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Selection for the Direct and Maternal Genetic Effects for Dystocia in Holsteins1
S e l e c t i o n for t h e Direct a n d M a t e r n a l G e n e t i c Effects for D y s t o c i a in H o l s t e i n s I K. M. BALCERZAK,2 A. E. FREEMAN, and R. L. WlLLHAM Iowa State University Ames 50011 ABSTRACT
a program of National Association of Animal Breeders (NAAB). Sires' transmitting abilities The effects of selection for the direct have been predicted by using a procedure with and matemal components of dystocia BLUP properties as described by Berger and were estimated for first, second and later, Freeman (1). Sires were evaluated within studs and all parifies. The effect of restricting through 1979, and, since then, have been evalumaternal change to zero and the effect of ated across studs. Only the direct effect of the selection for only the direct component sire on his calves' birth difflculty were used to were also examined. Gene flow procedure predict sires' transmitting abilities. Dystocia is was used to compute economic weights scored by dairy producers on a scale of 1 to 5, as 1 and .347 for the direct and maternal with 5 the most difficult birth. Data are coleffects, respectively. Genetic gain in aglected by the member organizations of NAAB. gregate genotype was the largest for first The data are screened by computer, and the parity. For all parities all the gain in the computauons are now done at Iowa State Uniaggregate genotype was accounted for by versity by P. J. Berger using an ordered catethe direct effects. At the same time, a gorical analysis to evaluate sires for dystocia slight decrease in the genetic maternal (4). These data, collected for sire evaluation, effects was observed. For all cases, selecprovided a basis for more extensive study of tion for both traits had almost no loss in birth difficulty and related traits. aggregate genotype or accuracy compared Dystocia is expressed with both direct and with when maternal changes were rematernal components. Thompson et ai. (9) estistricted to zero. Total genetic gain and mated the genetic correlation between direct genetic gain for the direct effect of dystoand maternal effects for dystocia as -.38 in first cia were greater and accuracy of selection parities and -.25 for older cows. These estiwas lower when selection was for the mates were made using the multitrait mixed genetic direct effect only versus the index model procedure described by Schaeffer et ai. that included both direct and maternal (6). Correlations were estimated from 19,237 effects. Selection for only the direct effects is not likely to produce any signifiheifer records from 199 sires and 69,458 cow cant change in dystocia as a maternal records from 323 sires. Recently Cue and tralt. Hayes (2), using a model that accounted for the weight of the dam, reported the direct maternal correlation as -.399 for heifers and .073 for INTRODUCTION adult cows. Thompson et ai. (9) postulated that Holstein sires used in artificial insemination a negative direct maternal correlation results have been evaluated for dystocia since 1977 as from small calves being bom with ease (11), then later they stated that small cows have increased dystocia. This hypothesis was later supported by Thompson et ai. (10) who reReceived June 22, 1988. Accepted October 28, 1988. ported that cow size does affect calving diffi]Journal Paper Number J-13115 of the lowa Agricul- culty at first and second parmritions. If selecture and Home Economics Experiment Station, Ames, tion was successful for dystocia as a direct Project 1053. ~%esent ad&ess: Institute of Cattle Bre¢ding and Dairy effect, it could conceivably become counterproScience of Warsaw Agricultural University, 05 840 Brwi- ductive or, at least, not effective because of the now, ul. Przejazd 4, Poland. antagonistic genetic relationship between direct 1989 J Dairy Sci 72:1273-1279
1273
1274
BALCERZAK ET AL.
and matemal effects. The objectives of this study were to estimate 1) the effect of selection for both direct and matemal effects by using economic weights computed by a gene flow procedure, 2) the effect of selecfion after restricting matemal change to zero, and 3) the effect of selection for only direct effects. PROCEDURE
The goal is to select sires for dystocia by considering direct (D) and matemal (M) effects as separate traits. Two sources of information are available for selecåon. The first is the average of single records measured on ni calves of the sire (Xi) representing direct sire effect for dystocia. The second source is the average of single records measured on nj calves bom from sire's daughters (Xj) representing the maternal effect of the sire. For one phenotypic tralt the overall economic value is determined partly by direct (GD) and partly by matemal (GM) geneåc component. So the aggregate genotype (H) for sires is: H = VDGD + VMGM and the index is I = blX i + b2Xj where VD, VM = economic values for the direct and the matemal contribution of dystocia, and b 1, b 2 = the index weights. Willham (12) showed that the matemal effect of the mother influenced the phenotype of her offspring. This effect is genetic with respect to the mother but acts as environmental with respect to offspring. Part of the matemal effect may be genefic and part may be environmental. Let PA and PB represent the phenotypic value of individuals A and B, respecUvely. If one assumes that the direct and the matemal effects influence the phenotypic expression of a trait, the model for a record on animal A is: PA = GDA + EDA + GMW + EMW and the model for a record on animal B is: PB = GDB + EDB + GMZ + EMZ where W and Z are mothers of A and B, Journal of Dalry Science Vol. 72, Nø. 5, 1989
respecfively; GDA and (]DB are the direct genetic effects associated with genotype of animais A and B; EDA and EDB are the nonmatemally caused environmental effects on A and B; GMW and GMZ are the geneUc maternal effects on A and B; and EMW and EMZ are environmental maternal effects on A and B. The genetic covariance between A and B can be found by the general rules for the covariance of linear functions. Assuming that any environmental covariances are zero,
CoV(PA,PB) = CoV(GDA,GDB) + CoV(GDA,GMz) + CoV(GMw,GD8) + cov(Guw,G~z). If only additive genetic effects are considered, this formula could be further simplified as: CoV(PA,PB) = aABO2D + awzO2M + (aAZ + awB)ODM where a's represent Wright's coefficient of relationship with nø inbreeding, O2D is the additive genetic variance for direct effects, O2M is additive genetic variance for maternal effects, and ODM represents the additive genetic covariance for direct and matemal effects. As an example, a formula for variance of single records (O2p) (covariance for the animal with itself) with direct and matemal effects considered is presented. This covariance contains genetic and environmental variances. If A is equal to B and W is equal to Z, relationship coefficients between these individuals (aAa and awz) are equal to 1 and aAW as well as aBz are equal to 1/2, then:
CoV(PA,PA) = O2p = O2D + O2M + ODM + O2E where O2E is composed of the nonadditive netic variance and environmental variance both direct and maternal effects. Following selection index theory, with direct and matemal effect considered, the pectation of the phenotypic variances and variance in the index are
gefor the exco-
DYSTOCIA IN HOLSTEINS
1275
TABLE 1. Expectation of genetic variances and covariances used to construct index equations (6). Parameters o2 OZM onu o~~-
Parity Second and later .0242 .0079 -.0035 .7600
First .045 .0365 -.0155 1.3828
O2Xi ---- (O2p + (ni - 1 ) (1/402D))/ni O2Xj - ((];2p .4- ( n i - 1) (1/1602D 4ODM + 1/402M))/nj OXiXj = 1/802D + 1/4ORM OXiH ---- V D (1/2021)) + V M (1/2ODM) OXj1.I = V D (1/402D + 1/2ODM)+ VM (1/4ORM + 1/202M)
where O2xi and O2Xj ale phenotypic variances of an average of single records for direct and matemal effects of dystocia, respecUvely; Oxixj is the phenotypic covariance between averages of records for D and M components; and Ox~ and OXjH represents right-hand sides of the index equations for direct and matemal effects The parameter estimates for genetic and environmental variances and genetic covariance (O2D, O2M, ODM, and O'2E) reported by Thompson (7) were used to construct selection index equations. These estimated parameters, presented in Table 1, were computed separately for first, second and later, and all parities. Only additive palts of the total genetic variance and covariance were considered. Values are needed for the economic weights for direct and materhal effects. As a result of one successful insemination, genes for both D and M effects of the sire are transferred to descendants. The transmittance of D and M effects ale not the same, however. When a sire's calf is bom (generation zero) maternal effects of the sire are not expressexi but one-half of sire's genes for the D component of dystocia is expressed. Consequently, when a sire's daughter calves (generation 1), one-half of the sire's matemal and onefourth of the direct effects are expressed. This leads to the conclusion that economic importance of direct and matemal effects for dystocia are different and should be computed by using a discounted gene flow procedure. FoUowing the method described by McClin-
All .0287 .0141 -.0061 .8817
tock and Cunningham (5), the number of possible expressions of sire's genotype resulting from one successful insemination in year zero could be calculated. Let NDgy and NM~ represent the numbers of possible descendants expressing the sire's genotype for direct (D) and matemal (M) component of dystocia in generatjon (g) and year (y). The method of compufing the number of possible descendants is presented in Table 2. To obtain the equivalent number of standard discounted expressions, the numbers of all possible individuals expressing the sire's genotype for direct and maternal effect of dystocia have to be adjusted for: 1.
2.
3.
The dilution of sire's genotype in his descendants. As it was shown before in generafion (g), (1/2)s of the matemal and (1/ 2) g+1 of the direct effects of the sire are expressed. The time elapsed from the insemination to each expression. Eally expressions are more economically valuable than later expressions. Thus, returns in year (y) should be discounted back to present values by multiplying by (1/1 + r) Y = RY, where r is rate of interest. The probability that each possible expression really occurs. If the average number of lactations per cow is L then the probability that parturition actually occurs in generation (g) is 1/Lg. If one takes into account that a sire genotype is expressed only when a sire's descendant is a female, then the probability that each possible expression actuaUy occurs is 1/(2L)g.
Let N'Dgy and N'Mgyrepresent the number of standard discounted expressions of a sire's genotype for direct and matemal effects of dystocia, respectively. Then: Journal of Dairy Science Vol. 72, Nø. 5, 1989
1276
BALCERZAK ET AI.,.
TABLE 2. Numbers of possible expressions of sire's genotype for the direct and the matemal effects following one successful insemination in year zero. Gencrations
Ye~s 0 1 2 3 4 5 6 7 8 9 10
0
1
Direct effects 2 3
4
0
1
1
1
1 1
1 1
1 2 3 2 1
1 3 6
1
7
4
N'Dgy = NDgy (1/2)• + 1 RY 1/(2L)g N'Mgy = Nlvlgy (1/2)g RY 1/(2L)g The standard discounted expressions of sires D and M components can now be summed over years and generations to give a measure of the total genetic contribution to the populaåon resulting from an insemination carried out in generation zero. Let ED and EM be the cumulative total numbers of discounted expressions for direct and maternal effect transmitted by a sire; then: G Y ED = Z ZN'Dgy g=O y=O and: G Y EM = Z ZN'M$y g=0 y=O where G is an investment period and Y is the total number of generations considered. The cumulative total number of discounted expressions can be used as economic weights to construct a selection index for maximizing galn in the aggregate genotype. Assuming that each cow calves the first time at 2.2 yr of age, the average number of lactations per cow is 3, the rate of interest (r) is .1, and the investment period (Y) is 10 yr, then the cumulative total number of expressions is: E D = .605 and E M = .210 Journal of Dairy Science VoL 72, Nø. 5, 1989
Maternal effects 2 3
1 2 3 2
4
1 3
1
6
1
7
4
For clarity, the economic weight for the direct effect can be set to 1. Therefore, economic weights used to construct selecuon index equations are: V D = 1 and
V M =
.347
It is likely that the economic weights are nonlinear as dystocia increases; however, one can assume that nonlinearity is similar for direct and maternal effect of the sire. In the present paper, the objective was to compare relative gains for the direct and maternal effects without taking into account any other traits. In such case, nonlinearity of economic weight was not considered. The genetic correlation between direct and maternal effects was a larger negative value for heifers than for older cows. For this reason, the expected changes in H, GD, and GM were estimated separately for first parity, second and later, and all parities. The number of progeny was always assumed equal (n i = nj) for sires and matemal grandsires. Random matings for sires and sire's daughters in the population were assumed. The aggregate genotype (H) was kept constant for all results. For computation of genetic gains in different selection alternatives, the SELIND program was used (3). RESULTS AND DISCUSSION
Table 3 gives the expected changes per standard deviation of selection on the index with
DYSTOCIA IN HOLSTEINS
1277
TABLE 3. Expected genetic galn (AH) and accuracyof selection (Rm) when sele¢ting for dystociaas both dire¢t (D) and maternal (M) effects. Nø. of
Parity 1
>1
All
progeny 20 80 200 1000 20 80 200 1000 20 80 200 1000
%
AH .074 .124 .155 .185 .059 .098 .121 .143 .063 .104 .130 .153
Rm .378 .632 .790 .943 .391 .647 .799 .947 .390 .646 .801 .948
economic weights computed by the gene flow procedure. Positive genetic gain in H and GI) indicates a decrease in dystocia score, whereas negative gain in GM indicates an increase in dystocia. Total genetic gain (AH) is largest for first parity when the number of progeny are equai for each parity. This is because heritabilities are higher in first than in later lactafions for both direct and maternai effects (9). It is unreaiistic to assume equai numbers for each parity. First parity records would normaily include 20 to 30% of all data. Thompson et ai. (9) showed that for direct effects, genetic gain was aiways largest when all records were used instead of only first parities. For this reason, results from all parities should be stressed. Genetic gain in H and GI) increases as the number of progeny increases as does the accuracy of selection (Rm). For all parities and economic weights computed by gene flow procedure, all the gain in H is accounted for by the gain in the direct effect. At the same time, a slightly negative AGM was observed. The negative gain in GM was greater as the number of progeny increased. The number of progeny was assumed equal for sires and maternai grandsires. In practice, the number of progeny would normaUy be greater for the maternal grandsire than for the sire. Therefore, there would be an increased gain (or lower negative gain) for the genetic maternal effect. Even for the extreme case with n i = 80 and nj = 1000, with use of data for all parities, 91% of the gain in H was accounted for by the gain in the direct effect.
D 102.4 102.5 102.6 102.6 100.9 101.0 101.0 101.3 101.4 101.5 101.7 101.8
of Gain in H M -2.4 -2.5 -2.6 -2.6 -.9 -1.0 -1.0 -1.3 -1.4 -1.5 - 1.7 -1.8
AGD .076 .127 .159 .190 .059 .098 .122 .145 .064 .106 .132 .156
AGra -.005 -.009 -.012 -.014 -.002 -.003 -.003 -.005 -.003 -.00,J, -.006 -.008
The additive direct effect for dystocia is clearly more important than the maternal effect in Holsteins. These results agree with Thompson et ai. (9) who reported that the direct effect was severai times greater than the maternal effect. With direct effects accounting for the major part of AH, maternal change was held constant to estimate the relative changes in AH and AGD. Parts of Table 3 are reproduced in Tables 4 and 5 to make comparison easier. In Table 4, the comparison of expected genetic gains when selecting for direct and maternal effects versus restricting maternal changes to zero is presented. Again, for all cases, total genetic gain is greater as the number of progeny increase. For all cases, there is aimost nø loss in AH or accuracy when maternai change is restricted to zero. At the same time, change in G D is slightly lower when AGM is restricted to zero versus selection for both direct and maternal effects, but this is at the expense of avoiding the decrease in GM. The difference in AGD for restricted versus the original index becomes larger as the number of progeny increases. These results again emphasize the importance of the direct effects of dystocia. It is useful to estimate the gain in H and the change in both the direct and maternai traits when selection is only for GD. Table 5 presents the results from selection for only direct genetic effects but using the maternal tralt as an aid to selection. This was done by setting VD = 1 and V M = 0 in the index equations. For all cases, total genetic gain and genetic gain for the direct Journal of Dalry Science Vol. 72, Nø. 5, 1989
1278
B A L C E R Z A K ET AL.
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DYSTOCIA IN HOLSTEINS
component of dystocia were greater and accuracy of selection was lower when selection is only for (3o versus the original index. At the same time, greater negative changes in maternal effects of dystocia were observed. As before, selection is increasingly effective as the number of progeny increases. In practice, sire selection is for other traits with litfle or nø pedigree selection for dystocia and little or nø culling of progeny tested sires for dystocia. The genetic correlation between transmitting abilities for dystocia with transmitting abilities for Predicted Difference milk and fat were estimated to be zero (8). There is, however, some selection for dystocia as a direct effect because some sires that are superior in calving ease are used more than those with greater expected dystocia in their progeny. Such selection for dystocia as a direct genetic effect would be difficult to quantitate, but the intensity must be low. Dystocia is not a selection criterion when selecting sires or dams of sons. These results clearly indicate the greater importance of the direct effect. It seems that there is little reason for concern that the current selection practices will increase calving difficulty as a maternal effect in the Holstein population. If direct selecUon is practiced for calving ease, attention may have to be given to maternal effects.
CONCLUSIONS
1) Direct effects are more important than matemal effects for dystocia in Holsteins. 2) Selection for dystocia using progeny from all lactations, with economic weights computed by gene flow procedure, would be expected to result in all the gain in aggregate genotype accounted for by the gain in the direct component with slight negative gain in matemal component. 3) Selection for only the direct effects
1279
is not likely to produce any significant change in dystocia as a maternal trait. ACKNOWLEDGMENTS
The financial support of Krzysztof Balcerzak during his stay at Iowa State University by The Kosciuszko Foundation is gratefully acknowledged. This research was supported in part by Grant 1-629-83-RE of the US-Israel Binational Agricultural Research and Development Fund. REFERENCES 1 Berger, P. J., and A. E. Freeman. 1978. Prediction of sire merit for calving difficulty. J. Dairy Sci. 61:1146. 2 Cue, R. I., and J. F. Hayes. 1985. Correlations of various direct and matemal effects for calvmg case. J. Dairy Sci. 68:374. 3 Ctmningham, E. P. 1970. SELIND-a FORTRAN program for genetic selecfion index. User's guide. The Agric. Inst., IXmsinea, Castleknock, Co. Dublin, Ireland. 4 Djemali, M., P. J. Berger, and A. E. Freeman. 1987. Ordered categorical sire evaluation for dystocia in Holsteins. J. Dairy Sci. 70:2374. 5 McClintock, A. E., and E. P. Cunningham. 1974. Selection in dual purpose cattle populations: defining the breeding objective. Anim. Prod. 18:237. 6 Schaeffer, L. R., J. W. Wilton, and R. Thompson. 1978. Simultaneous estimation of variance and covariance components from multitrait mixed model equations. Biometrics 34:199. 7 Thompson, J. R. 1980. Dystocia in dairy cattle. Age of dam and matemal considerauons, and relationships with economic traits. Ph.D. diss., Iowa State Univ., Ames. Univ. Microfilm Nø. 8106 064. 8 Thompson, J. R., A. E. Freeman, and P. J. Berger. 1980. Relationships of Dystocia transmitting ability with type and production transmitting ability in Holstein bulls. J. Dairy Sci. 63:1462. 9 Thompson, J. R., A. E. Freeman, and P. J. Berger. 1981. Age of dam and matemal effects for dystocia in Holsteins. J. Dairy Sci. 64:1603. 10 Thompson, J. R., E. J. Pollak, and C. L. Pelissier. 1983. Interrelationships of parturition problems, production of subsequent lactauon, reproduction, and age of first calving. J. Dairy Sci. 66:1119. 11 Thompson, J. R., and J.E.O. Rege. 1984. Influence of dam on calving difficuhy and early calf mortality. J. Dairy Sci. 67:847. 12 Willham, R. L. 1963. The covariance between relatives for characters composed of components contributed by related individuals. Biornetrics 19:18.
Journal of Dairy Science VoL 72, Nø. 5, 1989
a program of National Association of Animal Breeders (NAAB). Sires' transmitting abilities The effects of selection for the direct have been predicted by using a procedure with and matemal components of dystocia BLUP properties as described by Berger and were estimated for first, second and later, Freeman (1). Sires were evaluated within studs and all parifies. The effect of restricting through 1979, and, since then, have been evalumaternal change to zero and the effect of ated across studs. Only the direct effect of the selection for only the direct component sire on his calves' birth difflculty were used to were also examined. Gene flow procedure predict sires' transmitting abilities. Dystocia is was used to compute economic weights scored by dairy producers on a scale of 1 to 5, as 1 and .347 for the direct and maternal with 5 the most difficult birth. Data are coleffects, respectively. Genetic gain in aglected by the member organizations of NAAB. gregate genotype was the largest for first The data are screened by computer, and the parity. For all parities all the gain in the computauons are now done at Iowa State Uniaggregate genotype was accounted for by versity by P. J. Berger using an ordered catethe direct effects. At the same time, a gorical analysis to evaluate sires for dystocia slight decrease in the genetic maternal (4). These data, collected for sire evaluation, effects was observed. For all cases, selecprovided a basis for more extensive study of tion for both traits had almost no loss in birth difficulty and related traits. aggregate genotype or accuracy compared Dystocia is expressed with both direct and with when maternal changes were rematernal components. Thompson et ai. (9) estistricted to zero. Total genetic gain and mated the genetic correlation between direct genetic gain for the direct effect of dystoand maternal effects for dystocia as -.38 in first cia were greater and accuracy of selection parities and -.25 for older cows. These estiwas lower when selection was for the mates were made using the multitrait mixed genetic direct effect only versus the index model procedure described by Schaeffer et ai. that included both direct and maternal (6). Correlations were estimated from 19,237 effects. Selection for only the direct effects is not likely to produce any signifiheifer records from 199 sires and 69,458 cow cant change in dystocia as a maternal records from 323 sires. Recently Cue and tralt. Hayes (2), using a model that accounted for the weight of the dam, reported the direct maternal correlation as -.399 for heifers and .073 for INTRODUCTION adult cows. Thompson et ai. (9) postulated that Holstein sires used in artificial insemination a negative direct maternal correlation results have been evaluated for dystocia since 1977 as from small calves being bom with ease (11), then later they stated that small cows have increased dystocia. This hypothesis was later supported by Thompson et ai. (10) who reReceived June 22, 1988. Accepted October 28, 1988. ported that cow size does affect calving diffi]Journal Paper Number J-13115 of the lowa Agricul- culty at first and second parmritions. If selecture and Home Economics Experiment Station, Ames, tion was successful for dystocia as a direct Project 1053. ~%esent ad&ess: Institute of Cattle Bre¢ding and Dairy effect, it could conceivably become counterproScience of Warsaw Agricultural University, 05 840 Brwi- ductive or, at least, not effective because of the now, ul. Przejazd 4, Poland. antagonistic genetic relationship between direct 1989 J Dairy Sci 72:1273-1279
1273
1274
BALCERZAK ET AL.
and matemal effects. The objectives of this study were to estimate 1) the effect of selection for both direct and matemal effects by using economic weights computed by a gene flow procedure, 2) the effect of selecfion after restricting matemal change to zero, and 3) the effect of selection for only direct effects. PROCEDURE
The goal is to select sires for dystocia by considering direct (D) and matemal (M) effects as separate traits. Two sources of information are available for selecåon. The first is the average of single records measured on ni calves of the sire (Xi) representing direct sire effect for dystocia. The second source is the average of single records measured on nj calves bom from sire's daughters (Xj) representing the maternal effect of the sire. For one phenotypic tralt the overall economic value is determined partly by direct (GD) and partly by matemal (GM) geneåc component. So the aggregate genotype (H) for sires is: H = VDGD + VMGM and the index is I = blX i + b2Xj where VD, VM = economic values for the direct and the matemal contribution of dystocia, and b 1, b 2 = the index weights. Willham (12) showed that the matemal effect of the mother influenced the phenotype of her offspring. This effect is genetic with respect to the mother but acts as environmental with respect to offspring. Part of the matemal effect may be genefic and part may be environmental. Let PA and PB represent the phenotypic value of individuals A and B, respecUvely. If one assumes that the direct and the matemal effects influence the phenotypic expression of a trait, the model for a record on animal A is: PA = GDA + EDA + GMW + EMW and the model for a record on animal B is: PB = GDB + EDB + GMZ + EMZ where W and Z are mothers of A and B, Journal of Dalry Science Vol. 72, Nø. 5, 1989
respecfively; GDA and (]DB are the direct genetic effects associated with genotype of animais A and B; EDA and EDB are the nonmatemally caused environmental effects on A and B; GMW and GMZ are the geneUc maternal effects on A and B; and EMW and EMZ are environmental maternal effects on A and B. The genetic covariance between A and B can be found by the general rules for the covariance of linear functions. Assuming that any environmental covariances are zero,
CoV(PA,PB) = CoV(GDA,GDB) + CoV(GDA,GMz) + CoV(GMw,GD8) + cov(Guw,G~z). If only additive genetic effects are considered, this formula could be further simplified as: CoV(PA,PB) = aABO2D + awzO2M + (aAZ + awB)ODM where a's represent Wright's coefficient of relationship with nø inbreeding, O2D is the additive genetic variance for direct effects, O2M is additive genetic variance for maternal effects, and ODM represents the additive genetic covariance for direct and matemal effects. As an example, a formula for variance of single records (O2p) (covariance for the animal with itself) with direct and matemal effects considered is presented. This covariance contains genetic and environmental variances. If A is equal to B and W is equal to Z, relationship coefficients between these individuals (aAa and awz) are equal to 1 and aAW as well as aBz are equal to 1/2, then:
CoV(PA,PA) = O2p = O2D + O2M + ODM + O2E where O2E is composed of the nonadditive netic variance and environmental variance both direct and maternal effects. Following selection index theory, with direct and matemal effect considered, the pectation of the phenotypic variances and variance in the index are
gefor the exco-
DYSTOCIA IN HOLSTEINS
1275
TABLE 1. Expectation of genetic variances and covariances used to construct index equations (6). Parameters o2 OZM onu o~~-
Parity Second and later .0242 .0079 -.0035 .7600
First .045 .0365 -.0155 1.3828
O2Xi ---- (O2p + (ni - 1 ) (1/402D))/ni O2Xj - ((];2p .4- ( n i - 1) (1/1602D 4ODM + 1/402M))/nj OXiXj = 1/802D + 1/4ORM OXiH ---- V D (1/2021)) + V M (1/2ODM) OXj1.I = V D (1/402D + 1/2ODM)+ VM (1/4ORM + 1/202M)
where O2xi and O2Xj ale phenotypic variances of an average of single records for direct and matemal effects of dystocia, respecUvely; Oxixj is the phenotypic covariance between averages of records for D and M components; and Ox~ and OXjH represents right-hand sides of the index equations for direct and matemal effects The parameter estimates for genetic and environmental variances and genetic covariance (O2D, O2M, ODM, and O'2E) reported by Thompson (7) were used to construct selection index equations. These estimated parameters, presented in Table 1, were computed separately for first, second and later, and all parities. Only additive palts of the total genetic variance and covariance were considered. Values are needed for the economic weights for direct and materhal effects. As a result of one successful insemination, genes for both D and M effects of the sire are transferred to descendants. The transmittance of D and M effects ale not the same, however. When a sire's calf is bom (generation zero) maternal effects of the sire are not expressexi but one-half of sire's genes for the D component of dystocia is expressed. Consequently, when a sire's daughter calves (generation 1), one-half of the sire's matemal and onefourth of the direct effects are expressed. This leads to the conclusion that economic importance of direct and matemal effects for dystocia are different and should be computed by using a discounted gene flow procedure. FoUowing the method described by McClin-
All .0287 .0141 -.0061 .8817
tock and Cunningham (5), the number of possible expressions of sire's genotype resulting from one successful insemination in year zero could be calculated. Let NDgy and NM~ represent the numbers of possible descendants expressing the sire's genotype for direct (D) and matemal (M) component of dystocia in generatjon (g) and year (y). The method of compufing the number of possible descendants is presented in Table 2. To obtain the equivalent number of standard discounted expressions, the numbers of all possible individuals expressing the sire's genotype for direct and maternal effect of dystocia have to be adjusted for: 1.
2.
3.
The dilution of sire's genotype in his descendants. As it was shown before in generafion (g), (1/2)s of the matemal and (1/ 2) g+1 of the direct effects of the sire are expressed. The time elapsed from the insemination to each expression. Eally expressions are more economically valuable than later expressions. Thus, returns in year (y) should be discounted back to present values by multiplying by (1/1 + r) Y = RY, where r is rate of interest. The probability that each possible expression really occurs. If the average number of lactations per cow is L then the probability that parturition actually occurs in generation (g) is 1/Lg. If one takes into account that a sire genotype is expressed only when a sire's descendant is a female, then the probability that each possible expression actuaUy occurs is 1/(2L)g.
Let N'Dgy and N'Mgyrepresent the number of standard discounted expressions of a sire's genotype for direct and matemal effects of dystocia, respectively. Then: Journal of Dairy Science Vol. 72, Nø. 5, 1989
1276
BALCERZAK ET AI.,.
TABLE 2. Numbers of possible expressions of sire's genotype for the direct and the matemal effects following one successful insemination in year zero. Gencrations
Ye~s 0 1 2 3 4 5 6 7 8 9 10
0
1
Direct effects 2 3
4
0
1
1
1
1 1
1 1
1 2 3 2 1
1 3 6
1
7
4
N'Dgy = NDgy (1/2)• + 1 RY 1/(2L)g N'Mgy = Nlvlgy (1/2)g RY 1/(2L)g The standard discounted expressions of sires D and M components can now be summed over years and generations to give a measure of the total genetic contribution to the populaåon resulting from an insemination carried out in generation zero. Let ED and EM be the cumulative total numbers of discounted expressions for direct and maternal effect transmitted by a sire; then: G Y ED = Z ZN'Dgy g=O y=O and: G Y EM = Z ZN'M$y g=0 y=O where G is an investment period and Y is the total number of generations considered. The cumulative total number of discounted expressions can be used as economic weights to construct a selection index for maximizing galn in the aggregate genotype. Assuming that each cow calves the first time at 2.2 yr of age, the average number of lactations per cow is 3, the rate of interest (r) is .1, and the investment period (Y) is 10 yr, then the cumulative total number of expressions is: E D = .605 and E M = .210 Journal of Dairy Science VoL 72, Nø. 5, 1989
Maternal effects 2 3
1 2 3 2
4
1 3
1
6
1
7
4
For clarity, the economic weight for the direct effect can be set to 1. Therefore, economic weights used to construct selecuon index equations are: V D = 1 and
V M =
.347
It is likely that the economic weights are nonlinear as dystocia increases; however, one can assume that nonlinearity is similar for direct and maternal effect of the sire. In the present paper, the objective was to compare relative gains for the direct and maternal effects without taking into account any other traits. In such case, nonlinearity of economic weight was not considered. The genetic correlation between direct and maternal effects was a larger negative value for heifers than for older cows. For this reason, the expected changes in H, GD, and GM were estimated separately for first parity, second and later, and all parities. The number of progeny was always assumed equal (n i = nj) for sires and matemal grandsires. Random matings for sires and sire's daughters in the population were assumed. The aggregate genotype (H) was kept constant for all results. For computation of genetic gains in different selection alternatives, the SELIND program was used (3). RESULTS AND DISCUSSION
Table 3 gives the expected changes per standard deviation of selection on the index with
DYSTOCIA IN HOLSTEINS
1277
TABLE 3. Expected genetic galn (AH) and accuracyof selection (Rm) when sele¢ting for dystociaas both dire¢t (D) and maternal (M) effects. Nø. of
Parity 1
>1
All
progeny 20 80 200 1000 20 80 200 1000 20 80 200 1000
%
AH .074 .124 .155 .185 .059 .098 .121 .143 .063 .104 .130 .153
Rm .378 .632 .790 .943 .391 .647 .799 .947 .390 .646 .801 .948
economic weights computed by the gene flow procedure. Positive genetic gain in H and GI) indicates a decrease in dystocia score, whereas negative gain in GM indicates an increase in dystocia. Total genetic gain (AH) is largest for first parity when the number of progeny are equai for each parity. This is because heritabilities are higher in first than in later lactafions for both direct and maternai effects (9). It is unreaiistic to assume equai numbers for each parity. First parity records would normaily include 20 to 30% of all data. Thompson et ai. (9) showed that for direct effects, genetic gain was aiways largest when all records were used instead of only first parities. For this reason, results from all parities should be stressed. Genetic gain in H and GI) increases as the number of progeny increases as does the accuracy of selection (Rm). For all parities and economic weights computed by gene flow procedure, all the gain in H is accounted for by the gain in the direct effect. At the same time, a slightly negative AGM was observed. The negative gain in GM was greater as the number of progeny increased. The number of progeny was assumed equal for sires and maternai grandsires. In practice, the number of progeny would normaUy be greater for the maternal grandsire than for the sire. Therefore, there would be an increased gain (or lower negative gain) for the genetic maternal effect. Even for the extreme case with n i = 80 and nj = 1000, with use of data for all parities, 91% of the gain in H was accounted for by the gain in the direct effect.
D 102.4 102.5 102.6 102.6 100.9 101.0 101.0 101.3 101.4 101.5 101.7 101.8
of Gain in H M -2.4 -2.5 -2.6 -2.6 -.9 -1.0 -1.0 -1.3 -1.4 -1.5 - 1.7 -1.8
AGD .076 .127 .159 .190 .059 .098 .122 .145 .064 .106 .132 .156
AGra -.005 -.009 -.012 -.014 -.002 -.003 -.003 -.005 -.003 -.00,J, -.006 -.008
The additive direct effect for dystocia is clearly more important than the maternal effect in Holsteins. These results agree with Thompson et ai. (9) who reported that the direct effect was severai times greater than the maternal effect. With direct effects accounting for the major part of AH, maternal change was held constant to estimate the relative changes in AH and AGD. Parts of Table 3 are reproduced in Tables 4 and 5 to make comparison easier. In Table 4, the comparison of expected genetic gains when selecting for direct and maternal effects versus restricting maternal changes to zero is presented. Again, for all cases, total genetic gain is greater as the number of progeny increase. For all cases, there is aimost nø loss in AH or accuracy when maternai change is restricted to zero. At the same time, change in G D is slightly lower when AGM is restricted to zero versus selection for both direct and maternal effects, but this is at the expense of avoiding the decrease in GM. The difference in AGD for restricted versus the original index becomes larger as the number of progeny increases. These results again emphasize the importance of the direct effects of dystocia. It is useful to estimate the gain in H and the change in both the direct and maternai traits when selection is only for GD. Table 5 presents the results from selection for only direct genetic effects but using the maternal tralt as an aid to selection. This was done by setting VD = 1 and V M = 0 in the index equations. For all cases, total genetic gain and genetic gain for the direct Journal of Dalry Science Vol. 72, Nø. 5, 1989
1278
B A L C E R Z A K ET AL.
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DYSTOCIA IN HOLSTEINS
component of dystocia were greater and accuracy of selection was lower when selection is only for (3o versus the original index. At the same time, greater negative changes in maternal effects of dystocia were observed. As before, selection is increasingly effective as the number of progeny increases. In practice, sire selection is for other traits with litfle or nø pedigree selection for dystocia and little or nø culling of progeny tested sires for dystocia. The genetic correlation between transmitting abilities for dystocia with transmitting abilities for Predicted Difference milk and fat were estimated to be zero (8). There is, however, some selection for dystocia as a direct effect because some sires that are superior in calving ease are used more than those with greater expected dystocia in their progeny. Such selection for dystocia as a direct genetic effect would be difficult to quantitate, but the intensity must be low. Dystocia is not a selection criterion when selecting sires or dams of sons. These results clearly indicate the greater importance of the direct effect. It seems that there is little reason for concern that the current selection practices will increase calving difficulty as a maternal effect in the Holstein population. If direct selecUon is practiced for calving ease, attention may have to be given to maternal effects.
CONCLUSIONS
1) Direct effects are more important than matemal effects for dystocia in Holsteins. 2) Selection for dystocia using progeny from all lactations, with economic weights computed by gene flow procedure, would be expected to result in all the gain in aggregate genotype accounted for by the gain in the direct component with slight negative gain in matemal component. 3) Selection for only the direct effects
1279
is not likely to produce any significant change in dystocia as a maternal trait. ACKNOWLEDGMENTS
The financial support of Krzysztof Balcerzak during his stay at Iowa State University by The Kosciuszko Foundation is gratefully acknowledged. This research was supported in part by Grant 1-629-83-RE of the US-Israel Binational Agricultural Research and Development Fund. REFERENCES 1 Berger, P. J., and A. E. Freeman. 1978. Prediction of sire merit for calving difficulty. J. Dairy Sci. 61:1146. 2 Cue, R. I., and J. F. Hayes. 1985. Correlations of various direct and matemal effects for calvmg case. J. Dairy Sci. 68:374. 3 Ctmningham, E. P. 1970. SELIND-a FORTRAN program for genetic selecfion index. User's guide. The Agric. Inst., IXmsinea, Castleknock, Co. Dublin, Ireland. 4 Djemali, M., P. J. Berger, and A. E. Freeman. 1987. Ordered categorical sire evaluation for dystocia in Holsteins. J. Dairy Sci. 70:2374. 5 McClintock, A. E., and E. P. Cunningham. 1974. Selection in dual purpose cattle populations: defining the breeding objective. Anim. Prod. 18:237. 6 Schaeffer, L. R., J. W. Wilton, and R. Thompson. 1978. Simultaneous estimation of variance and covariance components from multitrait mixed model equations. Biometrics 34:199. 7 Thompson, J. R. 1980. Dystocia in dairy cattle. Age of dam and matemal considerauons, and relationships with economic traits. Ph.D. diss., Iowa State Univ., Ames. Univ. Microfilm Nø. 8106 064. 8 Thompson, J. R., A. E. Freeman, and P. J. Berger. 1980. Relationships of Dystocia transmitting ability with type and production transmitting ability in Holstein bulls. J. Dairy Sci. 63:1462. 9 Thompson, J. R., A. E. Freeman, and P. J. Berger. 1981. Age of dam and matemal effects for dystocia in Holsteins. J. Dairy Sci. 64:1603. 10 Thompson, J. R., E. J. Pollak, and C. L. Pelissier. 1983. Interrelationships of parturition problems, production of subsequent lactauon, reproduction, and age of first calving. J. Dairy Sci. 66:1119. 11 Thompson, J. R., and J.E.O. Rege. 1984. Influence of dam on calving difficuhy and early calf mortality. J. Dairy Sci. 67:847. 12 Willham, R. L. 1963. The covariance between relatives for characters composed of components contributed by related individuals. Biornetrics 19:18.
Journal of Dairy Science VoL 72, Nø. 5, 1989