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Estimates of variances due to direct and maternal effects for reproductive traits of Romanov sheep
SmallRuminant Research Small Ruminant Research18 (1995) 69-73
Estimates of variances due to direct and maternal effects for reproductive traits of Romanov sheep G.A. Maria* Animal Production Department, University of Zaragoza, Miguel Server 177,
(50013)Zaragoza, Spain
Accepted20 January 1995
Abstract A total of 2003 records of 352 Romanov ewes from 15 sires collected between 1985 and 1990 were analyzed. Natural and artificial insemination were used with lambing season centered in February, June and October. Lambing interval (LI) averaged 331 days with extremes of 168 and 469 days. Fractions of total variance and covariances due to direct and maternal genetic effects, and permanent environmental effects (c*) for litter size and LI were estimated. Traits analyzed were litter size score (LSS), standardized for each seasonX age ewe group, and LI. Variance components were estimated using derivative-free restricted maximum likelihood (DFREML) with an animal model including fixed effects of year X season, parity and mating system, the direct genetic effect of the animal ( h2), the maternal genetic effect (m’), the permanent environmental effect (c*), and random residual effect. Estimates of h*, &, and c* respectively, as a proportion of phenotypic variance, were 0.07,0.08, and 0.05 (LSS) and 0.09, 0.09, and 0.0 (LI). The low heritability estimates for these traits may hinder their rapid improvement through selection. Keywords: Sheep; Romanov;
Spain; Reproductive
traits; Variance components
1. Introduction Litter size is defined as number of lambs born per ewe. This trait is a major determinant of productivity and economic efficiency in sheep production systems (Nitter, 1987; Gabifia, 1989) and is a composite trait with two main components: ovulation rate and embryo survival. Litter size is easy to measure under supervised lambing, whereas measuring ovulation rate requires surgical methods such as endoscopy. Improvement of litter size is of great economic interest in meat sheep flocks in the Aragon region of Spain (Gabiiia, 1989). Two main methods for genetic * Fax: 34 76 591994. Email: LEVRINO CC.UNIZAR.ES. 0921~4488/95/$9.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO921-4488(95)00717-2
improvement of litter size are selection within local breeds and crossbreeding with hyperprolific breeds (e.g. Romanov) to simultaneously exploit both additive and non-additive genetic effects (Dickerson, 1969; Gabifia, 1989). Prolific breeds of sheep have been extensively used in crossbreeding systems. First cross (F,) ewes with Romanov and Finnish Landrace sires are superior to purebred local ewes for overall productivity (Donald et al., 1968; Dickerson, 1977; Ricordeau et al., 1990). In Spain, the Romanov breed has performed better than the Finnish Landrace as sires of autochthonous ewes (Valls, 1983b). When Romanov X Aragonesa F, ewes were used, the advantage provided by crossbreeding over purebred local schemes was estimated to be about 40% more lambs per ewe per year (Valls, 1983a). However, crossbreeding systems
70
G.A. Maria/Small Ruminant Research 18 (1995) 69-73
require an intensification of management that increases production costs (Sierra, 1985). The Romanov, a breed native of Russia, was introduced to France in 1963 and to Spain in 1973 (Valls, 1983a; Sierra, 1985; Ricordeau et al., 1990) because of its high litter size (2.6-3.1). Two composite breeds, the Salz and Marine strains, have been created in Spain using local ewes and Romanov sires (Sierra, 1985; A. Marine, personal communication, 1985). To take advantage of different systems of breed utilization, the genetic parameters involved should be known (Boujenane and Bradford, 1991). In addition, the heritability and repeatability of ewe productive and reproductive traits must be known for effective selection and designing culling programs (Clarke et al., 1983). The objective of this study was to estimate variances and covariances due to direct and maternal genetic effects for litter size and lambing interval using an animal model with data from Romanov sheep.
2. Materials and methods The source of data was a flock of Romanov sheep maintained at the Ovhi farm situated in Talavera de la Reina (South-Central Spain). A total of 2003 records of 352 purebred Romanov ewes from 15 sires, collected between 1985 and 1990, were analyzed. The Ovhi program uses recording and standardization methods for litter size applied by ITOVIC in France (Amiche, 1980). Natural (single-sire groups, SG) and artificial insemination (AI) were used with lambing seasons centered in February, June and October, according to the reproduction system described by Valls ( 1983a). Because of seasonal fertility, October lambing resulted from oestrus synchronized using intravaginal pessaries and pregnant mare serum gonadotrophin (Intervet, Spain). During the suckling period, ewes were fed a ration supporting 3.50 Meal of metabolizable energy and 240 g of crude protein per head per day. After weaning, which occurred at about 40 days of lamb age, ewes were fed 300 g of concentrate (barley 100%) and 1 kg of ammonia-treated straw per head per day, supporting the maintenance requirements (ARC, 1980). Two reproductive traits were considered for analysis: litter size (LS) and lambing interval (LI) . In order to account for the correlation between mean and vari-
ante that is present in categorical data like litter size, a standardized litter size score (LSS) was calculated for each ewe using the following expression: LSS= (LS-LSG)/(SDo&
+ 100
where LSG is the average LS of the ewe group (season X age group) and SDoso, is the standard deviation of LS in the ewe group. To avoid negative values, 100 was added to the score. Lambing interval was calculated as the interval in days between consecutive lambing. The DFREML programs of Meyer ( 1988) modified for use with SPARSPAK (Boldman and Van Vleck, 1991) were used for the animal model analysis. Derivative free restricted maximum likelihood (DFREML) was described by Smith and Graser ( 1986) and Meyer (1988). To save computing time, the SPARSPAK package (George and Ng, 1981) was used to reorder symbolically the mixed model equations once. Then the equations were updated each round and solved, and the log of the likelihood calculated by Cholesky factorization rather than by the Gaussian elimination algorithm used by the original DFREML programs. The full model (Model 8 of Meyer, 1988) was:
Y=Xb+Zaa+Zmm+Zcc+e where Y is N X 1 vector of records, X associates records in Y with the fixed effects in b, Zaa associates records in Y with random direct genetic effects, Zmm associates records in Y with random maternal genetic effects, Zcc associates records in Y with random permanent environmental effects of the ewe and e denotes the residual terms. The assumed variance-covariance structure was as follows:
Au2a aam 0 AgamArr2mo0
0 0
0
0
Icu2c0
0
0
0
Inu2e
where A is the numerator relationship matrix, Zc is an identity matrix with order number of ewes and In is an identity matrix with order number of records. Fixed effects included in model were year x season ( 16)) parity ( 1 to 6 + ) , and mating system (SG or AI).
G.A. Maria /Small Ruminant Research 18 (1995) 69-73
3. Results and discussion
Table 2
Records from first lambing ewes represented 20% of the sample whereas those from second, third, fourth, and fifth or more lambings represented 15.5, 14, 12.5 and 38% of the sample, respectively. Actual litter size means by parities are presented in Table 1. Mean LSS was 100.2 and ranged from 97.5 to 104.5 across parities. As described above, and due to the recording method used in the Ovhi farm, values of LSS are deviations from the mean of the contemporary group of the ewe. Lambing interval (LI) averaged 331 days with extremes of 168 and 469 days. Estimates of variance components are given in Table 2. The variance of the direct genetic effect of the animal (heritability) for LSS was 0.07 of total variance and the variance of the maternal genetic effect (maternal heritability) was 0.08 of total variance. The fraction due to permanent environmental effects of the ewe was 0.05. An estimate of repeatability can be obtained as the sum of fractions of variance due to the direct animal effects and permanent environmental effects (0.07 + 0.05 = 0.12). In general, results obtained in this study agree with those reported in the literature. Gabifia ( 1989) found estimates of heritability and repeatability for LS in the Rasa Aragonesa breed of 0.10 and 0.13, respectively. Cardellino et al. (1991) with Corriedale ewes, estimated repeatability for LS of 0.09. Fogarty et al. ( 1985) reported estimates of repeatability ranging from 0.06 to 0.15 and of heritability of 0.11 in five composite breeds containing genes from Suffolk, Rambouillet, Dorset, Targhee, and Finnsheep breeds. Nevertheless, Fahmy ( 1990) in DLS (Dorset, Leicester and Suffolk) composite ewes and Notter ( 198 1) in Finnsheep crosses, reported repeatability estimates for LS of 0.24 and 0.37, respectively. Clarke and Hohenboken ( 1983), working with eight sets of Table 1 Actual litter sizea means and standard deviations parity
Mean
SD
1 2 3 4 5+
2.06 2.50 2.45 2.45 2.51
0.82 0.66 0.69 0.79 0.83
“Average lambs born per ewe.
11
(SD) by parities
Summary of estimates of variance components for litter size score (LSS) and lambing interval (LI) using DFREML with an animal model” Trait
u*
h=
mz
c2
c,ln
rzBnl
2 UE-
LSS LI
0.997 17 358
0.07 0.09
0.08 0.09
0.05 0.00
-0.07 -0.09
-0.98 -0.98
0.875 15 729
a Model 8 (Meyer, 1988). CT’,total phenotypic variance; h2, fraction of total variance due to direct genetic effects; a?, fraction of total variance due to maternal genetic effects; c2, fraction of total variance due to permanent environmental effect of ewe; c,, covariance between animal direct and maternal genetic effects as a proportion of the total variance; i,, correlation between direct and maternal genetic animal effects; a:, error variance.
crosses (Suffolk and Columbia ewes with Finnsheep, Dorset, Cheviot and Romney sires), found estimates of heritability for number of lambs born of 0.12 and repeatability of 0.19. On the other hand, Ricordeau et al. ( 1990)) for Romanov ewes, reported estimates of heritability for LS of 0.02. Large negative estimates of correlation ( - 0.98 and -0.99) between direct and maternal effects were found. It is difficult to find a biological explanation for this high correlation, but the estimates may be due to the data structure of the sample (i.e. number of generations with animals measured as individuals and as dams). This is a common occurrence with many small data sets, and even in some that are not so small (Boldman et al., 1991). It is necessary to mention the observed deficiencies of DFREML procedures in estimating r,, with this type of commercial data set. We have seen that problem with small data sets and especially those of poor structure, i.e. those with only few dams with measurements themselves. In order to avoid this type of problem, three generation data are needed (Van Vleck, personal communication, 1992). Sheep data also seem to behave badly, probably because of low heritability (direct or maternal) for some traits. Nevertheless, high r,, estimates using DFREML have been reported by several authors working with large data sets of various domestic species (Gama et al., 1991a,b; Eler et al., 1993; Boldman et al., 1991). For LI, the fraction of variance due to direct genetic effects was 0.09. A similar estimate was found for maternal animal effects. A large negative correlation between direct and maternal animal effects was esti-
12
G.A. Maria /Small Ruminant Research 18 (1995) 69-73
mated ( - 0.98). These estimates of heritability for LI are slightly smaller than those obtained by Gabiiia (1989) for the Aragonesa breed. Variation in lambs’ ability to survive is influenced by intrauterine and postnatal maternal influences (Gama et al., 1991a). Nevertheless, these permanent environmental effects seem to have no important effect on the reproductive traits of the ewe lamb, as reflected by the low estimates of c* for LSS and for LI. The low heritability and repeatability estimates for LSS and LI interval with values very close to zero may hinder their rapid improvement through selection. Advantages of the use of a sparse matrix package (SPARSPAK) include smaller memory and central processing unit time requirements, and the availability at convergence of BLUE and BLUP solutions for all fixed and random effects (Boldman and Van Vleck, 1991). In consequence, the use of this type of routine greatly reduces computing cost and the amount of computer resources required for the estimation of breeding values of the animals. According to the likelihoods and from the theoretical point of view, Model 8 performed very well in the estimation of variance components for LSS with repeated measures. However, because the data structure might have produced the high correlations between direct and maternal genetic effects, models ignoring the correlation between direct and maternal effects might be recommended until more data become available. Analyses of Meyer et al. ( 1994)) working with a large cattle data set, were carried out ignoring and allowing for a direct and maternal covariance, i.e. fitting Models 5 and 6 of Meyer ( 1988). On the other hand, Cantet et al. (1992) suggested the inclusion of ‘phantom’ dams in order to avoid misspecification of maternal additive variance and additive covariance between direct and maternal effects, when dam information is missing. Likewise, Mallinckrodt et al. (1993) reported the impact of data falsification and selective reporting on estimates of genetic parameters using REML techniques. For these authors data falsification influenced estimates of the direct-maternal correlation (ram) and in BLUP it may be better to assume that r,,,, is zero than to use an estimate from selectively reported data. Burfening and Kress ( 1993) estimated direct and maternal effects in sheep for birth and weaning weights using the least-squares method proposed by Eisen ( 1967). This study found that the covariance between additive
direct and additive maternal effects is important and negative ( - 0.88). As a result of the large negative covariance between direct and maternal effect, these authors suggest that the total additive genetic contribution to a maternally influenced trait is expected to be low. From a practical point of view, it is hard to interpret the high correlations between maternal and direct genetic effect observed, but we have to recognize that this is a common finding when DFREML techniques are applied to low heritability traits derived from field data. The reliability of parameter estimates needs to be tested and further studies are necessary in order to find a logical explanation for these unlikely results. The results of this study provide an indication that direct and maternal heritability and permanent environmental effect of litter size and interval between lambing are close to zero. Knowledge of this fact should be taken into account when considering alternative selection strategies.
Acknowledgements Appreciation is extended to K. Meyer who provided the DFREML programs. The authors gratefully acknowledge Keith G. Boldman and Dale van Vleck for helping in the computing task and their useful comments. This study was carried out using the computing facilities of the University of Nebraska-Lincoln and supported by a grant from Ministerio de Educacidn y Ciencia, Spain.
References Amiche, L., 1980. Performances de reproduction des bmvis caussenardes du lot de la base de selection conduites en rythme acCelere% (Reproductive performance of Caussenardes sheep in accelerated lambing systems. In: Memoite de Fin d’Etude. ITPA, France, 66 pp. ARC, 1980. The Nutrient Requirement of Ruminant Livestock. Agticultural Research Council, Slough, 35 1 pp. Boldman, KG. and van Vleck, L.D., 1991a. Derivative-free restricted maximum likelihood estimation in animal models with a Sparse Matrix Solver. I. Dairy Sci., 74: 4337-4343. Boldman, KG., van Vleck, L.D., Gregory, K.E. and Cundiff, L.D., 1991b. Estimates of direct and maternal parameters for 200 d weight in purebred and composite lines of beef cattle. J. Anim. Sci., 69 (Suppl. 1): 203, abstract.
GA. Maria /Small Ruminant Research 18 (1995) 69-73
Boujenane, I. and Bndford, G.E., 1991. Genetic effects on ewe productivity of crossing D’man and sardi breeds of sheep. J. Anim. Sci., 69: 525-530. Burfening, P.J. and Kress, D.D., 1993. Direct and maternal effects on birth and weaning weight in sheep. Small Rumin. Res., 10: 153-163. Cantet, R.J.C., Schaeffer, L.R. and Smith, C., 1992. Reduced animal model with differential genetic grouping for direct and maternal effects. J. Anim. Sci., 70: 1730-1741. Cardellino, R.A., Siewerdt F. and Azzarini, M., 1991. Repeatability of reproductive and wool production traits in Corriedale sheep. Prod. Ovina, 3: 47-54. Clarke, S.E. and Hohenboken, W.D., 1983. Estimation of repeatability, heritability and breed difference for lamb production, J. Anim. Sci., 56: 309-315. Dickerson, G.E., 1969. Techniques for research in quantitative animal genetics. In: J.K. Loosli (Editor), Techniques and Procedures Animal Science Research. ASAS, Champaign, IL, pp. 3779. Dickerson, G.E., 1977. Crossbreeding evaluation of Finsheep and some U.S. breeds for market lamb production. North Central Regional Publ. No. 246, USDA and University of Nebraska, Lincoln, NE. Donald, H.P., Read, J.L. and Russell, W.S., 1968. A comparative trial ofcrossbreedewes by Finish Landrace and other sires. Anim. Prod., 10: 413421. Eisen, E.J., 1967. Mating designs for estimating direct and maternal genetic variances and direct-maternal genetic covariances. Can. J. Genet. Cytol., 9: 13-21. Eler, J.P., van Vleck, L.D., Lobo, R.B. and Message, Jr., A., 1993. Estimation of variances due to direct and maternal genetic effects in Nelore cattle. J. Anim. Sci., 71 (Suppl. 1): 107, abstract. Fahmy, M.H., 1990. Development of DLS breed of sheep: genetic and phenotypic parameters of date of lambing and litter size. Can. J. Anim. Sci., 70: 771-778. Fogarty, N.M., Dickerson, G.E. and Young, L.D., 1985. Lamb production and its components in pure breeds and composite lines. 111.Genetic parameters. J. Anim. Sci., 60: 40-57. Gabhia, D., 1989. Improvement of the reproductive performance of Rasa Aragonesa flocks in frequent lambing systems. II. Repeat-
73
ability and heritability of sexual precocity, fertility and litter size. Selection strategies. Livest. Prod. Sci., 22: 87-97. Gama, L.T., Dickerson, G.E., Young, L.D. and Leymaster, K.A., 1991a. Effects of breed, heterosis, age of dam, litter size, and birth weight on lamb mortality. J. Anim. Sci., 69: 2727-2743. Gama, L.T., Boldman, K.G. and Johnson, R.K., 1991b. Estimatesof genetic parameters for direct and maternal effects on embryonic survival in swine. J. Anim. Sci., 69: 4801-4809. George, A. and Ng, E., 1981. A brief description of SPARSPAK. Waterloo Sparse Linear Equations Package. SIGNUM NewsI., 16: 17-20. Mallinckrodt, C.H., Golden, B.L. and Bourdon, R.M., 1993. The impact of data falsification and selective reporting on estimates of genetic parameters. J. Anim. Sci., 71 (Suppl. 1): 98, abstract. Meyer, K., 1988. Programs to estimate variance components for individual animal models by restricted maximum likelihood (REML). User Notes. University of Edinburgh, 12 pp. Meyer, K., Carrick, M.J. and Donnelly, B.J.P., 1994. Genetic parameters for milk production of Australian beef cows and weaning weight of their calves. J. Anim. Sci., 72: 1177-I 165. Nitter, G., 1987. Economic response to increasing genetic potential for reproductive performance. In: I.M.F. Marai and J.B. Owen (Editors), New Techniques in Sheep Production. Butterworths, London, pp. 271-280. Notter, D.R., 1981. Repeatability of conception rate and litter size for ewes in accelerated lambing system. J. Anim. Sci., 53: 643650. Ricordeau, G., Thimonier, J., Poivei, J.P., Driancourt, M.A., Hochereau-de-Reviers, M.T. and Tchamitchian, L., 1990. INRA research on the Romanov sheep breed in France: a review. Livest. Prod. Sci., 24: 305-331. Sierra, I., 1985. The Salz sheep breed. Development and performance. Ibercaja, Zaragoza, 95 pp. Smith, S.P. and Graser, H.U., 1986. Estimating variance components in a class of mixed models by restricted maximum likelihood. J. Dairy Sci., 69: 1156-l 165. Valls, M., 1983a. Frequent lambing of sheep flocks in Spain: productivity and management consequences. Livest. Prod. Sci., IO: 49. Valls, M., 1983b. The performance of Romanov and FinishLandrace sheep in Spain. Ann. INIA, 18: 63-81.
Estimates of variances due to direct and maternal effects for reproductive traits of Romanov sheep G.A. Maria* Animal Production Department, University of Zaragoza, Miguel Server 177,
(50013)Zaragoza, Spain
Accepted20 January 1995
Abstract A total of 2003 records of 352 Romanov ewes from 15 sires collected between 1985 and 1990 were analyzed. Natural and artificial insemination were used with lambing season centered in February, June and October. Lambing interval (LI) averaged 331 days with extremes of 168 and 469 days. Fractions of total variance and covariances due to direct and maternal genetic effects, and permanent environmental effects (c*) for litter size and LI were estimated. Traits analyzed were litter size score (LSS), standardized for each seasonX age ewe group, and LI. Variance components were estimated using derivative-free restricted maximum likelihood (DFREML) with an animal model including fixed effects of year X season, parity and mating system, the direct genetic effect of the animal ( h2), the maternal genetic effect (m’), the permanent environmental effect (c*), and random residual effect. Estimates of h*, &, and c* respectively, as a proportion of phenotypic variance, were 0.07,0.08, and 0.05 (LSS) and 0.09, 0.09, and 0.0 (LI). The low heritability estimates for these traits may hinder their rapid improvement through selection. Keywords: Sheep; Romanov;
Spain; Reproductive
traits; Variance components
1. Introduction Litter size is defined as number of lambs born per ewe. This trait is a major determinant of productivity and economic efficiency in sheep production systems (Nitter, 1987; Gabifia, 1989) and is a composite trait with two main components: ovulation rate and embryo survival. Litter size is easy to measure under supervised lambing, whereas measuring ovulation rate requires surgical methods such as endoscopy. Improvement of litter size is of great economic interest in meat sheep flocks in the Aragon region of Spain (Gabiiia, 1989). Two main methods for genetic * Fax: 34 76 591994. Email: LEVRINO CC.UNIZAR.ES. 0921~4488/95/$9.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO921-4488(95)00717-2
improvement of litter size are selection within local breeds and crossbreeding with hyperprolific breeds (e.g. Romanov) to simultaneously exploit both additive and non-additive genetic effects (Dickerson, 1969; Gabifia, 1989). Prolific breeds of sheep have been extensively used in crossbreeding systems. First cross (F,) ewes with Romanov and Finnish Landrace sires are superior to purebred local ewes for overall productivity (Donald et al., 1968; Dickerson, 1977; Ricordeau et al., 1990). In Spain, the Romanov breed has performed better than the Finnish Landrace as sires of autochthonous ewes (Valls, 1983b). When Romanov X Aragonesa F, ewes were used, the advantage provided by crossbreeding over purebred local schemes was estimated to be about 40% more lambs per ewe per year (Valls, 1983a). However, crossbreeding systems
70
G.A. Maria/Small Ruminant Research 18 (1995) 69-73
require an intensification of management that increases production costs (Sierra, 1985). The Romanov, a breed native of Russia, was introduced to France in 1963 and to Spain in 1973 (Valls, 1983a; Sierra, 1985; Ricordeau et al., 1990) because of its high litter size (2.6-3.1). Two composite breeds, the Salz and Marine strains, have been created in Spain using local ewes and Romanov sires (Sierra, 1985; A. Marine, personal communication, 1985). To take advantage of different systems of breed utilization, the genetic parameters involved should be known (Boujenane and Bradford, 1991). In addition, the heritability and repeatability of ewe productive and reproductive traits must be known for effective selection and designing culling programs (Clarke et al., 1983). The objective of this study was to estimate variances and covariances due to direct and maternal genetic effects for litter size and lambing interval using an animal model with data from Romanov sheep.
2. Materials and methods The source of data was a flock of Romanov sheep maintained at the Ovhi farm situated in Talavera de la Reina (South-Central Spain). A total of 2003 records of 352 purebred Romanov ewes from 15 sires, collected between 1985 and 1990, were analyzed. The Ovhi program uses recording and standardization methods for litter size applied by ITOVIC in France (Amiche, 1980). Natural (single-sire groups, SG) and artificial insemination (AI) were used with lambing seasons centered in February, June and October, according to the reproduction system described by Valls ( 1983a). Because of seasonal fertility, October lambing resulted from oestrus synchronized using intravaginal pessaries and pregnant mare serum gonadotrophin (Intervet, Spain). During the suckling period, ewes were fed a ration supporting 3.50 Meal of metabolizable energy and 240 g of crude protein per head per day. After weaning, which occurred at about 40 days of lamb age, ewes were fed 300 g of concentrate (barley 100%) and 1 kg of ammonia-treated straw per head per day, supporting the maintenance requirements (ARC, 1980). Two reproductive traits were considered for analysis: litter size (LS) and lambing interval (LI) . In order to account for the correlation between mean and vari-
ante that is present in categorical data like litter size, a standardized litter size score (LSS) was calculated for each ewe using the following expression: LSS= (LS-LSG)/(SDo&
+ 100
where LSG is the average LS of the ewe group (season X age group) and SDoso, is the standard deviation of LS in the ewe group. To avoid negative values, 100 was added to the score. Lambing interval was calculated as the interval in days between consecutive lambing. The DFREML programs of Meyer ( 1988) modified for use with SPARSPAK (Boldman and Van Vleck, 1991) were used for the animal model analysis. Derivative free restricted maximum likelihood (DFREML) was described by Smith and Graser ( 1986) and Meyer (1988). To save computing time, the SPARSPAK package (George and Ng, 1981) was used to reorder symbolically the mixed model equations once. Then the equations were updated each round and solved, and the log of the likelihood calculated by Cholesky factorization rather than by the Gaussian elimination algorithm used by the original DFREML programs. The full model (Model 8 of Meyer, 1988) was:
Y=Xb+Zaa+Zmm+Zcc+e where Y is N X 1 vector of records, X associates records in Y with the fixed effects in b, Zaa associates records in Y with random direct genetic effects, Zmm associates records in Y with random maternal genetic effects, Zcc associates records in Y with random permanent environmental effects of the ewe and e denotes the residual terms. The assumed variance-covariance structure was as follows:
Au2a aam 0 AgamArr2mo0
0 0
0
0
Icu2c0
0
0
0
Inu2e
where A is the numerator relationship matrix, Zc is an identity matrix with order number of ewes and In is an identity matrix with order number of records. Fixed effects included in model were year x season ( 16)) parity ( 1 to 6 + ) , and mating system (SG or AI).
G.A. Maria /Small Ruminant Research 18 (1995) 69-73
3. Results and discussion
Table 2
Records from first lambing ewes represented 20% of the sample whereas those from second, third, fourth, and fifth or more lambings represented 15.5, 14, 12.5 and 38% of the sample, respectively. Actual litter size means by parities are presented in Table 1. Mean LSS was 100.2 and ranged from 97.5 to 104.5 across parities. As described above, and due to the recording method used in the Ovhi farm, values of LSS are deviations from the mean of the contemporary group of the ewe. Lambing interval (LI) averaged 331 days with extremes of 168 and 469 days. Estimates of variance components are given in Table 2. The variance of the direct genetic effect of the animal (heritability) for LSS was 0.07 of total variance and the variance of the maternal genetic effect (maternal heritability) was 0.08 of total variance. The fraction due to permanent environmental effects of the ewe was 0.05. An estimate of repeatability can be obtained as the sum of fractions of variance due to the direct animal effects and permanent environmental effects (0.07 + 0.05 = 0.12). In general, results obtained in this study agree with those reported in the literature. Gabifia ( 1989) found estimates of heritability and repeatability for LS in the Rasa Aragonesa breed of 0.10 and 0.13, respectively. Cardellino et al. (1991) with Corriedale ewes, estimated repeatability for LS of 0.09. Fogarty et al. ( 1985) reported estimates of repeatability ranging from 0.06 to 0.15 and of heritability of 0.11 in five composite breeds containing genes from Suffolk, Rambouillet, Dorset, Targhee, and Finnsheep breeds. Nevertheless, Fahmy ( 1990) in DLS (Dorset, Leicester and Suffolk) composite ewes and Notter ( 198 1) in Finnsheep crosses, reported repeatability estimates for LS of 0.24 and 0.37, respectively. Clarke and Hohenboken ( 1983), working with eight sets of Table 1 Actual litter sizea means and standard deviations parity
Mean
SD
1 2 3 4 5+
2.06 2.50 2.45 2.45 2.51
0.82 0.66 0.69 0.79 0.83
“Average lambs born per ewe.
11
(SD) by parities
Summary of estimates of variance components for litter size score (LSS) and lambing interval (LI) using DFREML with an animal model” Trait
u*
h=
mz
c2
c,ln
rzBnl
2 UE-
LSS LI
0.997 17 358
0.07 0.09
0.08 0.09
0.05 0.00
-0.07 -0.09
-0.98 -0.98
0.875 15 729
a Model 8 (Meyer, 1988). CT’,total phenotypic variance; h2, fraction of total variance due to direct genetic effects; a?, fraction of total variance due to maternal genetic effects; c2, fraction of total variance due to permanent environmental effect of ewe; c,, covariance between animal direct and maternal genetic effects as a proportion of the total variance; i,, correlation between direct and maternal genetic animal effects; a:, error variance.
crosses (Suffolk and Columbia ewes with Finnsheep, Dorset, Cheviot and Romney sires), found estimates of heritability for number of lambs born of 0.12 and repeatability of 0.19. On the other hand, Ricordeau et al. ( 1990)) for Romanov ewes, reported estimates of heritability for LS of 0.02. Large negative estimates of correlation ( - 0.98 and -0.99) between direct and maternal effects were found. It is difficult to find a biological explanation for this high correlation, but the estimates may be due to the data structure of the sample (i.e. number of generations with animals measured as individuals and as dams). This is a common occurrence with many small data sets, and even in some that are not so small (Boldman et al., 1991). It is necessary to mention the observed deficiencies of DFREML procedures in estimating r,, with this type of commercial data set. We have seen that problem with small data sets and especially those of poor structure, i.e. those with only few dams with measurements themselves. In order to avoid this type of problem, three generation data are needed (Van Vleck, personal communication, 1992). Sheep data also seem to behave badly, probably because of low heritability (direct or maternal) for some traits. Nevertheless, high r,, estimates using DFREML have been reported by several authors working with large data sets of various domestic species (Gama et al., 1991a,b; Eler et al., 1993; Boldman et al., 1991). For LI, the fraction of variance due to direct genetic effects was 0.09. A similar estimate was found for maternal animal effects. A large negative correlation between direct and maternal animal effects was esti-
12
G.A. Maria /Small Ruminant Research 18 (1995) 69-73
mated ( - 0.98). These estimates of heritability for LI are slightly smaller than those obtained by Gabiiia (1989) for the Aragonesa breed. Variation in lambs’ ability to survive is influenced by intrauterine and postnatal maternal influences (Gama et al., 1991a). Nevertheless, these permanent environmental effects seem to have no important effect on the reproductive traits of the ewe lamb, as reflected by the low estimates of c* for LSS and for LI. The low heritability and repeatability estimates for LSS and LI interval with values very close to zero may hinder their rapid improvement through selection. Advantages of the use of a sparse matrix package (SPARSPAK) include smaller memory and central processing unit time requirements, and the availability at convergence of BLUE and BLUP solutions for all fixed and random effects (Boldman and Van Vleck, 1991). In consequence, the use of this type of routine greatly reduces computing cost and the amount of computer resources required for the estimation of breeding values of the animals. According to the likelihoods and from the theoretical point of view, Model 8 performed very well in the estimation of variance components for LSS with repeated measures. However, because the data structure might have produced the high correlations between direct and maternal genetic effects, models ignoring the correlation between direct and maternal effects might be recommended until more data become available. Analyses of Meyer et al. ( 1994)) working with a large cattle data set, were carried out ignoring and allowing for a direct and maternal covariance, i.e. fitting Models 5 and 6 of Meyer ( 1988). On the other hand, Cantet et al. (1992) suggested the inclusion of ‘phantom’ dams in order to avoid misspecification of maternal additive variance and additive covariance between direct and maternal effects, when dam information is missing. Likewise, Mallinckrodt et al. (1993) reported the impact of data falsification and selective reporting on estimates of genetic parameters using REML techniques. For these authors data falsification influenced estimates of the direct-maternal correlation (ram) and in BLUP it may be better to assume that r,,,, is zero than to use an estimate from selectively reported data. Burfening and Kress ( 1993) estimated direct and maternal effects in sheep for birth and weaning weights using the least-squares method proposed by Eisen ( 1967). This study found that the covariance between additive
direct and additive maternal effects is important and negative ( - 0.88). As a result of the large negative covariance between direct and maternal effect, these authors suggest that the total additive genetic contribution to a maternally influenced trait is expected to be low. From a practical point of view, it is hard to interpret the high correlations between maternal and direct genetic effect observed, but we have to recognize that this is a common finding when DFREML techniques are applied to low heritability traits derived from field data. The reliability of parameter estimates needs to be tested and further studies are necessary in order to find a logical explanation for these unlikely results. The results of this study provide an indication that direct and maternal heritability and permanent environmental effect of litter size and interval between lambing are close to zero. Knowledge of this fact should be taken into account when considering alternative selection strategies.
Acknowledgements Appreciation is extended to K. Meyer who provided the DFREML programs. The authors gratefully acknowledge Keith G. Boldman and Dale van Vleck for helping in the computing task and their useful comments. This study was carried out using the computing facilities of the University of Nebraska-Lincoln and supported by a grant from Ministerio de Educacidn y Ciencia, Spain.
References Amiche, L., 1980. Performances de reproduction des bmvis caussenardes du lot de la base de selection conduites en rythme acCelere% (Reproductive performance of Caussenardes sheep in accelerated lambing systems. In: Memoite de Fin d’Etude. ITPA, France, 66 pp. ARC, 1980. The Nutrient Requirement of Ruminant Livestock. Agticultural Research Council, Slough, 35 1 pp. Boldman, KG. and van Vleck, L.D., 1991a. Derivative-free restricted maximum likelihood estimation in animal models with a Sparse Matrix Solver. I. Dairy Sci., 74: 4337-4343. Boldman, KG., van Vleck, L.D., Gregory, K.E. and Cundiff, L.D., 1991b. Estimates of direct and maternal parameters for 200 d weight in purebred and composite lines of beef cattle. J. Anim. Sci., 69 (Suppl. 1): 203, abstract.
GA. Maria /Small Ruminant Research 18 (1995) 69-73
Boujenane, I. and Bndford, G.E., 1991. Genetic effects on ewe productivity of crossing D’man and sardi breeds of sheep. J. Anim. Sci., 69: 525-530. Burfening, P.J. and Kress, D.D., 1993. Direct and maternal effects on birth and weaning weight in sheep. Small Rumin. Res., 10: 153-163. Cantet, R.J.C., Schaeffer, L.R. and Smith, C., 1992. Reduced animal model with differential genetic grouping for direct and maternal effects. J. Anim. Sci., 70: 1730-1741. Cardellino, R.A., Siewerdt F. and Azzarini, M., 1991. Repeatability of reproductive and wool production traits in Corriedale sheep. Prod. Ovina, 3: 47-54. Clarke, S.E. and Hohenboken, W.D., 1983. Estimation of repeatability, heritability and breed difference for lamb production, J. Anim. Sci., 56: 309-315. Dickerson, G.E., 1969. Techniques for research in quantitative animal genetics. In: J.K. Loosli (Editor), Techniques and Procedures Animal Science Research. ASAS, Champaign, IL, pp. 3779. Dickerson, G.E., 1977. Crossbreeding evaluation of Finsheep and some U.S. breeds for market lamb production. North Central Regional Publ. No. 246, USDA and University of Nebraska, Lincoln, NE. Donald, H.P., Read, J.L. and Russell, W.S., 1968. A comparative trial ofcrossbreedewes by Finish Landrace and other sires. Anim. Prod., 10: 413421. Eisen, E.J., 1967. Mating designs for estimating direct and maternal genetic variances and direct-maternal genetic covariances. Can. J. Genet. Cytol., 9: 13-21. Eler, J.P., van Vleck, L.D., Lobo, R.B. and Message, Jr., A., 1993. Estimation of variances due to direct and maternal genetic effects in Nelore cattle. J. Anim. Sci., 71 (Suppl. 1): 107, abstract. Fahmy, M.H., 1990. Development of DLS breed of sheep: genetic and phenotypic parameters of date of lambing and litter size. Can. J. Anim. Sci., 70: 771-778. Fogarty, N.M., Dickerson, G.E. and Young, L.D., 1985. Lamb production and its components in pure breeds and composite lines. 111.Genetic parameters. J. Anim. Sci., 60: 40-57. Gabhia, D., 1989. Improvement of the reproductive performance of Rasa Aragonesa flocks in frequent lambing systems. II. Repeat-
73
ability and heritability of sexual precocity, fertility and litter size. Selection strategies. Livest. Prod. Sci., 22: 87-97. Gama, L.T., Dickerson, G.E., Young, L.D. and Leymaster, K.A., 1991a. Effects of breed, heterosis, age of dam, litter size, and birth weight on lamb mortality. J. Anim. Sci., 69: 2727-2743. Gama, L.T., Boldman, K.G. and Johnson, R.K., 1991b. Estimatesof genetic parameters for direct and maternal effects on embryonic survival in swine. J. Anim. Sci., 69: 4801-4809. George, A. and Ng, E., 1981. A brief description of SPARSPAK. Waterloo Sparse Linear Equations Package. SIGNUM NewsI., 16: 17-20. Mallinckrodt, C.H., Golden, B.L. and Bourdon, R.M., 1993. The impact of data falsification and selective reporting on estimates of genetic parameters. J. Anim. Sci., 71 (Suppl. 1): 98, abstract. Meyer, K., 1988. Programs to estimate variance components for individual animal models by restricted maximum likelihood (REML). User Notes. University of Edinburgh, 12 pp. Meyer, K., Carrick, M.J. and Donnelly, B.J.P., 1994. Genetic parameters for milk production of Australian beef cows and weaning weight of their calves. J. Anim. Sci., 72: 1177-I 165. Nitter, G., 1987. Economic response to increasing genetic potential for reproductive performance. In: I.M.F. Marai and J.B. Owen (Editors), New Techniques in Sheep Production. Butterworths, London, pp. 271-280. Notter, D.R., 1981. Repeatability of conception rate and litter size for ewes in accelerated lambing system. J. Anim. Sci., 53: 643650. Ricordeau, G., Thimonier, J., Poivei, J.P., Driancourt, M.A., Hochereau-de-Reviers, M.T. and Tchamitchian, L., 1990. INRA research on the Romanov sheep breed in France: a review. Livest. Prod. Sci., 24: 305-331. Sierra, I., 1985. The Salz sheep breed. Development and performance. Ibercaja, Zaragoza, 95 pp. Smith, S.P. and Graser, H.U., 1986. Estimating variance components in a class of mixed models by restricted maximum likelihood. J. Dairy Sci., 69: 1156-l 165. Valls, M., 1983a. Frequent lambing of sheep flocks in Spain: productivity and management consequences. Livest. Prod. Sci., IO: 49. Valls, M., 1983b. The performance of Romanov and FinishLandrace sheep in Spain. Ann. INIA, 18: 63-81.