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Age of Dam and Maternal Effects for Dystocia in Holsteins1
Age of Dam and Maternal Effects for Dystocia in Holsteins 1 J. R. THOMPSON, A. E. FREEMAN, and P. J. BERGER Department of Animal Science Iowa State University Ames 50011
ABSTRACT
genes affecting dystocia in all parities and would allow inclusion of data from later parity animals for improved accuracy in evaluating sires for use on virgin heifers. Discussion also exists as to whether dystocia should be considered a trait of the calf or a trait of the dam. The NAAB calving-ease summary estimates sire transmitting ability for the ease with which his progeny are born (trait of the calf). Correlations of sire rankings as a trait of the calf with sire rankings as a trait of the dam have produced small or zero values (3, 9). A negative relationship between direct (trait o f the calf) and maternal effects would reduce progress from selecting against the direct effect. Philipsson (6) reported a negative - . 1 9 correlation for direct with maternal. The purpose of our study was to estimate genetic correlation for dystocia in first with later parities and to estimate correlation of maternal with direct effects o f dystocia.
Genetic correlations between dystocia in first with later parities and between direct with maternal effects for dystocia were estimated. Dystocia in first and later parities represent similar traits because of a large genetic correlation of .84. This similarity should allow calving reports on older dams and heifers to be combined in predicting a bull's calving performance. Correlations for direct with maternal effects were - . 3 8 for the heifer population and - . 2 5 for the cow (second and greater parities) population. This correlation would reduce progress from selecting for reduced dystocia if only direct effects were considered. Breeding programs to reduce dystocia should consider both direct and maternal performance. INTRODUCTION
Researchers (1, 3, 6) have suggested that dystocia in first and later parities should be considered separate traits. The present National Association of Animal Breeders (NAAB) calving ease summary, however, assumes that dystocia in first and later parities represents the same trait and uses progeny from all parities of dam to rank sires for dystocia. This assumption was made because the larger volume of data from older dams should improve accuracy of sire evaluation for use on virgin heifers if the traits are similar. Correlation of sire rankings from first with sire rankings from later parity data has resulted in correlations of .50 to .60 (1, 3, 8, 13). These correlations underestimate the genetic relationship (4). A large genetic correlation between dystocia in first with later parities indicates major influence of the same
Received September 15, 1980. 1Journal Paper No. J-9971 of the Iowa Agriculture and Home Economics Experiment Station, Ames. Project No. 1053. 1981 J Dairy Sci 64:1603-1609
DATA
Dystocia data were obtained from NAAB. These data were collected by individual bull studs from calving reports sent to dairymen. Information requested from all calvings in a herd were: date of calving - two seasons were defined, October through March and April through September; sex of calf; identification of calf, sire, dam, and maternal grandsire; parity of dam - lactation number initiated by calving; difficulty of calving - scored: 1 ) n o problem, 2) slight problem, 3) needed assistance, 4 ) c o n siderable force, 5) extreme difficulty; livability of calf - scored: 1) alive, 2) dead at birth, 3) dead by 48 hours postpartum; calf condition scored: 1) normal, 2) weak, 3) deformed. Holstein data were 177,455 records from 15 bull studs. Difficulty score was the measure of dystocia. Evaluator differences in difficulty score were removed by absorbing herd-yearseasons provided that a single person scored all calvings in a herd-year-season and was consistent in scoring.
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1604
THOMPSON ET AL. METHODS
The genetic correlation b e t w e e n dystocia in first and later parities was estimated by assuming dystocia in each age group a separate trait. Data were f r o m sires with progeny resulting f r o m b o t h first and later parity dams. A multitrait m i x e d - m o d e l procedure ( I 0 ) was used to estimate sire c o m p o n e n t s of variance and covariance for the t w o traits f r o m the m o d e l : Yi = Wihi + Xibi + Ziui + ei where Yi is the n i x 1 vector of observed difficulty scores for i = 1, first parity dams and i = 2, second and greater parity dams. n i is the n u m b e r of observations in the ith parity group. Wi is a k n o w n n i x nhi incidence matrix for herd-year-seasons. nh i is the n u m b e r of herd-year-seasons for the i th trait. Xi is a k n o w n n i X 2 incidence matrix for sex o f calf. bi is an u n k n o w n 2 x 1 vector of fixed sexof-calf effects. Zi is a k n o w n n i x n s incidence matrix for sires. ui is an u n k n o w n n s × 1 vector of r a n d o m sire transmitting abilities. e i is an u n k n o w n n i × I vector of r a n d o m residuals. The multitrait procedure (10) ignored error covariance b e t w e e n traits; thus, the error structure was
Var
= 2
\e2]
In2 0%
Sire variance structure was
:
ttnJs,,~
l. sa~:
_]
where n s is the n u m b e r of sires and the same sires included for b o t h traits. In an application of their procedure, Schaeffer et al. (10) considered estimating components of variance and covariance for male Journal of Dairy Science Vol. No. 64,
7, 1981
and female yearling weights. The assumption of zero error covariance was realistic in this situation. A similar situation w o u l d exist in our s t u d y if no dam in the first parity group was included in the later parity group. Verification o f this restriction was difficult because o f p o o r dam identification; however, a check of available dam identification indicated that o n l y 7% of the identified first parity dams were in the later parity group. Records o f dams that appeared in b o t h groups were affected by differe n t environments, which should m i n i m i z e error covariance but n o t eliminate it. The overall error covariance induced by the small n u m b e r o f dams in b o t h groups should be small in respect to error variance; thus, the a s s u m p t i o n o f zero error covariance should be nearly met. Sires were required to have progeny in five herds by each dam group. This restriction improved herd-year-season ties. The five herds with first parity calvings were allowed to be identical with or c o m p l e t e l y u n i q u e f r o m the five herds with older dam calvings. The m i x e d - m o d e l equations after absorption of herd-year-seasons were: TiXiQiXi +
¢
"YiZiQiXi
~ "/iXiQiZi
b
+7iZiQiZi J + Is * g -
u
TiXi(~iy t Lz+ 3tiZiQiYd
where Y~+ denotes the direct sum m a t r i x o p e r a t o r (12) * denotes the direct p r o d u c t m a t r i x o p e r a t o r (12) "Yi = 1/o2i , the inverse of the error comp o n e n t of variance for trait i Qi results f r o m the absorption of herd-yearseason effects equal lni -- Wi(W'iWi) -1 W I g - l is the variance-covariance m a t r i x a m o n g sires equal -1
AGE AND MATERNAL EFFECTS FOR DYSTOCIA Tong et al. (15) reported the computational procedure in detail. The basic methodology was to compute sire solutions with initial estimates for components of variance and covariance, use a quadratic form of the sire solutions to compute new components of variance and covariance, and use the new variance components again to compute sire solutions. This process was repeated iteratively until variance components stabilized. Our study made use of two techniques to expedite component stabilization. The common intercept approach (C1A) of Schaeffer (11) was used to obtain starting estimates for components of variance and covariance. The CIA procedure involved choosing high and low preliminary components of variance, obtaining new component estimates from each preliminary estimate, computing the slope of the line connecting new with preliminary estimates, and extrapolating lines until they intersected. The point of intersection was a satisfactory starting estimate for iteration. The second technique was to use the sum of squared deviations (SSD) or residue norm (5) of actual right-hand sides (TiXiQiYi) from righthand sides estimated at each round of iteration as a measure of stability of sire solutions. The basis of this procedure was the set of solutions that satisfied the mixed-model equations multiplied by the left-hand members (estimated right-hand sides) should regenerate the righthand members. A simple example from ordinary least squares is: normal equations,
1605
right-hand side was an adequate indicator of a satisfactory solution. The SSD used for solution was, thus, .0001 times the number of equations. The SSD also was an indicator for stable components of variance and covariance. A small change in components of variance would result in a small change in sire solutions. A small SSD from the first round of solution iteration after a new set of components o f variance and covariance were applied was, thus, an indicator of stable variance components. The preliminary study supported this and indicated that a SSD of .00015 times the number of equations from the first round o f iteration with new variance components was an indicator of stable components of variance. The same m e t h o d o l o g y was used to estimate components of variance and covariance for the maternal-direct relationship. Data included the same bull as both a sire and maternal grandsire. Dystocia represented separate traits for influence of the sire and maternal grandsire. A single record was not permitted to be in both data groups (i.e., a record with identified sire and maternal grandsire was assigned to one group randomly); thus, zero error covariance was realistic. Sire and maternal grandsire components of variance were obtained. Needed to estimate the direct-maternal correlation were the additive genetic variance (o~), maternal variance ( o ~ ) , and the additive-maternal covariance (OAM). These were estimated by equating components of variance to their genetic expectation (16):
X'Xfl = X'y o~ = o ~ / 4 , and solutions fi = (XIx) - t X'y; thus, if fl satisfies the normal equations /%
OS.MG S = 0 1 / 8 + aAM/4, and
^
X ' y = X'Xfl = X ' y
O~IGS = O~/16 + a~,i/4 + OAM/4.
^
a measure of accuracy of fl might be /N
SSD = (X'y - X ' y ) ' ( X ' y - X~'y) The SSD was calculated in our study from both fixed effect and sire solutions. A SSD below a preset number signaled a satisfactory solution to the mixed-model equations. A preliminary study o f data of similar form and solutions from a direct inverse indicated that a squared deviation of .0001 or less for each
The correlation between direct and maternal effects was estimated from:
rA~ = OA~/(O~ + Oh ) ' s .
RESULTS
Table 1 characterizes data for the age-ofdam analysis. A total o f 143,495 records from 14,170 herd-year-seasons were available. Heifer (first parity) calvings sired by 650 bulls acJournal of Dairy Science Vol. 64, No. 7, 1981
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THOMPSON ET AL.
TABLE 1. (~baracteristics of data to estimate sire components of variance and covariance from first and later parity data. Parity classification
Sires Records Herd-year-seasons
Heifers
Cows
650 29,099 7,004
650 114,386 11,876
Total 650 a 143,485 14,170 b
aMultitrait analysis procedures require the same set of sires to be included for all traits. bseveral herd-year-seasons included both heifer and cow calvings.
c o u n t e d for 20.3% o f the total data. High and low preliminary and starting (after CIA) comp o n e n t s of variance are in Table 2. The initial low estimate c o r r e s p o n d e d to a heritability of .02, the high to a heritability of .12. A zero sire c o m p o n e n t o f covariance was used during this portion of the p r o c e d u r e . The two covariance estimates o b t a i n e d during application of C I A to variances were averaged and used f r o m a low preliminary covariance of zero. The covariance corresponding to a genetic correlation of 1.0 and the starting variances then were used for a high preliminary estimate. The starting estimates in Table 2 were applied t o w a r d final estimates for c o m p o n e n t s of variance and covariance (Table 2). Twelve rounds of iteration were required to m e e t the outlined covergence criteria. Final heritabilities were .04 for cows and .08 for heifers. These estimates are slightly smaller
than prior estimates for US cattle (9, 13) b u t are c o m p a r a b l e to E u r o p e a n and Israeli estimates (1, 7). The genetic correlation b e t w e e n d y s t o c i a in heifers and cows was .84. Variation a m o n g heifers was twice that in cows. Sex-ofcalf differences also were a b o u t twice as large in the heifer p o p u l a t i o n (.36 for heifers versus .16 for cows), males born with m o r e difficulty. More dystocia in male calvings is consistent with previous w o r k (1, 3, 6, 9, 13), and size o f sex-of-calf differences are consistent with Teixeira (13). Larger sex-of-calf differences for first versus later parity calvings m a y in part be f r o m larger variation. The direct-maternal relationship was evaluated separately for heifers and cows. This partitioning was to d e t e r m i n e w h e t h e r estimates differed b e t w e e n heifers and cows. Data to estimate the maternal relationship are described in Table 3. More direct records, 62% o f
TABLE 2. Preliminary, a starting, b and final estimates for components of variance and covariance.
Preliminary low (h 2 = .02) Preliminary high (h 2 = .12) Starting Final
OsI c
0 2
.00658
.00334
.04050 .02400 .02473
.02058 .00680 .00640
S2
Os
02
o 2
0
1.3095
.6653
0
0 .00904 .01050
1.3095 1.2545 1.2624
.6653 .6511 .6527
0 0 0
t ,2
el
e2
(:}reI j2
d
aEstimates chosen to correspond to h 2 of .02 (low) and .12 (high) before application of common intercept approach. bEstimates after application of common intercept approach. CSubscript 1 refers to first parity dams, subscript 2 to second and greater parity. dError covariance defined zero. Journal of Dairy Science Vol. 64, No. 7, 1981
AGE AND MATERNAL EFFECTS FOR DYSTOCIA
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TABLE 3. Characteristics of data to estimate components of variance for direct-maternal relationships. Heifers
Sires Progeny Herd-year-seasons
Directc
Matemald
199 11,854 3,054
199 7,383 2,510
Cows Total
Direct
Maternal
199a 19,237 5,409 b
323 48,746 8,156
323 20,712 4,651
Total 323 a 69,458 11,280 b
aThe multitrait procedure required the same set of sires for all traits. bseveral herd-year-seasons contained both direct and maternal records. CDirect records considered sire of calf.
dMaternal records considered sire of dam or maternal grandsire of calf.
the total for heifers and 70% for cows, were available than maternal records (bull appeared as a maternal grandsire). The heifer population consisted of 19,237 records from 199 bulls and 5,409 herd-year-seasons whereas the cow population was 69,458 records from 323 sires and 11,280 h erd-year-seasons. Final sire and maternal grandsire components of variance and covariance are in Table 4. These components are equated to their genetic expectations to obtain additive and maternal components plus their covariance (Table 4). Total variation for heifers again was larger than variation for cows. Variation for dystocia as a trait of the calf was larger than variation as a trait of the dam. Sire-maternal grandsire covariance was one exception where heifer variation was not larger than cow variation but approximately equal (.0018 versus .0026). Additive genetic variation was larger than maternal variation and the additivematernal covariance was negative for both heifer and cow populations. Additive-maternal correlations were - . 3 8 for heifers and --.25 for cows. These agreed in sign but were slightly larger than the - . 1 9 of Philipsson (7) from heifer data. DISCUSSION
The large genetic correlation for dystocia in first with later parities indicated that the traits were influenced largely by the same genes. Data from second and later parities should increase accuracy of sire evaluations. The situation for dystocia parallels that for
milk production in which the genetic correlation between production in different lactations is not one, but the traits are considered the same. The question of including all data or only data from first parity calvings was addressed by comparing two sire evaluation methods. The first (Method I) was the present method of using all data. Heritability was .05 in this method. The second method was analysis of only data from heifer calvings. Advantages of the latter were 1) fewer data would be collected and analyzed, and 2) it would take advantage of the larger heritability in the heifer population. Accuracy of a progeny test from n progeny was defined as (nh2/(4 + (n - 1)h 2)'s. Table 5 compares accuracy of sire evaluation under each scheme. Several numbers of prog-
TABLE 4. Components of variance and covariance to estimate direct-maternal correlations. Population Hei~rs Final o~ Final O~GS Final Os.MGS Final O~s Final 2 °eMGS Additive genetic variation Maternal variation Additive-maternal covariance
.0112 .0080 .O018 1.3811 1.1560 .0450 .0365 -.0155
Cows .0060 .0021 .0026 .7587 .5686 .0242 .0079 -.0035
Journal of Dairy Science Vol. 64, No. 7, 1981
THOMPSON ET AL.
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TABLE 5. Comparison of two sire evaluation procedures for dystocia. Number of progeny (total) 10 50 100 500 1,000 5,000
Heifer data only Combined analysis Accuracya .34 .62 .75 .93 .96 .99
Recordsb
Accuracy
2 10 20 100 200 1,000
.20 .41 .54 .82 .90 .98
aAccuracy defined to be [nh2/(4 + (n - 1)h2)l .s b20% of total records assumed to be from first parity dams.
eny per sire were chosen, and accuracy of a progeny test was computed for all progeny (Method I) and 20% of the total progeny and heritability .08 (Method II). The 20% was the percentage of first parity calvings in our study. Method I always resulted in a greater accuracy, but accuracy was comparable for progeny numbers greater than 500. Most bulls in the present sire evaluation have less than 100 progeny; thus, Method I is recommended unless large numbers are available. The negative direct-maternal correlation indicated that females born with ease may tend to have difficulty in giving birth. This relationship possibly exists because small calves born with less difficulty (8) may result in small cows, which have increased difficulty in birth (9). The negative additive-maternal relationship should have little impact because bulls entering AI are not selected for calving performance, and the correlation between breeding values for production and dystocia is zero (14). The negative correlation should be considered, however, if bulls entering AI are selected for calving performance. Selecting against the direct effect for dystocia over several generations also would result in less response than expected. The direct effect of the maternal grandsire also is passed through the dam, which offsets the maternal effect to some extent. The size of the correlations for direct with maternal effects allows some bulls to be desirable for both traits. Ranking bulls for maternal effects is not recommended at this time but should be considered before selection against dystocia is applied to bulls entering AI. Journal of Dairy Science Vol. 64, No. 7, 1981
CONCLUSIONS
The genetic correlation for dystocia in first with later parities is large indicating that the traits have a similar genetic base. Continuation of the practice of including all data in sire evaluation for dystocia and adjusting for unequal age-of-dam variation is recommended. Additive effects are negatively correlated with maternal effects. Sire evaluation for maternal effects is not recommended but should be considered before selecting bulls entering artificial insemination on calving performance.
ACKNOWLEDGMENT
This research was supported by grant No. I-3-79 of the Binational Agricultural Research Development Fund (BARD).
REFERENCES
1 Bar-Anan, R., M. Soller, and J. C. Bowman. 1976.
Genetic and environmental factors affecting the incidence of difficult calving and perinatal calf mortality in IsraeI-Friesian dairy herds. Anita. Prod. 22:299. 2 Berger, P. J., and A. E. Freeman. 1978. Prediction of sire merit for calving difficulty. J. Dairy Sci. 61 : 1146. 3 Cady, R. A. 1980. Evaluation of Holstein bulls for dystocia. Ph.D. dissertation. Comell University, Ithaca, NY. 4 Calo, L. L., R. E. McDowell, L. D. Van Vieck, and P. D. Miller. 1973. Genetic aspects of beef production among Holstein-Friesians pedigree selected for milk production. J. Anita. Sci. 37:676. 5 Gerog, D. D., and R. F. Keller. 1973. Criteria for ordering columns in two-dimensional projection
AGE AND MATERNAL EFFECTS FOR DYSTOCIA methods. Publ. IS-3147, Ames Lab., USAEC, Ames, IA. 6 Philipsson, J. 1976. Studies on calving difficulty, stillbirth and associated factors in Swedish cattle breeds. II. Effects of non-genetic factors. Acta Agric. Scand. 26:165. 7 Philipsson, J. 1976. Studies on calving difficulty, stillbirth and associated factors in Swedish cattle breeds. III. Genetic parameters. Acta Agric. Scand. 26:211. 8 Pollak, E. J. 1975. Dystocia in Holsteins. Ph.D. dissertation, Iowa State University, Ames. Microfilm No. 76-1866, Univ. Microfilms, Ann Arbor, MI. 9 Pollak, E. J., and A. E. Freeman. 1976. Parameter estimation and sire evaluation for dystocia and calf size in Holsteins. J. Dairy Sci. 59:1817. 10 Schaeffer, L. R., J. W. Wilton, and R. Thomson. 1978. Simultaneous estimation of variance and covariance components from multitrait mixed model equations. Biometrics 34:199. 11 Schaeffer, L. R. 1979. Estimation of variance and
12 13
14
15
16
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covariance components for average daily gain and backfat thickness in swine. Variance components and animal breeding. Proc. Conf. in honor of C. R. Henderson. Cornell University, Ithaca, NY. Searle, S. R. 1966. Matrix algebra for the biological sciences. John Wiley and Sons, Inc., New York, NY. Teixeira, N. M. 1978. Genetic differences in dystocia, calf condition, and calf livability in Holsteins. Ph.D. dissertation. Iowa State University, Ames. Thompson, J. R., A. E. Freeman, and P. J. Berger. 1980. Relationship of dystocia transmitting ability with type and production transmitting abilities in Holstein bulls. J. Dairy Sci. 63:1462. Tong, A.K.W., B. W. Kennedy, and J. E. Moxley. 1979. Heritabilities and genetic correlations for the first three lactations from records subject to culling. J. Dairy Sci. 62:1784. Wiliham, R. L. 1972. The role of maternal effects in animal breeding: III. Biometrical aspects of maternal effects in animals. J. Anim. Sci. 36:1288.
Journal of Dairy Science Vol. 64, No. 7, 1981
ABSTRACT
genes affecting dystocia in all parities and would allow inclusion of data from later parity animals for improved accuracy in evaluating sires for use on virgin heifers. Discussion also exists as to whether dystocia should be considered a trait of the calf or a trait of the dam. The NAAB calving-ease summary estimates sire transmitting ability for the ease with which his progeny are born (trait of the calf). Correlations of sire rankings as a trait of the calf with sire rankings as a trait of the dam have produced small or zero values (3, 9). A negative relationship between direct (trait o f the calf) and maternal effects would reduce progress from selecting against the direct effect. Philipsson (6) reported a negative - . 1 9 correlation for direct with maternal. The purpose of our study was to estimate genetic correlation for dystocia in first with later parities and to estimate correlation of maternal with direct effects o f dystocia.
Genetic correlations between dystocia in first with later parities and between direct with maternal effects for dystocia were estimated. Dystocia in first and later parities represent similar traits because of a large genetic correlation of .84. This similarity should allow calving reports on older dams and heifers to be combined in predicting a bull's calving performance. Correlations for direct with maternal effects were - . 3 8 for the heifer population and - . 2 5 for the cow (second and greater parities) population. This correlation would reduce progress from selecting for reduced dystocia if only direct effects were considered. Breeding programs to reduce dystocia should consider both direct and maternal performance. INTRODUCTION
Researchers (1, 3, 6) have suggested that dystocia in first and later parities should be considered separate traits. The present National Association of Animal Breeders (NAAB) calving ease summary, however, assumes that dystocia in first and later parities represents the same trait and uses progeny from all parities of dam to rank sires for dystocia. This assumption was made because the larger volume of data from older dams should improve accuracy of sire evaluation for use on virgin heifers if the traits are similar. Correlation of sire rankings from first with sire rankings from later parity data has resulted in correlations of .50 to .60 (1, 3, 8, 13). These correlations underestimate the genetic relationship (4). A large genetic correlation between dystocia in first with later parities indicates major influence of the same
Received September 15, 1980. 1Journal Paper No. J-9971 of the Iowa Agriculture and Home Economics Experiment Station, Ames. Project No. 1053. 1981 J Dairy Sci 64:1603-1609
DATA
Dystocia data were obtained from NAAB. These data were collected by individual bull studs from calving reports sent to dairymen. Information requested from all calvings in a herd were: date of calving - two seasons were defined, October through March and April through September; sex of calf; identification of calf, sire, dam, and maternal grandsire; parity of dam - lactation number initiated by calving; difficulty of calving - scored: 1 ) n o problem, 2) slight problem, 3) needed assistance, 4 ) c o n siderable force, 5) extreme difficulty; livability of calf - scored: 1) alive, 2) dead at birth, 3) dead by 48 hours postpartum; calf condition scored: 1) normal, 2) weak, 3) deformed. Holstein data were 177,455 records from 15 bull studs. Difficulty score was the measure of dystocia. Evaluator differences in difficulty score were removed by absorbing herd-yearseasons provided that a single person scored all calvings in a herd-year-season and was consistent in scoring.
1603
1604
THOMPSON ET AL. METHODS
The genetic correlation b e t w e e n dystocia in first and later parities was estimated by assuming dystocia in each age group a separate trait. Data were f r o m sires with progeny resulting f r o m b o t h first and later parity dams. A multitrait m i x e d - m o d e l procedure ( I 0 ) was used to estimate sire c o m p o n e n t s of variance and covariance for the t w o traits f r o m the m o d e l : Yi = Wihi + Xibi + Ziui + ei where Yi is the n i x 1 vector of observed difficulty scores for i = 1, first parity dams and i = 2, second and greater parity dams. n i is the n u m b e r of observations in the ith parity group. Wi is a k n o w n n i x nhi incidence matrix for herd-year-seasons. nh i is the n u m b e r of herd-year-seasons for the i th trait. Xi is a k n o w n n i X 2 incidence matrix for sex o f calf. bi is an u n k n o w n 2 x 1 vector of fixed sexof-calf effects. Zi is a k n o w n n i x n s incidence matrix for sires. ui is an u n k n o w n n s × 1 vector of r a n d o m sire transmitting abilities. e i is an u n k n o w n n i × I vector of r a n d o m residuals. The multitrait procedure (10) ignored error covariance b e t w e e n traits; thus, the error structure was
Var
= 2
\e2]
In2 0%
Sire variance structure was
:
ttnJs,,~
l. sa~:
_]
where n s is the n u m b e r of sires and the same sires included for b o t h traits. In an application of their procedure, Schaeffer et al. (10) considered estimating components of variance and covariance for male Journal of Dairy Science Vol. No. 64,
7, 1981
and female yearling weights. The assumption of zero error covariance was realistic in this situation. A similar situation w o u l d exist in our s t u d y if no dam in the first parity group was included in the later parity group. Verification o f this restriction was difficult because o f p o o r dam identification; however, a check of available dam identification indicated that o n l y 7% of the identified first parity dams were in the later parity group. Records o f dams that appeared in b o t h groups were affected by differe n t environments, which should m i n i m i z e error covariance but n o t eliminate it. The overall error covariance induced by the small n u m b e r o f dams in b o t h groups should be small in respect to error variance; thus, the a s s u m p t i o n o f zero error covariance should be nearly met. Sires were required to have progeny in five herds by each dam group. This restriction improved herd-year-season ties. The five herds with first parity calvings were allowed to be identical with or c o m p l e t e l y u n i q u e f r o m the five herds with older dam calvings. The m i x e d - m o d e l equations after absorption of herd-year-seasons were: TiXiQiXi +
¢
"YiZiQiXi
~ "/iXiQiZi
b
+7iZiQiZi J + Is * g -
u
TiXi(~iy t Lz+ 3tiZiQiYd
where Y~+ denotes the direct sum m a t r i x o p e r a t o r (12) * denotes the direct p r o d u c t m a t r i x o p e r a t o r (12) "Yi = 1/o2i , the inverse of the error comp o n e n t of variance for trait i Qi results f r o m the absorption of herd-yearseason effects equal lni -- Wi(W'iWi) -1 W I g - l is the variance-covariance m a t r i x a m o n g sires equal -1
AGE AND MATERNAL EFFECTS FOR DYSTOCIA Tong et al. (15) reported the computational procedure in detail. The basic methodology was to compute sire solutions with initial estimates for components of variance and covariance, use a quadratic form of the sire solutions to compute new components of variance and covariance, and use the new variance components again to compute sire solutions. This process was repeated iteratively until variance components stabilized. Our study made use of two techniques to expedite component stabilization. The common intercept approach (C1A) of Schaeffer (11) was used to obtain starting estimates for components of variance and covariance. The CIA procedure involved choosing high and low preliminary components of variance, obtaining new component estimates from each preliminary estimate, computing the slope of the line connecting new with preliminary estimates, and extrapolating lines until they intersected. The point of intersection was a satisfactory starting estimate for iteration. The second technique was to use the sum of squared deviations (SSD) or residue norm (5) of actual right-hand sides (TiXiQiYi) from righthand sides estimated at each round of iteration as a measure of stability of sire solutions. The basis of this procedure was the set of solutions that satisfied the mixed-model equations multiplied by the left-hand members (estimated right-hand sides) should regenerate the righthand members. A simple example from ordinary least squares is: normal equations,
1605
right-hand side was an adequate indicator of a satisfactory solution. The SSD used for solution was, thus, .0001 times the number of equations. The SSD also was an indicator for stable components of variance and covariance. A small change in components of variance would result in a small change in sire solutions. A small SSD from the first round of solution iteration after a new set of components o f variance and covariance were applied was, thus, an indicator of stable variance components. The preliminary study supported this and indicated that a SSD of .00015 times the number of equations from the first round o f iteration with new variance components was an indicator of stable components of variance. The same m e t h o d o l o g y was used to estimate components of variance and covariance for the maternal-direct relationship. Data included the same bull as both a sire and maternal grandsire. Dystocia represented separate traits for influence of the sire and maternal grandsire. A single record was not permitted to be in both data groups (i.e., a record with identified sire and maternal grandsire was assigned to one group randomly); thus, zero error covariance was realistic. Sire and maternal grandsire components of variance were obtained. Needed to estimate the direct-maternal correlation were the additive genetic variance (o~), maternal variance ( o ~ ) , and the additive-maternal covariance (OAM). These were estimated by equating components of variance to their genetic expectation (16):
X'Xfl = X'y o~ = o ~ / 4 , and solutions fi = (XIx) - t X'y; thus, if fl satisfies the normal equations /%
OS.MG S = 0 1 / 8 + aAM/4, and
^
X ' y = X'Xfl = X ' y
O~IGS = O~/16 + a~,i/4 + OAM/4.
^
a measure of accuracy of fl might be /N
SSD = (X'y - X ' y ) ' ( X ' y - X~'y) The SSD was calculated in our study from both fixed effect and sire solutions. A SSD below a preset number signaled a satisfactory solution to the mixed-model equations. A preliminary study o f data of similar form and solutions from a direct inverse indicated that a squared deviation of .0001 or less for each
The correlation between direct and maternal effects was estimated from:
rA~ = OA~/(O~ + Oh ) ' s .
RESULTS
Table 1 characterizes data for the age-ofdam analysis. A total o f 143,495 records from 14,170 herd-year-seasons were available. Heifer (first parity) calvings sired by 650 bulls acJournal of Dairy Science Vol. 64, No. 7, 1981
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THOMPSON ET AL.
TABLE 1. (~baracteristics of data to estimate sire components of variance and covariance from first and later parity data. Parity classification
Sires Records Herd-year-seasons
Heifers
Cows
650 29,099 7,004
650 114,386 11,876
Total 650 a 143,485 14,170 b
aMultitrait analysis procedures require the same set of sires to be included for all traits. bseveral herd-year-seasons included both heifer and cow calvings.
c o u n t e d for 20.3% o f the total data. High and low preliminary and starting (after CIA) comp o n e n t s of variance are in Table 2. The initial low estimate c o r r e s p o n d e d to a heritability of .02, the high to a heritability of .12. A zero sire c o m p o n e n t o f covariance was used during this portion of the p r o c e d u r e . The two covariance estimates o b t a i n e d during application of C I A to variances were averaged and used f r o m a low preliminary covariance of zero. The covariance corresponding to a genetic correlation of 1.0 and the starting variances then were used for a high preliminary estimate. The starting estimates in Table 2 were applied t o w a r d final estimates for c o m p o n e n t s of variance and covariance (Table 2). Twelve rounds of iteration were required to m e e t the outlined covergence criteria. Final heritabilities were .04 for cows and .08 for heifers. These estimates are slightly smaller
than prior estimates for US cattle (9, 13) b u t are c o m p a r a b l e to E u r o p e a n and Israeli estimates (1, 7). The genetic correlation b e t w e e n d y s t o c i a in heifers and cows was .84. Variation a m o n g heifers was twice that in cows. Sex-ofcalf differences also were a b o u t twice as large in the heifer p o p u l a t i o n (.36 for heifers versus .16 for cows), males born with m o r e difficulty. More dystocia in male calvings is consistent with previous w o r k (1, 3, 6, 9, 13), and size o f sex-of-calf differences are consistent with Teixeira (13). Larger sex-of-calf differences for first versus later parity calvings m a y in part be f r o m larger variation. The direct-maternal relationship was evaluated separately for heifers and cows. This partitioning was to d e t e r m i n e w h e t h e r estimates differed b e t w e e n heifers and cows. Data to estimate the maternal relationship are described in Table 3. More direct records, 62% o f
TABLE 2. Preliminary, a starting, b and final estimates for components of variance and covariance.
Preliminary low (h 2 = .02) Preliminary high (h 2 = .12) Starting Final
OsI c
0 2
.00658
.00334
.04050 .02400 .02473
.02058 .00680 .00640
S2
Os
02
o 2
0
1.3095
.6653
0
0 .00904 .01050
1.3095 1.2545 1.2624
.6653 .6511 .6527
0 0 0
t ,2
el
e2
(:}reI j2
d
aEstimates chosen to correspond to h 2 of .02 (low) and .12 (high) before application of common intercept approach. bEstimates after application of common intercept approach. CSubscript 1 refers to first parity dams, subscript 2 to second and greater parity. dError covariance defined zero. Journal of Dairy Science Vol. 64, No. 7, 1981
AGE AND MATERNAL EFFECTS FOR DYSTOCIA
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TABLE 3. Characteristics of data to estimate components of variance for direct-maternal relationships. Heifers
Sires Progeny Herd-year-seasons
Directc
Matemald
199 11,854 3,054
199 7,383 2,510
Cows Total
Direct
Maternal
199a 19,237 5,409 b
323 48,746 8,156
323 20,712 4,651
Total 323 a 69,458 11,280 b
aThe multitrait procedure required the same set of sires for all traits. bseveral herd-year-seasons contained both direct and maternal records. CDirect records considered sire of calf.
dMaternal records considered sire of dam or maternal grandsire of calf.
the total for heifers and 70% for cows, were available than maternal records (bull appeared as a maternal grandsire). The heifer population consisted of 19,237 records from 199 bulls and 5,409 herd-year-seasons whereas the cow population was 69,458 records from 323 sires and 11,280 h erd-year-seasons. Final sire and maternal grandsire components of variance and covariance are in Table 4. These components are equated to their genetic expectations to obtain additive and maternal components plus their covariance (Table 4). Total variation for heifers again was larger than variation for cows. Variation for dystocia as a trait of the calf was larger than variation as a trait of the dam. Sire-maternal grandsire covariance was one exception where heifer variation was not larger than cow variation but approximately equal (.0018 versus .0026). Additive genetic variation was larger than maternal variation and the additivematernal covariance was negative for both heifer and cow populations. Additive-maternal correlations were - . 3 8 for heifers and --.25 for cows. These agreed in sign but were slightly larger than the - . 1 9 of Philipsson (7) from heifer data. DISCUSSION
The large genetic correlation for dystocia in first with later parities indicated that the traits were influenced largely by the same genes. Data from second and later parities should increase accuracy of sire evaluations. The situation for dystocia parallels that for
milk production in which the genetic correlation between production in different lactations is not one, but the traits are considered the same. The question of including all data or only data from first parity calvings was addressed by comparing two sire evaluation methods. The first (Method I) was the present method of using all data. Heritability was .05 in this method. The second method was analysis of only data from heifer calvings. Advantages of the latter were 1) fewer data would be collected and analyzed, and 2) it would take advantage of the larger heritability in the heifer population. Accuracy of a progeny test from n progeny was defined as (nh2/(4 + (n - 1)h 2)'s. Table 5 compares accuracy of sire evaluation under each scheme. Several numbers of prog-
TABLE 4. Components of variance and covariance to estimate direct-maternal correlations. Population Hei~rs Final o~ Final O~GS Final Os.MGS Final O~s Final 2 °eMGS Additive genetic variation Maternal variation Additive-maternal covariance
.0112 .0080 .O018 1.3811 1.1560 .0450 .0365 -.0155
Cows .0060 .0021 .0026 .7587 .5686 .0242 .0079 -.0035
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THOMPSON ET AL.
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TABLE 5. Comparison of two sire evaluation procedures for dystocia. Number of progeny (total) 10 50 100 500 1,000 5,000
Heifer data only Combined analysis Accuracya .34 .62 .75 .93 .96 .99
Recordsb
Accuracy
2 10 20 100 200 1,000
.20 .41 .54 .82 .90 .98
aAccuracy defined to be [nh2/(4 + (n - 1)h2)l .s b20% of total records assumed to be from first parity dams.
eny per sire were chosen, and accuracy of a progeny test was computed for all progeny (Method I) and 20% of the total progeny and heritability .08 (Method II). The 20% was the percentage of first parity calvings in our study. Method I always resulted in a greater accuracy, but accuracy was comparable for progeny numbers greater than 500. Most bulls in the present sire evaluation have less than 100 progeny; thus, Method I is recommended unless large numbers are available. The negative direct-maternal correlation indicated that females born with ease may tend to have difficulty in giving birth. This relationship possibly exists because small calves born with less difficulty (8) may result in small cows, which have increased difficulty in birth (9). The negative additive-maternal relationship should have little impact because bulls entering AI are not selected for calving performance, and the correlation between breeding values for production and dystocia is zero (14). The negative correlation should be considered, however, if bulls entering AI are selected for calving performance. Selecting against the direct effect for dystocia over several generations also would result in less response than expected. The direct effect of the maternal grandsire also is passed through the dam, which offsets the maternal effect to some extent. The size of the correlations for direct with maternal effects allows some bulls to be desirable for both traits. Ranking bulls for maternal effects is not recommended at this time but should be considered before selection against dystocia is applied to bulls entering AI. Journal of Dairy Science Vol. 64, No. 7, 1981
CONCLUSIONS
The genetic correlation for dystocia in first with later parities is large indicating that the traits have a similar genetic base. Continuation of the practice of including all data in sire evaluation for dystocia and adjusting for unequal age-of-dam variation is recommended. Additive effects are negatively correlated with maternal effects. Sire evaluation for maternal effects is not recommended but should be considered before selecting bulls entering artificial insemination on calving performance.
ACKNOWLEDGMENT
This research was supported by grant No. I-3-79 of the Binational Agricultural Research Development Fund (BARD).
REFERENCES
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Genetic and environmental factors affecting the incidence of difficult calving and perinatal calf mortality in IsraeI-Friesian dairy herds. Anita. Prod. 22:299. 2 Berger, P. J., and A. E. Freeman. 1978. Prediction of sire merit for calving difficulty. J. Dairy Sci. 61 : 1146. 3 Cady, R. A. 1980. Evaluation of Holstein bulls for dystocia. Ph.D. dissertation. Comell University, Ithaca, NY. 4 Calo, L. L., R. E. McDowell, L. D. Van Vieck, and P. D. Miller. 1973. Genetic aspects of beef production among Holstein-Friesians pedigree selected for milk production. J. Anita. Sci. 37:676. 5 Gerog, D. D., and R. F. Keller. 1973. Criteria for ordering columns in two-dimensional projection
AGE AND MATERNAL EFFECTS FOR DYSTOCIA methods. Publ. IS-3147, Ames Lab., USAEC, Ames, IA. 6 Philipsson, J. 1976. Studies on calving difficulty, stillbirth and associated factors in Swedish cattle breeds. II. Effects of non-genetic factors. Acta Agric. Scand. 26:165. 7 Philipsson, J. 1976. Studies on calving difficulty, stillbirth and associated factors in Swedish cattle breeds. III. Genetic parameters. Acta Agric. Scand. 26:211. 8 Pollak, E. J. 1975. Dystocia in Holsteins. Ph.D. dissertation, Iowa State University, Ames. Microfilm No. 76-1866, Univ. Microfilms, Ann Arbor, MI. 9 Pollak, E. J., and A. E. Freeman. 1976. Parameter estimation and sire evaluation for dystocia and calf size in Holsteins. J. Dairy Sci. 59:1817. 10 Schaeffer, L. R., J. W. Wilton, and R. Thomson. 1978. Simultaneous estimation of variance and covariance components from multitrait mixed model equations. Biometrics 34:199. 11 Schaeffer, L. R. 1979. Estimation of variance and
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covariance components for average daily gain and backfat thickness in swine. Variance components and animal breeding. Proc. Conf. in honor of C. R. Henderson. Cornell University, Ithaca, NY. Searle, S. R. 1966. Matrix algebra for the biological sciences. John Wiley and Sons, Inc., New York, NY. Teixeira, N. M. 1978. Genetic differences in dystocia, calf condition, and calf livability in Holsteins. Ph.D. dissertation. Iowa State University, Ames. Thompson, J. R., A. E. Freeman, and P. J. Berger. 1980. Relationship of dystocia transmitting ability with type and production transmitting abilities in Holstein bulls. J. Dairy Sci. 63:1462. Tong, A.K.W., B. W. Kennedy, and J. E. Moxley. 1979. Heritabilities and genetic correlations for the first three lactations from records subject to culling. J. Dairy Sci. 62:1784. Wiliham, R. L. 1972. The role of maternal effects in animal breeding: III. Biometrical aspects of maternal effects in animals. J. Anim. Sci. 36:1288.
Journal of Dairy Science Vol. 64, No. 7, 1981