- Email: [email protected]
Effects of Errors in the Age Adjustment of First Lactations
Effects of Errors in the Age Adjustment of First Lactations R. H. MILLER, B. T. McDANIEL, and R. D. PLOWMAN
U. S. Department of Agriculture, Beltsville, Maryland Abstract
justed for age by two different sets of multiplicative factors: a) the original Dairy Herd Improvement Association (DHIA) factors developed by Kendrick (5), and b) the new D H I A factors recently reported by McDaniel et al. (7). The latter factors employ different percentage corrections for two seasons of freshening, milk and fat, and various geographical regions of the United States.
The Dairy Herd Improvement Association (DHIA) age factors of Kendrick and MeDaniel were compared using 10,620 first lactations made in Michigan Holstein herds during the period 1961-63. The effectiveness of the alternative age adjustments was judged by the impact on sire ranking and on the statistical properties of the standardized records. Bulls were found to rank almost identically, regardless of the manner of age adjustment. Rank correlations between proofs based on actual and age-corrected records were about .95. There were significant regressions of age-adjusted production on age, for both sets of factors. I t was concluded that standard age adjustments may not be satisfactory in research applications requiring a high degree of accuracy.
Data
Searle and Henderson (9) discussed alternative ways of adjusting production records for variation in age at calving. They compared the Statistical properties of lactation records adjusted for age by three different procedures: (1) multiplicative, (2) herd level, and (3) additive corrections. Among the criteria considered were repeatability, coefficients of variation, and residual variance due to age. Searle and Henderson concluded that there is no single criterion for choosing a best method of age correction. They did not directly consider age adjustments from the standpoint of their effects on sire evaluation. Recently, many workers have suggested the use of separate age adjustments according to season of calving [Gravir and Hickman (2), McDaniel et al. (7), Syrstad {11), and Miller et al. (8)]. ~¢~an Vleek and Henderson (12) previously advocated simultaneous adjustnmnt for age and season effects. Butcher (1), Gravir and Hickman (2), McDaniel et al. (7), and Miller et al. (8) also reported that nfilk and fat age adjustment factors should be different, since fat per cent shows a slight decline from first lactation to maturity. The purpose of the present study was to compare the properties of first-lactation records adReceived for publication September 1, 1967.
The data were 10,620 first lactations (ages at calving less than 36 months) from Michigan Holstein herds using artificial service. These data have been described in detail by Miller et al. (9). There were 1,003 herd years represented and the calving dates were restricted to 1961-63. Approximately 25% of the records were by naturally sired cows, although all herds used artificial service to some extent. Only records of registered cows were used. All records terminated by culling were extended to a 305-day basis. There were 1,095 different sires represented, but only 40 artificial insemination (AI) bulls were studied individually. The remaining sires were allotted to a group cmuparison of non-AI bulls versus the remaining AI sires. Results and Discussion
Several aspects of age-adjusted records were considered. The primary objective was to determine whether the use of different sets of age factors would alter the ranking of bulls evaluated on the basis of first lactation daughters and contemporaries. The age range employed (up to 36 months) represents only about one-fourth of all lactations made in D H I A herds. However, major portions of the sire selection decisions in artificial insemination are based largely on progeny records in this age range. I n addition, certain statistical properties of age-adjusted first lactations were investigated. These included the effects of age adjustments on 1) coefficients of variation, 2) magnitude of estimated seasonal effects, 3) reduction in variation associated with age, and 4) year-to-year homogeneity of the regression of production on age. Effects on sire evaluation. I n another report (9), results of a study of three different meth-
378
379
L A C T A T I O N ADJUST1V[ENT
ods of sire evaluation are presented. This discussion considered the relative r a n k correlations a m o n g the three evaluation procedures. U s i n g the same data, sires were also evaluated on the basis of m a t u r e e q u i v a l e n t ( M E ) p r o d u c tion of t h e i r p r o g e n y , as estinmted b y the K e n drick age f a c t o r s a n d b y the new D t t I A factors r e p o r t e d b y M c D a n i e l et al. (7). A t the same time sires were also evaluated on the actual first l a c t a t i o n p r o d u c t i o n of p r o g e n y , u s i n g the following least-squares m o d e l :
where h~ is a n effect common to o b s e r v a t i o n s in the i ~h h e r d year, aj is a n effect p r e s e n t f o r all observations in the j*~ season of calving, b~ is a n element p e c u l i a r to the k TM y e a r of birth, (ab)j~ is a n effect possessed b y all observations in the j r , season a n d k th y e a r of birth, s~,~ is a n effect common to all d a u g h t e r s of the m TM sire in the 1~h g r o u p (the i n d e x 1 r e f e r s to two g r o u p s : G r o u p 1 r e p r e s e n t s all n o n - A I a n d res i d u a l - A I bulls, G r o u p 2 r e p r e s e n t s the 40 bulls t h a t were fitted u n i q u e l y ) , a n d e~j~,,~, is a r a n dora e r r o r p e c u l i a r to the n "~ d a u g h t e r of the m th sire. Table 1 contains the r a n k correlations a m o n g h e r d n m t e c o m p a r i s o n a n d least-squares sire proofs, f o r b o t h sets of age f a c t o r s a n d f o r b o t h milk a n d fat. I n addition, r a n k correlations between all M E measures of b r e e d i n g value a n d least-squares p r o o f s f o r actual milk a n d f a t yields are presented. The c o m p a r i s o n s of pl~imary i n t e r e s t in Table I are those between p r o o f s b a s e d on the diff e r e n t age f a c t o r s f o r the same m e t h o d of comp u t a t i o n . F o r example, r~ is the r a n k correlation f o r p r o o f s based on M E milk-yield a n d c o m p u t e d b y h e r d m a t e c o m p a r i s o n s f o r the two a l t e r n a t i v e a g e - a d j u s t m e n t procedures.
This correlation is 0.99. I n fact, all similar correlations (yield t r a i t held c o n s t a n t ) between sire e v a l u a t i o n s based on the different age factors are 0.99. A p p a r e n t l y , the use of different age a d j u s t m e n t f a c t o r s h a d essentially no imp a c t u p o n the relative s t a n d i n g of the 40 sires. The new D t I I A f a c t o r s a p p l y different p e r centage corrections to nfilk a n d f a t a n d to the two different seasons of calving ( N o v e m b e r J u n e , J u l y - O c t o b e r ) . The K e n d r i c k f a c t o r s a r e a h n o s t the same as the new D t t I A factors f o r milk in the N o v e m b e r - J u n e season in the Midwest. T h a t the use of different M E f a c t o r s would alter r a n k i n g v e r y little can be i n f e r r e d from the high rank correlations between M E p r o o f s a n d those based on a c t u a l p r o d u c t i o n , regardless of m e t h o d of c o m p u t a t i o n . F o r example, the r a n k correlations between leastsquares p r o o f s based on actual milk yield a n d those c o m p u t e d f r o m M E milk yield b y the h e r d n m t e c o m p a r i s o n are a b o u t .95. The correlations of p r o o f s b a s e d on a c t u a l yield with M E measures of b r e e d i n g value c o m p u t e d b y least s q u a r e s are a r o u n d .99. This indicates t h a t bulls which e n t e r service d u r i n g tile same general p e r i o d of time will r a n k a b o u t the same on actual first l a c t a t i o n p r o d u c t i o n as on a n M E basis. This s u p p o r t s the g e n e r a l l y held view t h a t t r u e c o n t e m p o r a x y c o m p a r i s o n s (based on only first l a c t a t i o n s ) will minimize r a n k i n g era'ors a r i s i n g f r o m inaccuracies of age factors. I t n m s t be r e m e m b e r e d t h a t these results do n o t a p p l y to bulls e n t e r i n g service a t w i d e r i n t e r v a l s of time, or to p r o o f s cmnpiled f o r all available lactations f o r bulls t h a t have been in selwice f o r widely different periods of time. Effects on analysis of ,variance. Table 2 presents the means, s t a n d a r d deviations, a n d coefficients of v a r i a t i o n f o r the v a r i o u s p r o d u c t i o n measures. The means f o r M E p r o d u c t i o n b a s e d
TABLE 1 Spearman rank correlations among different measures of breeding value of 40 artificia.1 insemination sires ~
1
2 3 4 5 6 7 8 9
2
3
4
5
6
7
8
.79
.99 .80
.79 .99 .81
.94 .77 .95 .78
.78 .96 .80 .96 .83
.93 .76 .94 .77 .99 .83
.76 .96 .79 .97 .82 .99 .82
i ----Herdmate milk (new D H I A factors). 3 = tterdmate milk (Kendrick factors). 5 =- Least-squares milk (new D H I A factors). 7 ----Least-squares milk (Kendrick factors). 9 ----Least-squares milk (actual production).
2 4 6 8 10
= IIerdmate f a t = Herdmate f a t = Least-squares --= Least-squares -= Least-squares
9
10
.94 .78 .95 .78 .99 .83 .99 .82
.79 .97 .81 .96 .84 .99 .84 .99 .84
(new D H I A factors). (Kendrick factors). f a t (new D t t I A factors). f a t (Kendrick factors). f a t (actual production).
g. DAIRY SCIENCE VOL, 51, NO. 3
380
Means,
M I L L E R , M c D A N I E L , AND P L O W M A N
standard
TABLE 2 deviations, and var£ation ~
Trait ME milk-new DHIA factors ME milk-Kendrick factors Actual milk ME fat-new DHIA factors ME fat-Kendrick factors Actual fat
Mean
coefficients SD ~
of
+1 +t +1 +[ +1 +1
CV b
6,310
1,034
16.38
6,405 5,082
1,047 838
16.34 16.48
224
35.6
15.87
233 185
36.9 29.6
15.82 16.00
,at r~
" P r o d u c t i o n in k i l o g r a n l u n i t s . " Within herd years.
on the new D H I A factors are lower than those computed for mature yield estimated by the K e n d r i c k factors. This is expected because the new D H I A factors are lower, on the average, for ages under 36 months in the Midwest region. The standard deviations were lower for ME yield estimated using the new D H I A factors, but the coefficients of variation were virtually identical, indicating that variability among records changed only as a result of changes in the mean. I n the computation of least-squares estimates of sire effects, the model also contained season and birth-year effects. The model was fitted on a within herd and year of calving basis. Two seasons (November-April and May-October) and f o u r birth-year categories (1958-61) were employed. The least-squares estimates of the effects are shown in Table 3 for the two different sets of age factors and for aetual production. All seasonal effects were statistically significant except for actual fat production. The magnitude of the estimates of seasonal effects varied greatly according to the manner of age adjustment. Seasonal effects were small for actual production, but were larger when the new D H I A factors were used to compute M E yield. Production adjusted by the K e n drick factors showed somewhat smaller seasonal effects compared to ME production based on the new D H I A factm's. The estimates of effects for the different sets of age factors are not strictly comparable because of the difference in the standard deviations. The differences in the estimates of seasonal effects may be due in p a r t to the presence of an age × season interaction. V a n Vleek and tIendet~on (12), W u n d e r and McGilliard (13), and Syrstad (11) have reported such an interaction for the entire age range. I t may be postulated that this interaction also exists within the first lactation age range~-'The new D H I A J. DAIRY SCIENCE ~OL. 51, NO. 3
+1 +1 +1 +1 +1 +1
+1 +1 +[ +1 +1 +1
d
+1 +l +l +1 +1 +1
+t +I +I +l +I +l
-d 45 "E
.5
z~
LACTATION
age factors are different for the two seasonal classifications and records age-adjusted by these factors exhibited the greatest amount of seasonal variation. I f an age X season interaction exists, the new D H I A factors may attribute a portion of the age × season interaction to seasons. The Kendriek factors are constant across seasons and the ME records exhibit less seasonal variance. I t might be supposed that apparent seasonal variance found in the analysis of the actual records would be increased because age was ignored in the analysis, but this apparently did not occur. The size of the birth-year effects also varied greatly, depending upon the mode of age adjustment. Birth-year differences were significant for actual production (P < .01), for ME yield based on the new D H I A factors (P .05). and nonsignificant for ME production computed with the Kendrick factors. These relationships may be influenced by the confounding of year of birth and age in the data. Late-calving heifers would be present only in 1958 or 1959 birth years, due to the way in which the data were selected. I f the age factors are inaccurate, birth-year comparisons may not be an appropriate measure of genetic changes, due to the presence of a bias arising from age differences. The trends for both actual production and ME yield based on the new D I t I A factors were distinctly negative. Estimates for actual production indicate a decrease of about 48 kg of milk from 1958 to 1961, a conclusion which is somewhat suspect. F o r example, the comparison of the 1958 birth year to the 1961 birth year may be biased for actual production, because the mean age of calving would be higher for 1958. This bias may also be present to a lesser extent for ME yield if age differences remain. That age effects biased the birth-year comparisons for actual yield was shown by repeating the analysis with the inclusion of a quadratic regression on age. When this was done there was no consistent pattern for birthyear effects and the F-value was nonsignificant. Effects on residual age variance and age X year variance. The following model was fitted
381
ADJUSTMENT
¢$
¢$
o
"a
O9
to the data:
Y , ~ = ~ + h. + ~ ( x . ~ - - ~ ) + ~.(x-~,. - ~x )
+
t~l~(X~--x)
+ / 3 ~ (x-~,~ - x~ )
+ e,~
where h,~ refers to the joint effects of the i t~ herd and the jt~ year of calving and X , ~ refers to the age at calving of the k t~ cow in the jth year and the i ~h herd. According to this model a separate quadratic regression is fitted for each year of calving. The procedure for fitting
¢9 °
J-. DAT]ZY S C I E N C E V O L . 51, NO. 3
382
M I L L E R , McDANIEL, AND PLOWMAN
this model has been described by H a r v e y (3). The results are presented in Table 4 f o r the different production criteria. I n all cases the average linear and quadratic regressions on age were significant, but the individual y e a r regressions were not significantly different f r o m the average coefficient. Table 4 indicates that neither set of age factors removed all of the variance associated with age at calving. The residual variance was greater for the new D H I A factors than f o r production based on the K e n d r i c k factors. Ho~z ever, the coefficient of variation based on the error mean square was only slightly larger for the new D H I A factors (16.7 to 16.6). The results in Table 4 indicate that there was little yearly variation in the relationship of age and first-lactation production, confirming the results of Hillers and F r e e m a n (4). A stepwise procedure was employed to discard nonsignificant effects f r o m the model. The analysis of variance and regression coefficients for the final model are given in Tables 5 and 6, respectively. I n interpreting these results it must be remembered that the ranges of ages and years studied were very limited. I f data characterized by wider variations in age and time are studied, interactions between ages and years may be observed. The results in Table 5 and 6 indicate that neither set of age factors was v e r y effective in reducing variation in first lactation records associated with age. The regressions of actual milk yield and the M E yields on age are shown graphically in F i g u r e 1. Searle and Henderson (10) pointed out that it may not be desirable for age factors to remove all the a p p a r e n t variance due to age, especially if other variables are confounded with age. Nevertheless, the present results indicate that the factors used removed very little of the age variation in production. The regression coefficients f o r M E yield in Table 6 are similar to those f o r actual production. These
% ,-d
o
TABLE 6 Regression coefficients for quadratic regression of production on age ~
£
Production measure
V
Linear
New D H I A factors Milk 216 -+47.5 Fat 7.7± 1.6 Kendrick factors Milk 159 -+48.0 Fat 5.4_+ 1.7 Actual production Milk 189 -+38.1 Fat 6.6-+ 1.4
Quadratic --15.5+_3.72 --0.1-+ .01 --13.2-+3.76 --0.1-+ .01 --11.8-+3.06 --0.1___ .01
Milk and fat coded in kilogram units. J. DAIRY SOIENCE VOL. 5], NO. 3
LACTATION
75~
650
.-J hA >- 500 -.A
• N[kl FRCTO~S & OLD F'ETORS X ~K~TURL YIELO
DEVIRTION FROM HERO RVERRGERGE [MO.l FIG. 1. l~egresslon of first lactation mature equivalent and actual milk Field on deviation of age from herd average age at first calving. results agree to some extent with those of Lee and I I i c k m a n (6), who found statistically significant regressions of nmture-equivalent production on age. They also found that the pooled within-herd regressions differed markedly f r o m one season of calving to another. Summary and Conclusions The D H I A age factors of K e n d r i c k (5) and McDaniel et al. (7) were compared, using 10,620 first lactations f r o m Michigan Holstein herds that had used artificial service. Calving dates were restricted to 1961-63. F o r t y A I bulls were studied individually, by both cont e m p o r a r y comparison and least-squares evaluation procedures. Bulls were found to rank almost identically when proofs were computed in the same manner, using both sets of age factors. These results s u p p o r t the view that the effect of age factor errors on sire r a n k i n g m a y be minimized by basing sire proofs on first lactations of progeny and herdmates. Differences in the results of analyses of variance due to the use of different age factors were studied. The new D H I A factors lowered the mean slightly, but the coefficients of variation were vi~¢ually identical. Seasonal effects were largest f o r M E production based on the new D H I A factors, intermediate f o r M E yield estimated by the K e n d r i c k factors, and smallest for actual production. I t was concluded that the new D H I A factors may enhance seasonal variance if an age × season interaction exists.
ADJUSTMENT
383
Birth-year comparisons were estimated by least squares as a criterion of genetic changes. The results varied greatly, depending upon the mode of age adjustment. I t was concluded that the comparisons may have been biased by age differences. Quadratic regressions on age were fitted on an intra-herd-year basis. The regressions were significant for both ME measures and for actual yield. The regressions were homogeneous f r o m one calving year to another. The residual variation was of comparable size for both ME measures, as reflected by the coefficients of variation. These results indicate that age factors computed for an over-all population may not fit individual subsets of the population v e r y closely. Research applications requiring precise age adjustment, such as the estimation of genetic trends, should consider other methods to account for age variation, such as regression. References (1) Butcher, ~ . F. 1966. Environmental and Genetic Factors Affecting the Composition of Cow's Milk. M.S. thesis, North Carolina State University. p. 108. (2) Gravir, K., and Hickma~, C. G. 1966. Importance of Lactation Number, Age, and Season of Calving for Dalry Cattle Breed Improvement. Publ. no. 1230, Canada Dept. Agr. (3) Harvey, W. R. 1964. Computing Procedures for a Generalized Least-Squares Analysis Program. Mimeographed report. (4) Hillers, J. K., and Freeman, A. E. 1965. Differences Between Sires in Ra£e of Maturity of Their Daughters. J. Dairy Set., 48 : 1680. (5) Kendrick, J. F. 1955. Standardizing DairyHerd Improvement Association Records in Proving Sires. Dairy Herd Improvement Letter, ARS-52-1. U.S. Dept. Agr. (6) Lee, A. J., and Hickmaa, C. G. 1967. YieldAge Regression in Age-Corrected Records. J. Dairy Sci., 50: 986. (Abstract.) (7) McDaniel, B. T., Miller, R. H., Corley, E. L., and Plowman, R. D. 1967. D H I A Age Adjustment Factors for Standardizing Lactations to a Mature Basis. Dairy Herd Improvement Letter, ARS-44-188. U.S. Dept. Agr. (8) Miller, R. H., Haxvey, W. R., Tablet, K. A., McDaniel, B. T., and Corley, E. L. 1966. Maximum Likelihood Estimates of Age Effects. J. Dairy Sci., 49: 65. (9) Miller, R. H., McDaniel, B. T., and Plowman, 1~. D. 1968. Compaxison of Three Methods of Sire Evaluation. J. Dairy Sci., 51: Accepted for publication. J. DAIRY SCIENCE VOL. 51, N0.
3
384
MILLER, McDANIEL, AND PLOWMAN
(10) Searle, S. R., and Henderson, C. R. 1960. Judging the Effectiveness of Age-Correction Factors. J. Dalry Sci., 43: 966. (11) Syrstad, O. 1965. Studies on Dairy Herd Records. II. Effect of Age and Season of Calving. Acta Agr., Scand., 15:1. (12) Van ¥1eck, L. D., and Henderson, C. R. 1961. Ratio Factors for Adjusting Monthly
J. DAIRY SOlEXC~:-VOL. 51, No. 3
Test-Day Data for Age and Season of Calving and Ratio Factors for Extending P a r t Lactation Records. J. Dairy Sci., 44 : 1093. (13) Wunder, W. W., aa~d McGilliard, L. D. 1967. Seasons of Calving a~d Their Interactions with Age for Lactational Milk Yield. J. Dairy Sci., 50: 986. (Abstract.)
U. S. Department of Agriculture, Beltsville, Maryland Abstract
justed for age by two different sets of multiplicative factors: a) the original Dairy Herd Improvement Association (DHIA) factors developed by Kendrick (5), and b) the new D H I A factors recently reported by McDaniel et al. (7). The latter factors employ different percentage corrections for two seasons of freshening, milk and fat, and various geographical regions of the United States.
The Dairy Herd Improvement Association (DHIA) age factors of Kendrick and MeDaniel were compared using 10,620 first lactations made in Michigan Holstein herds during the period 1961-63. The effectiveness of the alternative age adjustments was judged by the impact on sire ranking and on the statistical properties of the standardized records. Bulls were found to rank almost identically, regardless of the manner of age adjustment. Rank correlations between proofs based on actual and age-corrected records were about .95. There were significant regressions of age-adjusted production on age, for both sets of factors. I t was concluded that standard age adjustments may not be satisfactory in research applications requiring a high degree of accuracy.
Data
Searle and Henderson (9) discussed alternative ways of adjusting production records for variation in age at calving. They compared the Statistical properties of lactation records adjusted for age by three different procedures: (1) multiplicative, (2) herd level, and (3) additive corrections. Among the criteria considered were repeatability, coefficients of variation, and residual variance due to age. Searle and Henderson concluded that there is no single criterion for choosing a best method of age correction. They did not directly consider age adjustments from the standpoint of their effects on sire evaluation. Recently, many workers have suggested the use of separate age adjustments according to season of calving [Gravir and Hickman (2), McDaniel et al. (7), Syrstad {11), and Miller et al. (8)]. ~¢~an Vleek and Henderson (12) previously advocated simultaneous adjustnmnt for age and season effects. Butcher (1), Gravir and Hickman (2), McDaniel et al. (7), and Miller et al. (8) also reported that nfilk and fat age adjustment factors should be different, since fat per cent shows a slight decline from first lactation to maturity. The purpose of the present study was to compare the properties of first-lactation records adReceived for publication September 1, 1967.
The data were 10,620 first lactations (ages at calving less than 36 months) from Michigan Holstein herds using artificial service. These data have been described in detail by Miller et al. (9). There were 1,003 herd years represented and the calving dates were restricted to 1961-63. Approximately 25% of the records were by naturally sired cows, although all herds used artificial service to some extent. Only records of registered cows were used. All records terminated by culling were extended to a 305-day basis. There were 1,095 different sires represented, but only 40 artificial insemination (AI) bulls were studied individually. The remaining sires were allotted to a group cmuparison of non-AI bulls versus the remaining AI sires. Results and Discussion
Several aspects of age-adjusted records were considered. The primary objective was to determine whether the use of different sets of age factors would alter the ranking of bulls evaluated on the basis of first lactation daughters and contemporaries. The age range employed (up to 36 months) represents only about one-fourth of all lactations made in D H I A herds. However, major portions of the sire selection decisions in artificial insemination are based largely on progeny records in this age range. I n addition, certain statistical properties of age-adjusted first lactations were investigated. These included the effects of age adjustments on 1) coefficients of variation, 2) magnitude of estimated seasonal effects, 3) reduction in variation associated with age, and 4) year-to-year homogeneity of the regression of production on age. Effects on sire evaluation. I n another report (9), results of a study of three different meth-
378
379
L A C T A T I O N ADJUST1V[ENT
ods of sire evaluation are presented. This discussion considered the relative r a n k correlations a m o n g the three evaluation procedures. U s i n g the same data, sires were also evaluated on the basis of m a t u r e e q u i v a l e n t ( M E ) p r o d u c tion of t h e i r p r o g e n y , as estinmted b y the K e n drick age f a c t o r s a n d b y the new D t t I A factors r e p o r t e d b y M c D a n i e l et al. (7). A t the same time sires were also evaluated on the actual first l a c t a t i o n p r o d u c t i o n of p r o g e n y , u s i n g the following least-squares m o d e l :
where h~ is a n effect common to o b s e r v a t i o n s in the i ~h h e r d year, aj is a n effect p r e s e n t f o r all observations in the j*~ season of calving, b~ is a n element p e c u l i a r to the k TM y e a r of birth, (ab)j~ is a n effect possessed b y all observations in the j r , season a n d k th y e a r of birth, s~,~ is a n effect common to all d a u g h t e r s of the m TM sire in the 1~h g r o u p (the i n d e x 1 r e f e r s to two g r o u p s : G r o u p 1 r e p r e s e n t s all n o n - A I a n d res i d u a l - A I bulls, G r o u p 2 r e p r e s e n t s the 40 bulls t h a t were fitted u n i q u e l y ) , a n d e~j~,,~, is a r a n dora e r r o r p e c u l i a r to the n "~ d a u g h t e r of the m th sire. Table 1 contains the r a n k correlations a m o n g h e r d n m t e c o m p a r i s o n a n d least-squares sire proofs, f o r b o t h sets of age f a c t o r s a n d f o r b o t h milk a n d fat. I n addition, r a n k correlations between all M E measures of b r e e d i n g value a n d least-squares p r o o f s f o r actual milk a n d f a t yields are presented. The c o m p a r i s o n s of pl~imary i n t e r e s t in Table I are those between p r o o f s b a s e d on the diff e r e n t age f a c t o r s f o r the same m e t h o d of comp u t a t i o n . F o r example, r~ is the r a n k correlation f o r p r o o f s based on M E milk-yield a n d c o m p u t e d b y h e r d m a t e c o m p a r i s o n s f o r the two a l t e r n a t i v e a g e - a d j u s t m e n t procedures.
This correlation is 0.99. I n fact, all similar correlations (yield t r a i t held c o n s t a n t ) between sire e v a l u a t i o n s based on the different age factors are 0.99. A p p a r e n t l y , the use of different age a d j u s t m e n t f a c t o r s h a d essentially no imp a c t u p o n the relative s t a n d i n g of the 40 sires. The new D t I I A f a c t o r s a p p l y different p e r centage corrections to nfilk a n d f a t a n d to the two different seasons of calving ( N o v e m b e r J u n e , J u l y - O c t o b e r ) . The K e n d r i c k f a c t o r s a r e a h n o s t the same as the new D t t I A factors f o r milk in the N o v e m b e r - J u n e season in the Midwest. T h a t the use of different M E f a c t o r s would alter r a n k i n g v e r y little can be i n f e r r e d from the high rank correlations between M E p r o o f s a n d those based on a c t u a l p r o d u c t i o n , regardless of m e t h o d of c o m p u t a t i o n . F o r example, the r a n k correlations between leastsquares p r o o f s based on actual milk yield a n d those c o m p u t e d f r o m M E milk yield b y the h e r d n m t e c o m p a r i s o n are a b o u t .95. The correlations of p r o o f s b a s e d on a c t u a l yield with M E measures of b r e e d i n g value c o m p u t e d b y least s q u a r e s are a r o u n d .99. This indicates t h a t bulls which e n t e r service d u r i n g tile same general p e r i o d of time will r a n k a b o u t the same on actual first l a c t a t i o n p r o d u c t i o n as on a n M E basis. This s u p p o r t s the g e n e r a l l y held view t h a t t r u e c o n t e m p o r a x y c o m p a r i s o n s (based on only first l a c t a t i o n s ) will minimize r a n k i n g era'ors a r i s i n g f r o m inaccuracies of age factors. I t n m s t be r e m e m b e r e d t h a t these results do n o t a p p l y to bulls e n t e r i n g service a t w i d e r i n t e r v a l s of time, or to p r o o f s cmnpiled f o r all available lactations f o r bulls t h a t have been in selwice f o r widely different periods of time. Effects on analysis of ,variance. Table 2 presents the means, s t a n d a r d deviations, a n d coefficients of v a r i a t i o n f o r the v a r i o u s p r o d u c t i o n measures. The means f o r M E p r o d u c t i o n b a s e d
TABLE 1 Spearman rank correlations among different measures of breeding value of 40 artificia.1 insemination sires ~
1
2 3 4 5 6 7 8 9
2
3
4
5
6
7
8
.79
.99 .80
.79 .99 .81
.94 .77 .95 .78
.78 .96 .80 .96 .83
.93 .76 .94 .77 .99 .83
.76 .96 .79 .97 .82 .99 .82
i ----Herdmate milk (new D H I A factors). 3 = tterdmate milk (Kendrick factors). 5 =- Least-squares milk (new D H I A factors). 7 ----Least-squares milk (Kendrick factors). 9 ----Least-squares milk (actual production).
2 4 6 8 10
= IIerdmate f a t = Herdmate f a t = Least-squares --= Least-squares -= Least-squares
9
10
.94 .78 .95 .78 .99 .83 .99 .82
.79 .97 .81 .96 .84 .99 .84 .99 .84
(new D H I A factors). (Kendrick factors). f a t (new D t t I A factors). f a t (Kendrick factors). f a t (actual production).
g. DAIRY SCIENCE VOL, 51, NO. 3
380
Means,
M I L L E R , M c D A N I E L , AND P L O W M A N
standard
TABLE 2 deviations, and var£ation ~
Trait ME milk-new DHIA factors ME milk-Kendrick factors Actual milk ME fat-new DHIA factors ME fat-Kendrick factors Actual fat
Mean
coefficients SD ~
of
+1 +t +1 +[ +1 +1
CV b
6,310
1,034
16.38
6,405 5,082
1,047 838
16.34 16.48
224
35.6
15.87
233 185
36.9 29.6
15.82 16.00
,at r~
" P r o d u c t i o n in k i l o g r a n l u n i t s . " Within herd years.
on the new D H I A factors are lower than those computed for mature yield estimated by the K e n d r i c k factors. This is expected because the new D H I A factors are lower, on the average, for ages under 36 months in the Midwest region. The standard deviations were lower for ME yield estimated using the new D H I A factors, but the coefficients of variation were virtually identical, indicating that variability among records changed only as a result of changes in the mean. I n the computation of least-squares estimates of sire effects, the model also contained season and birth-year effects. The model was fitted on a within herd and year of calving basis. Two seasons (November-April and May-October) and f o u r birth-year categories (1958-61) were employed. The least-squares estimates of the effects are shown in Table 3 for the two different sets of age factors and for aetual production. All seasonal effects were statistically significant except for actual fat production. The magnitude of the estimates of seasonal effects varied greatly according to the manner of age adjustment. Seasonal effects were small for actual production, but were larger when the new D H I A factors were used to compute M E yield. Production adjusted by the K e n drick factors showed somewhat smaller seasonal effects compared to ME production based on the new D H I A factm's. The estimates of effects for the different sets of age factors are not strictly comparable because of the difference in the standard deviations. The differences in the estimates of seasonal effects may be due in p a r t to the presence of an age × season interaction. V a n Vleek and tIendet~on (12), W u n d e r and McGilliard (13), and Syrstad (11) have reported such an interaction for the entire age range. I t may be postulated that this interaction also exists within the first lactation age range~-'The new D H I A J. DAIRY SCIENCE ~OL. 51, NO. 3
+1 +1 +1 +1 +1 +1
+1 +1 +[ +1 +1 +1
d
+1 +l +l +1 +1 +1
+t +I +I +l +I +l
-d 45 "E
.5
z~
LACTATION
age factors are different for the two seasonal classifications and records age-adjusted by these factors exhibited the greatest amount of seasonal variation. I f an age X season interaction exists, the new D H I A factors may attribute a portion of the age × season interaction to seasons. The Kendriek factors are constant across seasons and the ME records exhibit less seasonal variance. I t might be supposed that apparent seasonal variance found in the analysis of the actual records would be increased because age was ignored in the analysis, but this apparently did not occur. The size of the birth-year effects also varied greatly, depending upon the mode of age adjustment. Birth-year differences were significant for actual production (P < .01), for ME yield based on the new D H I A factors (P .05). and nonsignificant for ME production computed with the Kendrick factors. These relationships may be influenced by the confounding of year of birth and age in the data. Late-calving heifers would be present only in 1958 or 1959 birth years, due to the way in which the data were selected. I f the age factors are inaccurate, birth-year comparisons may not be an appropriate measure of genetic changes, due to the presence of a bias arising from age differences. The trends for both actual production and ME yield based on the new D I t I A factors were distinctly negative. Estimates for actual production indicate a decrease of about 48 kg of milk from 1958 to 1961, a conclusion which is somewhat suspect. F o r example, the comparison of the 1958 birth year to the 1961 birth year may be biased for actual production, because the mean age of calving would be higher for 1958. This bias may also be present to a lesser extent for ME yield if age differences remain. That age effects biased the birth-year comparisons for actual yield was shown by repeating the analysis with the inclusion of a quadratic regression on age. When this was done there was no consistent pattern for birthyear effects and the F-value was nonsignificant. Effects on residual age variance and age X year variance. The following model was fitted
381
ADJUSTMENT
¢$
¢$
o
"a
O9
to the data:
Y , ~ = ~ + h. + ~ ( x . ~ - - ~ ) + ~.(x-~,. - ~x )
+
t~l~(X~--x)
+ / 3 ~ (x-~,~ - x~ )
+ e,~
where h,~ refers to the joint effects of the i t~ herd and the jt~ year of calving and X , ~ refers to the age at calving of the k t~ cow in the jth year and the i ~h herd. According to this model a separate quadratic regression is fitted for each year of calving. The procedure for fitting
¢9 °
J-. DAT]ZY S C I E N C E V O L . 51, NO. 3
382
M I L L E R , McDANIEL, AND PLOWMAN
this model has been described by H a r v e y (3). The results are presented in Table 4 f o r the different production criteria. I n all cases the average linear and quadratic regressions on age were significant, but the individual y e a r regressions were not significantly different f r o m the average coefficient. Table 4 indicates that neither set of age factors removed all of the variance associated with age at calving. The residual variance was greater for the new D H I A factors than f o r production based on the K e n d r i c k factors. Ho~z ever, the coefficient of variation based on the error mean square was only slightly larger for the new D H I A factors (16.7 to 16.6). The results in Table 4 indicate that there was little yearly variation in the relationship of age and first-lactation production, confirming the results of Hillers and F r e e m a n (4). A stepwise procedure was employed to discard nonsignificant effects f r o m the model. The analysis of variance and regression coefficients for the final model are given in Tables 5 and 6, respectively. I n interpreting these results it must be remembered that the ranges of ages and years studied were very limited. I f data characterized by wider variations in age and time are studied, interactions between ages and years may be observed. The results in Table 5 and 6 indicate that neither set of age factors was v e r y effective in reducing variation in first lactation records associated with age. The regressions of actual milk yield and the M E yields on age are shown graphically in F i g u r e 1. Searle and Henderson (10) pointed out that it may not be desirable for age factors to remove all the a p p a r e n t variance due to age, especially if other variables are confounded with age. Nevertheless, the present results indicate that the factors used removed very little of the age variation in production. The regression coefficients f o r M E yield in Table 6 are similar to those f o r actual production. These
% ,-d
o
TABLE 6 Regression coefficients for quadratic regression of production on age ~
£
Production measure
V
Linear
New D H I A factors Milk 216 -+47.5 Fat 7.7± 1.6 Kendrick factors Milk 159 -+48.0 Fat 5.4_+ 1.7 Actual production Milk 189 -+38.1 Fat 6.6-+ 1.4
Quadratic --15.5+_3.72 --0.1-+ .01 --13.2-+3.76 --0.1-+ .01 --11.8-+3.06 --0.1___ .01
Milk and fat coded in kilogram units. J. DAIRY SOIENCE VOL. 5], NO. 3
LACTATION
75~
650
.-J hA >- 500 -.A
• N[kl FRCTO~S & OLD F'ETORS X ~K~TURL YIELO
DEVIRTION FROM HERO RVERRGERGE [MO.l FIG. 1. l~egresslon of first lactation mature equivalent and actual milk Field on deviation of age from herd average age at first calving. results agree to some extent with those of Lee and I I i c k m a n (6), who found statistically significant regressions of nmture-equivalent production on age. They also found that the pooled within-herd regressions differed markedly f r o m one season of calving to another. Summary and Conclusions The D H I A age factors of K e n d r i c k (5) and McDaniel et al. (7) were compared, using 10,620 first lactations f r o m Michigan Holstein herds that had used artificial service. Calving dates were restricted to 1961-63. F o r t y A I bulls were studied individually, by both cont e m p o r a r y comparison and least-squares evaluation procedures. Bulls were found to rank almost identically when proofs were computed in the same manner, using both sets of age factors. These results s u p p o r t the view that the effect of age factor errors on sire r a n k i n g m a y be minimized by basing sire proofs on first lactations of progeny and herdmates. Differences in the results of analyses of variance due to the use of different age factors were studied. The new D H I A factors lowered the mean slightly, but the coefficients of variation were vi~¢ually identical. Seasonal effects were largest f o r M E production based on the new D H I A factors, intermediate f o r M E yield estimated by the K e n d r i c k factors, and smallest for actual production. I t was concluded that the new D H I A factors may enhance seasonal variance if an age × season interaction exists.
ADJUSTMENT
383
Birth-year comparisons were estimated by least squares as a criterion of genetic changes. The results varied greatly, depending upon the mode of age adjustment. I t was concluded that the comparisons may have been biased by age differences. Quadratic regressions on age were fitted on an intra-herd-year basis. The regressions were significant for both ME measures and for actual yield. The regressions were homogeneous f r o m one calving year to another. The residual variation was of comparable size for both ME measures, as reflected by the coefficients of variation. These results indicate that age factors computed for an over-all population may not fit individual subsets of the population v e r y closely. Research applications requiring precise age adjustment, such as the estimation of genetic trends, should consider other methods to account for age variation, such as regression. References (1) Butcher, ~ . F. 1966. Environmental and Genetic Factors Affecting the Composition of Cow's Milk. M.S. thesis, North Carolina State University. p. 108. (2) Gravir, K., and Hickma~, C. G. 1966. Importance of Lactation Number, Age, and Season of Calving for Dalry Cattle Breed Improvement. Publ. no. 1230, Canada Dept. Agr. (3) Harvey, W. R. 1964. Computing Procedures for a Generalized Least-Squares Analysis Program. Mimeographed report. (4) Hillers, J. K., and Freeman, A. E. 1965. Differences Between Sires in Ra£e of Maturity of Their Daughters. J. Dairy Set., 48 : 1680. (5) Kendrick, J. F. 1955. Standardizing DairyHerd Improvement Association Records in Proving Sires. Dairy Herd Improvement Letter, ARS-52-1. U.S. Dept. Agr. (6) Lee, A. J., and Hickmaa, C. G. 1967. YieldAge Regression in Age-Corrected Records. J. Dairy Sci., 50: 986. (Abstract.) (7) McDaniel, B. T., Miller, R. H., Corley, E. L., and Plowman, R. D. 1967. D H I A Age Adjustment Factors for Standardizing Lactations to a Mature Basis. Dairy Herd Improvement Letter, ARS-44-188. U.S. Dept. Agr. (8) Miller, R. H., Haxvey, W. R., Tablet, K. A., McDaniel, B. T., and Corley, E. L. 1966. Maximum Likelihood Estimates of Age Effects. J. Dairy Sci., 49: 65. (9) Miller, R. H., McDaniel, B. T., and Plowman, 1~. D. 1968. Compaxison of Three Methods of Sire Evaluation. J. Dairy Sci., 51: Accepted for publication. J. DAIRY SCIENCE VOL. 51, N0.
3
384
MILLER, McDANIEL, AND PLOWMAN
(10) Searle, S. R., and Henderson, C. R. 1960. Judging the Effectiveness of Age-Correction Factors. J. Dalry Sci., 43: 966. (11) Syrstad, O. 1965. Studies on Dairy Herd Records. II. Effect of Age and Season of Calving. Acta Agr., Scand., 15:1. (12) Van ¥1eck, L. D., and Henderson, C. R. 1961. Ratio Factors for Adjusting Monthly
J. DAIRY SOlEXC~:-VOL. 51, No. 3
Test-Day Data for Age and Season of Calving and Ratio Factors for Extending P a r t Lactation Records. J. Dairy Sci., 44 : 1093. (13) Wunder, W. W., aa~d McGilliard, L. D. 1967. Seasons of Calving a~d Their Interactions with Age for Lactational Milk Yield. J. Dairy Sci., 50: 986. (Abstract.)