- Email: [email protected]
Age Adjustment of Production Records: History and Basic Problems1
SYMPOSIUM: AGE ADJUSTMENT
Age Adiustment of Production Records: History and Basic Problems
1
A. E. FREEMAN Iowa State University, Ames 50010 Introduction
Few problems in dairy cattle breeding command as much interest and effort as the ageyield relation, implying its importance and lack of satisfactory solution. Adjusting both complete and incomplete records for age differences when phenotypes are expressed is necessary to compare genetic merit of females of different ages because yield increases with age to maturity then slowly declines. Progress has been made in exploring methodology and developing age-adjustment factors for the commercial dairy population. As the industry has changed (primarily from natural service progeny tests to multiple herd ones) and with easy availability of records and computers, emphasiS on removing biases in age adjustments has changed. Time will tell the adequacy of current methodology, but additional effort in both methodology and application should be productive. Most published work has been with completed lactations. Correction for age differences has received little attention for records in progress and terminal incomplete records (terminated for reasons other than a dry date), except incomplete records which have been extended then age adjusted. I will consider only complete lactations. The purpose of age correction to a mature basis is to correct a record for age only, that is, to estimate the cow's production under the same environmental conditions at maturity. This has been pointed out by Searle and Henderson (39), and its definition is necessary to discuss critically age factors and their effectiveness. Misunderstanding the purpose of age corrections has led to confusion. Development of Ideas
I will attempt to follow the development of knowledge in chronological order with selected works. Dependence of milk and milk fat yields on age has been prominent in literature since about 1900, though yield-age dependence was R.eceived July 23, 1971. lJournal Paper J-6976 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project 1053.
recognized even earlier. Gavin in 1912-13 stated the need for expressing a cow's ability to produce with a single number (9, 10). He further recognized that an important problem in estimating a cow's milking ability in later lactations from the first lactation was deciding on a figure to represent a cow's mature ability. He proposed maximum 3-day yield to measure phenotype and the lactation with the highest lifetime 3-day yield to measure mature production. This measure of phenotype was chosen, at least in part, because he thought it was relatively free of differences in length of lactation and time of service, and he adjusted it for age at calving and season of calving. In 1914, Pearl (35) published the law relating milk flow to age in dairy cattle; It was the equation, Y = a + bx + cx2 + d log x, where Y = amount of milk produced in a given time and x = age of the cow. Gowen in 1920 to 24 (11, 12, 13) working with large samples of data from Holstein and Jersey breeds substantially increased knowledge of age effects. He fitted curves of the type described by Pearl (35) and derived age correction factors for milk yield. He showed that coefficient of variation nearly was constant within age groups and yields were nearly distributed normally. He used regression techniques to describe effect of age on yields of milk, milk fat, solids-not-fat, and percentages of the last two. Up to this time, effects of selection, or culling, on age factors were discussed in literature. In 1928, Sanders (36) discussed the bias from culling in factors developed as gross comparisons. He avoided bias by comparing change in production from one lactation to the next of the same cow - a method known as paired comparisons. He recognized confounding effects of breeds, seasons, and service periods but did not mention bias in paired comparisons. After need for age-adjusting lactation records to compare cows of different ages was recognized, sets of factors were developed and used, coming mainly from data of breed associations. An example of development of gross factors and breeders' skepticism of their wide~ spread use is in the work of Norton (34) in 941
JOURNAL OF DAIRY SCIENCE
942
1932. Number of times milked per day was a problem. Sire proving work started on a national basis as part of the Dairy Herd Improvement Association's (DHIA) program in 1936 (1). Before 1932, sires were proven by the highest yearly record of both daughters and dams. From 1932 to 36, the highest 365-day record was used. Starting in 1936, age corrections to 2X, 305-day, mature-equivalent were used in the DHIA program. Ward and Campbell (43) in 1938 used regression techniques for age adjustments with New Zealand data. They recognized that herds, body weight, month of calving, and service period affected both mature and nonmature production but, as most authors did, judged the effects of these variables to be relatively minor to age differences. Use of most age corrections were within herds, but differences between herds were evident in estimating age adjustments. Johansson and Hansson (21) in 1940, with Swedish data, concluded that productive capacity depends not only on age but on number of pregnancies and length of calving interval. They used paired comparisons to develop age factors and worked with deviations from herdyear averages to evaluate their work. All research did not agree with adjusting records by age classifications. Gaines et al. (6, 7, 8) with fat-corrected milk as a measure of yield and age and live weight as independent variables came to substantially different conclusions from most authors about age-adjusting production records. They concluded it was biologically unsound to correct yield for age because age has no effect on yield independent of live weight. Their data were not large. In later study, they used cows with three or more lactations and based conclusions on regressions within cows of 4% fat-corrected milk on age and live weight. In 1949, Henderson (15) showed that least squares estimates of environmental effects were biased because of incomplete repeatability if records were greater or less than herd average. He pointed out that, theoretically, maximum likelihood estimates can take repeatability into account and use all records to estimate yearly environmental effects. He then used maximum likelihood methods to estimate age factors from a small set of data. The classical paper of Lush and Shrode (25) clarified some biases in estimating agecorrection factors from gross comparisons and paired comparisons. Three sources of bias are JOURNAL
OF
DAIRY
SCIENCE
VOL.
56,
No.
7
selection or culling with all animals not allowed to reach mature ages; time trends, either genetic or environmental; and incomplete repeatability. These sources are not independent. If effects of positive time trends that are wholly genetic or environmental and effects of effective culling are considered to act individually, biases in gross and paired comparisons factors might occur. Gross comparison factors are expected to be biased positively by culling and negatively by genetic trends, and envircnmental trends would cause little bias if records of all ages are affected equally. This is not likely because older cows would experience poorer environment when data are accumulated over time, causing a negative bias in the factor. Paired comparison factors would not be biased by genetic trends but would be by incomplete repeatability. Paired factors would be biased positively by environmental trends and negatively by culling. Lush and Shrode (25) compared bias in paired and ratio factors and showed that if repeatability is less than .5, bias in paired comparisons would be larger than in gross comparisons. Beardsley (3) applied the maximum likelihood method of Henderson (15) to data of the American Jersey Cattle Club. He included effects of herds, years of birth, years of production, cows, and ages in the model. The multiplicative ratio factors from this analysis were more like ratio factors used at the time than factors from paired comparisons. He stated it was not plausible that culling could account for large differences between paired and maximum likelihood factors. This application and earlier work of Henderson (15) constituted the first real use of methodology that attempted to account for all biases discussed by Lush and Shrode (25). Later work by Henderson (16) using the same methodology pointed out the biases in estimates of environmental trends caused by errors in age adjustment and repeatability. This general methodology was rewritten, expanded by Henederson et al. (17), and directed toward estimation of genetic and environmental trends but is generally the same theory applied to adjusting for age. In 1953, Kendrick (22) developed gross comparisons from DHIA data. He recognized that many other variables affect lactation records. However, he stated that at that time it was not practical to adjust lactations for many other variables but it was practical to adjust for age, times milked per day, and length to 305-days. This statement probably represented general thoughts of the industry in
SYMPOSIUM
1953 and the relatively complete acceptance of age-adjusting records. These factors were used extensively on a national basis for many years. Recent Research
During the late 1950's and 1960's, a great deal of effort was applied to age-yield relation. Most, if not all, of this work does not represent new ideas for sources of variability affecting the age-yield relation or new methodology. Rather, it represents quantitative exploration of the magnitudes of these effects, choices of appropriate models, and implementation of this work to estimate more accurately what a cow would have produced if she been mature under the same environmental conditions. The remainder of my discussion will be more problem-oriented than chronological. Differences Between Herds. A major source of bias likely to be troublesome in estimating age corrections is differences between herds. These influence the age-yield relation by ages being confounded partly with herds of different production and by differences between ages varying with production by herds. Searle and Henderson (38) developed additive age factors based on herd production. These corrections are regressions on age-corrected herd average. Their work indicated that age corrections should be larger in higherproducing than lower-producing herds and independent of the nonmature cow's production. This work outlined a method of computing herd-level factors and discussed inherent problems. On limited data, these herd-level factors were similar to multiplicative New York factors. Searle (37) applied the same techniques (38) to larger New Zealand herds and suggested that multiplicative factors introduced or magnified age by herd interactions whereas herd-level factors did not. He pointed out that herd-level factors gave all herdmates the same correction. This presumes that production of cows of different merit in the same herd increases by the same amount as they grow old. Multiplicative factors presume that production of cows of the same age in different herds increases in direct proportion to previous records, independently of herd effects except as the herd effect may have influenced cow's previous record. Neither presumption is necessarily true and failure would be detected as interaction of age with herd. Further work considering herd-level effects
943
on age-yield relation was by Lee (23) and by Hickman (18). Hickman (18) used standard Canadian age corrections and found a significant relation between age and yield remained in age-corrected yields. This is not an adequate test of age-correction factors, but he also found indication of herd by age interaction for milk yields. Season of Calving. Season of calving repeatedly has been associated with variations in lactation yield and change in production with age (14, 26, 27, 29, 30, 40, 44). Lee (24) found that 35% of variation in age at first freshening was associated with herd differences. He compared herd-level corrections with the Canadian BCA corrections. Regression within season and herd of age-corrected yield on age was large for both methods in first lactations but minor for BCA corrections in later lactations. Gravir and Hickman (14) found that season of calving (fall and spring) affected yield-age relation for all lactations and season of calving effects differed by lactation number. Differences in culling among cows within lactations seemed insignificant, but not so across lactations. Wunder and McGilliard (44) estimated effects of age and season and their interaction by maximum likelihood techniques. Cyclic variation usually associated with season of calving was masked partly by the interaction. Under drylot feeding conditions there was no consistent age by season interaction as under nondrylot conditions, thus suggesting a definable management effect on age-yield relation. Syrstad (40) in Norway came to conclusions similar to those of much work in the United States: seasonal effects were important and partly confounded with age at calving and lactation number, independent of age, had small effects on yields. However, increase in yield with age was similar for different production. McDaniel and Corley (26) using DHI data from all states found seasonal differences in data grouped into six regions. Seasonal differences of calving are important in the age-yield relation. Regional Differences. Regional differences in how production changes with age have been studied by USDA workers. By the early 1960's, sires had been evaluated in the nation long enough that regional differences in sire evaluation could be scrutinized. Age-correction factors were investigated, and Miller (30) compared gross and paired comparisons in different areas of the nation. Differences between JOURNAL
OF
DAIRY
SCIENCE
VOL.
56, No.
7
JOURNAL OF DAIRY SCIENCE
944
regions did exist; gross and paired comparisons differed most between Midwestern and Plains areas. This work was enlarged with gross compari~ sons by McDaniel and Corley (26), who con~ cluded that age corrections should be computed separately for milk and milk fat. Differences between regions, breeds, and seasons were judged important enough to be considered. These differences were large enough to cause biases in sire evaluation. In 1967, McDaniel et a1. (27) published sets of agecorrection factors for different regions and season of calving by breeds for milk and milk fat. Usage of these factors in all USDA sire and cow evaluation work became effective in February 1967 (27). Judging Effectiveness of Age Factors. Cri~ teria for judging effectiveness of age corrections is a difficult aspect of age correction. Difficulty stems from estimating the cow's pro~ duction had she been mature under identical environmental circumstances. Because this is physically impossible, all evluation of effective~ ness of age corrections must be indirect. Searle and Henderson (39) considered several criteria: repeatability; coefficient of variation; interaction of herd by age; and regressions within herd, year, and season of age-corrected yield on age. No single criterion or combination of criteria seemed adequate. Miller et al. (31) studied the factors of McDaniel et al. (27). They realized that elimination of all variability associated with age was not an absolute criterion by which age factors could be judged but reasoned that large age differences should not exist in age-corrected data. They computed the total and within herd-year-season regressions of matureequivalent production on age. The within regressions were larger than total regressions because of confounding of age with herd production. They concluded with sire evaluation based on deviations from herd-year-season averages, comparison of two sires could be biased by 500 kg of milk. Miller et al. (32) compared ranking of sires with factors of Kendrick (22) and McDaniel et al. (27) and other things constant. Sires ranked almost identically with the two procedures. Such an approach is useful for testing practical differences between procedures but not for testing unbiasness of either set of factors, as the authors realized. They also showed that for estimation of trends the two sets of factors gave large differences. How large must be differences in age factors JOURNAL
OF
DAIRY SCIENCE
VOL.
56, No. 7
to be important? The answer depends upon intended use. Lush and Shrode (25) suggested for estimating future production of a cow an error of .02 is inconsequential. They also pointed out that smaller errors could be consequential in specific instances, which is truer in sire evaluation now than many years ago. Sires now are compared between regions of the nation with daughers of varying ages in different years and seasons. Small differences are important in choosing sires for special mating to produce future bulls for artificial insemination. Such differences do not seem as important in choosing among sires for routine use within studs. Maximum Likelihood Estimation. Methods having the most appeal in estimating age corrections are those arising from mixed model techniques, described by C. R. Henderson as having the best linear prediction with unequal subclass numbers data (unpublished), or maximum likelihood estimates of age constants with a model that accounts for major sources of variability affecting age-yield relation. Miller et al. (33) used maximum likelihood techniques to estimate age effects. They used an easily understood example of why maxi~ mum likelihood estimators are superior theoretically to least squares estimators when random effects are in the model. For example, cows' records are not perfectly repeatable over years. Least squares estimates assume them constant (or perfectly repeatable) but maximum likelihood estimators do not and, therefore, are more realistic and unbiased. Their model included herd, cow, year, and age effects, and they compared maximum likelihood factors with those developed as gross and paired comparisons. Gross factors were more like the maximum likelihood factors than those from paired comparisons, particularly at older ages. An excellent example of a model combined with maximum likelihood estimation is the study of Miller et al. (29). They fitted monthage constants after accounting for effects of herds, years, and cows. This work presumably accounted for selection among cows by maximum likelihood technique resulting in addition of a ratio (error component of variance to the components of variance for cows) to the diagonal element of equation for each cow. This assumed that repeatability is known and constant for all lactations. Multiplicative factors then were computed from the agemonth constants. This work indicated that large interactions of month of calving by age
SYMPOSIUM
occurred, that monthly mature equivalent factors could not be grouped adequately into seasons, and ignoring such interactions could bias comparisons of individual records and sire evaluations. Wunder and McGilliard (44) through maximum likelihood also showed interaction of age by season to be important. Other work by Miller and Henderson (28) compared seasonal age factors from maximum likelihood with cows and sires as random variables to gross and paired comparisons. Maximum likelihood factors were intermediate between gross and paired comparisons adjusted for years. Other Problems. Another class of problems relative to age-yield relation is correcting out differences that are biologically real and not just age dependent. For example, Hickman and Henderson (19) estimated that heritability of maturity rate reflected in change of production with age was from one-third to onefourth that of production. Hillers and Freeman (20) showed that regression within sire of actual production on age differed significantly between sires. Other works (2,4, 5, 21) indicate that heritabilities and genetic correlations between different lactations are not constant while Van Vleck and Bradford (42) and Van Vleck (41) shows less difference between heritabilities of different lactations. If sires differ in rate of maturity of their daughters and production in lactations has different heritabilities and is controlled by different sets of genes, correction for age may be obscuring genetic differences. Because most sires are selected primarily on the daughter's first lactation, this may result in indirect selection for early maturity. Such selection is not necessarily detrimental. These examples do, however, point to a different class of age problems not thoroughly investigated. Adjusting records to an age other than a mature one has not received much research effort. This aspect of age-adjusting records should be considered for more unbiased age adjustments when records are corrected to a non-mature age. If this cannot be demonstrated, there is no reason to change the age base to one other than maturity. It is necessary to adjust for age differences to compare genetic merit of cows of different ages. Biases exist in age adjustment because of culling, time trends, and incomplete repeatability. Methodology has been developed to avoid major effects of these biases. Examination of DRI data has led to improvement in models describing major effects on age and
945
yield. Additional improvements surely will be made. References
(1) Arnold, F. J. 1956. Fifty years of D.H.IA. work. J. Dairy Sci., 39:792. (2) Barker, J. S. F., and Alan Robertson. 1966. Genetic and phenotypic parameters for the first three lactations in Friesian cows. Anim. Prod., 8:221. (3) Beardsley, J. P. 1952. A report of a study of age conversion factors to the Research Committee of the American Jersey Cattle Club. (Mimeo}. (4) Butcher, D. F., and A. E. Freeman. 1968. Heritabilities and repeatabilities of milk and milk fat production by lactations. J. Dairy Sci., 51:1387. (5) Freeman, A. E. 1960. Genetic relationships among the first three lactations of Holstein cows. J. Dairy Sci., 43:876. (Abstr.) (6) Gaines, W. L., C. S. Rhode, and J. G. Cash. 1940. Age, live weight and milk-energy yield in Illinois cows. J. Dairy Sci., 23: 1031. (7) Gaines, W. L., C. S. Rhode, and J. G. Cash. 1942. Age, live weight and milk-energy yield - a correction. J. Dairy Sci., 25:15. (8) Gaines, W. L., H. P. Davis, and R. F. Morgan. 1947. Within-cow regression of milkenergy yield on age and liveweight. J. Dairy Sci., 30:273. (9) Gavin, W. 1912. The interpretation of milk records. J. Roy. Scot. England, 73:153. (10) Gavin, W. 1913. Studies in milk records on the accuracy of estimating a cow's milking ability by her first lactation yield. J. Agr. Sci., 5:377. (11) Gowen, J. W. 1920a. Studies in milk secretion. V. On the variations and correlations of milk secretion with age. Genetics, 5:11. ( 12) Gowen, J. W. 1920b. Studies in milk secretion. VIII. On the influence of age on milk yield and butterfat percentage as determined from 365 day records of HolsteinFriesian cattle. Maine Agr. Exp. Sta. Bull. 293. (13) Gowen, J. W. 1924. Milk secretion. Williams and Wilkins, Baltimore, Maryland. (14) Gravir, K., and C. G. Hickman. 1966. Importance of lactation number, age and season of calving for dairy cattle breed improvement. Canadian Dep. Agr. Pub. 1239. (15) Henderson, C. R. 1949. Estimation of changes in herd environment. J. Dairy Sci., 32:706. (Abstr.) ( 16) Henderson, C. R. 1958. &timates of environmental trends and biases resulting from errors in age factors and repeatability. J. Dairy Sci., 41:747. (Abstr.) (17) Henderson, C. R., O. Kempthorne, S. R. Searle, and C. M. Von Krosigk. 1959. The estimation of genetic and environmental trends from records subject to culling. BiJOURNAL OF DAIRY SCIENCE VOL. 56, No. 7
JOURNAL OF DAIRY SCIENCE
946
ometrics, 15:192. ( 18) Hickman, C. G. 1962. Effects of level of herd environment. I. Relationship between yield and age. J. Dairy Sci., 45:861. (19) Hickman, C. G., and C. R. Henderson. 1955. Components of the relationship between level of production and rate of maturity in dairy cattle. J. Dairy Sci., 38:883. (20) Hillers, J. K., and A. E. Freeman. 1965. Differences between sires in rate of maturity of their daughters. J. Dairy Sci., 48:1680. (21) Johansson, I., and A. Hansson. 1940. Causes of variation in milk and butterfat yield of dairy cows. K. Lantbr. Akad. Handb., 79:1. (22) Kendrick, J. F. 1953. Standardizing DairyHerd-Improvement Association records in proving sires. U.S. Dep. Agr., Agr. Res. Serv., BDI-INF. 162. (23) Lee, A. J., and C. G. Hickman. 1969. Age and herd correction of first lactation milk yield records. J. Dairy Sci., 52:941. (Abstr.) (24) Lee, A. J., and C. G. Hickman. 1967. Yieldage regression in age-corrected records. J. Dairy Sci., 50:987. (Abstr.) (25) Lush, J. L., and R. R. Shrode. 1950. Changes in milk production with age and milking frequency. J. Dairy Sci., 33:338. (26) McDaniel, B. T., and E. L. Corley. 1966. Environmental Influences on age correction factors. J. Dairy Sci., 49: 736. (Abstr.) (27) McDaniel, B. T., R. H. Miller, E. L. Corley, and R. D. Plowman. 1967. DHIA age adjustment factors for standardization lactations to a mature basis. Dairy Herd Improvement Letter, ARS-44-188. U.S. Dep. Agr. (28) Miller, P. D., and C. R. Henderson. 1968. Seasonal age correction factors by maximum likelihood. J. Dairy Sci., 51 :958. (29) Miller, P. D., W. E. Lentz, and C. R. Henderson. 1970. Joint influence of month and age of calving on milk yield of Holstein cows in the Northeastern United States. J. Dairy Sci.. 53:351. (30) Miller, R. H. 1964. Biases in the estimation of the re!!ression of milk production on age. J. Dairy Sci., 47:855. (31) Miller, R. H., B. T. McDaniel, and F. N. Dickinson. 1970. Regression of mature-
JOURNAL
OF
DAIRY
SCIENCE
VOL,
56. No.
7
(32)
(33)
(34)
(35) (36)
(37) (38)
(39) (40) (41)
(42)
(43)
(44)
equivalent production on age at calving. J. Dairy Sci., 53:453. Miller, R. H., B. T. McDaniel, and R. D. Plowman. 1968. Effects of errors in the age adjustment of first lactations. J. Dairy Sci., 51:378. Miller, R. H., W. R. Harvey, K. A. Tabler, B. T. McDaniel, and E. L. Corley. 1966. Maximum likelihood estimates of age effects. J. Dairy Sci., 49:65. Norton, H. W., Jr. 1932. Adjusting records for comparison. Holstein-Friesian World, 29:799. Pearl, Raymond. 1914. On the law relating milk flow to age in dairy cattle. Proc. Soc. Exp. BioI. Med., 12:18. Sanders, H. G. 1928. The variation in milk yields caused by season of the year, service and dry period, and their elimination. J. Agr. Sci., 18:46. Searle, S. R. 1962. Age and herd effects in New Zealand dairy cow records. J. Dairy Sci., 45: 82. Searle, S. R., and C. R. Henderson. 1959. Establishing age-correction factors related to the level of herd production. J. Dairy Sci., 42:824. Searle, S. R., and C. R. Henderson. 1960. Judging the effectiveness of age-correction factors. J. Dairy Sci., 43:966. Syrstad, O. 1965. Studies on dairy herd records. II. Effect of age and season of calving. Acta. Agr. Scand., 15: 1. Van Vleck, L. D. 1966. Heritability estimates of milk production with different numbers of records per sire by herd subclass. J. Dairy Sci., 49:53. Van Vleck, L. D., and G. E. Bradford. 1966. Genetic and maternal influence on the first three lactations of Holstein cows. J. Dairy Sci., 49:45. Ward, A. H., and J. T. Campbell. 1938. The practical application of age conversion factors to dairy cattle production records. J. Agr. Sci., 28:509. Wunder, W. W., and L. D. McGilliard. 1967. Seasons of calving and their interactions with age for lactational milk yield. J. Dairy Sci., 50:986. (Abstr.)
Age Adiustment of Production Records: History and Basic Problems
1
A. E. FREEMAN Iowa State University, Ames 50010 Introduction
Few problems in dairy cattle breeding command as much interest and effort as the ageyield relation, implying its importance and lack of satisfactory solution. Adjusting both complete and incomplete records for age differences when phenotypes are expressed is necessary to compare genetic merit of females of different ages because yield increases with age to maturity then slowly declines. Progress has been made in exploring methodology and developing age-adjustment factors for the commercial dairy population. As the industry has changed (primarily from natural service progeny tests to multiple herd ones) and with easy availability of records and computers, emphasiS on removing biases in age adjustments has changed. Time will tell the adequacy of current methodology, but additional effort in both methodology and application should be productive. Most published work has been with completed lactations. Correction for age differences has received little attention for records in progress and terminal incomplete records (terminated for reasons other than a dry date), except incomplete records which have been extended then age adjusted. I will consider only complete lactations. The purpose of age correction to a mature basis is to correct a record for age only, that is, to estimate the cow's production under the same environmental conditions at maturity. This has been pointed out by Searle and Henderson (39), and its definition is necessary to discuss critically age factors and their effectiveness. Misunderstanding the purpose of age corrections has led to confusion. Development of Ideas
I will attempt to follow the development of knowledge in chronological order with selected works. Dependence of milk and milk fat yields on age has been prominent in literature since about 1900, though yield-age dependence was R.eceived July 23, 1971. lJournal Paper J-6976 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project 1053.
recognized even earlier. Gavin in 1912-13 stated the need for expressing a cow's ability to produce with a single number (9, 10). He further recognized that an important problem in estimating a cow's milking ability in later lactations from the first lactation was deciding on a figure to represent a cow's mature ability. He proposed maximum 3-day yield to measure phenotype and the lactation with the highest lifetime 3-day yield to measure mature production. This measure of phenotype was chosen, at least in part, because he thought it was relatively free of differences in length of lactation and time of service, and he adjusted it for age at calving and season of calving. In 1914, Pearl (35) published the law relating milk flow to age in dairy cattle; It was the equation, Y = a + bx + cx2 + d log x, where Y = amount of milk produced in a given time and x = age of the cow. Gowen in 1920 to 24 (11, 12, 13) working with large samples of data from Holstein and Jersey breeds substantially increased knowledge of age effects. He fitted curves of the type described by Pearl (35) and derived age correction factors for milk yield. He showed that coefficient of variation nearly was constant within age groups and yields were nearly distributed normally. He used regression techniques to describe effect of age on yields of milk, milk fat, solids-not-fat, and percentages of the last two. Up to this time, effects of selection, or culling, on age factors were discussed in literature. In 1928, Sanders (36) discussed the bias from culling in factors developed as gross comparisons. He avoided bias by comparing change in production from one lactation to the next of the same cow - a method known as paired comparisons. He recognized confounding effects of breeds, seasons, and service periods but did not mention bias in paired comparisons. After need for age-adjusting lactation records to compare cows of different ages was recognized, sets of factors were developed and used, coming mainly from data of breed associations. An example of development of gross factors and breeders' skepticism of their wide~ spread use is in the work of Norton (34) in 941
JOURNAL OF DAIRY SCIENCE
942
1932. Number of times milked per day was a problem. Sire proving work started on a national basis as part of the Dairy Herd Improvement Association's (DHIA) program in 1936 (1). Before 1932, sires were proven by the highest yearly record of both daughters and dams. From 1932 to 36, the highest 365-day record was used. Starting in 1936, age corrections to 2X, 305-day, mature-equivalent were used in the DHIA program. Ward and Campbell (43) in 1938 used regression techniques for age adjustments with New Zealand data. They recognized that herds, body weight, month of calving, and service period affected both mature and nonmature production but, as most authors did, judged the effects of these variables to be relatively minor to age differences. Use of most age corrections were within herds, but differences between herds were evident in estimating age adjustments. Johansson and Hansson (21) in 1940, with Swedish data, concluded that productive capacity depends not only on age but on number of pregnancies and length of calving interval. They used paired comparisons to develop age factors and worked with deviations from herdyear averages to evaluate their work. All research did not agree with adjusting records by age classifications. Gaines et al. (6, 7, 8) with fat-corrected milk as a measure of yield and age and live weight as independent variables came to substantially different conclusions from most authors about age-adjusting production records. They concluded it was biologically unsound to correct yield for age because age has no effect on yield independent of live weight. Their data were not large. In later study, they used cows with three or more lactations and based conclusions on regressions within cows of 4% fat-corrected milk on age and live weight. In 1949, Henderson (15) showed that least squares estimates of environmental effects were biased because of incomplete repeatability if records were greater or less than herd average. He pointed out that, theoretically, maximum likelihood estimates can take repeatability into account and use all records to estimate yearly environmental effects. He then used maximum likelihood methods to estimate age factors from a small set of data. The classical paper of Lush and Shrode (25) clarified some biases in estimating agecorrection factors from gross comparisons and paired comparisons. Three sources of bias are JOURNAL
OF
DAIRY
SCIENCE
VOL.
56,
No.
7
selection or culling with all animals not allowed to reach mature ages; time trends, either genetic or environmental; and incomplete repeatability. These sources are not independent. If effects of positive time trends that are wholly genetic or environmental and effects of effective culling are considered to act individually, biases in gross and paired comparisons factors might occur. Gross comparison factors are expected to be biased positively by culling and negatively by genetic trends, and envircnmental trends would cause little bias if records of all ages are affected equally. This is not likely because older cows would experience poorer environment when data are accumulated over time, causing a negative bias in the factor. Paired comparison factors would not be biased by genetic trends but would be by incomplete repeatability. Paired factors would be biased positively by environmental trends and negatively by culling. Lush and Shrode (25) compared bias in paired and ratio factors and showed that if repeatability is less than .5, bias in paired comparisons would be larger than in gross comparisons. Beardsley (3) applied the maximum likelihood method of Henderson (15) to data of the American Jersey Cattle Club. He included effects of herds, years of birth, years of production, cows, and ages in the model. The multiplicative ratio factors from this analysis were more like ratio factors used at the time than factors from paired comparisons. He stated it was not plausible that culling could account for large differences between paired and maximum likelihood factors. This application and earlier work of Henderson (15) constituted the first real use of methodology that attempted to account for all biases discussed by Lush and Shrode (25). Later work by Henderson (16) using the same methodology pointed out the biases in estimates of environmental trends caused by errors in age adjustment and repeatability. This general methodology was rewritten, expanded by Henederson et al. (17), and directed toward estimation of genetic and environmental trends but is generally the same theory applied to adjusting for age. In 1953, Kendrick (22) developed gross comparisons from DHIA data. He recognized that many other variables affect lactation records. However, he stated that at that time it was not practical to adjust lactations for many other variables but it was practical to adjust for age, times milked per day, and length to 305-days. This statement probably represented general thoughts of the industry in
SYMPOSIUM
1953 and the relatively complete acceptance of age-adjusting records. These factors were used extensively on a national basis for many years. Recent Research
During the late 1950's and 1960's, a great deal of effort was applied to age-yield relation. Most, if not all, of this work does not represent new ideas for sources of variability affecting the age-yield relation or new methodology. Rather, it represents quantitative exploration of the magnitudes of these effects, choices of appropriate models, and implementation of this work to estimate more accurately what a cow would have produced if she been mature under the same environmental conditions. The remainder of my discussion will be more problem-oriented than chronological. Differences Between Herds. A major source of bias likely to be troublesome in estimating age corrections is differences between herds. These influence the age-yield relation by ages being confounded partly with herds of different production and by differences between ages varying with production by herds. Searle and Henderson (38) developed additive age factors based on herd production. These corrections are regressions on age-corrected herd average. Their work indicated that age corrections should be larger in higherproducing than lower-producing herds and independent of the nonmature cow's production. This work outlined a method of computing herd-level factors and discussed inherent problems. On limited data, these herd-level factors were similar to multiplicative New York factors. Searle (37) applied the same techniques (38) to larger New Zealand herds and suggested that multiplicative factors introduced or magnified age by herd interactions whereas herd-level factors did not. He pointed out that herd-level factors gave all herdmates the same correction. This presumes that production of cows of different merit in the same herd increases by the same amount as they grow old. Multiplicative factors presume that production of cows of the same age in different herds increases in direct proportion to previous records, independently of herd effects except as the herd effect may have influenced cow's previous record. Neither presumption is necessarily true and failure would be detected as interaction of age with herd. Further work considering herd-level effects
943
on age-yield relation was by Lee (23) and by Hickman (18). Hickman (18) used standard Canadian age corrections and found a significant relation between age and yield remained in age-corrected yields. This is not an adequate test of age-correction factors, but he also found indication of herd by age interaction for milk yields. Season of Calving. Season of calving repeatedly has been associated with variations in lactation yield and change in production with age (14, 26, 27, 29, 30, 40, 44). Lee (24) found that 35% of variation in age at first freshening was associated with herd differences. He compared herd-level corrections with the Canadian BCA corrections. Regression within season and herd of age-corrected yield on age was large for both methods in first lactations but minor for BCA corrections in later lactations. Gravir and Hickman (14) found that season of calving (fall and spring) affected yield-age relation for all lactations and season of calving effects differed by lactation number. Differences in culling among cows within lactations seemed insignificant, but not so across lactations. Wunder and McGilliard (44) estimated effects of age and season and their interaction by maximum likelihood techniques. Cyclic variation usually associated with season of calving was masked partly by the interaction. Under drylot feeding conditions there was no consistent age by season interaction as under nondrylot conditions, thus suggesting a definable management effect on age-yield relation. Syrstad (40) in Norway came to conclusions similar to those of much work in the United States: seasonal effects were important and partly confounded with age at calving and lactation number, independent of age, had small effects on yields. However, increase in yield with age was similar for different production. McDaniel and Corley (26) using DHI data from all states found seasonal differences in data grouped into six regions. Seasonal differences of calving are important in the age-yield relation. Regional Differences. Regional differences in how production changes with age have been studied by USDA workers. By the early 1960's, sires had been evaluated in the nation long enough that regional differences in sire evaluation could be scrutinized. Age-correction factors were investigated, and Miller (30) compared gross and paired comparisons in different areas of the nation. Differences between JOURNAL
OF
DAIRY
SCIENCE
VOL.
56, No.
7
JOURNAL OF DAIRY SCIENCE
944
regions did exist; gross and paired comparisons differed most between Midwestern and Plains areas. This work was enlarged with gross compari~ sons by McDaniel and Corley (26), who con~ cluded that age corrections should be computed separately for milk and milk fat. Differences between regions, breeds, and seasons were judged important enough to be considered. These differences were large enough to cause biases in sire evaluation. In 1967, McDaniel et a1. (27) published sets of agecorrection factors for different regions and season of calving by breeds for milk and milk fat. Usage of these factors in all USDA sire and cow evaluation work became effective in February 1967 (27). Judging Effectiveness of Age Factors. Cri~ teria for judging effectiveness of age corrections is a difficult aspect of age correction. Difficulty stems from estimating the cow's pro~ duction had she been mature under identical environmental circumstances. Because this is physically impossible, all evluation of effective~ ness of age corrections must be indirect. Searle and Henderson (39) considered several criteria: repeatability; coefficient of variation; interaction of herd by age; and regressions within herd, year, and season of age-corrected yield on age. No single criterion or combination of criteria seemed adequate. Miller et al. (31) studied the factors of McDaniel et al. (27). They realized that elimination of all variability associated with age was not an absolute criterion by which age factors could be judged but reasoned that large age differences should not exist in age-corrected data. They computed the total and within herd-year-season regressions of matureequivalent production on age. The within regressions were larger than total regressions because of confounding of age with herd production. They concluded with sire evaluation based on deviations from herd-year-season averages, comparison of two sires could be biased by 500 kg of milk. Miller et al. (32) compared ranking of sires with factors of Kendrick (22) and McDaniel et al. (27) and other things constant. Sires ranked almost identically with the two procedures. Such an approach is useful for testing practical differences between procedures but not for testing unbiasness of either set of factors, as the authors realized. They also showed that for estimation of trends the two sets of factors gave large differences. How large must be differences in age factors JOURNAL
OF
DAIRY SCIENCE
VOL.
56, No. 7
to be important? The answer depends upon intended use. Lush and Shrode (25) suggested for estimating future production of a cow an error of .02 is inconsequential. They also pointed out that smaller errors could be consequential in specific instances, which is truer in sire evaluation now than many years ago. Sires now are compared between regions of the nation with daughers of varying ages in different years and seasons. Small differences are important in choosing sires for special mating to produce future bulls for artificial insemination. Such differences do not seem as important in choosing among sires for routine use within studs. Maximum Likelihood Estimation. Methods having the most appeal in estimating age corrections are those arising from mixed model techniques, described by C. R. Henderson as having the best linear prediction with unequal subclass numbers data (unpublished), or maximum likelihood estimates of age constants with a model that accounts for major sources of variability affecting age-yield relation. Miller et al. (33) used maximum likelihood techniques to estimate age effects. They used an easily understood example of why maxi~ mum likelihood estimators are superior theoretically to least squares estimators when random effects are in the model. For example, cows' records are not perfectly repeatable over years. Least squares estimates assume them constant (or perfectly repeatable) but maximum likelihood estimators do not and, therefore, are more realistic and unbiased. Their model included herd, cow, year, and age effects, and they compared maximum likelihood factors with those developed as gross and paired comparisons. Gross factors were more like the maximum likelihood factors than those from paired comparisons, particularly at older ages. An excellent example of a model combined with maximum likelihood estimation is the study of Miller et al. (29). They fitted monthage constants after accounting for effects of herds, years, and cows. This work presumably accounted for selection among cows by maximum likelihood technique resulting in addition of a ratio (error component of variance to the components of variance for cows) to the diagonal element of equation for each cow. This assumed that repeatability is known and constant for all lactations. Multiplicative factors then were computed from the agemonth constants. This work indicated that large interactions of month of calving by age
SYMPOSIUM
occurred, that monthly mature equivalent factors could not be grouped adequately into seasons, and ignoring such interactions could bias comparisons of individual records and sire evaluations. Wunder and McGilliard (44) through maximum likelihood also showed interaction of age by season to be important. Other work by Miller and Henderson (28) compared seasonal age factors from maximum likelihood with cows and sires as random variables to gross and paired comparisons. Maximum likelihood factors were intermediate between gross and paired comparisons adjusted for years. Other Problems. Another class of problems relative to age-yield relation is correcting out differences that are biologically real and not just age dependent. For example, Hickman and Henderson (19) estimated that heritability of maturity rate reflected in change of production with age was from one-third to onefourth that of production. Hillers and Freeman (20) showed that regression within sire of actual production on age differed significantly between sires. Other works (2,4, 5, 21) indicate that heritabilities and genetic correlations between different lactations are not constant while Van Vleck and Bradford (42) and Van Vleck (41) shows less difference between heritabilities of different lactations. If sires differ in rate of maturity of their daughters and production in lactations has different heritabilities and is controlled by different sets of genes, correction for age may be obscuring genetic differences. Because most sires are selected primarily on the daughter's first lactation, this may result in indirect selection for early maturity. Such selection is not necessarily detrimental. These examples do, however, point to a different class of age problems not thoroughly investigated. Adjusting records to an age other than a mature one has not received much research effort. This aspect of age-adjusting records should be considered for more unbiased age adjustments when records are corrected to a non-mature age. If this cannot be demonstrated, there is no reason to change the age base to one other than maturity. It is necessary to adjust for age differences to compare genetic merit of cows of different ages. Biases exist in age adjustment because of culling, time trends, and incomplete repeatability. Methodology has been developed to avoid major effects of these biases. Examination of DRI data has led to improvement in models describing major effects on age and
945
yield. Additional improvements surely will be made. References
(1) Arnold, F. J. 1956. Fifty years of D.H.IA. work. J. Dairy Sci., 39:792. (2) Barker, J. S. F., and Alan Robertson. 1966. Genetic and phenotypic parameters for the first three lactations in Friesian cows. Anim. Prod., 8:221. (3) Beardsley, J. P. 1952. A report of a study of age conversion factors to the Research Committee of the American Jersey Cattle Club. (Mimeo}. (4) Butcher, D. F., and A. E. Freeman. 1968. Heritabilities and repeatabilities of milk and milk fat production by lactations. J. Dairy Sci., 51:1387. (5) Freeman, A. E. 1960. Genetic relationships among the first three lactations of Holstein cows. J. Dairy Sci., 43:876. (Abstr.) (6) Gaines, W. L., C. S. Rhode, and J. G. Cash. 1940. Age, live weight and milk-energy yield in Illinois cows. J. Dairy Sci., 23: 1031. (7) Gaines, W. L., C. S. Rhode, and J. G. Cash. 1942. Age, live weight and milk-energy yield - a correction. J. Dairy Sci., 25:15. (8) Gaines, W. L., H. P. Davis, and R. F. Morgan. 1947. Within-cow regression of milkenergy yield on age and liveweight. J. Dairy Sci., 30:273. (9) Gavin, W. 1912. The interpretation of milk records. J. Roy. Scot. England, 73:153. (10) Gavin, W. 1913. Studies in milk records on the accuracy of estimating a cow's milking ability by her first lactation yield. J. Agr. Sci., 5:377. (11) Gowen, J. W. 1920a. Studies in milk secretion. V. On the variations and correlations of milk secretion with age. Genetics, 5:11. ( 12) Gowen, J. W. 1920b. Studies in milk secretion. VIII. On the influence of age on milk yield and butterfat percentage as determined from 365 day records of HolsteinFriesian cattle. Maine Agr. Exp. Sta. Bull. 293. (13) Gowen, J. W. 1924. Milk secretion. Williams and Wilkins, Baltimore, Maryland. (14) Gravir, K., and C. G. Hickman. 1966. Importance of lactation number, age and season of calving for dairy cattle breed improvement. Canadian Dep. Agr. Pub. 1239. (15) Henderson, C. R. 1949. Estimation of changes in herd environment. J. Dairy Sci., 32:706. (Abstr.) ( 16) Henderson, C. R. 1958. &timates of environmental trends and biases resulting from errors in age factors and repeatability. J. Dairy Sci., 41:747. (Abstr.) (17) Henderson, C. R., O. Kempthorne, S. R. Searle, and C. M. Von Krosigk. 1959. The estimation of genetic and environmental trends from records subject to culling. BiJOURNAL OF DAIRY SCIENCE VOL. 56, No. 7
JOURNAL OF DAIRY SCIENCE
946
ometrics, 15:192. ( 18) Hickman, C. G. 1962. Effects of level of herd environment. I. Relationship between yield and age. J. Dairy Sci., 45:861. (19) Hickman, C. G., and C. R. Henderson. 1955. Components of the relationship between level of production and rate of maturity in dairy cattle. J. Dairy Sci., 38:883. (20) Hillers, J. K., and A. E. Freeman. 1965. Differences between sires in rate of maturity of their daughters. J. Dairy Sci., 48:1680. (21) Johansson, I., and A. Hansson. 1940. Causes of variation in milk and butterfat yield of dairy cows. K. Lantbr. Akad. Handb., 79:1. (22) Kendrick, J. F. 1953. Standardizing DairyHerd-Improvement Association records in proving sires. U.S. Dep. Agr., Agr. Res. Serv., BDI-INF. 162. (23) Lee, A. J., and C. G. Hickman. 1969. Age and herd correction of first lactation milk yield records. J. Dairy Sci., 52:941. (Abstr.) (24) Lee, A. J., and C. G. Hickman. 1967. Yieldage regression in age-corrected records. J. Dairy Sci., 50:987. (Abstr.) (25) Lush, J. L., and R. R. Shrode. 1950. Changes in milk production with age and milking frequency. J. Dairy Sci., 33:338. (26) McDaniel, B. T., and E. L. Corley. 1966. Environmental Influences on age correction factors. J. Dairy Sci., 49: 736. (Abstr.) (27) McDaniel, B. T., R. H. Miller, E. L. Corley, and R. D. Plowman. 1967. DHIA age adjustment factors for standardization lactations to a mature basis. Dairy Herd Improvement Letter, ARS-44-188. U.S. Dep. Agr. (28) Miller, P. D., and C. R. Henderson. 1968. Seasonal age correction factors by maximum likelihood. J. Dairy Sci., 51 :958. (29) Miller, P. D., W. E. Lentz, and C. R. Henderson. 1970. Joint influence of month and age of calving on milk yield of Holstein cows in the Northeastern United States. J. Dairy Sci.. 53:351. (30) Miller, R. H. 1964. Biases in the estimation of the re!!ression of milk production on age. J. Dairy Sci., 47:855. (31) Miller, R. H., B. T. McDaniel, and F. N. Dickinson. 1970. Regression of mature-
JOURNAL
OF
DAIRY
SCIENCE
VOL,
56. No.
7
(32)
(33)
(34)
(35) (36)
(37) (38)
(39) (40) (41)
(42)
(43)
(44)
equivalent production on age at calving. J. Dairy Sci., 53:453. Miller, R. H., B. T. McDaniel, and R. D. Plowman. 1968. Effects of errors in the age adjustment of first lactations. J. Dairy Sci., 51:378. Miller, R. H., W. R. Harvey, K. A. Tabler, B. T. McDaniel, and E. L. Corley. 1966. Maximum likelihood estimates of age effects. J. Dairy Sci., 49:65. Norton, H. W., Jr. 1932. Adjusting records for comparison. Holstein-Friesian World, 29:799. Pearl, Raymond. 1914. On the law relating milk flow to age in dairy cattle. Proc. Soc. Exp. BioI. Med., 12:18. Sanders, H. G. 1928. The variation in milk yields caused by season of the year, service and dry period, and their elimination. J. Agr. Sci., 18:46. Searle, S. R. 1962. Age and herd effects in New Zealand dairy cow records. J. Dairy Sci., 45: 82. Searle, S. R., and C. R. Henderson. 1959. Establishing age-correction factors related to the level of herd production. J. Dairy Sci., 42:824. Searle, S. R., and C. R. Henderson. 1960. Judging the effectiveness of age-correction factors. J. Dairy Sci., 43:966. Syrstad, O. 1965. Studies on dairy herd records. II. Effect of age and season of calving. Acta. Agr. Scand., 15: 1. Van Vleck, L. D. 1966. Heritability estimates of milk production with different numbers of records per sire by herd subclass. J. Dairy Sci., 49:53. Van Vleck, L. D., and G. E. Bradford. 1966. Genetic and maternal influence on the first three lactations of Holstein cows. J. Dairy Sci., 49:45. Ward, A. H., and J. T. Campbell. 1938. The practical application of age conversion factors to dairy cattle production records. J. Agr. Sci., 28:509. Wunder, W. W., and L. D. McGilliard. 1967. Seasons of calving and their interactions with age for lactational milk yield. J. Dairy Sci., 50:986. (Abstr.)