(Key Words: Beef Cattle, Maternal Effects, Growth, Preweaning Period, ... There were three different phases of ... Henderson's method III was used, as out-.
DIRECT AND M A T E R N A L V A R I A N C E S A N D COVARIANCES A N D M A T E R N A L PHENOTYPIC EFFECTS ON PREWEANING GROWTH OF BEEF CATTLE I R.J.C. C a n t e r 2 , D. D. Kress a'4, D. C. A n d e r s o n s , D. E. D o o r n b o s s , P. J. B u r f e n i n g a a n d R. L. Blackwell a'6 N o r t h e r n A g r i c u l t u r a l R e s e a r c h C e n t e r , Havre, M T 59501 a n d M o n t a n a S t a t e University, B o z e m a n 5 9 7 1 7 ABST R A C T
Birth weights (BW) and weaning weights (WW) of 41423 non-creep-fed Hereford calves were used to estimate direct and maternal sources of variation and maternal phenotypic effects (fm). Seventeen different (co)variances among relatives were estimated through Henderson's Method III and restticted estimated maximum likelihood procedures. Direct and maternal (co)variances and fm were evaluated by multiple regression procedures. Estimates of h a for BW and WW were .28 and .28 respectively, by the paternal half-sib procedure and .45 and .88, respectively, based on full-sibs. Repeatability estimates were .21 for BW and .30 for WW. Heritabilities based on regression of offspring on dam and offspring on sire were .45 and .21 for BW and .28 and .06 for WW, respectively. Negative correlations were found between solutions for additive genetic direct and additive maternat effects (rG). Estimates of r G ranged from - . 8 6 to --1.05 for BW and from --.57 to - . 7 9 for WW. Estimates of heritability for direct effects (h~), for maternal effects (h~n) and for total additive genetic effects (h~) were .16 to .27, .18 to .63 and - . 0 2 to .05 for BW and .26 to .32, .27 to .67 and .10 to .20 for WW. Dominance affected both direct and maternal effects for BW and WW. Values of -.15 (BW) and -.25 (WW) were found for fm (path coefficient between the maternal phenotypes of dam and daughter). These results indicated that selection response would be decreased due to the negative genetic correlation between direct and maternal effects. (Key Words: Beef Cattle, Maternal Effects, Growth, Preweaning Period, Genetic Parameters.)
Introduction
Since t h e early w o r k o f K o c h a n d Clark ( 1 9 5 5 ) , m a t e r n a l effects h a v e b e e n r e c o g n i z e d as i m p o r t a n t in d e t e r m i n i n g t h e results o f select i o n for p r e w e a n i n g g r o w t h r a t e in b e e f c a t t l e ( K o c h et al., 1982). As p o i n t e d o u t b y H o h e n b o k e n a n d Brinks ( 1 9 7 1 ) a n d K o c h ( 1 9 7 2 ) , b e e f c a t t l e d a t a usually do n o t p r o v i d e e n o u g h d i f f e r e n t r e l a t i o n s h i p s a m o n g relatives to esti-
] Published with approval of the Director of Montana Agric. Exp. Sta., journal series no. J-2001. = Departamento de Zootecnia, Fac. de Agronomia, Univ. de Buenos Aires, Argentina. Present Address: Dept. of Anim. Sci., Univ. of If, Urbana. aDept, of Anim. and Range Sci., Montana State Univ., Bozeman 59717. 4 Direct reprint requests to this author. s Northern Agric. Res. Center, Star Route 36, Box 43, Havre, MT 59501. ~Authors gratefully acknowledge the helpful suggestions of Daniel Gianola. Received June 11, 1987. Accepted October 26, 1987.
m a t e all additive, d o m i n a n c e a n d e n v i r o n m e n t a l variances a n d c o v a r i a n c e s f o r d i r e c t a n d m a t e r nal effects. T h e r e f o r e , t h e reaI m a g n i t u d e o f s o m e o f these p a r a m e t e r s is n o t clear. A n o t h e r u n s o l v e d p r o b l e m suggested b y K o c h ( 1 9 7 2 ) is t h e q u a n t i f i c a t i o n o f t h e e f f e c t of the maternal phenotype of the female on the f u t u r e m a t e r n a l p h e n o t y p e s o f h e r daughters. Baker (1980) emphasized the importance of this p a t h in d e t e r m i n i n g t h e m a g n i t u d e o f t h e c o v a r i a n c e b e t w e e n a d d i t i v e g e n e t i c direct a n d m a t e r n a l effects ( O A o A m ) o n w e a n i n g weight. Because t h e values o f O A o A m i n f l u e n c e s r a t e o f progress to s e l e c t i o n f o r w e a n i n g w e i g h t ( V a n V l e c k et al., 1 9 7 7 ) , it is i m p o r t a n t t o e s t i m a t e a A o A m free o f m a t e r n a l p h e n o t y p i c effects. T h e p u r p o s e o f this s t u d y was t o e s t i m a t e direct a n d m a t e r n a l (co)variances a n d m a t e r n a l p h e n o t y p i c effects o n b i r t h a n d w e a n i n g w e i g h t o f H e r e f o r d c a t t l e using several d i f f e r e n t relat i o n s h i p s a m o n g relatives. Materials and Methods
Data were c o l l e c t e d at t h e N o r t h e r n Agricult u r a l R e s e a r c h C e n t e r ( N A R C ) , Havre, MT.
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J. Anim. Sci. 1988. 66:648--660
DIRECT AND MATERNAL EFFECTS IN BEEF CATTLE Birth weights (BW) and weaning weights (WW) were taken on 4,423 Hereford calves from 1938 to 1983. There were three different phases of data collection and breeding systems (Flower et al., 1963; Kress and Burfening, 1972; Kress et al., 1979a). Briefly, the first phase consisted of animals raised before 1946; these were cattle that originated at NARC. The second phase was characterized by the creation and development of closed lines and subsequent testing of crosslines of Hereford cattle. The process was initiated in 1946 and was maintained through 1975. These closed lines had low levels of inbreeding (Kress et al., 1979a). The third phase started in 1975 with stock purchased from the Livestock and Range Research Station (LARRS), Miles City, MT, in 1962 and 1963 and is still continuing. These purebred cattle were selected by the index: I = 365-d adjusted weight - 3.2 adjusted birth weight. Descriptions of the management procedures were given by Flower et al. (1963), Kress and Burfening (1972) and Kress et al. (1979a). Briefly, heifers were bred to calve first as 3-yr-olds before 1951 and as 2-yr-olds thereafter. The breeding season lasted approximately 60 d, beginning the 1st wk of June. During most years, natural service was used in single-sire pastures. Heifers and cows received supplement during the winter, and calves were not creep-fed. The total number o f sires that produced progeny was 202, but only 105 were raised at NARC. All of the latter had records available on their own BW and WW. The remaining bulls were raised at LARRS under different environmental conditions. Statistical Analyses. Seventeen different (co)variances among relatives existed within the database analyzed and were evaluated for BW and WW as shown in Figure 1. Family relationships were analyzed by least squares procedures as outlined by Harvey (1977). The basic model used was; Yijklm = # + li + aj + sk + (as)jk + bXijklm + gil + eij klmn where Yijklm = observation on the mth calf BW or WW, /a -- general mean common to all the observations, Ii = effect of the i th line-year, e.g., i = 150 (line 1, year 1950), 250, 350,
649
450, etc., aj = effect of the jth age of dam, j = 2, 3, 4, 5, 6 to 10, 11 or more, Sk = effect of the k th sex, k = 1 (heifer), 2 (bull), 3 (steer), (as)jk = effect of the interaction between the jth age of dam and k th sex, bXijklm = regression o f BW on birth date or WW on age at weaning, gil = random family effect (general term used for sire, maternal grandsire (MGS), paternal grandsire (PGS) and maternal great-grandsire nested within the ith line-year) and eijklm = random error. Due to the small number of observations within family subclass, the records were corrected for line-year effects in the paternal half-sib (PHS) + dam first cousins (DFC) and full-sib (FS) + parents paternal half-sibs (PPHS) models using constants obtained from a fixedeffects model. This model included the effects of age of dam, sex, line, year and the regressions of BW on birthdate and WW on weaning age. Estimates of residual variances were corrected for the number of degrees of freedom lost while adjusting for line-year. Dam components of variance were estimated from the full-sib model in which dams were nested within sire and from a model in which dams were nested within maternal grandams. Henderson's method III was used, as outlined by Harvey (1977), to estimate the variance components in all the analyses described above. Standard errors for heritability estimates obtained through analyses o f variance were calculated by formulas provided by Osborne and Patterson (1952). Covariances between offspring and dam (coy(O, D)), offspring and sire (coy(O, S)), offspring and maternal grandam (cov(O, MGD)), aunt (full-sib of dam) and niece (cov(MA, N)) and aunt (full-sib of sire) and nephew or niece (cov(PA, N)) were evaluated by simple linear regression procedures after adjusting both weights for all fixed effects (see Figure 1 for diagrams depicting relationships). A sire-MGS model and the restricted maximum likelihood (REML) method of estimating variance components was employed to improve the estimates of the sire and MGS variance components. The program used was P3V in the BMDP package, which is based on a combination of Fisher-scoring and Newton-Raphson
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GS
GD 1
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i n t e r a c t i o n c o r r e c t e d b y t h e f i x e d effects (line-year, age o f d a m , sex o f calf, age o f d a m x sex i n t e r a c t i o n a n d regression o n b i r t h date o r age at w e a n i n g ) was u s e d o n t h e 1 , 7 7 4 calves o f line 4. Final solutions for the direct and maternal g e n e t i c ( c o ) v a r i a n c e s were o b t a i n e d t h r o u g h o r d i n a r y least squares p r o c e d u r e s . E s t i m a t e s o f t h e (co)variances a m o n g relatives f o r BW a n d WW were regressed o n t h e c o e f f i c i e n t s f o r t h e direct a n d m a t e r n a l (co)variances in t h e exp e c t e d values ( T a b l e 1). T h e r e f o r e , e s t i m a t e s o f t h e d i r e c t a n d m a t e r n a l ( c o ) v a r i a n c e s were t h e regression c o e f f i c i e n t s o f a m o d e l w i t h zero i n t e r c e p t . T h e n i n e d i r e c t a n d m a t e r n a l (co)varia n c e s were:
GD 4
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Figure 1. Relationships a m o n g r e l a t i v e s where O = offspring, D = dam, S = sire, GD = grandam, GS = grandsire and GGS = great-grandsire. The relationships used were: 1) paternal half-sibs (PHS); 0 1 -- 0 6 ; 2) paternal grandsire (PGS): O t - Oa ; 3) maternal grandsire (MGS): 0 7 - 0 9 ; 4) maternal great grandsire (MGGS): O~ - 0 6 ; 5) maternal grandam (MGD): O~ -- Oz2 ; 6) covariance offspring and sire (coy(O, S): $3
02 Do = 02 Dm = ODoDm =
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7) covariance offspring and dam (cov(O D)): D a - - O14 ;
8) covariance offspring and maternal grandam (coy(O, MGD)): GD 2 -- 0 6 ; 9) covariance aunt (full-sib of dam) a n d n i e c e (cov(MA, N)): D 3 - O s ; 10) covariance aunt (full-sib of sire) and niece (cov(PA, N)): D t --0 3 ; 11) full-sibs (FS): Or0 -- Oll ; 12) maternal half-sibs (MHS): O a -- 0 9 ; 13) dam first cousins (DFC): O s -- O 6 ; 14) PHS + MGD: O14 - Ors ; 15) P H S + D F C : 0 7 - O 8; 16) FS + parents PHS (FS + PPHS): Or2 -- Ola; and 17) PHS + dams PHS (PHS + DPHS): 0 9 -- Or1.
OEoEm =
v a r i a n c e d u e to a d d i t i v e d i r e c t effects, v a r i a n c e d u e to a d d i t i v e m a t e r n a l effects, covariance between additive direct a n d a d d i t i v e m a t e r n a l effects, variance d u e t o d o m i n a n c e d i r e c t effects, variance d u e t o d o m i n a n c e m a t e r n a l effects, covariance between dominance d i r e c t a n d d o m i n a n c e m a t e r n a l effects, variance d u e t o d i r e c t e n v i r o n m e n t a l effects, v a r i a n c e d u e to m a t e r n a l environm e n t a l effects a n d c o v a r i a n c e b e t w e e n d i r e c t a n d mat e r n a l e n v i r o n m e n t a l effects.
T h e value o f f m (effect o f d a m m a t e r n a l phenotype on future daughter maternal phenot y p e as d e f i n e d b y K o c h , 1 9 7 2 ) was e s t i m a t e d by fitting Falconer's (1965) model through m u l t i p l e regression. T h e r e f o r e , t h e e s t i m a t e s o f t h e (co)variances a m o n g relatives w e r e regressed o n t h e c o e f f i c i e n t s f o r variance c o m p o n e n t s f o r t h e t e r m s in t h e r a n d o m m o d e l : P=A+fmPW+D+C+E where
algorithms (Jennrich and Sampson, 1976). Because t h e m a x i m u m n u m b e r o f cells t h e p r o g r a m c a n h a n d l e is c o n s t r a i n e d b y t h e system, a t w o - w a y r a n d o m m o d e l w i t h o u t
P = p h e n o t y p i c value o f a n individual meas u r e d as a d e v i a t i o n f r o m t h e p o p u l a tion mean, A -- b r e e d i n g value o f t h e individual, f m = partial regression c o e f f i c i e n t r e l a t i n g
DIRECT
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6 51
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