in which a cow freshens has a different effect on the relationship between total and part production for milk from what it does for butterfat. Previous studies of the influence of season of freshening on the relationship of total to part production have used the same seasonal grouping for butterfat 57 as for milk and have not been concerned as to whether the same grouping for seasons might not apply to both measures of production. The choice of whether to use separate seasonal groupings for milk and butterfat must be made on an individual basis. The use of separate groupings will increase the accuracy of the extended records but may also make their extending more complicated. However, the increasingly widespread use of machine processing of records makes it appear feasible that separate group— ings for seasons for milk and butterfat will not present any major problem. In case the decision is to use the same grouping for milk and butterfat, the grouping for milk (April to July and August to March) is best. This will not remove as much of the seasonal effect from the extended butterfat records as will the optimum grouping, but it will remove more than will the use of the grouping for butterfat (March to June and July to February) on milk records. The factors for monthly production for both milk and butterfat are, in general, larger for the eight-month fall and winter season than for the four- month spring and summer season for the first four months of the lactatiOn but are smaller during the remaining months of the lactation. In other words, the lactation curve is flatter for cows freshening during the fall and winter months. It is quite common that because of less competition from other farm chores, better management is provided for cows freshening during the fall and early winter months. In addition, these same cows often get a boost in production from early spring pastures during the latter part of their lactation 58 when production normally drops more rapidly. On the other hand, cows freshening during the spring and early summer months do not receive as much of a boost in production from spring pasture; and then just when they need additional feed to maintain a high level of production, the pastures hit a late summer slump and production drops rather drastically. Other factors, such as temperature and humidity, probably play an important role also in affecting the shape of the lactation curve of cows freshening during different seasons of the year. The ratio factors for cumulative production for both milk and butterfat are larger for records initiated during the fall and winter months than for those started in the spring and summer season. The difference is largest for the first month where the factors for fall and winter months are approx- imately 8 percent larger for milk and 5 percent larger for butterfat than those for spring and summer months. This difference declines rapidly until it is almost negligible by the eighth cumulative month. Adjusting for season of freshening does not appear as important as adjusting for age at freshening because the difference between seasons is not as large as the difference between ages. However, accounting for season of calving does have practical importance. Since it is practically as easy to adjust for both age and season simultaneously as for age alone by using the factors presented in tables 1-8, it is recommended that both be adjusted for in extending part records. 59 131221 Factors for both cumulative and monthly production differ between breeds. Holstein and Brown Swiss factors for milk tend to be alike, while Guernsey factors resemble Jersey factors even more closely. The Guernsey and Jersey factors for cumulative production of butterfat are very similar to each other and fall approximately midway between those for Holsteins and Brown Swiss, which differ widely. Except for the first month, the Holstein factors for monthly production of butterfat are very similar to the factors for Guernseys and Jerseys, while the factors for Brown Swiss are larger during the early months and smaller during the latter months of the lactation than those for the other three breeds. Thus, both Holstein and Brown Swiss factors show a tendency for a flatter lactation curve for milk, but only the Brown Swiss factors show this tendency for butterfat. Apparently the butter- fat test increases more rapidly towards the end of the lactation for Brown Swiss than for the other three breeds. Because of this flatter lactation curve, Brown Swiss factors for both milk and butterfat, if applied to cumulative production for any of the other breeds, will overestimate 305-day production. Holstein factors will over- estimate cumulative Guernsey and Jersey milk production but underestimate cumulative Guernsey and Jersey butterfat production. Guernsey factors for both milk and butterfat will overestimate Jersey production for younger cows but underestimate it for older cows. However, the difference between Guern— sey and Jersey factors is so slight as to make little practical difference be- tween the two in actual use. The overestimates in all cases are larger during 60 early lactation, decrease as production for each succeeding month is added to the cumulative total and become almost. negligible after the eighth cumula- tive month. A comparison of the ratio factors indicates a definite difference between factors for extending milk records and those for extending butterfat produc- tion for at least the first eight cumulative months. Except for the first month for Brown Swiss and the first two months for Holsteins, the ratio factors for cumulative production of butterfat will overestimate milk production for the lactation in all breeds. These overestimates are larger for Guernseys and Jerseys than for Holsteins or Brown Swiss. Milk production for the lactation will be overestimated by factors for non-cumulative production of butterfat for the first five months but underestimated when extended by factors for butterfat for the last five months. The shape of the lactation curve for butter- fat is flatter than the shape of the curve for milk production; hence, separate factors should be used for extending milk and butterfat records to estimate more accurately 305—day yield. In View of the results obtained, breed, age, and season of freshening influence the relationship between total and part production and should be adjusted for in extending part records to a 305—day basis. Furthermore. separate factors should be used for extending milk and butterfat records. In order to remove adequately the effects of age from the extending of the rec-— ords, separate factors are needed for milk records initiated before 36 months of age and for those started at 36 months or older, while separate sets of factors are needed to extend butterfat records started at less than 36 months, 61 36 to 47 months, and 48 months or older. Season of freshening can be adjust- ed for by extending records started during a four month spring and summer period separately from the other eight months. Bhenotypic Correlations Phenotypic correlations between segments of lactations are useful to give an indication of the probable accuracy with which a part record can be extended to completion. A phenotypic correlation between the total and a part of the same record or between a part of one lactation and the total of a succeeding lactation can result from either environmental or genetic causes or a combination of both. If both the environmental and the genetic correlations between a total and a part record are positive and the correlation between the genes and the envi- ronment is positive, the resulting phenotypic correlation should also be posi- tive and fairly large. If both the environmental and genetic correlations are negative and the correlation between the genes and the environment is positive, the resulting phenotypic correlation should be negative and fairly large. If both the environmental and the genetic correlations are of the same sign but the correlation between the genes and the environment is negative, the re- sulting phenotypic correlation may be either positive or negative but should be close to zero. If the environmental and genetic correlations are of opposite sign or if one or both of them are zero, the resulting phenotypic correlation should be close to zero. 62 A small phenotypic correlation between the total and a part of the same record would indicate little or no value to extending part records. The larger the correlation is, the greater the expected accuracy with which a part rec- ord could be extended to full length. The phenotypic correlation reflects the frequency with which individual estimates may be expected to deviate in var- ious amounts from the actual record. Although a large positive phenotypic correlation between part. and total may indicate a large degree of accuracy for extending records, the genetic progress in total production to be achieved from selection based on part rec- ords is dependent upon the genetic correlation between the two traits. Al— though the phenotypic correlations may indicate that estimates of total pro- duction made from cumulative production for 6 or 7 months are accurate enough for all practical purposes, they do not indicate what effect the use of such an estimate may have on genetic progress. Genetic correlations and the relative efficiency of selection will be discussed in subsequent sections. Phenotypic correlations between production for a single month and total production for the same lactation are shown in table 9, while those between production for cumulative months and total production for the same lactation are given in table 10. The phenotypic correlations between monthly production and total yield are largest for the fifth month followed closely by the fourth and sixth months. For cows in their first lactation, production for the third month is almost as closely correlated with total production as is production for the fourth or sixth months, while for older cows the seventh month is the next most 63 Table 9. Phenotypic correlations between monthly production and total production for the same lactation for Holsteins Eflflk Lactation Month of lactation number D F 1 2 3 4 5 6 7 8 9 10 1 1,628 .68 .80 .84 .86 .86 .85 .83 .77 .73 .60 2 2,311 .62 .76 .79 .83 .85 .85 .83 .80 .71 .55 3a 5,737 .54 .71 .78 .81 .84 .83 .82 .77 .69 .54 Butterfat Lactation Month of lactation number D F 1 2 3 4 5 6 7 8 9 10 1 1,628 .71 .75 .81 .83 .82 .80 .78 .73 .70 .56 2 2,311 .62 .71 .75 .80 .81 .81 .79 .76 .68 .56 3a 5,737 .61 .70 .75 .77 .78 .80 .79 .75 .70 .57 aThird or later lactation. Table 10. 64 Phenotypic correlations between cumulative production and total production for the same lactation for Holsteins Milk Lactation Number of cumulative months number D F 1 2 3 4 5 6 7 8 9 1 1,628 .68 .81 .87 .91 .93 .95 .97 .98 .99 2 2,311 .62 .76 .83 .87 .91 .93 .96 .98 .99 3a 5,737 .54 .70 .79 .84 .89 .92 .95 .97 .99 Butterfat Lactation Number of cumulative months number D F 1 2 3 4 5 6 7 8 9 1 1,628 .71 .81 .86 .90 .93 .95 .97 .98 .99 2 2,311 .62 .74 .81 .86 .90 .93 .95 .97 .99 3a 5,737 .61 .74 .82 .86 .90 .93 .96 .98 .99 aThird or later lactation. 653 accurate predictor of total yitld 101‘ the la:. tation. The difference between first 1' alf heifers and mature cows suggests that the condition of the older cows at the time of freshening may influence the early months of the lactation in ways that do not carry through for the com- plete lactation, thereby reducing the value of early months for estimating total yield for the lactation. On the other hand, early production of first calf heifers may not be as easily influenced by conditioning prior to freshen» ing or condition prior to freshening may affect the entire record. In all cases the correlations between the first and last months and total yield are the low- est, indicating that these months are more subject to temporary influences than are the center months of the lactation. The correlations between monthly production and total production for the same lactation are larger for first lactations than for later lactations indi— cating that yield for the first lactation can be more accurately estimated from a single test than can production for later lactations. Correlations for second lactations are also larger than those for third and later making second lacta- tions next best in accuracy of estimating from a single test. These results suggest that mature cows may be more susceptible to temporary environmen- tal influences which affect some parts of the lactation but not other parts of the whole lactation than are younger cows, I)31'llt"l.llal‘ly those in their first lactation. It is also possible that different genes may be affecting production at different ages and that the genes operating at younger ages have more of an influence on both the part and the total record than do the genes Operating in mature cows. The same effect could also be obtained by an increase in 66 the variation between records as the age increased, with no change in either the genetic or the environmental influence on the relationship between total and part records. The correlations between monthly production and total yield are slightly larger for milk than for butterfat; thus, extended milk records should be slightly more accurate measures of the actual records than extended butter— fat records. The phenotypic correlations between cumulative and total production in- crease rapidly until the fifth or sixth month and then more slowly until the end of the lactation. The biggest increase in accuracy of predicting total records from cumulative production comes with the addition of the second month. Correlations reach . 90 by the fourth month for first lactation, by the fifth month for second lactations, and by the sixth month for third and later records. They are . 95 by the sixth month for first records and by the seventh month for later records, and reach . 99 by the ninth month for all records. The results of this study are in agreement with those of Kennedy and Seath (36) that cumulative production for the first four months is at least as valuable as any single month for predicting total production for the lactation. For all practical purposes, total yield for the lactation can be estimated accurately enough from cumulative production for 6 or 7 months to make waiting for the ten-month total needless. 67 The magnitude of the phenotypic correlations between monthly and total production and between cumulative and total production, and the months which are the most accurate for extending part records are in agreement with the results of other investigations (5, 13, 23, 31, 46, 54, 56, 59, 62, 69, 73). The phenotypic correlations between monthly production for a given lac- tation and total production for succeeding adjacent and non-adjacent lactations and between cumulative production for a given lactation and total production for succeeding adjacent and non-adjacent lactations are reported in tables 11—14. These correlations are of interest. in that they give an indication as to what degree of accuracy may be expected on the average in predicting the total of a future record of a cow from a monthly or cumulative part of a present record by the same cow. As would be expected, the accuracy of a part record in predicting a future record is much less than for predicting the total of the current record. Correlations between monthly production and total production for the same lactation reach . 86, whereas the highest cor- relation between monthly production and total produced for a succeeding lac- tation is . 54 for adjacent and . 51 for non-adjacent lactations. For cumula- tive production the correlations reach . 99 for the same lactation but only . 56 and . 53 for succeeding adjacent and non-adjacent records, respectively. The phenotypic correlations between monthly production in one lactation and total production for a succeeding lactation are small for the first month, increase steadily to the seventh month, and decline rapidly to the tenth month. The correlations are slightly larger for milk than for butterfat. In general, na- Table 11. Phenotypic. correlations between monthly production and total production for the Sllt‘t'WniFdlng adjacent lactation for Holsteins Milk Lactation Month of lactation numbera D F 1 2 3 4 5 6 7 8 9 10 I 1,246 35 40 43 .46 .46 4% .50 45 42 .31 2 955 .27 .35 .38 .45 .50 .51 .54 .54 .45 .33 b . . . . . 3 1,956 .56 .31 .37 .41 .44 .42 .45 .42 .37 .27 39481294.: Lactation Month of lactation L numbera D F 1 2 3 4 5 6 7 8 9 10 1 1,246 .29 .31 .38 .41 .38 .41 .42 .39 .37 .26 2 955 2.3. .30 .35 .44 .45 .45 .50 .48 .38 .33 3'0 1, 956 .22 .26 .32. .34. .373; .36 .41 .38 . 36 .29 allefers to the first recorded lactation of a pair of adjacent lactations. b . . Thlrd or later lactation. 69 Table 12. Phenotypic correlations between monthly production and total production for a succeeding non-adjacent lactation for Holsteins Milk Lactation Month of lactation number“ D F 1 2 3 4 5 6 7 3 9 1 332 .23 .31 .40 .39 .34 .42 .42 .33 .30 2 110 .35 .36 .40 .45 .47 .43 .51 .46 .34 3b 139 .16 .25 .27 .33 .39 .33 .41 .33 .23 Butterfat Lactation Month of lactation numbera D F 1 2 3 4 5 6 7 8 9 1 332 .23 .35 .35 .37 .26 .33 .30 .30 .25 2 110 .42 .41 .40 .46 .42 .39 .47 .43 .32 3b 139 .21 . 17 .24 . 35 . 33 . 36 . 39 . 33 . 33 aRefers to the first recorded lactation of a pair of non-adjacent lactations. bThird or later lactation. Table 13. Phenotypic mrrelations between cumulative production and total production for the succeeding adjacent lactation for Holsteins ---.-... k... . _--.--—_.—_._ .——-.-. hfijk Lac-tation _H_____ ”Nttgttgrjtiu‘rnulative months nu mbera D F 1 2 3 4 5 . 6 7 8 9 1 1,246 .35 .41 .44 .47 .48 .50 ..2. .53 .54 .3. 955 .27 .34 .38‘ .42 .46 .49 .51 54 .56 3b 1,956 .26 .31 .36 .40 .43 .45 .47 .49 .50 otter-fat Lactation Number of cumulative months tuunbera I)I? 1 2 3 4 5 6 7 3 9 1 1,246 29 .34 .37 .40 2 43 .45 .46 .47 2 955 2’ .39 .33 38 .42 .45 .48 50 .51 3b 1,956 22 ”7 .31 .35 .37 39 .41 .43 .44 aRcfers to the first recorded lat-tation of a pair of adjacent lactations. bThird or later lactation. 71 Table 14. Phenotypic correlations t..