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Genetic and Phenotypic Parameters for a Profit Function and Selection Method for Optimizing Profit in Dairy Cattle1
Genetic and P h e n o t y p i c Parameters f o r a P r o f i t F u n c t i o n and Selection M e t h o d f o r O p t i m i z i n g Profit in D a i r y Cattle I G. S. GILL 2 and F. R. ALLAIRE Department of Dairy Science Ohio State University and Ohio Agricultural Research and Development Center Columbus 43210
INTRODUCTION
ABSTRACT
The basic objective in animal improvement through breeding is to select individuals with the highest breeding values to serve as parents of the next generation. The challenge is to find a method which makes best use of phenotypic values when breeding values are less than perfectly correlated with the phenotypic measures. The larger the number of characteristics involved in actual merit the more difficult it is to define objective methods. Complexity and difficulty increase as the number of traits increases. A main objective for commercial dairy cattle breeding is to increase milk yield as an indirect method of increasing profit. Little is known about possible operational definitions for profit and genetic and phenotypic relationships between profit and milk yield. This study reports on genetic and phenotypic parameters of a profit function, milk yield, herdlife and other performance, and reproduction traits. Index systems are compared relative to their efficiency for maximizing profit/day of herdlife by selection.
Genetic and phenotypic relationships were estimated on a profit function for 933 Holstein cows. Methods of selection among cows were investigated for profit per day of herdlife. The profit function included production, reproduction, and body weight. Heritability for profit/day during first lactation was .50 -+ .12 compared to .28 + .10 for milk/day in the first lactation. Correlations (genetic, phenotypic) between first lactation and lifetime records per day of herdtife were (.93, .74) for milk production and (.79, .65) for profit. Correlations between milk/day-first and profit/day-life were (.85, .55). Correlations for total lifetime production and profit were (.95, .97) and per day of herdlife were (.94, .87). Herdlife compared to lifetime traits had larger correlations with profit/day than yield/day (.64 versus .40, .69 versus .48) indicating the profit function contained important factors related to herdlife besides lactation performance. Correlations between age at first calving with total lifetime production and profit were negative ( - . 1 5 to - . 3 2 , - . 1 6 to -.07), suggesting an increase in these traits can be expected in selection for younger age at first calving. Genetic gain expected in profit/day of life from selection on profit/day-first lactation was 24% more efficient than milk/day-first. A simplified profit function may be effective for increasing profitability in dairy production by selection.
Description of Data and Analytical Procedure
Received November 24, 1975. ~Journal Article Number 129-75, Ohio Agricultural Research and Development Center. 2Department of Animal Sciences, Punjab Agricultural University, Ludhiana (Punjab), India.
The description of the data and definition of the profit function are given by Gill and Allaire (2). Data were from 933 Holstein cows sired by 93 bulls in 8 herds managed by the Ohio Department of Corrections and were herds in the Ohio NC-2 Project. Measurements on individual cows were incorporated into an estimated profit quantity for life up to date of second and last calving. Information on individual cows included: age at each calving, actual milk production with fat percent for each lactation, number of days in milk, number of breeding services, and weight estimated from girth circumference. Daily performance was on the first calving interval and total herdlife to last calving. Average income and expense inde-
1325
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GILL AND ALLAIRE
pendent of recorded information terms were constant and assigned to each cow. Heritabilities of traits and genetic correlations among the traits were estimated from variance-covariance analyses of sire effects of paternal half-sisters where all traits were adjusted for herd, year, and season fixed effects at time of first calving in a linear mixed model (6). Alternative selection methods were investigated by computing genetic gain expected from direct and indirect selection on single traits or indexes. The theoretical responses were computed from admissible parameter estimates substituted into the following equations. The genetic response in the k th trait from single trait selection on the ith trait is AGk; i = (~-)rkihkhiO k and response from selection on an index (I) developed to maximize jth trait is
TABLE 1. Heritability estimates for production and reproduction variables. Heritability Trait
Estimate
SEa
First lactation milk First lactation fat Milk/day of first lactation Life milk Life fat Milk/day of life First lactation profit Profit/day of first lactation Life profit Profit/day of life Age at first calving Weight at first calving First intercalving period Herdlife Number of calvings Total life Percent days dry Percent days open
.12 .14 .28 .25 .26 .40 .47 .50 .26 .31 .51 .18 -.01 .25 .23 .26 .30 .11
.08 .08 .10 .09 .09 .11 .11 .12 .10 .10 .12 .09 .07 .09 .09 .09 .10 .08
AGk; I = (-~)hkOk(.~birkihioi)/ 1
(h join. birjihiGi). 5
astandard errors by modifying procedures described by Swiger et al. (14) and Tallis (15).
1
The genetic response is a function of standardized selection differential 0-), genetic correlations r, heritabilities h 2, selection index coefficients b, and phenotypic standard deviations e. The ratios of the AG's for different selection systems were computed to compare the relative selection efficiency for gain under alternative criteria of selection. The accuracy of predicting breeding value for economic lifetime return from single trait selection on ith trait or an index was obtained as the correlation r G l and given as rGi = (.~birkihiOk) "5 1
where k refers to the lifetime trait. RESULTS AND DISCUSSION Heritabilities
Heritability estimates for production, profit, and reproduction traits are in Table 1. Estimates for first lactation yields ranged from .12 to .14 and were lower than estimates commonly reported for standardized 305-day mature-equivalent yields. The lower heritabilities were expected since days in milk and age at first calving varied among cows, introducing more nongenetic variation compared to stanJournal of Dairy Science Voh 59, No. 7
dardized lactations. Per day heritability was .28 and within the range commonly reported for first lactation yield. Yield per day would be analogous to a standardized lactation for actual yield. Heritabilities for total lifetime yield were about .25 and would reflect not only genetic variability for yield/day but also variability in herdlife associated with bull progeny groups. A larger heritability of .40 occurred when yield was per day. To the extent yield is included in culling, differences among means of progeny groups would be expected. Larger differences tend to increase heritability estimates for a lifetime trait if lower producers were culled and maturing survivors continued in production with no increase in average calving interval. Heritabilities for estimated profit to the end of the first lactation were larger than for yield for the same period. The comparison was .50 versus .28 on daily basis. It appears that differences among bull progeny groups other than milk yield, perhaps aspects of reproductive efficiency, are contributing importantly to variations in profit. When heritabilities (or variations among progeny groups) were compared for first lactation versus lifetime traits, a decrease for profit and increase for milk yield
PARAMETERS AND SELECTION METHODS FOR PROFIT occurred. Variance components among bullprogeny groups increased for both profit and milk yield although greater variation within bull-progeny group occurred for profit than changes for milk yield traits. Environmental variations seemed to accumulate, and variation increased as length of herdlife increased. Heritabilities for herdlife, number of calvings, and total life ranged from .23 to .25 and were slightly larger than in other studies (4, 7, 11, 12). Reproductive traits, % days open in lifetime, and days between 1st and 2nd parturitions had heritabilities. 11 and .00. Age at first calving had a high heritability at .51 suggesting rate of sexual development and/ or reproductive management practices were associated with bull progeny groups. Other workers (7, 9) attributed a large heritability for age at first calving with confounding the sequential use of breeding bulls and the disproportionately greater number of calvings in autumn-season. Larson et al. (10) reported no evidence for a nonzero heritability for age at first calving. Differences in age at first insemination may be associated with progeny groups, as would be expected when heifers are bred only after reaching a minimum size since size exhibits genetic variability. Such a policy in reproductive management would lead to variations of progeny group in age at first calving not necessarily due to genetic variations in conception rate or sexual maturity. First Lactation and Lifetime Traits
Phenotypic and genetic correlations are in Table 2 for sets of first lactation and lifetime traits. Age at first calving was correlated negatively with total lifetime production and profit traits both genetically and phenotypically with profit/day having largest negative (genetic, phenotypic) correlations (-.41, -.24). Larson et al. (10) reported negative phenotypic correlation ( - . 2 7 ) between age at first calving and total production to 84 mo of age. The genetic correlation indicates cow calving at younger ages were more profitable cows for reasons associated with progeny groups. The relatively large genetic correlation (.51) between age at first calving and % days open indicates there may be a genetic basis to variations in reproductive efficiency at later ages. In spite of small positive phenotypic correlations with milk/day
1327
(.05 for life and .16 for first lactation), there were negative correlations with herdlife, both genetically, - . 0 8 , and phenotypically, - . 1 0 . This series of correlations and the relatively large negative corrrelation between age at first calving and profit, though mostly not statistically different from zero, seem to indicate variation in age at first calving was more reflective of variation in herdlife .or reproductive efficiency than variation in total or daily production for life. Greater production during first lactation by later first calvers does not overcome associated costs of shorter herdlife. Weight at first calving had a slight negative phenotypic correlation with total lifetime performance traits - . 0 3 to - . 1 3 except for milk/ day .08. The genetic correlations were larger than the phenotypic and were positive, ranging from .24 to .39. These relationships suggest a negative environmental relationship between weight at first calving and lifetime performance characteristics. This conclusion would be consistent with results from nutritional experiments (13, 14). The pattern of phenotypic correlations indicated there were larger correlations between early and lifetime .performance per day (.5 to .7) than on a total basis (.2 to .4). Among genetic correlations, correlations for per day ranged .7 to .9 compared to 1.0 for total production and smaller correlations (.4 to .7) for total profit. The larger genetic correlations seem to indicate a closer association between bull progeny means than individual cow performance. Reasons for the inconsistency in genetic correlations for total milk and fat in first lactation are not clear but may suggest these traits have more of a role in culling than production per day or the defined profit trait. The high genetic correlation would arise in part because animals culled after only one lactation would have lifetime production equal to first lactation production. Cows having two calvings, but only one complete lactation, represented 32% of the data. Negative genetic correlations (--.2 to - . 3 ) between percent days open and profit (total or per day) in first lactation indicated the more efficient reproduction was associated positively on a genetic basis with profit/day in first lactation. The phenotypic correlations, however, were positive and smaller reflecting the effect of a lower heritability for percent days Journal of Dairy Science Vol. 59, No. 7
to 00
t~ TABLE 2. Phenotypic and genetic correlations among the production and reproduction variables of the first lactation and lifetime performance traits a. Lifetime production traits <
Reproduction traits
Total fat
Total profit
Milk /day
Profit /day
Herdlife
Age at first calving
-.08 -.15
-.07 -.15
-.16 -.32
.05 -.22
-.24 -.41
-.10 -.08
.05 .51
-.11 -.12
-.10 .12
Weight at first calving
-.03 .31
-.03 .30
-,08 .39
.08 .24
-,13 .27
-.06 .21
-.04 -.49
-.05 .26
.01 -.14
Total milk
.23 1.03
.24 1.05
.26 1.10
.56 1.04
.42 1.00
.13 .81
.51 .02
.05 .82
.20 .91
Total fat
.22 1.05
.23 1.08
.24 1.11
.55 1.02
.39 1.00
.12 .83
.51 .06
.04 .85
.19 .96
Total profit
.29 .47
.29 .48
.41 .67
.64 .74
.65 .80
.19 .27
.13 -.29
.17 .31
.08 .19
Milk/day
.25 .49
.25 .51
.33 .69
.74 .93
.55 .85
.12 .23
.00 ,00
.12 .27
.14 .24
Profit/day
.29 .44
.29 .46
.40 .64
.64 .73
.65 .79
.19 .26
.11 -.16
.17 .28
.07 .19
.19-.36
.19-.36
.17-.35
.07-.28
.10-.33
.23-.38
.23-.43
.29-.44
First lactation traits
.q
Standard erlor of genetic correlation b (low-high)
aphenotypic correlation above genetic correlation. Maximum standard error is .03 for phenotypic correlations. bstandard errors are m i n i m u m and approximate (14).
% Days open
.32-.59
No. calvings
No. services
Total milk
O
.q Z 2t" F"
P A R A M E T E R S A N D SELECTION METHODS FOR PROFIT
open and positive environmental correlations .22 to .29. Genetic correlations between first lactation and lifetime yield or profit per day were high (.8), but correlations between first lactation traits and herdlife were low (.2). It appears herdlife was associated more closely with cumulative nongenetic factors affecting lifetime production or profit/day then the genetic factors. Probably one of these factors is partial culling on low production which would tend to increase environmental correlations at a faster rate than genetic ones since heritability of production is less than 50%. Environmental correlations were larger than genetic correlations between milk/day-life or profit/day-life each with length of herdlife. These were .53 versus .40 and .72 versus .64.
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Genetic and Phenotypic Relationships Among Lifetime Traits
Knowledge of the interrelationship of lifetime traits is important to predict the expected correlated changes with selection. Phenotypic and genetic correlations among lifetime traits are in Table 3. An important limitation in the interpretation of the analyses on lifetime traits is the inability to assess clearly effects of selection on computed correlations. According to Brown and Turner (3), selection on one trait theoretically will lead to estimates nearer zero than correlations from unselected populations. Genetic and phenotypic correlations among total lifetime performance traits were about .9. Interestingly, profit/day had higher correlations with total performance traits than did milk/ day. Phenotypic correlations were .77 to .83 versus .63 to .72, and genetically .84 to .97 versus .62 to .81. This suggests the cows having largest total yield or profit were those with higher production, reproductive efficiency, and herdlife than those with only higher production. The profit function seems to be measuring characters important for total production beyond milk alone. This interpretation is supported further by the larger phenotypic correlations between profit/day and herdlife (.69) than milk/day and herdlife (.48). The genetic and phenotypic correlations are consistent among traits of total performance. The importance of increasing the number of calvings to increase total production and profit/day is indicated by the large phenotypic correlations ranging from .70 to .99. Percent
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Journal o f Dairy Science Vol. 59, No. 7
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GILL AND ALLAIRE
days open as a measure of reproductive efficiency up to last calving was correlated only slightly with total or daily production, or profit on a phenotypic basis. Correlations ranged .02 to .10. E f f i c i e n c y of A l t e r n a t i v e Selection Systems
Responses expected from selection for a single trait when selection intensity is unity 0-= 1.0) are in Table 4 to assess the relative effect of direct and indirect selection alternatives. Direct selection on a single trait resulted in greater advances in the desired direction than indirect selection for only 4 of 13 traits. These traits were age at first calving, life fat, milk/ day-life, and herdlife. Nine traits show larger response from indirect selection in one or more traits than direct selection indicating the indirect selection traits had higher heritabilities than the trait of interest along with a large genetic correlation. First lactation milk and fat had unusually large and unrealistic genetic correlation resulting in high responses from indirect selection. Genetic correlations equal to 1.0 were substituted for those estimates exceeding 1.00. Other traits favoring indirect selection may to some unknown extent reflect sampling error in estimates of genetic parameters. Greater gain in total performance of first lactation was expected by selection on traits expressed per day. This occurred because total performance traits, not standardized per day, had lower heritabilities than analogous traits per day. Profit in first lactation led to at least 25% greater gains in milk in first lactation compared to direct selection when traits were defined on a total or per-day basis. These results reflect the result of high genetic correlations and larger heritability for the profit trait compared to the milk-yield trait. Selection on profit/day in the first lactation resulted in larger gains in profit/day of herdlife than milk/day in the first lactation ($.14 versus $.11). This result indicates there are factors besides yield which have some genetic basis in profit during first lactation which also contribute to profit throughout herdlife. Selection on all production or profit traits had a negative correlated response for age at first calving, suggesting more efficient production and larger total production can be expected from animals which calve at an early age. This result may reflect a combination of Journal of Dairy Science Vol. 59, No. 7
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PARAMETERS AND SELECTION METHODS FOR PROFIT early sexual m a t u r i t y as well as higher relative reproductive efficiency t h r o u g h o u t life. Selection on some f u n c t i o n of performance traits of first lactation seems most desirable for changing lifetime performance since selections on lifetime traits are n o t practical. Delaying selection until i n f o r m a t i o n is available o n lifetime traits would increase greatly costs of maintaining potential replacement stocks awaiting records on dam or awaiting records on bull progeny. More importantly, genetic progress per year would become d e p e n d e n t on longer generation intervals. Five selection indexes were developed to compare relative efficiencies with selection for a single trait for expected gains in profit/day-life. The indexes were constructed by incorporating i n f o r m a t i o n available at the end of the first lactation. Traits chosen were age at first calving (P1), milk/day (P2), profit/ day (P3), and first lactation profit (P4)- Five c o m b i n a t i o n s of the four traits were defined and selection indexes developed for predicting indirectly profit/day of life. The indexes given in original units of the traits and in terms of proportionality weights and standard deviation units, respectively, were: I1 = - . 0 0 1 0 P 1 + .0513P2 + .0316P3; - . 7 0 8 0 ( P 1 / o 1 ) + (P2/o2) + .0878(P3/o3) I2 = - . 0 0 1 1 P 1 + . 0 5 5 2 P 2 ; - . 7 2 3 8 ( P I / o l ) + (P2/O2)
1331
I3 = --.0002P1 + .4028P3 ; --.1262(P1/ol ) + (P3/03) 14 = .0048P2 + .3981P3 ; .0002(P2/o2) + (P3/03 ) I s = --.0002P1 + .0010P4 ;--.1271(P1/ol) + (P4/u4 ) The proportionality weights for the various traits in the indexes take into a c c o u n t the relative i n f o r m a t i o n in first lactation traits i n d e p e n d e n t of p h e n o t y p i c variation. The relative efficiency of various single first lactation traits and indexes for indirect selection are compared in Table 5. The single most import a n t first lactation trait is profit/day during first lactation. The rGi value a n d expected responses from selection on P3 were larger than the corresponding results for P1, P2, or P4 singly. The indexes suggest the c o m b i n e d i n f o r m a t i o n from P1 and P2 is about equal to that of P3This conclusion is drawn since 11 was only 4% more efficient than P3 alone and I2 had a b o u t equal efficiency with I1 . T h e index 12 based on PI a n d P2 will, however, be simpler to calculate. Age at first calving had surprisingly large heritability and genetic correlations with profit during first lactation and life. The genetic correlations were total profit for first - . 7 8 + .22, profit/day for first - . 7 6 +- .21, and profit/day for life - . 4 1 + .23. Genetic parameters associated with age at first calving were
TABLE 5. Relative efficiency of different selection criteria for maximizing genetic gain in profit/day of life. Relative efficiency (%) Selection criterion
rGi
Response a ($)
Profit/ day-first
Milk/ day-first
Direct selection Profit/day of life
.557
.140
100
124
Indirect selection with first lactation traits Age at calving (P1) Milk/day (P2) Index (Is): P1, P2 Profit/clay (P3) Index (I 1): P1, P~, P3 Index (13): P1, P3 Index (I4): P:, P3 Total profit (P4) Index (I5): P1, P4
.293 .4.50 .581 .559 .582 .561 .559 .548 .553
.070 .113 .146 .140 .146 .141 .140 .137 .139
53 81 104 100 104 101 100 98 99
65 10_.O0 129 124 129 125 124 122 123
aResponse is given for selection differential equal to one standard deviation of selection criterion. Journal of Dairy Science VoL 59, No. 7
1332
GILL AND ALLAIRE
reduced by 33% to determine the effect of smaller values on selection efficiencies in Table 5. The index for P1 and P2 had efficiencies 91% and 112% compared to 104% and 129%, respectively. Lower genetic parameters for age at first calving (P~) would support the calculation of estimated profit (P3) compared to the use of an index including P1 and P2. The expected gain in profit/day for life was $.140 for selection on Ps which was equal to direct selection. A desirable simplifying result was that gain by indirect selection on age at first calving and milk/day in first lactation accounted for essentially all the information in profit/day for first lactation with regard to gain in profit/day for life. Greatest utilization of milk yield as a component of culling occurs during first lactation (1, 2). Alternative selection methods directed at maximizing profit/ day-life are compared for relative efficiency with respect to milk/day-first. This comparison indicates profit/day-first (P3) was +24% more efficient than milk/day while combination of P~, P2 was +29%. The expected correlated responses on economically important traits from first lactation single trait or index selection are in Table 6. Selection on the most efficient index I 1 relative to selection on milk/day alone will result in animals younger by 24 days in age of first calving, 2.5 more kg body weight, .18 more kg milk/day in first lactation, $.04 more profit/ day in life, and 7 more days of herdlife. Selection on I2 which was simpler and about as efficient as I~, results in greater gain than selection on milk/day-first by more rapidly decreasing age at first calving by - 2 6 0 % and increasing milk/day by +28% in first lactation and +8% for lifetime and increasing herdlife by +17%. Selection differentials, resulting in equal correlated responses, might be known as the relative selection value of each trait. Comparing correlated genetic responses in profit/day of life, a selection differential of 1 kg of milk/day in first lactation is equal to a selection differential of - 5 7 days for age at first calving (i.e., 1 kg: - 5 7 days). Relative economic values as defined by Hazel (8) may be obtained as the simple genetic regression of profit/day-life on each trait. These were .1742 (S/kg) for milk/ day-first and - . 0 0 1 7 (S/day) for age at first calving, giving relative economic values of 1 kg J o u r n a l o f D a i r y S c i e n c e Vol. 59, No. 7
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PARAMETERS AND SELECTION METHODS FOR PROFIT m i l k / d a y - f i r s t e q u a l t o - 1 0 2 days age. T h e relative e c o n o m i c values o n a p h e n o t y p i c basis w o u l d b e t h e simple p h e n o t y p i c regressions. These were .107 ($/kg) f o r m i l k / d a y - f i r s t a n d - . 0 0 1 3 ( S / d a y ) for age, giving relative econ o m i c value o n p h e n o t y p i c basis 1 kg e q u a l t o - 8 2 days. CONCLUSIONS
L i f e t i m e e c o n o m i c m e r i t f r o m a simplified p r o f i t f u n c t i o n i n c l u d i n g individual c o w prod u c t i o n , r e p r o d u c t i o n , a n d w e i g h t traits h a d a larger h e r i t a b i l i t y t h a n milk yield u p t o s e c o n d p a r t u r i t i o n . E x p e c t e d gains in p r o f i t / d a y - l i f e b y selecting o n p r o f i t / d a y - f i r s t o r selecting o n age at first calving a n d m i l k / d a y - f i r s t were g r e a t e r t h a n gains f r o m selecting o n m i l k / d a y - f i r s t or b y direct s e l e c t i o n o n p r o f i t / d a y - l i f e . A p r o f i t function shown to be representative for a broad range of c o n d i t i o n s can increase t h e e f f i c i e n c y of selection f o r p r o f i t a b i l i t y . ACKNOWLEDGMENT
T h e a u t h o r s wish t o t h a n k U S A I D p r o g r a m for f u n d s s u p p o r t i n g this research a n d T. M. L u d w i c k a n d E. R. R a d e r for c o o p e r a t i o n a n d access t o d a t a c o l l e c t e d u n d e r t h e Ohio NC-2 Project. REFERENCES
1 Allaire, F. R., and C. R. Henderson. 1966. Selection practiced among dairy cows. II. Total production over a sequence of lactations. J. Dairy Sci. 49:1435. 2 Allaire, F. R., and C. R. Henderson. 1967. Selection practiced among dairy cows. III. Type appraisal and lactation traits. J. Dairy Sci. 50:194. 3 Brown, G. H., and H. N. Turner. 1968. Response to selection in Australian Merino sheep. II. Esti-
1 333
mates of phenotypic and genetic parameters for some production traits in Merino ewes and an analysis of the possible effects of selection on them. Aust. J. Agr. Res. 19:303. 4 Evans, D. L., C. Branton, and B. R. Farthing. 1964. Heritability estimates and interrelationships among production per day of productive life, longevity, breeding efficiency, and type in a herd of Holstein cows. J. Dairy Sci. 47:699. (Abstr.) 5 Gill, G. S., and F. R. Allaire. 1976. Relationship of age at first calving, days open, days dry, and herdlife to a profit function for dairy cattle. J. Dairy Sci. 59:1131. 6 Harvey, W. R. 1970. Estimation of variance and covariance components in a mixed model. Biometrics 26:485. 7 Harville, D. A., and C. R. Henderson. 1966. Interrelationships among age, body weight, and production traits during first lactations of dairy cattle. J. Dairy Sci. 49:1254. 8 Hazel, L. N. 1943. The genetic basis for constructing selection indexes. Genetics 28:476. 9 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. 10 Larson, C. J., A. B. Chapman, and L. E. Casida. 1951. Butterfat production per day of life as a criterion of selection in dairy cattle. J. Dairy Sci. 34:1163. 11 Miller, P., L. D. Van Vleck, and C. R. Henderson. 1967. Relationships among herdlife, milk production, and calving interval. J. Dairy Sci. 50:1283. 12 Plowman, R. D., and R. F. Gaalaas. 1960. Heritability estimates of longevity in Holstein-Friesian cattle. J. Dairy Sci. 43:877. (Abstr.) 13 Schultz, L. H. 1969. Relationship of rearing rate of diary heifers to mature performance. J. Dairy Sci. 52:1321. 14 Swanson, E. W. 1967. Optimum growth patterns for dairy cattle. J. Dairy Sci. 50:244. 15 Swiger, L. A., W. R. Harvey, D. O. Everson and K. E. Gregory. 1964. The variance of intraclass correlation involving groups with one observation. Biometrics 20:818. 16 Tallis, G. M. 1959. Sampling errors of genetic correlation coefficients calculated from analyses of variance and covariance. Aust. J. Stat. 1: 35.
Journal of Dairy Science Vol. 59, No. 7
INTRODUCTION
ABSTRACT
The basic objective in animal improvement through breeding is to select individuals with the highest breeding values to serve as parents of the next generation. The challenge is to find a method which makes best use of phenotypic values when breeding values are less than perfectly correlated with the phenotypic measures. The larger the number of characteristics involved in actual merit the more difficult it is to define objective methods. Complexity and difficulty increase as the number of traits increases. A main objective for commercial dairy cattle breeding is to increase milk yield as an indirect method of increasing profit. Little is known about possible operational definitions for profit and genetic and phenotypic relationships between profit and milk yield. This study reports on genetic and phenotypic parameters of a profit function, milk yield, herdlife and other performance, and reproduction traits. Index systems are compared relative to their efficiency for maximizing profit/day of herdlife by selection.
Genetic and phenotypic relationships were estimated on a profit function for 933 Holstein cows. Methods of selection among cows were investigated for profit per day of herdlife. The profit function included production, reproduction, and body weight. Heritability for profit/day during first lactation was .50 -+ .12 compared to .28 + .10 for milk/day in the first lactation. Correlations (genetic, phenotypic) between first lactation and lifetime records per day of herdtife were (.93, .74) for milk production and (.79, .65) for profit. Correlations between milk/day-first and profit/day-life were (.85, .55). Correlations for total lifetime production and profit were (.95, .97) and per day of herdlife were (.94, .87). Herdlife compared to lifetime traits had larger correlations with profit/day than yield/day (.64 versus .40, .69 versus .48) indicating the profit function contained important factors related to herdlife besides lactation performance. Correlations between age at first calving with total lifetime production and profit were negative ( - . 1 5 to - . 3 2 , - . 1 6 to -.07), suggesting an increase in these traits can be expected in selection for younger age at first calving. Genetic gain expected in profit/day of life from selection on profit/day-first lactation was 24% more efficient than milk/day-first. A simplified profit function may be effective for increasing profitability in dairy production by selection.
Description of Data and Analytical Procedure
Received November 24, 1975. ~Journal Article Number 129-75, Ohio Agricultural Research and Development Center. 2Department of Animal Sciences, Punjab Agricultural University, Ludhiana (Punjab), India.
The description of the data and definition of the profit function are given by Gill and Allaire (2). Data were from 933 Holstein cows sired by 93 bulls in 8 herds managed by the Ohio Department of Corrections and were herds in the Ohio NC-2 Project. Measurements on individual cows were incorporated into an estimated profit quantity for life up to date of second and last calving. Information on individual cows included: age at each calving, actual milk production with fat percent for each lactation, number of days in milk, number of breeding services, and weight estimated from girth circumference. Daily performance was on the first calving interval and total herdlife to last calving. Average income and expense inde-
1325
1326
GILL AND ALLAIRE
pendent of recorded information terms were constant and assigned to each cow. Heritabilities of traits and genetic correlations among the traits were estimated from variance-covariance analyses of sire effects of paternal half-sisters where all traits were adjusted for herd, year, and season fixed effects at time of first calving in a linear mixed model (6). Alternative selection methods were investigated by computing genetic gain expected from direct and indirect selection on single traits or indexes. The theoretical responses were computed from admissible parameter estimates substituted into the following equations. The genetic response in the k th trait from single trait selection on the ith trait is AGk; i = (~-)rkihkhiO k and response from selection on an index (I) developed to maximize jth trait is
TABLE 1. Heritability estimates for production and reproduction variables. Heritability Trait
Estimate
SEa
First lactation milk First lactation fat Milk/day of first lactation Life milk Life fat Milk/day of life First lactation profit Profit/day of first lactation Life profit Profit/day of life Age at first calving Weight at first calving First intercalving period Herdlife Number of calvings Total life Percent days dry Percent days open
.12 .14 .28 .25 .26 .40 .47 .50 .26 .31 .51 .18 -.01 .25 .23 .26 .30 .11
.08 .08 .10 .09 .09 .11 .11 .12 .10 .10 .12 .09 .07 .09 .09 .09 .10 .08
AGk; I = (-~)hkOk(.~birkihioi)/ 1
(h join. birjihiGi). 5
astandard errors by modifying procedures described by Swiger et al. (14) and Tallis (15).
1
The genetic response is a function of standardized selection differential 0-), genetic correlations r, heritabilities h 2, selection index coefficients b, and phenotypic standard deviations e. The ratios of the AG's for different selection systems were computed to compare the relative selection efficiency for gain under alternative criteria of selection. The accuracy of predicting breeding value for economic lifetime return from single trait selection on ith trait or an index was obtained as the correlation r G l and given as rGi = (.~birkihiOk) "5 1
where k refers to the lifetime trait. RESULTS AND DISCUSSION Heritabilities
Heritability estimates for production, profit, and reproduction traits are in Table 1. Estimates for first lactation yields ranged from .12 to .14 and were lower than estimates commonly reported for standardized 305-day mature-equivalent yields. The lower heritabilities were expected since days in milk and age at first calving varied among cows, introducing more nongenetic variation compared to stanJournal of Dairy Science Voh 59, No. 7
dardized lactations. Per day heritability was .28 and within the range commonly reported for first lactation yield. Yield per day would be analogous to a standardized lactation for actual yield. Heritabilities for total lifetime yield were about .25 and would reflect not only genetic variability for yield/day but also variability in herdlife associated with bull progeny groups. A larger heritability of .40 occurred when yield was per day. To the extent yield is included in culling, differences among means of progeny groups would be expected. Larger differences tend to increase heritability estimates for a lifetime trait if lower producers were culled and maturing survivors continued in production with no increase in average calving interval. Heritabilities for estimated profit to the end of the first lactation were larger than for yield for the same period. The comparison was .50 versus .28 on daily basis. It appears that differences among bull progeny groups other than milk yield, perhaps aspects of reproductive efficiency, are contributing importantly to variations in profit. When heritabilities (or variations among progeny groups) were compared for first lactation versus lifetime traits, a decrease for profit and increase for milk yield
PARAMETERS AND SELECTION METHODS FOR PROFIT occurred. Variance components among bullprogeny groups increased for both profit and milk yield although greater variation within bull-progeny group occurred for profit than changes for milk yield traits. Environmental variations seemed to accumulate, and variation increased as length of herdlife increased. Heritabilities for herdlife, number of calvings, and total life ranged from .23 to .25 and were slightly larger than in other studies (4, 7, 11, 12). Reproductive traits, % days open in lifetime, and days between 1st and 2nd parturitions had heritabilities. 11 and .00. Age at first calving had a high heritability at .51 suggesting rate of sexual development and/ or reproductive management practices were associated with bull progeny groups. Other workers (7, 9) attributed a large heritability for age at first calving with confounding the sequential use of breeding bulls and the disproportionately greater number of calvings in autumn-season. Larson et al. (10) reported no evidence for a nonzero heritability for age at first calving. Differences in age at first insemination may be associated with progeny groups, as would be expected when heifers are bred only after reaching a minimum size since size exhibits genetic variability. Such a policy in reproductive management would lead to variations of progeny group in age at first calving not necessarily due to genetic variations in conception rate or sexual maturity. First Lactation and Lifetime Traits
Phenotypic and genetic correlations are in Table 2 for sets of first lactation and lifetime traits. Age at first calving was correlated negatively with total lifetime production and profit traits both genetically and phenotypically with profit/day having largest negative (genetic, phenotypic) correlations (-.41, -.24). Larson et al. (10) reported negative phenotypic correlation ( - . 2 7 ) between age at first calving and total production to 84 mo of age. The genetic correlation indicates cow calving at younger ages were more profitable cows for reasons associated with progeny groups. The relatively large genetic correlation (.51) between age at first calving and % days open indicates there may be a genetic basis to variations in reproductive efficiency at later ages. In spite of small positive phenotypic correlations with milk/day
1327
(.05 for life and .16 for first lactation), there were negative correlations with herdlife, both genetically, - . 0 8 , and phenotypically, - . 1 0 . This series of correlations and the relatively large negative corrrelation between age at first calving and profit, though mostly not statistically different from zero, seem to indicate variation in age at first calving was more reflective of variation in herdlife .or reproductive efficiency than variation in total or daily production for life. Greater production during first lactation by later first calvers does not overcome associated costs of shorter herdlife. Weight at first calving had a slight negative phenotypic correlation with total lifetime performance traits - . 0 3 to - . 1 3 except for milk/ day .08. The genetic correlations were larger than the phenotypic and were positive, ranging from .24 to .39. These relationships suggest a negative environmental relationship between weight at first calving and lifetime performance characteristics. This conclusion would be consistent with results from nutritional experiments (13, 14). The pattern of phenotypic correlations indicated there were larger correlations between early and lifetime .performance per day (.5 to .7) than on a total basis (.2 to .4). Among genetic correlations, correlations for per day ranged .7 to .9 compared to 1.0 for total production and smaller correlations (.4 to .7) for total profit. The larger genetic correlations seem to indicate a closer association between bull progeny means than individual cow performance. Reasons for the inconsistency in genetic correlations for total milk and fat in first lactation are not clear but may suggest these traits have more of a role in culling than production per day or the defined profit trait. The high genetic correlation would arise in part because animals culled after only one lactation would have lifetime production equal to first lactation production. Cows having two calvings, but only one complete lactation, represented 32% of the data. Negative genetic correlations (--.2 to - . 3 ) between percent days open and profit (total or per day) in first lactation indicated the more efficient reproduction was associated positively on a genetic basis with profit/day in first lactation. The phenotypic correlations, however, were positive and smaller reflecting the effect of a lower heritability for percent days Journal of Dairy Science Vol. 59, No. 7
to 00
t~ TABLE 2. Phenotypic and genetic correlations among the production and reproduction variables of the first lactation and lifetime performance traits a. Lifetime production traits <
Reproduction traits
Total fat
Total profit
Milk /day
Profit /day
Herdlife
Age at first calving
-.08 -.15
-.07 -.15
-.16 -.32
.05 -.22
-.24 -.41
-.10 -.08
.05 .51
-.11 -.12
-.10 .12
Weight at first calving
-.03 .31
-.03 .30
-,08 .39
.08 .24
-,13 .27
-.06 .21
-.04 -.49
-.05 .26
.01 -.14
Total milk
.23 1.03
.24 1.05
.26 1.10
.56 1.04
.42 1.00
.13 .81
.51 .02
.05 .82
.20 .91
Total fat
.22 1.05
.23 1.08
.24 1.11
.55 1.02
.39 1.00
.12 .83
.51 .06
.04 .85
.19 .96
Total profit
.29 .47
.29 .48
.41 .67
.64 .74
.65 .80
.19 .27
.13 -.29
.17 .31
.08 .19
Milk/day
.25 .49
.25 .51
.33 .69
.74 .93
.55 .85
.12 .23
.00 ,00
.12 .27
.14 .24
Profit/day
.29 .44
.29 .46
.40 .64
.64 .73
.65 .79
.19 .26
.11 -.16
.17 .28
.07 .19
.19-.36
.19-.36
.17-.35
.07-.28
.10-.33
.23-.38
.23-.43
.29-.44
First lactation traits
.q
Standard erlor of genetic correlation b (low-high)
aphenotypic correlation above genetic correlation. Maximum standard error is .03 for phenotypic correlations. bstandard errors are m i n i m u m and approximate (14).
% Days open
.32-.59
No. calvings
No. services
Total milk
O
.q Z 2t" F"
P A R A M E T E R S A N D SELECTION METHODS FOR PROFIT
open and positive environmental correlations .22 to .29. Genetic correlations between first lactation and lifetime yield or profit per day were high (.8), but correlations between first lactation traits and herdlife were low (.2). It appears herdlife was associated more closely with cumulative nongenetic factors affecting lifetime production or profit/day then the genetic factors. Probably one of these factors is partial culling on low production which would tend to increase environmental correlations at a faster rate than genetic ones since heritability of production is less than 50%. Environmental correlations were larger than genetic correlations between milk/day-life or profit/day-life each with length of herdlife. These were .53 versus .40 and .72 versus .64.
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Genetic and Phenotypic Relationships Among Lifetime Traits
Knowledge of the interrelationship of lifetime traits is important to predict the expected correlated changes with selection. Phenotypic and genetic correlations among lifetime traits are in Table 3. An important limitation in the interpretation of the analyses on lifetime traits is the inability to assess clearly effects of selection on computed correlations. According to Brown and Turner (3), selection on one trait theoretically will lead to estimates nearer zero than correlations from unselected populations. Genetic and phenotypic correlations among total lifetime performance traits were about .9. Interestingly, profit/day had higher correlations with total performance traits than did milk/ day. Phenotypic correlations were .77 to .83 versus .63 to .72, and genetically .84 to .97 versus .62 to .81. This suggests the cows having largest total yield or profit were those with higher production, reproductive efficiency, and herdlife than those with only higher production. The profit function seems to be measuring characters important for total production beyond milk alone. This interpretation is supported further by the larger phenotypic correlations between profit/day and herdlife (.69) than milk/day and herdlife (.48). The genetic and phenotypic correlations are consistent among traits of total performance. The importance of increasing the number of calvings to increase total production and profit/day is indicated by the large phenotypic correlations ranging from .70 to .99. Percent
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GILL AND ALLAIRE
days open as a measure of reproductive efficiency up to last calving was correlated only slightly with total or daily production, or profit on a phenotypic basis. Correlations ranged .02 to .10. E f f i c i e n c y of A l t e r n a t i v e Selection Systems
Responses expected from selection for a single trait when selection intensity is unity 0-= 1.0) are in Table 4 to assess the relative effect of direct and indirect selection alternatives. Direct selection on a single trait resulted in greater advances in the desired direction than indirect selection for only 4 of 13 traits. These traits were age at first calving, life fat, milk/ day-life, and herdlife. Nine traits show larger response from indirect selection in one or more traits than direct selection indicating the indirect selection traits had higher heritabilities than the trait of interest along with a large genetic correlation. First lactation milk and fat had unusually large and unrealistic genetic correlation resulting in high responses from indirect selection. Genetic correlations equal to 1.0 were substituted for those estimates exceeding 1.00. Other traits favoring indirect selection may to some unknown extent reflect sampling error in estimates of genetic parameters. Greater gain in total performance of first lactation was expected by selection on traits expressed per day. This occurred because total performance traits, not standardized per day, had lower heritabilities than analogous traits per day. Profit in first lactation led to at least 25% greater gains in milk in first lactation compared to direct selection when traits were defined on a total or per-day basis. These results reflect the result of high genetic correlations and larger heritability for the profit trait compared to the milk-yield trait. Selection on profit/day in the first lactation resulted in larger gains in profit/day of herdlife than milk/day in the first lactation ($.14 versus $.11). This result indicates there are factors besides yield which have some genetic basis in profit during first lactation which also contribute to profit throughout herdlife. Selection on all production or profit traits had a negative correlated response for age at first calving, suggesting more efficient production and larger total production can be expected from animals which calve at an early age. This result may reflect a combination of Journal of Dairy Science Vol. 59, No. 7
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PARAMETERS AND SELECTION METHODS FOR PROFIT early sexual m a t u r i t y as well as higher relative reproductive efficiency t h r o u g h o u t life. Selection on some f u n c t i o n of performance traits of first lactation seems most desirable for changing lifetime performance since selections on lifetime traits are n o t practical. Delaying selection until i n f o r m a t i o n is available o n lifetime traits would increase greatly costs of maintaining potential replacement stocks awaiting records on dam or awaiting records on bull progeny. More importantly, genetic progress per year would become d e p e n d e n t on longer generation intervals. Five selection indexes were developed to compare relative efficiencies with selection for a single trait for expected gains in profit/day-life. The indexes were constructed by incorporating i n f o r m a t i o n available at the end of the first lactation. Traits chosen were age at first calving (P1), milk/day (P2), profit/ day (P3), and first lactation profit (P4)- Five c o m b i n a t i o n s of the four traits were defined and selection indexes developed for predicting indirectly profit/day of life. The indexes given in original units of the traits and in terms of proportionality weights and standard deviation units, respectively, were: I1 = - . 0 0 1 0 P 1 + .0513P2 + .0316P3; - . 7 0 8 0 ( P 1 / o 1 ) + (P2/o2) + .0878(P3/o3) I2 = - . 0 0 1 1 P 1 + . 0 5 5 2 P 2 ; - . 7 2 3 8 ( P I / o l ) + (P2/O2)
1331
I3 = --.0002P1 + .4028P3 ; --.1262(P1/ol ) + (P3/03) 14 = .0048P2 + .3981P3 ; .0002(P2/o2) + (P3/03 ) I s = --.0002P1 + .0010P4 ;--.1271(P1/ol) + (P4/u4 ) The proportionality weights for the various traits in the indexes take into a c c o u n t the relative i n f o r m a t i o n in first lactation traits i n d e p e n d e n t of p h e n o t y p i c variation. The relative efficiency of various single first lactation traits and indexes for indirect selection are compared in Table 5. The single most import a n t first lactation trait is profit/day during first lactation. The rGi value a n d expected responses from selection on P3 were larger than the corresponding results for P1, P2, or P4 singly. The indexes suggest the c o m b i n e d i n f o r m a t i o n from P1 and P2 is about equal to that of P3This conclusion is drawn since 11 was only 4% more efficient than P3 alone and I2 had a b o u t equal efficiency with I1 . T h e index 12 based on PI a n d P2 will, however, be simpler to calculate. Age at first calving had surprisingly large heritability and genetic correlations with profit during first lactation and life. The genetic correlations were total profit for first - . 7 8 + .22, profit/day for first - . 7 6 +- .21, and profit/day for life - . 4 1 + .23. Genetic parameters associated with age at first calving were
TABLE 5. Relative efficiency of different selection criteria for maximizing genetic gain in profit/day of life. Relative efficiency (%) Selection criterion
rGi
Response a ($)
Profit/ day-first
Milk/ day-first
Direct selection Profit/day of life
.557
.140
100
124
Indirect selection with first lactation traits Age at calving (P1) Milk/day (P2) Index (Is): P1, P2 Profit/clay (P3) Index (I 1): P1, P~, P3 Index (13): P1, P3 Index (I4): P:, P3 Total profit (P4) Index (I5): P1, P4
.293 .4.50 .581 .559 .582 .561 .559 .548 .553
.070 .113 .146 .140 .146 .141 .140 .137 .139
53 81 104 100 104 101 100 98 99
65 10_.O0 129 124 129 125 124 122 123
aResponse is given for selection differential equal to one standard deviation of selection criterion. Journal of Dairy Science VoL 59, No. 7
1332
GILL AND ALLAIRE
reduced by 33% to determine the effect of smaller values on selection efficiencies in Table 5. The index for P1 and P2 had efficiencies 91% and 112% compared to 104% and 129%, respectively. Lower genetic parameters for age at first calving (P~) would support the calculation of estimated profit (P3) compared to the use of an index including P1 and P2. The expected gain in profit/day for life was $.140 for selection on Ps which was equal to direct selection. A desirable simplifying result was that gain by indirect selection on age at first calving and milk/day in first lactation accounted for essentially all the information in profit/day for first lactation with regard to gain in profit/day for life. Greatest utilization of milk yield as a component of culling occurs during first lactation (1, 2). Alternative selection methods directed at maximizing profit/ day-life are compared for relative efficiency with respect to milk/day-first. This comparison indicates profit/day-first (P3) was +24% more efficient than milk/day while combination of P~, P2 was +29%. The expected correlated responses on economically important traits from first lactation single trait or index selection are in Table 6. Selection on the most efficient index I 1 relative to selection on milk/day alone will result in animals younger by 24 days in age of first calving, 2.5 more kg body weight, .18 more kg milk/day in first lactation, $.04 more profit/ day in life, and 7 more days of herdlife. Selection on I2 which was simpler and about as efficient as I~, results in greater gain than selection on milk/day-first by more rapidly decreasing age at first calving by - 2 6 0 % and increasing milk/day by +28% in first lactation and +8% for lifetime and increasing herdlife by +17%. Selection differentials, resulting in equal correlated responses, might be known as the relative selection value of each trait. Comparing correlated genetic responses in profit/day of life, a selection differential of 1 kg of milk/day in first lactation is equal to a selection differential of - 5 7 days for age at first calving (i.e., 1 kg: - 5 7 days). Relative economic values as defined by Hazel (8) may be obtained as the simple genetic regression of profit/day-life on each trait. These were .1742 (S/kg) for milk/ day-first and - . 0 0 1 7 (S/day) for age at first calving, giving relative economic values of 1 kg J o u r n a l o f D a i r y S c i e n c e Vol. 59, No. 7
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PARAMETERS AND SELECTION METHODS FOR PROFIT m i l k / d a y - f i r s t e q u a l t o - 1 0 2 days age. T h e relative e c o n o m i c values o n a p h e n o t y p i c basis w o u l d b e t h e simple p h e n o t y p i c regressions. These were .107 ($/kg) f o r m i l k / d a y - f i r s t a n d - . 0 0 1 3 ( S / d a y ) for age, giving relative econ o m i c value o n p h e n o t y p i c basis 1 kg e q u a l t o - 8 2 days. CONCLUSIONS
L i f e t i m e e c o n o m i c m e r i t f r o m a simplified p r o f i t f u n c t i o n i n c l u d i n g individual c o w prod u c t i o n , r e p r o d u c t i o n , a n d w e i g h t traits h a d a larger h e r i t a b i l i t y t h a n milk yield u p t o s e c o n d p a r t u r i t i o n . E x p e c t e d gains in p r o f i t / d a y - l i f e b y selecting o n p r o f i t / d a y - f i r s t o r selecting o n age at first calving a n d m i l k / d a y - f i r s t were g r e a t e r t h a n gains f r o m selecting o n m i l k / d a y - f i r s t or b y direct s e l e c t i o n o n p r o f i t / d a y - l i f e . A p r o f i t function shown to be representative for a broad range of c o n d i t i o n s can increase t h e e f f i c i e n c y of selection f o r p r o f i t a b i l i t y . ACKNOWLEDGMENT
T h e a u t h o r s wish t o t h a n k U S A I D p r o g r a m for f u n d s s u p p o r t i n g this research a n d T. M. L u d w i c k a n d E. R. R a d e r for c o o p e r a t i o n a n d access t o d a t a c o l l e c t e d u n d e r t h e Ohio NC-2 Project. REFERENCES
1 Allaire, F. R., and C. R. Henderson. 1966. Selection practiced among dairy cows. II. Total production over a sequence of lactations. J. Dairy Sci. 49:1435. 2 Allaire, F. R., and C. R. Henderson. 1967. Selection practiced among dairy cows. III. Type appraisal and lactation traits. J. Dairy Sci. 50:194. 3 Brown, G. H., and H. N. Turner. 1968. Response to selection in Australian Merino sheep. II. Esti-
1 333
mates of phenotypic and genetic parameters for some production traits in Merino ewes and an analysis of the possible effects of selection on them. Aust. J. Agr. Res. 19:303. 4 Evans, D. L., C. Branton, and B. R. Farthing. 1964. Heritability estimates and interrelationships among production per day of productive life, longevity, breeding efficiency, and type in a herd of Holstein cows. J. Dairy Sci. 47:699. (Abstr.) 5 Gill, G. S., and F. R. Allaire. 1976. Relationship of age at first calving, days open, days dry, and herdlife to a profit function for dairy cattle. J. Dairy Sci. 59:1131. 6 Harvey, W. R. 1970. Estimation of variance and covariance components in a mixed model. Biometrics 26:485. 7 Harville, D. A., and C. R. Henderson. 1966. Interrelationships among age, body weight, and production traits during first lactations of dairy cattle. J. Dairy Sci. 49:1254. 8 Hazel, L. N. 1943. The genetic basis for constructing selection indexes. Genetics 28:476. 9 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. 10 Larson, C. J., A. B. Chapman, and L. E. Casida. 1951. Butterfat production per day of life as a criterion of selection in dairy cattle. J. Dairy Sci. 34:1163. 11 Miller, P., L. D. Van Vleck, and C. R. Henderson. 1967. Relationships among herdlife, milk production, and calving interval. J. Dairy Sci. 50:1283. 12 Plowman, R. D., and R. F. Gaalaas. 1960. Heritability estimates of longevity in Holstein-Friesian cattle. J. Dairy Sci. 43:877. (Abstr.) 13 Schultz, L. H. 1969. Relationship of rearing rate of diary heifers to mature performance. J. Dairy Sci. 52:1321. 14 Swanson, E. W. 1967. Optimum growth patterns for dairy cattle. J. Dairy Sci. 50:244. 15 Swiger, L. A., W. R. Harvey, D. O. Everson and K. E. Gregory. 1964. The variance of intraclass correlation involving groups with one observation. Biometrics 20:818. 16 Tallis, G. M. 1959. Sampling errors of genetic correlation coefficients calculated from analyses of variance and covariance. Aust. J. Stat. 1: 35.
Journal of Dairy Science Vol. 59, No. 7