Estimation of maternal effects on birth and weaning weight of Hereford cattle by Rodolfo Juan Carlos Cantet A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Animal Science Montana State University © Copyright by Rodolfo Juan Carlos Cantet (1984) Abstract: Evidence has been found that maternal effects are important sources of variation in mammals. In beef cattle, evidence has been found to support the hypothesis that maternal effects can reduce the expected response to selection for growth traits, especially preweaning growth. It is not clear whether maternal effects in preweaning growth of beef cattle are genetic or environmental. Therefore, the present research was conducted to study the nature and. magnitude of maternal effects in birth and weaning weight of Hereford cattle. The data used were the records of 4,423 noncreep-fed beef calves raised at the Northern Agricultural Research Center, Havre, Mt from 1938 to 1983. Least-squares, fitting constants method (Henderson III) and Restricted Maximum Likelihood procedures were used to estimate eighteen covariances between different types of relatives. The basic models included the fixed effects of line-year, age of dam, sex of calf, age of dam by sex interaction and the regressions of birth weight on birthdate of calf and weaning weight on weaning age of calf. The source of variation depicting the relative relationship was considered a random effect. Multiple regression procedures were used to obtain the nine parameters: additive genetic, dominance genetic and environmental direct and maternal variances and the covariance between the direct and maternal source in each case. All solutions showed a negative additive genetic correlation between additive direct effects and additive maternal effects (rG). The results were not clear regarding to the magnitude of rG for birth weight but the probable value for weaning weight was around -.60 to -.75. There was also evidence for a negative environmental correlation for maternal phenotype of the dam and daughter in the case of weaning weight. This path coefficient (fm) was calculated to be .08 for birth weight and -.10 for weaning weight. After correcting the expectations of the covariances between relatives for fm, rG was still present and negative for both weights. The solutions showed that dominance was also involved in determining maternal effects in preweaning growth of beef cattle but its effects may be confounded with epistasis.  ESTIMATION OF MATERNAL. EFFECTS ON BIRTH AND WEANING WEIGHT OF HEREFORD CATTLE by R odolfo Juan C arlos Cantet A t h e s i s subm itted i n p a r t i a l f u l f i l l m e n t o f the req u irem en ts f o r the degree o f Master o f S c ie n c e i n Animal S c ie n c e MONTANA STATE UNIVERSITY Bozeman, Montana May, 1984 APPROVAL o f a t h e s i s subm itted by R odolfo Juan C arlos Cantet This t h e s i s has been read by each member o f the t h e s i s com m ittee and h a s b een fo u n d to be s a t i s f a c t o r y r e g a r d i n g c o n t e n t , E n g l i s h usage , fo rm a t , c i t a t i o n s , b ib l io g r a p h ic s t y l e , and c o n s is t e n c y , and i s ready f o r su b m iss io n to th e C o l leg e o f Graduate S t u d ie s . S'/z sr / ______ fD D Date C hairperson , Graduate Committee Approved fo r th e Major Department ___S . , - ^ Date Head, Major Department Approved f o r the C o l leg e o f Graduate S t u d ie s Graduate DeanDate i l l STATEMENT OF PERMISSION TO USE I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f th e r e q u i r e m e n t s f o r a m a s t e r ’s d e g r e e a t M ontana S t a t e U n i v e r s i t y , I ag ree t h a t th e L ibrary s h a l l make i t a v a i l a b l e to borrow ers under the r u l e s o f th e L ibrary . B r i e f q u o t a t io n s from t h i s t h e s i s are a l lo w a b le w ith o u t s p e c i a l p e r m is s io n , provided t h a t a c c u r a te acknowledgement o f sou rce i s made. P e r m iss io n f o r e x t e n s i v e q u o ta t io n from or r e p r o d u c t io n o f t h i s , t h e s i s may be granted by my major p r o f e s s o r , or i n h i s ab sen ce , by the D ir e c to r o f L ib r a r ie s when, i n th e o p in io n o f e i t h e r , th e proposed use o f the m a te r ia l i s f o r s c h o la r l y purposes . Any copying or use o f the m a t e r i a l i n t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w ith o u t my w r i t t e n p e r m iss io n . S ig n a tu r e Mous 2S , I9%4 Date To ray w i f e , to ray mother and to th e memory o f ray f a th e r V VITA R o d o l f o Juan C a r lo s C a n te t was born t o Mr. and Mrs. R o d o lfo Manuel Cantet i n Buenos A ir e s , A rgentina , on March 17, 1954. He a tten d ed L ic e o M i l i t a r General San M artin H ighschool and was ad m itted to the F acu ltad de Agronomia, U n ivers idad de Buenos A ires i n 1972. He graduated as an In g e n ier o Agronomo i n 1978. He h a s w orked a s a r e s e a r c h e r i n B e e f C a t t l e B r e e d in g a t t h e Departamento de Z o o teen ia , U n iversidad de Buenos A ir e s , from 1978 to p r e s e n t . In September 1982, he was a d m itted to Montana S t a t e U n iv e r s i ty f o r h i s M aster's degree i n Animal S c ie n c e (Animal B reeding). He m arried P a t r i c i a Prandini i n 1982. v i ACKNOWLEDGMENTS I w an t t o e x p r e s s my d eep a p p r e c i a t i o n and a d m i r a t i o n t o Dr. D. D. K r e s s . H is r e s e a r c h w as t h e r e a s o n f o r t r a v e l l i n g t h e l o n g d is ta n c e from Buenos A ir e s to Bozeman. His a d v ic e , common s e n se and k n o w le d g e c o u ld be t h e r e a s o n s f o r d o in g t h a t t r a v e l s e v e r a l t i m e s a g a i n . I a l s o w an t t o th an k t h e m em bers o f my g r a d u a t e c o m m i t t e e , Drs . P. J. B u r f e n i n g and M. D. H uffm an f o r t h e i r a d v i c e and h e l p f u l com m en ts . To Dr. R. L. B l a c k w e l l , f o r h i s k i n d n e s s a s a p e r s o n and h i s w is e n e s s as an anim al breeder. To Dr. R. C. C h r is ten son from whom I lea r n e d th e u s e fu l s k i l l s o f th e l i n e a r m odels. S p e c i a l th a n k s t o D a le T r o w b r id g e , D ia n e Doede and my f e l l o w s graduate s tu d e n ts fo r t h e i r f r i e n d s h ip , h e lp and p a t ie n c e . A n o te o f g r a t i t u d e to Juan F. Chavez f o r the good moments we shared d i s c u s s in g over anim al breed ing . To my p r o f e s s o r s and g u i d e s a t B u en os A i r e s , Drs . J. Lopez S e c o , J. G a r c ia Tobar and In g . Agr. L. F. S a n ta Colom a. . They b e l i e v e d i n me from t h e b e g i n n i n g . To Mrs. F r a n c i s c a P e r r i e r de M agnin , t o whom I owe t h e f a c t o f h a v in g s t u d i e d i n U.S.A. To A r g e n t in a , f o r a l l t h e b e a u t i f u l th in g s my country has g iv e n to me. F i n a l ly , I would l i k e to thank my parents because I am what th ey tau gh t me. To my s i s t e r and aunt Leonor fo r b e in g a s th ey are. To my w i f e , P a t r i c i a , f o r b e in g the b e a u t i f u l p a s t , the s u p p o r t iv e p r e se n t and th e prom ising f u t u r e . v i i TABLE OF CONTENTS LIST OF TABLES . . . . LIST OF FIGURES . . . ABSTRACT ............................. INTRODUCTION .................... REVIEW OF LITERATURE . x x i I 4 v i i i E st im ation o f d i r e c t and m aternal so u r c e s o f v a r i a t i o n Problems i n e s t im a t in g d i r e c t and m aternal g e n e t i c c o v a r ia n c e s ...................................................................................... 1. Standard error o f the e s t im a t e s and non independence o f the c o e f f i c i e n t s i n the ex p ected v a lu e s . . . . ..................................................... 2 . Small number o f r e l a t i v e s in v o lv e d i n the e s t im a t io n i n b e e f c a t t l e f i e l d data . . . , 3 . Maternal e f f e c t s e v a lu a t io n l e n g h te n s the tim e t conduct th e s t u d y ..................................................... .... • E s t im a tes o f d i r e c t and m aternal g e n e t i c v a r ia n c e s and c o v a r ia n c e s f o r b ir th w e igh t and weaning w e ig h t i n b e e f c a t t l e .................................. .... ............................................... 1. B ir th w e igh t ........................................................................ » 2 . Weaning w e i g h t .................................. .... ................................. 4 18 19 21 21 22 22 24 MATERIALS AND METHODS 31 Weather .......................................................... S o i l s ............................................................... Range c o n d i t io n s .................................. Experim ental an im als ........................ Management o f the b reed in g herd . S e l e c t i o n and b reed in g procedures. S t a t i s t i c a l Procedures .................... 31 32 32 32 33 34 36 RESULTS AND DISCUSSION . 46 SUMMARY .78 LITERATURE CITED 82 APPENDIX 89 v i i i LIST OF TABLES Table Page 1 C o e f f i c i e n t s f o r the d i r e c t and m aternal v a r ia n c e s and c o v a r ia n c e s i n th e ex p ec ted v a lu e s o f the c o v a r ia n c e s between r e l a t i v e s ............................................ . . . 11 2 E st im ates o f d i r e c t and m aternal a d d i t iv e v a r ia n c e s and c o v a r ia n c e s on b ir th w e ig h t o f c a t t l e ............................. 23 3. E s t im a tes o f d i r e c t and m aternal a d d i t iv e g e n e t i c , v a r ia n c e s and co v a r ia n ce o f c a l f growth through w e a n i n g ..................................................................................... 25 4 D i s t r i b u t io n o f r e co r d s by l i n e s and by y e a r s .................... 40 5 A n alyses o f v a r ia n ce fo r s i r e - t y p e r e l a t i v e s ..................... 47 6 L e a s t -s q u a r e s means f o r age o f dam, s e x , age o f dam by s e x s u b c l a s s e s and r e g r e s s i o n s i n t h e PHS m od el . 48 7 A n alyses o f v a r ia n c e f o r c o u s in s f a m i l i e s . ............................... 49 8 A n alyses o f v a r ia n ce fo r f u l l - s i b s and dam-maternal granddam m odels ...................................... 50 9 E st im a tes o f h e r i t a b i l i t i e s and c o r r e l a t i o n s f o r b ir th w e ig h t and weaning w e ig h t .................... . . . . . . . . . . 52 10 Covariance between r e l a t i v e s : e s t i m a t e s , d e g r e e s o f freedom f o r e s t im a t io n and ex p e c te d v a lu e s i n terms o f d i r e c t and m aternal c o v a r ia n c e s . . . . . . ....................... 53 11 Asym ptotic v a r ia n c e -c o v a r ia n c e m a tr ic e s f o r the s ir e - m a t e r nalgrand s i r e model ... ......................................................... 60 12 C o e f f i c i e n t s o f c o v a r ia n c e s between r e l a t i v e s and s o lu t i o n s fo r F a lc o n e r ' s (1965) model . 62 13 S o lu t io n s f o r d i r e c t and m aternal co v a r ia n ces used by o th e r workers ....................................... 63 14 S o lu t io n s f o r the d i r e c t and m aternal v a r ia n c e s , c o v a r ia n c e s and h e r i t a b i l i t i e s 66 i x LIST OF TABLES (CONTINUED) Table Page 15 Sim ple c o r r e l a t i o n c o e f f i c i e n t s among the c o e f f i c i e n t s o f d i r e c t and m aternal v a r ia n c e s and c o v a r i a n c e s ............................. .............................................................. 73 LIST OF FIGURES Path c o e f f i c i e n t diagram o f D ic k e r so n ’ s (1947) model . A path c o e f f i c i e n t diagram d e s c r ib in g F a lc o n e r ’ s (1965) m aternal e f f e c t s model . . . . . .................... A path c o e f f i c i e n t diagram d e s c r ib in g Koch’s (1972) model ..................................................... .... ....................... .... A path c o e f f i c i e n t diagram d e s c r ib in g the c o v a r ia n c e between m aternal grand progeny .................... . x i ABSTRACT E v id e n c e h a s b een fo u n d t h a t m a t e r n a l e f f e c t s a r e i m p o r t a n t s o u r c e s o f v a r i a t i o n i n m amm als. In b e e f c a t t l e , e v i d e n c e h a s b een found to supp ort the h y p o t h e s i s t h a t m aternal e f f e c t s can reduce the e x p e c t e d r e s p o n s e t o s e l e c t i o n f o r g r o w t h t r a i t s , e s p e c i a l l y p r e w e a n in g g r o w t h . I t i s n o t c l e a r w h e th e r m a t e r n a l e f f e c t s i n p r e w e a n in g g r o w th o f b e e f c a t t l e a r e g e n e t i c or e n v i r o n m e n t a l . T h erefore , th e p r e se n t r e se a r c h was conducted to study th e nature and m agnitude o f m aternal e f f e c t s i n b ir th and weaning w e ig h t o f Hereford c a t t l e . The d a t a u s e d w e r e t h e r e c o r d s o f 4 ,4 2 3 n o n c r e e p - f e d b e e f c a lv e s r a i s e d a t th e Northern A g r ic u l t u r a l Research Center, Havre, Mt from 1938 to 1983. L e a s t -s q u a r e s , f i t t i n g c o n s ta n ts method (Henderson I I I ) and R e s t r i c t e d Maximum L i k e l i h o o d p r o c e d u r e s w e r e u s e d t o e s t i m a t e e i g h t e e n c o v a r i a n c e s b e t w e e n d i f f e r e n t ty p e s o f r e l a t i v e s . The b a s i c m odels in c lu d e d th e f i x e d e f f e c t s o f l i n e - y e a r , age o f dam, s e x o f c a l f , a g e o f dam by s e x i n t e r a c t i o n and t h e r e g r e s s i o n s o f b ir th w e ig h t on b ir th d a te o f c a l f and weaning w e ig h t on weaning age o f c a l f . The sou rce o f v a r i a t i o n d e p ic t in g th e r e l a t i v e r e l a t i o n s h i p was c o n s id er e d a random e f f e c t . M u lt ip le r e g r e s s io n procedures were used t o o b ta in th e n in e param eters: a d d i t iv e g e n e t i c , dominance g e n e t i c and en v iron m en ta l d i r e c t and m aterna l v a r ia n c e s and the c o v a r ia n c e between th e d i r e c t and m aternal sou rce i n each c a se . A l l s o l u t i o n s sh ow ed a n e g a t i v e a d d i t i v e g e n e t i c c o r r e l a t i o n b e t w e e n a d d i t i v e d i r e c t e f f e c t s and a d d i t i v e m a t e r n a l e f f e c t s ( r G). The r e s u l t s were not c l e a r r e g a rd in g to th e magnitude o f rg f o r b ir th w e ig h t but th e probable v a lu e fo r weaning w e ig h t was around - .6 0 to - . 7 5 . T h e r e w a s a l s o e v i d e n c e f o r a n e g a t i v e e n v i r o n m e n t a l c o r r e l a t i o n f o r m aternal phenotype o f th e dam and daughter i n the case o f weaning w e ig h t . This path c o e f f i c i e n t (fm) was c a l c u l a t e d to be .08 fo r b i r t h w e ig h t and - .1 0 f o r weaning w e ig h t . A fter c o r r e c t in g the e x p e c t a t io n s o f the c o v a r ia n c e s betw een r e l a t i v e s f o r fm, rg was s t i l l p r e s e n t and n e g a t i v e f o r b o th w e i g h t s . The s o l u t i o n s show ed th a t dominance was a l s o in v o lv e d i n d e ter m in in g m aternal e f f e c t s i n p r e w e a n in g g r o w th o f b e e f c a t t l e b u t i t s e f f e c t s may be c o n fo u n d e d w ith e p i s t a s i s . I . INTRODUCTION The s u c c e s s o f a . b r e e d in g sc h e m e t o im p r o v e p e r fo r m a n c e c h a r a c t e r i s t i c s o f f a r m a n i m a l s d e p e n d s on how g e n e t i c and en v iron m en ta l so u r c e s o f v a r i a t i o n are taken i n t o account. Like o th er d o m e st ic mammals, b e e f c a t t l e are s u b j e c t to m aternal environm ent from t h e e a r l y m om ents o f g e s t a t i o n th r o u g h w e a n in g t im e . A m a te r n a l e f f e c t i s an e f f e c t c o n t r i b u t e d t o the" p h e n o t y p i c v a l u e o f an in d i v id u a l by i t s dam (W illham , 1980). Although m aternal e f f e c t s are e n v i r o n m e n t a l s o f a r a s t h e i r i n f l u e n c e on o f f s p r i n g i s c o n c e r n e d , they are determ ined by g e n e t i c and env iron m enta l f a c t o r s (Koch, 1972). B i r t h w e i g h t i s t h e r e s u l t o f g e s t a t i o n a l g r o w th r a t e and g e s t a t i o n l e n g th . Weaning w e ig h t i s th e consequence o f b ir th w e igh t and g r o w th d u r in g t h e s u c k l i n g p e r io d . B oth t r a i t s a r e m ea su red a s t h e p h e n o t y p i c v a l u e o f t h e c a l f , b u t t h e y a r e com p osed o f a t l e a s t two com ponents, o f f s p r i n g g e n e t i c s f o r growth and a m aternal e f f e c t c o n t r i b u t e d by t h e dam. T h is l a t t e r i n f l u e n c e i s p rod u ced by n u t r i e n t s provided by th e u te r u s ( in th e c a se o f b ir th w e ig h t) and the mammary g la n d ( i n t h e c a s e o f w e a n in g w e i g h t ) . As R o b iso n (1 9 8 1 ) comments, i t has r e c e n t ly become apparent t h a t o th e r f a c t o r s may be i n v o l v e d i n t h i s a c t i o n , p e r h a p s th r o u g h c i r c u l a t i n g h o r m o n e s , c y to p la s m ,e t c . The o th e r c o n t r ib u t io n o f the dam to th e phenotyp ic v a lu e o f the o f f s p r i n g i s a sam ple h a l f o f her gen es to the c a l f . T herefore , w h i le t h e s i r e c o n t r i b u t e s t o t h e p h e n o t y p i c v a l u e o f t h e o f f s p r i n g by p a s s i n g a s a m p le h a l f o f h i s g e n e s t o t h e o f f s p r i n g , t h e dam 2 c o n t r ib u t e s i n a t l e a s t two ways. Willham (1980) p o in t s ou t t h a t the confounding o f th e two c o n t r ib u t io n s from the dam and the p o s s i b i l i t y o f a n e g a t i v e g e n e t i c c o r r e l a t i o n b e t w e e n t h e d i r e c t and m a te r n a l e f f e c t c o n s t i t u t e the b a se s f o r the paramount problem s i n e s t im a t in g m aternal e f f e c t s . I t i s c l e a r th a t h e r i t a b i l l t i e s (h2 ) can be b ia sed because o f the p resen ce o f m aternal e f f e c t s (Robison, 1981). The m o d e l i n g p r o c e s s t o e s t i m a t e m a te r n a l e f f e c t s h a s been i n i t i a t e d by D i c k e r s o n ( 1 9 4 7 ) . K em pthorne (1 9 5 5 ) w as an im p o r t a n t p ap er i n s o l v i n g t h e p rob lem o f t h e e s t i m a t i o n o f g e n e t i c and en v iron m en ta l v a r ia n c e s based on c o v a r ia n c e s betw een r e l a t i v e s . The p r e s e n t a t i o n i n c l u d e d t h e b a s i s o f t h e a c t u a l t h e o r y f o r m e a s u r in g m aternal and d i r e c t v a r ia t i o n . Koch and Clark (1955b) was th e f i r s t paper to e s t i m a t e th e a d d i t iv e g e n e t i c co v a r ia n c e betw een d i r e c t and m aternal e f f e c t s ( a AoAm) i n b e e f c a t t l e , by u s in g path c o e f f i c i e n t s theory . F i n a l ly , Willham (1963) d eve lop ed a l i n e a r model theory fo r e s t i m a t i n g d i r e c t and m aternal g e n e t i c c o v a r ia n c e s and v a r ia n c e s by an e x te n s io n o f the procedures f i r s t deve lop ed by Kempthorne (1955). The u s e o f W i l lh a m 's m ethod a p p l i e d to c a t t l e r e c o r d s h a s been r e p o r t e d by E v e r e t t and Magee ( 1 9 6 5 ) , H i l l ( 1 9 6 5 ) , Brown and G a lv ez ( 1 9 6 9 ) , V e s e l y and R o b is o n ( 1 9 7 1 ) , Koch ( 1 9 7 2 ) , P h i l i p s s o n ( 1 9 7 6 ) , F i s h e r and W i l l i a m s (1 9 7 8 ) and B u r f e n i n g e t a l (1 9 8 1 ) f o r b i r t h w e i g h t . H i l l e t a l ( 1 9 6 5 ) , D e e s e and R oger ( 1 9 6 7 ) , H ohenboken and B r in k s ( 1 9 6 7 ) , V e s e l y and R o b iso n ( 1 9 7 1 ) , Koch ( 1 9 7 2 ) , B e l t r a n Bru (1978) and K ress e t a l (1979) d e a l t w i th weaning w e ig h t . The g en era l c o n c lu s io n s from th e r e v ie w e d l i t e r a t u r e were t h a t h e r i t a b i l i t y fo r a d d i t iv e g e n e t i c d i r e c t e f f e c t s (h2o) was l a r g e r f o r b i r t h w e ig h t than 3 t h e c o n t r i b u t i o n s o f a d d i t i v e g e n e t i c m a t e r n a l e f f e c t s (hm^). The co n v erse was tru e f o r weaning w e ig h t . A n e g a t iv e g e n e t i c antagonism betw een a d d i t iv e g e n e t i c d i r e c t and a d d i t iv e g e n e t i c m aterna l e f f e c t s ( i . e . , n e g a t iv e v a lu e o f oAoAm) has been found f o r both t r a i t s . The m a g n itu d e o f oAoAm i s l i k e l y t o be r e l a t i v e l y g r e a t e r f o r w e a n in g w e ig h t than f o r b i r t h w e ig h t . However, the e x a c t v a lu e o f AoAm has b e e n t h e m a t t e r o f som e d i s c u s s i o n (Koch, 1972; B a k er , 1 9 8 0 ) . Van V ieck e t a l (1977) have shown t h a t th 6 v a lu e o f a AoAm d e ter m in es the lo n g term r esp on se to s e l e c t i o n f o r weaning w e igh t . T o tu s e k ( 1 9 6 8 ) , Mangus and B r in k s ( 1 9 7 1 ) , K r e s s and B u r f e n in g (1972), M artin e t a l (1981) and Ochoa e t a l (1981) have found th a t the e n v ir o n m e n t i n w h ic h t h e h e i f e r c a l f i s r a i s e d a f f e c t s h e r f u t u r e m aterna l phenotype t h a t she p ro v id es f o r her c a lv e s . This c o m p lic a te s t h e m a t t e r o f t h e r e l a t i v e m a g n itu d e o f e n v i r o n m e n t a l and g e n e t i c s o u r c e s o f v a r i a t i o n on t h e e x p r e s s i o n o f m a te r n a l e f f e c t s , a s Koch (1972) and Hohenboken (1973) d i s c u s s . The o b j e c t i v e s o f th e p r e se n t s tu dy were: 1) to e s t i m a t e the amount o f v a r i a t i o n due to a d d i t iv e g e n e t i c d i r e c t and a d d i t i v e g e n e t i c m a t e r n a l e f f e c t s i n b i r t h w e i g h t and w e a n in g w e ig h t o f H ereford b e e f c a lv e s , 2 ) t o c l a r i f y th e problem o f the r e l a t i v e im portance o f genotype and environm ent f o r the e x p r e s s io n o f m aterna l e f f e c t s on both t r a i t s , and 3 ) t o e s t i m a t e t h e a d d i t i v e g e n e t i c c o v a r i a n c e b e t w e e n d i r e c t and m aternal e f f e c t s f o r both b ir th w e ig h t and weaning w e ig h t o f Hereford b e e f c a lv e s . 4 REVIEW OF LITERATURE .EaMroatlon o f d i r e c t and m aternal s o u r c e s o f v a r i a t i o n As i n m o s t o t h e r a n im a l b r e e d in g p r o b le m s , m a t e r n a l e f f e c t s theory i s s t r o n g ly r e l a t e d t o q u a d r a t ic e s t im a t io n . The m odels used to e s t i m a t e v a r ia n c e components due to m aternal e f f e c t s s t a r t e d from the v a r ia n c e o f the c l a s s i c model: O2P = O2G + O 2 E (I) w h er e a 2 P i s t h e t o t a l p h e n o t y p i c v a r i a n c e , a 2 G i s t h e v a r i a n c e due t o g e n e t i c e f f e c t s , and Ct2 E i s t h e e n v i r o n m e n t a l v a r i a n c e . D u rin g t h e e n t i r e m o d e l i n g p r o c e s s , no a t t e m p t h a s b een made t o i n c o r p o r a t e t h e g e n o t y p e by e n v i r o n m e n t a l i n t e r a c t i o n s o u r c e o f v a r i a t i o n ( a 2GE) i n t o m aternal e f f e c t s q u a d ra t ic e s t im a t io n . A f u r th e r p a r t i t i o n o f a 2G can be made as f o l l o w s : O2G = O2 A + d 2D + c £ l (2) where a 2 A i s th e v a r ia n c e due to a d d i t i v e g e n e t i c e f f e c t s , a 2D i s the v a r ia n c e due to dominance e f f e c t s ( i . e . , i n t r a l o c u s i n t e r a c t i o n ) an d a2 I i s t h e v a r i a n c e d u e t o e p i s t a s i s ( i . e . , i n t e r l o c u s i n t e r a c t i o n ) . D i c k e r s o n (1 9 4 7 ) made t h e f i r s t p a r t i t i o n o f t h e v a r i a n c e s i n m o d e l ( I ) t o i n c o r p o r a t e m a t e r n a l e f f e c t s . He d id n o t c o n s i d e r dominance or e p i s t a s i s i n h i s model a s shown below: a 2 P = O2 Ao + O2 Am + o Ao Am + O2 Em + O2Eo ( 3 ) The terms o f model ( 3 ) are O2 Ao = v a r ia n c e due to a d d i t iv e d i r e c t e f f e c t s , O2 Am s v a r ia n c e due to a d d i t iv e m aternal e f f e c t s , 5 crAoAm = c o v a r ia n c e betw een a d d i t iv e m aternal and a d d i t iv e d i r e c t e f f e c t s , p a Em = v a r ia n c e due to m aternal env iron m enta l e f f e c t s common to f u l l - s i b s and m aternal h a l f - s i b s , and a^Eo = v a r ia n c e due to random environm ent. The m od el w as u s e d t o e s t i m a t e m a t e r n a l and d i r e c t c o v a r i a n c e s i n c a r c a s s d a t a o f s w i n e . D i c k e r s o n ( 19 4 7 ) d e v e l o p e d t h e p a t h c o e f f i c i e n t diagram shown i n F igure I. The p h e n o ty p e o f X (Px) i s t h e r e s u l t o f i t s own g e n o t y p e f o r d i r e c t e f f e c t s (Gox) p lu s a commmon or m aternal environm ent component among l i t t e r m ates (Pmw)s where w i n d i c a t e s the dam o f X. D ickerson (1947) d id n o t in c lu d e th e random en v iron m en ta l sou rce o f v a r ia t i o n i n t h e d ia g r a m b u t i n t h e a n a l y s i s . The t r a n s m i s s i b l e g e n o t y p e or a d d i t iv e g e n e t i c e f f e c t s are s p l i t i n t o two components: 0 ( d ir e c t ) and m (m a tern a l) . The Gmx component w i l l be e x p ressed o n ly i f in d iv id u a l X s u b s e q u e n t l y b e c o m e s a dam (W il lh a m , 19 6 3 ) . The co m p o n en t Pmw i s a f f e c t e d by t h e m a t e r n a l g e n o t y p e o f W ( i . e . , Gmw). T here was no i n t e n t i o n t o r e l a t e t h e m a t e r n a l p h e n o ty p e o f w w i t h t h e m a te r n a l p h e n o ty p e o f h er dam, h e r m a t e r n a l gran d dam and so on. 6 F ig u re I . Path c o e f f i c i e n t diagram o f D i c k e r s o n ' s ( 1947) model. 7 In term s o f the path c o e f f i c i e n t s o f F igure I , th e h e r i t a b i l i t y or r e g r e s s i o n o f t r a n s m i t t e d a b i l i t y (Gox + Gmx) on i n d i v i d u a l perform ance (X) i s b(Go + Gmx) Px = go2 + 3 / 2 gogm Pgogm + 1 /2 gm2 (4) This e x p r e s s io n i s the numerator f o r what i s c a l l e d h e r i t a b i l i t y f o r t o t a l e f f e c t s w h er e " t o t a l " s t a n d s f o r a d d i t i v e g e n e t i c d i r e c t p lu s a d d i t iv e g e n e t i c m aternal e f f e c t s . The m ain c o n t r i b u t i o n s o f K em pthorne ( 1955) t o t h e t h e o r y o f m aternal e f f e c t s was th e i n c l u s i o n o f dominance i n the model and the d e s c r i p t i o n o f t h e b a s i s f o r t h e c o e f f i c i e n t s o f t h e d i r e c t and m aterna l c o v a r ia n c e s i n t o the e x p e c t a t i o n o f th e c o v a r i a n c e b e tw e e n r e l a t i v e s . H is t h e o r y a s s u m e s t h a t t h e g e n o t y p i c v a l u e o f an in d iv id u a l i s a d d i t i v e l y determ ined by th e j o i n t e f f e c t s o f the genes p o s s e s s e d by the in d i v id u a l and i t s mother. The g e n e t i c v a r ia n ce o f h i s m od e l i s O2 G = Cf2 Ao + O2 Am + a AoAm + cr^Do + o + CDoDm (5) w h er e O2Do and O2Dm a r e t h e v a r i a n c e s due t o d o m in a n c e d i r e c t and d o m in a n c e m a t e r n a l d e v i a t i o n s , r e s p e c t i v e l y , and ODoDm i s t h e co v a r ia n c e betw een the dominance e f f e c t s . Kempthorne ( 1955) d id not c o n s id e r th e common or m aternal source o f en v iron m en ta l v a r i a t i o n ( i . e . , C2Em). The o th er e x p r e s s io n s der ived a r e t h e c o v a r i a n c e s b e t w e e n o f f s p r i n g and s i r e (c o v (0 ,S ) ) , o f f s p r in g and dam (cov(0,D )) and among f u l l - s i bs (cov(FS)) as cov ( 0 ,S ) = pq C 2Ao + 1 /2 pq C AoAm, cov (0 ,D ) = pq C 2 Ao + pq C 2 Am + 5 /4 C 2 AoAm + c DoDm, and 8 cov (FS) = 1 /2 a2 Ao + O2 Am + 2 pq aAoAm + i/H a2Do + O2Dm. p and q are th e gene f r e q u e n c ie s f o r g en es A and a , r e s p e c t i v e l y . The most commonly used model f o r e s t i m a t i n g m aternal e f f e c t s o f b i r t h w e i g h t and w e a n in g w e i g h t i n c a t t l e was d e r i v e d by W illham ( 1 9 6 3 ) . B a s i c a l l y , he g e n e r a l i z e d t h e work o f K em pthorne (1 9 5 5 ) a d d in g e p i s t a s i s t o t h e m o d e l . H ow ever, t h i s i n t e r l o c u s g en e e x p r e s s io n h as a lw ays been assumed to be z e r o or n e g l i g i b l e f o r both b i r t h w e i g h t and w e a n in g w e i g h t . P e r h a p s t h e m o st u s e f u l r e s u l t o f W il lh a m 's p a p e r w as t h e d e r i v a t i o n o f t h e c o e f f i c i e n t s f o r t h e a d d i t iv e and dominance c o v a r ia n c e s i n th e ex p ected v a lu e s o f v a r io u s kin d s o f r e l a t i v e s . The c o e f f i c i e n t s t h a t K e m p t h o r n e (1 9 5 5 ) had e x p r e s s e d a s f u n c t io n s o f W right’s c o e f f i c i e n t o f r e l a t i o n s h i p w ith no in b r e ed in g or M a l e c o t ’s " c o e f f i c i e n t de p a r e n te " r e c e i v e d c o n c r e t e n u m e r ic a l v a lu e s w ith th e work o f Willham. Willham (1963) showed t h a t the g e n o ty p ic c o v a r ia n ce between the phenotypes o f i n d i v i d u a l s X and I , w ith r e s p e c t i v e m others W and Z, i s equal to c o v ( G x , Gy) % c o v ( G o x ,G o y ) + c o v (G o x ,G m z ) + c o v (G m w ,G o y ) + cov(Gmw,Gmz) (6) w h er e Gox and Goy a r e t h e g e n o t y p i c v a l u e s o f X and Y f o r d i r e c t e f f e c t s , and Gmw and Gmz a r e the g e n o ty p ic v a lu e s o f the dams W and Z f o r m a t e r n a l e f f e c t s . Thus, t h e p r o b lem was r e d u c e d t o c a l c u l a t i n g the fou r c o v a r ia n c e s i n (6). 9 The f i r s t c o v a r ia n c e betw een X and Y f o r component o was g iv e n by Kempthorne (1957) a s 2pxy O2Ao + uxy O2Do + (2px y ) r (ux y ) s O2 (Ar Ds ) 0 f o r 21r+siN where O2 (Ar Ds )0 i s th e e p i s t a t i c component o f g e n o ty p ic v a r ia n c e fo r the d i r e c t co m p o n e n t o. For t h i s t e r m , r and s r e f e r t o t h e number o f l o c i i n v o l v e d i n t h e i n t e r a c t i o n and N r e f e r s t o t h e number o f l o c i s e g r e g a t in g f o r component o. The term pxy i s W right’s c o e f f i c i e n t o f r e l a t i o n s h i p w i t h no i n b r e e d i n g or t w i c e M alecot’s " c o e f f i e c i e n t de parente". The c o e f f i c i e n t uxy i s the p r o b a b i l i t y t h a t th e two genes a t a l o c u s i n in d i v id u a l x a r e i d e n t i c a l by d e s c e n t w i th th e two genes a t t h a t l o c u s i n i n d i v i d u a l y. The v a l u e o f uYV i s z e r o u n l e s s t h e two i n d i v i d u a l s are r e l a t e d by two l i n e s o f d e s c e n t such a s f u l l s i b s or doub le f i r s t c o u s in s . The s e c o n d and t h i r d t e r m s i n ( 6 ) a r e t h e g e n o t y p i c c o v a r i a n c e s betw een th e i n d i v i d u a l s and t h e i r m others f o r components o e x p ressed i n x or y. and co m p o n en t m e x p r e s s e d i n y or x , r e s p e c t i v e l y . S i n c e Mode and Robinson ( 1959) showed t h a t th e g e n o ty p ic c o v a r ia n c e betw een c h a r a c t e r s , or i n t h i s c a s e c o m p o n e n ts o f a c h a r a c t e r can be p a r t i t i o n e d i n an a n a l o g u e s manner t o t h e g e n o t y p i c v a r i a n c e , t h o s e term s are 2 pxz a AoAm + uxz CfDoDm + r ^ s (2 Px z ) r ûXz)8 Cf(Ar D3 )0 (Ar Ds )m 2£r+s£M and 10 2 pyw CTAoAm + uyw CT DoDm + (2pyw) r (uyw) s CT(Ar Ds )0 (Ar Ds )m 2^r+s£M Cf (Ar Ds )0 (Ar Ds )m i s the e p i s t a t i c co v a r ia n c e between o and m„ M i s th e number o f l o c i s e g r e g a t in g t h a t a f f e c t both 6 and m. A g e n e r a l e x p r e s s io n f o r the cov(Gx,Gy) assum ing th a t e p i s t a s i s i s equal to z e r o i s : cov(Gx,Gy) = 2 Pxy Cf2 Ao + (2 Pxz + 2 pyw) cfAoAm + 2 pwz a 2Am + Ux y Cf2Do + ( U x z + uyw) CfDoDm + uwz CT2Dm (7) Table I shows th e c o e f f i c i e n t s 2p and u f o r s e v e r a l r e l a t i v e s and i s b a se d on t h e r e l a t i o n s h i p s c o n s i d e r e d by W illh a m ( 1963) and Van V leck and Hart (1966) fo r th e g e n e t i c components o f (7) w ith the more g e n e r a l e x p r e s s io n s f o r the en v iron m en ta l components o f v a r ia t i o n a s show n i n Thompson ( 1 9 7 6 ) . Then, when x and y h a v e t h e sam e m a te r n a l grand s i r e we have 2 Pxy = ( 1 /2 ) = 1/16, 2 Pxz - 1/8; .2 Pyw = 1/8; 2 Pzw - (1 /2 )^ - 1/4 S in c e x and y are not r e la t e d by two l i n e s o f d e s c e n t a l l u’s are z e ro . T h erefore , th e ex p e c te d v a lu e o f a 2 ^ c s i s E( Cf2JdQg) = 2 pxy CT2 Ao + (2 pxz + 2 Pyw) Cf AoAm + 2 pwz Cf2Am E( Cf 2MqS) = 1/16 Cf2Ao + 1/4 CfAoAM + 1/4 Cf2Am Any k in d o f r e l a t i v e r e l a t i o n s h i p can be e v a l u a t e d i n th e same way. C o v a r ia n c e s i n T a b le I w e r e d i v i d e d i n t o t h r e e g r o u p s . In th e f i r s t grou p s i r e - t y p e r e l a t i o n s h i p s a r e c o n s i d e r e d ; h e n c e , t h e TABLE I . COEFFICIENTS FOR THE DIRECT AND MATERNAL VARIANCES AND COVARIANCES IN THE EXPECTED VALUES OF THE COVARIANCES BETWEEN RELATIVES Relatives cf2flO 0 V m Q ro a 2C 0 0 V m aX Q £ ° x Paternal Half-Sibs (PHS) IA O Sire-tvne O erouD 0 0 0 0 0 0 Paternal Grand S ire-S ibs (PGS) 1/16 O O 0 0 0 0 0 0 Maternal Grand S ire-S ibs (MGS) 1/16 1/4 1/4 ' 0 0 0 o . 0 0 Maternal Great Grand S ire-S ibs (MGGS) 1/64 1/16 1/16 0 0 0 0 0 0 Maternal Grand Dam-Sibs (MGD) 1/16 1/4 1/4 0 0 0 0 0 0 IIBIaIBIIS■ • o . « - C= C -— Offspring and S ire (COV(O1S)) 1/2 Covariance erouo 1/4 O O 0 0 0 0 0 Offspring and Dam (COV(OjD)) 1/2 5/4 1/2 0 I 0 0 . I 0 Offspring and Maternal Grand Dam (COV(OjMjD)) 1/4 5/8 1/4 0 0 0 0 0 0 Maternal Grand S ire Progeny and Grand Offspring COV(SjMGS) 1/8 1/4 O 0 0 0 0 0 0 Maternal F u ll-S ib Aunt and Offspring (COV(MAjN)) 1/4 3/4 1/2 0 1/4 0 0 0 0 Paternal F u ll-S ib Aunt and Offspring (COV(PAjN)) 1/4 3/4 1/2 0 1/4 0 0 0 0 R elative re la t ion sh ip s involving dominance F u ll-S ibs (FS) 1/2 I I 1/4 0 I 0 0 I Maternal Half-Sibs (MHS) 1/4 I I 0 0 I 0 0 I S ingle F ir s t Cousins (SFC) 1/8 1/2 1/2 0 0 1/4 0 0 0 PHS plus Dams MHS (PHS + MHSD) 5/16 1/4 1/4 1/16 0 0 0 0 0 PHS + SFC 3/8 1/2 1/2 1/8 0 1/4 0 0 0 FS plus PHS parents (FS + PHS) 5/8 5/4 I 25/64 0 I 0 0 I PHS + PHS Dams (PHS + PHSD) 5/16 1/4 1/4 1/64 0 0 0 0 I 12 e x p e c t a t i o n s o n l y i n v o l v e s a d d i t i v e e f f e c t s . The s e c o n d grou p c o n t a in s c o v a r ia n c e s betw een th e o f f s p r i n g g e n e r a t i o n and a c l o s e l y r e l a t e d i n d i v i d u a l o f t h e p a r e n t a l g e n e r a t i o n . The l a s t grou p i s composed by th e term s i n v o lv i n g dominance. The error term s f o r m odels i n which t h e r e i s on ly one f a m i ly component have not been e x t e n s i v e l y u s e d . An u n c l e a r i n t e r p r e t a t i o n o f t h e c o m p o n e n ts i n v o l v e d i n t h e e x p e c t a t io n f o r th o se er ro r term s i s th e p o s s i b l e reason . So f a r i t h a s b e e n a s su m e d t h e r e i s no e f f e c t o f t h e dam e n v ir o n m e n t on t h e f u t u r e m a t e r n a l a b i l i t y o f th e fe m a le o f f s p r in g . T h is i s l i k e l y to o c c u r f o r w e a n in g w e i g h t i n b e e f c a t t l e , a s Koch ( 1972) p o i n t e d o u t . I f t h i s i s t r u e , m a t e r n a l e n v ir o n m e n t w i l l be a f f e c t e d by gran d m a t e r n a l e n v ir o n m e n t and th e l a t t e r by m a t e r n a l g r e a t g ra n d dam e n v ir o n m e n t and s o on. In t h i s s e n s e , t h e m a te r n a l e f f e c t i s v iew ed a s p a r t i a l l y a f f e c t e d by. m aternal env ironm ent from p r e v io u s g e n e r a t io n s . The f i r s t a t te m p t to in c o r p o r a te th e s e e f f e c t s i n t o the model was made by F a lco n er (1965). The v a r ia n ce o f h i s model i s : CT2 P = Ct 2A + CT2M + 2 CTAM + CT2D + CT2Em + Ct2Eo ( 8 ) where CT2 A i s the v a r ia n c e o f a d d i t iv e e f f e c t s , Ct2 M i s the v a r ia n c e due to the m aternal e f f e c t s to which th e in d iv id u a l i s s u b j e c t , CT AM i s the c o v a r ia n c e betw een a d d i t iv e arid m aternal e f f e c t s ; Ct2D i s the v a r ia n c e due to dominance d e v i a t i o n s (F a lconer in c lu d e d h e r e a l s o the e p i s t a t i c d e v i a t i o n s i n v o lv i n g dom inance), CT2 Em i s th e v a r ia n c e due t o m a t e r n a l or common e n v i r o n m e n t , a s b e f o r e , and Ct2 Eo i s t h e v a r i a n c e due t o random e n v ir o n m e n t . The m a te r n a l e f f e c t s (M) a r e d e f in e d a s a l i n e a r f u n c t io n , fm, o f th e m other’s p h en otyp ic m aternal 13 v a lu e , P», measured as a d e v ia t io n from the p o p u la t io n mean, so th a t M = fm P' ( 9) F a l c o n e r (1 9 6 5 ) a d m i t t e d t h a t t h e way M i s d e f i n e d i s r a t h e r r e s t r i c t e d b e c a u s e i t e x c l u d e s a l l m a tern a l i n f l u e n c e s t h a t are not c o r r e la t e d w ith the m other’s p henotyp ic m aternal v a lu e . But he a l s o p o i n t s o u t t h a t i f t h e s e o t h e r i n f l u e n c e s a r e p r e s e n t t h e y w i l l be in c lu d e d w ith th e r e s t o f the common or m aternal environm ent ( a 2Em). The c o e f f i c i e n t fm i s d e f in e d to be "a p a r t ia l r e g r e s s io n c o e f f i c i e n t r e l a t i n g d a u g h t e r s t o m o t h e r s ’ p h e n o t y p i c v a l u e s i n t h e a b s e n c e o f g e n e t i c v a r i a t i o n among t h e m o th e r s" . W hether t h e r e l a t i o n s h i p i s r e a l l y l i n e a r i s , o f c o u r s e , op en t o q u e s t i o n . O b v io u s l y , a l i n e a r r e l a t i o n s h i p i s e a s i e r to e v a lu a te . I t should a l s o be noted th a t the D, Em and Eo term s i n the model are u n c o r r e la te d w ith P’. H en ce ,a l l o t h e r c o v a r i a n c e s i n ( 8 ) a r e z e r o b u t a AM. An i n t e r p r e t a t i o n o f model ( 8) i n term s o f path c o e f f i c i e n t s i s shown i n F igu re 2. The p r im e i n t h e grap h i n d i c a t e s t h e p r e v io u s g e n e r a t i o n . The arrow p o i n t i n g a t M’ from t h e l e f t i n d i c a t e s th e c a r r y i n g o v e r o f m aternal e f f e c t s from p r e v io u s g e n e r a t io n s . F a lconer ( I965) der ived the cov(0,D) i n term s o f fm as c o v (0 ,D ) = a 2A ( 1 / ( 2 - fm)) + fm a 2 Pm’ I t i s worth n o t in g the d e r iv a t io n o f a AM. By d e f i n i t i o n M = fm Pm’ = fm (A’ + M» + D» + Em’ + E o') . S in c e D’, Em’ and Eo' a r e n o t c o r r e l a t e d w i t h A, th e y can be o m i t t e d w h i l e d e r iv in g a AM. T h erefore , th e r e le v a n t p a r t o f M can be w r i t t e n as M = fm (A' + fm P” ) = fm (A’ + fm (A” + fm P’ ” ) ) 14 F i g u r e 2 . A p a th c o e f f i c i e n t d ia g r a m d e s c r i b i n g F a l c o n e r ' s (1 9 6 5 ) m aternal e f f e c t s model. P i s the phenotype o f the in d i v id u a l ; A, h i s a d d i t i v e g e n o t y p e ; D, h i s d o m i n a n c e d e v i a t i o n ; Em a r e t h e en v iron m en ta l f a c t o r s common to f u l l - s i b s and m aternal h a l f - s i b s th a t are not in c lu d e d i n th e m aternal e f f e c t ; M i s the m aternal e f f e c t ; Eo are o th er en v iron m en ta l f a c t o r s p a r t ic u l a r to the in d iv id u a l and r AM i s t h e c o r r e l a t i o n b e t w e e n a d d i t i v e g e n e t i c and m a t e r n a l e f f e c t s . Path c o e f f i c i e n t s ( e 0 , a , d, m, e m, .5 and fm ) a r e s t a n d a r d p a r t i a l r e g r e s s i o n c o e f f i c i e n t s . 15 T herefore = fm (A». + fm (.Ag 1 + fm (Aggg + . . . . e t c ) CAM = fm OAAg + fm2 OAAgg + fm3 OAAggg + . . . . OAM = O2A ( 1 /2 fm + 1/1} fm2 + 1 /8 fm3 + . . . . The e x p r e s s io n i n b r a c k e ts i s th e g e o m e tr ic s e r i e s w ith common r a t i o 1/2 fm. I f l f m l < I the s e r i e s c on verges w ith sum ( 1/ 2 ) fm fm —— — —— —— = I - fm/ 2 2 - fm Hence fm oAM = O2 A -------------- ' 2 - fm Thompson (1 9 7 6 ) h a s d e r i v e d t h e c o e f f i c i e n t s f o r fm i n t h e e x p e c te d v a lu e s o f some r e l a t i v e r e l a t i o n s h i p s . W illh a m (1 9 7 2 ) c o n s i d e r e d a m od el i n w h ic h t h e e f f e c t o f t h e m aternal grand dam i s p r e se n t . The g e n o ty p ic c o v a r ia n ce between any tw o r e l a t i v e s i s e v a l u a t e d a s i n ( 6 ) , b u t w i t h n in e c o v a r i a n c e s i n s t e a d o f f o u r . An a d d i t i v e g e n e t i c term f o r t h e v a r i a t i o n due to gran d m a t e r n a l e f f e c t s ( i . e . O2 An) i s a l s o d e f i n e d . For g e n e t i c e f f e c t s o n ly th e v a r ia n c e o f t h i s model i s O2 A = O2 Ao + o AoAm + OAoAn + O2 Am + OAmAn + O 2 An (9 ) where OAoAn and OAmAn are th e c o v a r ia n c e s between d i r e c t and grand m a t e r n a l a d d i t i v e e f f e c t s and m a t e r n a l and gran d m a t e r n a l a d d i t i v e e f f e c t s , r e s p e c t i v e l y . From a t h e o r e t i c a l p o i n t o f v i e w , i t i s n o t c l e a r w h e th e r to p r e f e r t h e m a t e r n a l - g r a n d m a t e r n a l a d d i t i v e m odel t o t h e m a te r n a l 16 a d d i t iv e model. Using th e same r e a so n in g , i t i s p o s s i b l e to in c lu d e g r e a t grand m aternal e f f e c t s i n t o the model and so on. A d d i t i v e g e n e t i c e f f e c t s a r e c a r r i e d by t h e dam s i d e th ro u g h s e v e r a l g e n e r a t i o n s . H ow ever , t h e sam e t h e o r y o f t h e c o v a r i a n c e betw een r e l a t i v e s (Kempthorne, 1955) shows a h igh l e v e l o f r e l i a b i l i t y i n t h e e v a l u a t i o n o f t h e a d d i t i v e g e n o t y p e or b r e e d in g v a l u e by c o n s id e r in g o n ly one g e n e r a t io n p r e v io u s to the one c on s id ered . As a r e s u l t o f t h e s e i d e a s , Koch ( 1972) d e f i n e d t h e m o s t b i o l o g i c a l l y m e a n in g f u l m odel t o e v a l u a t e m a t e r n a l e f f e c t s i n b e e f c a t t l e b i r t h w e i g h t and w e a n in g w e i g h t . The m od el co m b in ed W i l lh a m 's ( 1963) a d d i t i v e and d o m in a n t c o m p o n e n ts w i t h F a l c o n e r ' s (1 9 6 5 ) c o n c e p t o f t r a n s m it t e d m aternal phenotype e f f e c t s . The c o v a r ia n ce betw een random en v iron m en ta l and m aternal or common en v iron m en ta l e f f e c t s ( a EoEm) was a l s o added. The v a r ia n c e o f Koch's (1972) model can be exp ressed as a 2 p = o^ko + a AoAm + o^Am + a 2-Do + a DoDm + a ̂ Dm + + a 2eo + a EoEm + a ^Em (10) The o r i g i n a l e x p r e s s i o n i n t h e p ap er d o e s n o t d i f f e r e n t i a t e betw een o^jjo ando^Eo. I t a l s o does not s p l i t a 2Dm and a 2Em. These f o u r v a r i a n c e s a p p e a r i n tw o t e r m s : a 2Do + a 2 Eo and a 2Dm +O2 Em. The c l a s s i c a l g e n e t i c theory assum es no c o v a r ia n ce betw een dominance and e n v i r o n m e n t a l d e v i a t i o n s o f any k in d ( F a l c o n e r , 1 9 8 1 ) . Koch ( 1972 ) j u s t i f i e d h i s p r o c e d u r e by s a y i n g t h a t t h e r e l a t i o n s h i p s u s u a l l y a v a i l a b l e i n b e e f c a t t l e d a t a do n o t p r o v id e c r i t i c a l c o n t r a s t s f o r s e p a r a t in g dominance and env iron m enta l d e v ia t io n s . 17 F igu re 3. A path c o e f f i c i e n t diagram d e s c r ib in g Koch’s (1972) model. Po i s the p h en otyp ic , Go i s the a d d i t iv e g e n e t i c , Do i s the dominance and Eo i s th e en v iron m en ta l v a lu e fo r b ir th w e ig h t or weaning w e igh t e x p r e s s e d by i n d i v i d u a l s . Pm, Cm, Dm and Em a r e c o r r e s p o n d in g m a t e r n a l e f f e c t s . P r im e s on v a l u e s r e p r e s e n t p a r e n t a l v a l u e s and double prim es r e p r e s e n t grandparent v a lu e s . Path c o e f f i c i e n t s between s y m b o l s ( . 5 , g , d , e , p , fm ) a r e s t a n d a r d p a r t i a l r e g r e s s i o n c o e f f i c i e n t s . Double arrow s r e p r e s e n t r e s id u a l c o r r e l a t i o n s between t r a i t s 18 F i g u r e 3 i s t h e p a th d ia g r a m w h ic h s u m m a r iz e s t h e c o n c e p t s o f Koch ( 19 7 2 ) . In t h i s d ia g r a m P0 ^ , P1o2 and P1o1 r e p r e s e n t t h e p h e n o ty p e f o r b i r t h w e i g h t or w e a n in g w e i g h t o f t h e o f f s p r i n g , s i r e and dam, r e s p e c t i v e l y . I f a l l the p o s s i b l e paths e x i s t , then cov(0,D) = 1 /2 cf^Ao + 5 /4 crAoAm + 1 /2 cf^Am + a DoDm + f^m + + (1+fm) CTEoEm + fm /(2 -fm ) ( 1 /2 CT2 Am + 5 /4 Cf AoAm) (1 1 ) Note t h a t i f fm = 0 , t h i s e x p r e s s io n r e d u c e s to cov(0,D) = 1/2 Cf ^Ao + 5 /4 Cf AoAm + 1/2 CT̂ Am + a DoDm + Cf EoEm (12) a s show n i n Thompson ( 1 9 7 6 ) . The f o r m u l a s (11 ) or (1 2 ) show t h a t i f g e n e t i c or en v iron m en ta l c o v a r ia n c e term s are n e g a t iv e , the cov(OjD) can be lo w e r than a n t i c i p a t e d from d i r e c t g e n e t i c or m aternal g e n e t i c e f f e c t s (Koch,1972). This e x p la in s p a r t o f the d isa g reem en t between t h e e s t i m a t e s o f h2 by p a t e r n a l h a l f - s i b a n a l y s i s a s com pared t o r e g r e s s i o n o f o f f s p r i n g on dam (h 2 bgD = 2 c o v ( 0 , D ) / Cf 2 P, F a l c o n e r , 1 981 ) . The m odels f o r e s t i m a t i n g d i r e c t and m aternal v a r i a t i o n o f b ir th w e ig h t and weaning w e ig h t i n b e e f c a t t l e have been c o n s id er e d i n order o f c o m p le x i ty . Some d i f f i c u l t i e s a r i s e i n th e a p p l i c a t i o n o f the more c o m p le x m o d e ls to b e e f c a t t l e . That i s th e s u b j e c t o f th e n e x t s e c t i o n . P ro b lem s .in e s t im a t in g d i r e c t and m aternal g e n e t ic c o v a r ia n c e s There are some problem s i n e s t i m a t i n g m aternal v a r i a t i o n i n any a n im a l s p e c i e s . A l s o , t h e r e a r e s p e c i f i c p r o b le m s i n e s t i m a t i n g m aternal and d i r e c t c o v a r ia n c e s i n b e e f c a t t l e . The order i n which the problem s are p r e sen te d i m p l i e s no order o f im portance. 19 1. Standard e r r o r o f th e e s t i m a t e s and non independence o f th e c o e f f i c i e n t s i n th e ex p ec ted v a lu e s T h is i s a g e n e r a l p r o b le m . The l a r g e s ta n d a r d e r r o r o f th e e s t i m a t e s o f m aternal c o v a r ia n c e s i s due to the g e n e r a l ly s m a l l number o f r e l a t i v e s in v o lv e d ( s p e c i a l l y i n b e e f c a t t l e ) and th e m u l t i p l i e r s u s e d ( i . e . , 1 / 2 , 1 / 4 , 1 / 8 , 1 /1 6 ) (K och, 1972; W i l l h a m ,1 9 8 0 ) . As Koch ( 1972) p o in t s o u t , e r r o r s o f e s t i m a t e s i n one component tend to cause o th e r components to d i f f e r i n the o p p o s i t e d i r e c t io n s in c e the sum o f components i s f o r c e d t o equal th e whole. In g e n e r a l , i t i s exp e c te d t h a t i n c r e a s i n g the number o f r e l a t i v e r e l a t i o n s h i p s i n v o l v e d w o u ld d e c r e a s e t h e s ta n d a r d e r r o r s o f e s t im a t io n . D esigned ex p e r im en ts t h a t y i e l d s p e c i f i c u s e f u l c o v a r ia n c e s t h a t a r e u n c o r r e l a t e d h a v e b een s u g g e s t e d by W illh a m (1 9 6 3 ) and E is e n ( 1 9 6 7 ) . B o n d a r i e t a l (1 9 7 8 ) u s e d tw o d e s i g n s s u g g e s t e d by W illham ( 1963) i n T r i b o l i u in C-astaneum t o i n v e s t i g a t e g e n e t i c m a te r n a l i n f l u e n c e s on pupa w e ig h t and f a m i ly s i z e . The d e s ig n s were based on c r e a t i n g a s y s t e m o f m a t i n g s b e t w e e n f a m i l i e s o f f u l l - s i b s and p a te r n a l h a l f - s i b s . M atings between d i f f e r e n t f u l l - s i b f a m i l i e s are a l s o i n v o l v e d . At l e a s t t h r e e g e n e r a t i o n s a r e r e q u i r e d i n a l l t h e d e s ig n s . The g e n e r a t io n i n t e r v a l i n T ribo lium i s 30 days (Bondari e t a l , I 9 78 ); w h i l e i n b e e f c a t t l e t h e g e n e r a t i o n i n t e r v a l i s 4.3 y e a r s (Koch e t a l , I 9 8 2 ) . The p rob lem i s a g g r a v a t e d by t h e f a c t t h a t th e f e c u n d i t y r a t e i n c a t t l e i s low and r e p e a te d m atings to produce f u l l - s i b f a m i l i e s s h o u ld t a k e p l a c e i n d i f f e r e n t y e a r s . The r e s u l t 20 in c r e a s e s th e g e n e r a t io n i n t e r v a l . T h erefore , th e d e s ig n s are b e t t e r s u i t e d f o r la b o r a to r y a n im a ls than f o r b e e f c a t t l e . In c a se t h e r e are more c o v a r ia n c e s between r e l a t i v e s than d i r e c t and m aternal c o v a r ia n c e s to e v a lu a te , a method to s o lv e s im u lta n e o u s ly f o r t h e p a r a m e t e r s s h o u ld n e c e s s a r i l y be u se d . Van V le c k and H art (1966) have used I e a s t - s q u a r e s , w e ig h t in g the eq u a t io n s by the numbers o f o b s e r v a t i o n s u s e d i n t h e e s t i m a t e o f t h e r e l a t i v e r e l a t i o n s h i p . For the d e s ig n s d i s c u s s e d i n the p r e v io u s paragraph, E isen (1967) has s u g g e s t e d t h e u s e o f t h e d i a g o n a l e l e m e n t s o f (X’X)” 1 t o w e i g h t th e e q u a t i o n s . He h a s a l s o i n d i c a t e d t h a t t h e p r o c e d u r e i s n o t f u l l y o f f i c i c n t i f th e v a r ia n c e s o f th e e s t i m a t e s o f the c o v a r ia n c e s between r e l a t i v e s are not homogeneous. This i s l i k e l y to occur when d i f f e r e n t m e th o d s a r e u s e d t o e s t i m a t e t h e v a r i a n c e c o m p o n e n ts , and when t h e number o f r e c o r d s u s e d f o r t h e e s t i m a t e a r e e n t i r e l y d i f f e r e n t , a s u s u a l ly happens w ith b e e f c a t t l e . To overcome t h i s problem, Thompson (1976) has d eve lop ed a m o d if ie d maximun l i k e l i h o o d procedure. A fter assum ing t h a t th e o b s e r v a t io n s are norm ally d i s t r i b u t e d , the lo g o f in dependent m a tr ic e s o f sum o f squares i s m aximized. I t i s n ecessa ry t o s o l v e t h e e q u a t i o n s . i t e r a t i v e l y . The c a s e w h ere p a r e n t s a r e s u b j e c t to c u l l i n g was a l s o c o n s id er e d by Thompson (1976). However, th e f a c t t h a t in dependent sum o f sq u ares i s r eq u ired p r e c lu d e s the use o f th e p r o c e d u r e when t h e d a t a a r e n o t c o l l e c t e d u n d er a d e s ig n e d e x p e r im e n t . A n oth er p rob lem i s t h a t t h e m ethod can n o t a v o id t h e e f f e c t s o f the c o r r e l a t i o n s betw een the c o e f f i c i e n t s even though the d e s ig n i s good (Thompson, 1976). 21 2. Sm all number o f r e l a t i v e s in v o lv e d i n th e e s t i m a t i o n in b e e f c a t t l e f i e l d data T h is p r o b le m h a s p a r t i a l l y b e e n e x p l a i n e d i n t h e p r e c e d in g s e c t i o n . Hohenboken (1973) s a id t h a t i t i s d i f f i c u l t to l o c a t e enough ty p e s o f f a m i l i e s to equal th e number o f unknowns o f i n t e r e s t , and i t i s d i f f i c u l t to account s t a t i s t i c a l l y f o r a l l en v iron m en ta l cau ses o f l i k e n e s s b e t w e e n r e l a t i v e s . Koch (1 9 7 2 ) u s e d s e v e n r e l a t i v e r e l a t i o n s h i p s and the er ro r o f m aternal h a l f - s i b s model. There i s no o t h e r p ap er u s i n g m ore r e l a t i v e r e l a t i o n s h i p s th a n Koch( 1 9 72 ) . The d i r e c t consequence i s th a t some term s must be dropped from the model to s o lv e fo r the r e s t . I f the. term dropped i s not z e r o , th e s o lu t io n i s b i a s e d and t h e o t h e r c o m p o n e n ts a r e e i t h e r u n d e r e s t i m a t e d or o v e r e s t im a te d . The m agnitude o f the error depends on th e c o r r e l a t i o n among the term s f o r th a t p a r t ic u la r s e t o f r e l a t i v e s and the s i z e o f th e term dropped. 3 . M aternal e f f e c t s e v a lu a t io n l e n a h te n s th e tim e to conduct th e study i' As Willham (1980) p o in t s ou t m aternal e f f e c t s are: 1) a t l e a s t a g e n e r a t i o n b e h i n d t h e d i r e c t e f f e c t s i n t h e i r e x p r e s s io n , 2 ) s e x l i m i t e d , and 3 ) occur l a t e i n th e l i f e o f th e fem a le . A ll th e s e f a c t o r s le n g th e n the e v a lu a t io n t im e. I f the r e co r d s a r e t a k e n o v e r a l o n g p e r i o d o f t i m e , t h e r e i s t h e p o s s i b i l i t y o f i n t r o d u c i n g e n v i r o n m e n t a l c o r r e l a t i o n s ( E i s e n , 1967) ; y e a r by s i r e i n t e r a c t i o n i s a l s o p o s s i b l e tq occur which i n turn ten d s to i n f l a t e the s i r e v a r ia n c e component (Koch, 1972). 22 J5aj^mat.e-a-.Pf._.dJ.r-e.Q.t-,.and_ma.ternal g e n e t i c v a r ia n c e s and c o v a r ia n c e s f o r b ir t h w e ig h t and weaning w e ig h t i n b e e f c a t t l e The e s t i m a t e s r e v i e w e d i n t h i s s e c t i o n a r e t h e r e s u l t s o f a p p l y i n g t h e W illh a m (1 9 6 3 ) and Koch (1 9 7 2 ) p r o c e d u r e s . The f i r s t approach to th e problem was made by Koch and Clark (1955b). I . B ir th w e igh t Table 2 sum m arizes th e e s t i m a t e s o f p u b lish ed r e p o r t s on b ir th w e ig h t . Three e s t i m a t e s o f d a ir y c a t t l e are a l s o in c lu d ed . In g e n e r a l , t h e r e i s a trend fo r h2o to be g r e a te r than h2m. The means s u g g e s t t h a t a d d i t iv e d i r e c t i n f l u e n c e s are two t im e s the amount o f a d d i t iv e m aternal i n f l u e n c e s . The c o r r e l a t i o n b e t w e e n a d d i t i v e d i r e c t and a d d i t iv e m aternal e f f e c t s ( r g ) w as n e g a t i v e i n a l m o s t a l l t h e e s t i m a t e s . The few e s t i m a t e s and t h e b i g r a n g e o f t h e v a l u e s p ro d u c e u n c e r t a i n t y ab o u t the r e a l m agnitude o f rg. A p o s s ib l e b i o l o g i c a l e x p la n a t io n g iv en by F is h e r and W il l ia m s (1978) i s t h a t th e two opposing a d d i t i v e - e f f e c t s t e n d t o p r e v e n t e x c e s s e s i n b i r t h w e i g h t t h e r e b y p r o t e c t i n g th e s u r v iv a l o f both c a l f and cow a t p a r t u r i t io n . This h y p o t h e s i s i s supported by th e f a c t t h a t the e s t i m a t e s o f r G f o r d y s t o c ia , a t r a i t s t r o n g ly dependent on b ir th w e ig h t (B urfen ing e t a l , 1 9 7 8 ) , w e r e - . 1 9 f o r P h i l i p s s o n ( 1 9 7 6 ) , - . 5 4 f o r B u r f e n i n g e t a l (1981) and - .38 ( h e i f e r s ) and - .2 5 (cow s) fo r Thompson e t a l (1981). The f i f t h c o lu m n i n T a b le 2 w as i n c l u d e d s i n c e Koch (1 9 7 2 ) and B ak er (1 9 8 0 ) p o s t u l a t e d t h a t , when c o v (0 ,D ) i s e x c lu d e d from the. a n a l y s i s , t h e v a l u e s o f OA0 Am and r G a r e c l o s e t o z e r o . The s i m p l e TABLE 2 . ESTIMATES OF DIRECT AND MATERNAL ADDITIVE GENETIC VARIANCES AND COVARIANCES ON BIRTH WEIGHT OF CATTLE H e r i ta b i l i t ie s Genetic corre la tion Inclusion Direct Maternal Total between addit ive o f COV Number of e f f e c t s e f f e c t s e f f e c t s d ir ec t and add it ive (OsD) in records Breed Authors Ch20 J Ch2mJ Ch2t J maternal e f f e c t s the so lu tion used (rG) .35 - .42 >0 No 4,553 Hereford Koch and Clark (1955c) .22 .04 .00 - .9 3 Noa 1,064 Holstein Everett and Magee (1965) .65 .15 .27 - .9 8 Nob .56 .30 .36 - .5 8 Yes 789 Hereford Brown and Galvez (1969) .14 .25 .17 - .3 9 Yes 932 Angus .72 .48 - - .5 5 to —.89 Yes 1,962 Hereford Vesely and Robinson (1971) .44 inO to to .40 .12 - - .1 7 to .27 Yes 4,060 Hereford Koch (1972) .44 .04 to .19 - - .0 7 to .30 No .19 .08 ” - .5 3 No 6,724 Swedish- Philipsson (1976) Friesian .51 k .44 — .36 Yes 1,534 H olstein Fisher and Williams (1978) .21 .11 — -.2 4 No 11,552 Sinmental Burfening e t a l . (1981) .40 .17 .27 & Averages ^Relatives included: O2PHS, O2MGS, COV(S,MGS) "Relatives included: o^PGS, oZ^GS, COV(SsMGS) 24 mean o f t h e e s t i m a t e s w i t h o u t Cov(OilD) i s e q u a l t o - . 3 5 . T h is v a l u e does not seem to su p p ort t h a t h y p o th e s is . The o n l y tw o r e p o r t s i n w h ic h d o m in a n c e and e n v i r o n m e n t a l m aternal e f f e c t s were in c lu d e d w ere Brown and Galvez (1969) and Koch ( 1 9 7 2 ) . H ow ever, b o th p a p e r s a ssu m e d a DoDm and oEoEm t o be z e r o . The dominance d i r e c t e f f e c t s accounted f o r 9 and 17 % o f i n Angus and H ereford, r e s p e c t i v e l y (Brown and G alvez , 1969). The e s t im a t e of a ^Dm was n e g a t iv e which i s p o s s ib ly s u g g e s t in g th a t a n e g a t iv e source o f v a r i a t i o n w as l e f t o u t from t h e m o d e l . Koch (1 9 7 2 ) p r e s e n t e d a term f o r o^Dm + a ^Em t h a t a c c o u n t e d f o r 10 % o f a ^P. T h is a u th o r concluded t h a t th e env iron m enta l m aternal a b i l i t y o f dams did not have a s i g n i f i c a n t d i r e c t e f f e c t on m a t e r n a l a b i l i t y i n t h e n e x t g e n e r a t io n . 2 . Weaning w e igh t E s t i m a t e s o f d i r e c t and m a t e r n a l a d d i t i v e g e n e t i c s o u r c e s o f v a r i a t i o n on prew eaning growth are shown i n Table 3. C o n tr a r y t o b i r t h w e i g h t , a v e r a g e d a i l y g a i n or w e a n in g w e i g h t have more v a r i a t i o n f o r a d d i t iv e m aterna l e f f e c t s than f o r a d d i t iv e d i r e c t e f f e c t s . The mean o f t h e e s t i m a t e s o f r Q i s h i g h l y n e g a t i v e . Koch (1972) em phasized th e f a c t t h a t the e s t i m a t e s o f r^ when the cov (0 ,D ) was e x c l u d e d from t h e s o l u t i o n w e r e s m a l l e r and s u g g e s t e d an o v e r e s t im a t io n o f a AoAm. However, th e l a s t two e s t i m a t e s i n Table 3 i n d i c a t e t h a t t h i s i s n o t n e c e s s a r i l y t h e c a s e . I t s h o u l d be n o te d t h a t i t i s very d i f f i c u l t to compare e s t i m a t e s coming from d i f f e r e n t g e n e t i c m o d e ls . The o n l y s t u d y i n w h ic h r Q w as e v a l u a t e d by a s o l u t i o n which o n ly c o n t a in s a d d i t iv e e f f e c t s i s the one o f Kress e t P 1P 3I TABLE 3« ESTIMATES OF DIRECT AMD MATERNAL ADDITIVE GEMETIC VARIANCES AND COVARIANCE OF CALF GHOHTH THROUGH WEANING H er lta M Iit ie s Direct Maternal Total e f f e c t s e f f e c t s e f f e c t s Ch20 ) Ch2m) Ch2t ) Genetic corre la tion between addit ive d ir e c t and add it ive maternal e f f e c t s Inclusion of COV (OjD) in the so lu tion (rG) Number of records Breed Authors used .21 - .12 -.65 .18 .15 .25. .0 .40 .46 .17 - .7 3 No 4,553 Hereford Koch and Clark (1955c) Yes 725 Brahman Deese and Roger (1967) Yes 466 Brahman x Shorthorn No 4,060 Hereford Koch (1972) Averages HeapifflgJfeight .32 .29 .34 - .3 1 Yes 717^ Hereford H il l (1965) .31 .50 .34 - .4 6 Yes b •37 - .17 —.73 to —1.07 Yes 1,692 Hereford Vesely and Robison (1971) .23 .54 .08 - .7 9 Yes 2,618 Hereford Hohenboken and Brinks (1971a) .23 .34 COCVJ - . 2 8 No .14 .64 - -1 .1 4 Yes .14 .34 .32 - .0 7 No 228 Charolais Baker (1980) .20 .53 .09 - .9 0 Yes 3,765 Brahman Beltran Bru (1978) .20 .47 .02 - .7 5 No .12 .05 . “ —.68 No 13,682 Sinsnental Kress e t a l . (1979) Crossesa .41 OCV • - . 6 5 Averages R elatives included: iiPHSj ^MGSj COV(SjMGS) R elatives included: 2PGSj 2MGSj COV(SjMGS) roUl 26 a l ( 1 9 7 9 ) . In t h e r e m a i n i n g o n e s , t h e s o l u t i o n s w e r e o b t a in e d assum ing th a t some o f the d i r e c t and m aterna l c o v a r ia n c e s were zero . As d i s c u s s e d b e f o r e , e r r o r s i n t h e e s t i m a t e o f one c o v a r i a n c e c a u s e t h e o t h e r c o m p o n e n ts t o d i f f e r i n th e o p p o s i t e d i r e c t i o n , s i n c e th e sum i s f o r c e d t o e q u a l t h e t o t a l . When c o v (0 ,D ) was i n c l u d e d i n th e s o l u t i o n , ODoDm and a EoEm were a lw ays assumed to be z e ro . I f th e se term s are not n u l l , then th e i n c l u s i o n o f th e cov(0,D) i n th e s o lu t i o n ten d s to o v e r e s t im a t e th e v a lu e o f a AoAm and as a consequence, a l s o ° f r G. The im portance o f d e ter m in in g th e e x a c t magnitude o f oAoAm comes from the f a c t t h a t r e sp o n se to s e l e c t i o n f o r preweahing growth r e l i e s m o s t l y on i t s v a l u e a s shown by Van V le c k e t a l ( 1 9 7 7 ) . I t i s r e a so n a b le to suppose t h a t a AoAm i s n e g a t iv e s in c e a l l i t s e s t im a t e s h a v e t h i s s i g n ( T a b le 3 ) . T h is m eans t h a t m ost o f t h e p r o g r e s s made i n one g e n e r a t i o n due to s e l e c t i o n f o r g r o w th r a t e i s o v e r co m e by m a t e r n a l e f f e c t s i n t h e n e x t g e n e r a t i o n . A f t e r r e v i e w i n g t h e l i t e r a t u r e o f s e l e c t i o n e x p er im en ts i n b e e f c a t t l e , Koch e t a l (1982) concluded t h a t the r e a l i z e d h2 (th e p o r t io n o f the t o t a l or phenotypic c h a n g e due to g e n e t i c p r o g r e s s ) w as .45 f o r b i r t h w e i g h t , .24 f o r weaning w e ig h t , .35 fo r postw ean ing ga in ; .41 fo r f i n a l w e ig h t a t the perform ance t e s t and .33 f o r g a in e f f i c i e n c y . Thus, s e l e c t i o n would be l e s s s u c c e s s f u l f o r w e a n in g w e i g h t th a n f o r o t h e r g r o w th and e f f i c i e n c y t r a i t s . I m p o r t a n t e v i d e n c e f o r t h e p r e s e n c e o f m a te r n a l e f f e c t s on w eaning w e ig h t are g iv e n by the com parison o f m aternal and p a tern a l g e n e t i c param eters. Koch e t a l (1982) i n d ic a t e d t h a t m aternal h a l f - 27 s i b c o r r e l a t i o n s are l a r g e r than p a te rn a l h a l f - s i b c o r r e l a t i o n s (.34 v s . .0 7 ) . H ohenboken and B r in k s ( 1 9 7 1 a ) r e p o r t e d a d i s a g r e e m e n t b e t w e e n t h e c o v ( 0 ,S ) (4 8 .7 k g 2 ) and t h e cov (Oj D) (1 8 .7 k g 2 ) . The a v e r a g es o f s i r e and dam c o n t r ib u t io n s to g e n e t i c trend s i n w e a n in g w e i g h t o f c o m m e r c ia l h e r d s w e r e 1 .74 and .27 kg (Kennedy and H e n d e r s o n , 1977 ) and 1 .30 and .86 ( Z o l l i n g e r and N i e l s e n , 1984) . I f th e s e e s t i m a t e s measured o n ly t r a n s m it t e d or d i r e c t e f f e c t s i n a la r g e c l o s e d h e r d o v e r s e v e r a l y e a r s w i t h c o n s i s t e n t s e l e c t i o n p r a c t i c e s from year to y e a r , s i r e and dam c o n t r ib u t io n s would be ex p ec ted to be e q u a l . T h e r e f o r e , i f a AoAm (o r aEoEm) i s n e g a t i v e , t h e l o w e r dam trend would be ex p ec ted a s compared to th e trend e s t i m a t e fo r s i r e s ( Z o l l i n g e r and N i e l s e n , 1 9 8 4 ) . H ohenboken and B r in k s (1 9 7 1 b ) fo u n d n e g a t i v e g e n e t i c c o r r e l a t i o n s b e t w e e n t h e m a t e r n a l a b i l i t y o f b e e f h e i f e r s and g r o w th t r a i t s o f p a t e r n a l h a l f - s i b b r o t h e r s t e e r s . The r e v i e w e d v a l u e s f o r t h e c o r r e l a t i o n b e t w e e n m i l k y i e l d o f d a i r y h e i f e r s w i t h b e e f t r a i t s o f p a t e r n a l h a l f - s i b s b r o t h e r i s c l o s e t o z e r o (W h ite e t a l , 1 9 8 1 ) . H i l l (1 9 6 5 ) h a s fo u n d t h a t r Q f o r w e a n in g w e i g h t s w e r e - . 1 6 , - .3 1 and - . 4 5 , a t 15 0 , 180 and 210 d o f a g e , r e s p e c t i v e l y , which s u g g e s t s t h a t an im p ortan t part o f the n e g a t iv e a s s o c i a t i o n betw een d i r e c t and m aternal e f f e c t s i s env iron m enta l and g i v e s a p a r t i a l e x p l a n a t i o n f o r su c h a s m a l l c o r r e l a t i o n i n d a i r y c a t t l e . The a b o v e p a ra g ra p h h a s i n t r o d u c e d one o f t h e m o s t im p o r t a n t problem s i n the a s s o c i a t i o n o f d i r e c t and m aternal e f f e c t s f o r weaning w e i g h t . The p rob lem i s t o d e t e r m in e how much o f t h i s n e g a t i v e c o r r e l a t i o n i s g e n e t i c and how much i s en v iron m en ta l. I M a te r n a l a b i l i t y o f a b e e f cow i s u s u a l l y m ea su r e d u s i n g h er "m ost p r o b a b le p r o d u c in g a b i l i t y " (MPPA) (L ush , 1 9 4 5 ) . There i s e v i d e n c e t h a t e n v i r o n m e n t a l s o u r c e s o f v a r i a t i o n a f f e c t t h e r e l a t i o n s h i p betw een e a r ly growth o f a b e e f f em a le and her subsequent m a t e r n a l a b i l i t y . For e x a m p le , t h e p h e n o t y p i c c o r r e l a t i o n b e tw e e n b i r t h y e a r m eans o f t h e cow and MPPA w a s fo u n d to be - . 5 2 , - . 2 0 and - .11 and th e c o r r e l a t i o n betw een age o f dam e f f e c t s and MPPA fo r the tw o t r a i t s w as - . 7 0 , - . 6 8 and - . 1 9 , a s r e p o r t e d by E l l i c o t e t a l ( 1 9 7 0 ) , Mangus and B r in k s (1 9 7 1 ) and K r e s s and B u r f e n i n g ( 1 9 7 2 ) . T h ese l a t t e r a u t h o r s a l s o r e p o r t e d a p o s i t i v e t r e n d (b = .06 + .03) f o r weaning w e ig h t on b ir th d a te and a n e g a t iv e trend (b = - .1 0 ± .02) f o r MPPA on b ir t h d ate . Hence, the d a ta in d ic a t e d t h a t a t l e a s t part o f t h e n e g a t i v e a s s o c i a t i o n b e t w e e n g r o w th r a t e and s u b s e q u e n t m aternal a b i l i t y (or betw een d i r e c t and m aternal e f f e c t s ) was caused by en v iron m en ta l s o u r c e s o f v a r ia t io n . The b a s i c c a l f f o o d d u r in g t h e p r e w e a n in g p e r i o d i s t h e m i lk p ro d u ced by h i s m o th e r . C a n t e t ( 1 9 8 3 ) c a l c u l a t e d a n a v e r a g e c o r r e l a t i o n b e t w e e n cow m i l k p r o d u c t io n and c a l f w e a n in g g a i n or w e i g h t o f .58 fro m 26 s t u d i e s . T h e r e f o r e , a h ig h a v e r a g e d a i l y g a i n o f t h e h e i f e r c a l f i s p o s i t i v e l y a s s o c i a t e d w i t h h e r m o th e r 's m i lk p ro d u ction and n e g a t iv e ly a s s o c i a t e d to her f u tu r e m aterna l a b i l i t y . Hence, th e ex p e c te d r e l a t i o n s h i p betw een weaning w e ig h t o f a cow and h e r s u b s e q u e n t m i lk p r o d u c t i o n w ou ld be n e g a t i v e . C h r i s t i a n e t a l (1965) found n e g a t iv e c o r r e l a t i o n s betw een dam weaning w e ig h t and m ilk ii and b u t t e r f a t p r o d u c t io n . T o tu s e k (1 9 6 8 ) fo u n d t h a t c o w s r a i s e d on low p la n e s o f n u t r i t i o n p r e v io u s to 240 d o f age, weaned c a lv e s t h a t 28 29 w e ig h e d 8 and 10 kg m ore th a n c a l v e s w eaned by c o w s r a i s e d on t h e medium and h igh p la n e s o f n u t r i t i o n , r e s p e c t i v e l y . Johnsson and Obst (1984) found t h a t th e r a t e o f growth b e fo r e weaning had more in f lu e n c e on s u b s e q u e n t m a t e r n a l a b i l i t y i n t h e f i r s t t h r e e l a c t a t i o n s than e i t h e r g r o w th b e t w e e n 8 t o 14 mo o f a g e or p r e m a t in g l i v e w e i g h t o f H ereford h e i f e r s . A major p a r t o f th e developm ent o f th e mammary g land ta k e s p lace between b ir th and f i r s t c a lv in g (S e jr s e n , 1978). Many s t u d i e s rev iew ed by Koch ( 1 9 7 2 ) , K r e s s and B u r f e n i n g (1 9 7 2 ) and S e j r s e n (1 9 7 8 ) show t h a t h i g h l e v e l s o f e n e r g y i n t h e r e a r i n g p e r io d r e s u l t e d i n a d e c r ea se o f subsequent m ilk y i e l d o f d a ir y h e i f e r s . The mechanism o f t h i s p h e n o m e n o n i s r e l a t e d t o a d e c r e a s e i n g r o w t h h o r m o n e c o n c e n t r a t i o n i n t h e b lo o d and an i n c r e a s e i n t h e a m ou n ts o f f a t i n t h e u d d e r , e i t h e r a t t h e s a m e p h y s i o l o g i c a l o r a t t h e sa m e c h r o n o lo g ic a l age, a s th e l e v e l o f energy i n th e d i e t i n c r e a s e s during t h e r e a r i n g p e r i o d ( S e j r s e n , 1 9 7 8 ) . M a r t in e t a l (1 9 8 1 ) and Ochoa e t a l (1 9 8 1 ) r e p o r t e d t h a t c r e e p - f e e d i n g h e i f e r c a l v e s r e s u l t e d i n a d ecrea sed l i f e t i m e p r o d u c t iv i t y and MPPA f o r weaning w e ig th which i s c o n s i s t e n t w ith th e e a r l i e r f in d in g s o f i n f e r i o r udder developm ent. From th e s t u d i e s r e v i e w e d a b o v e i t . i s c l e a r t h a t t h e cow s t h a t had h ig h e r weaning w e ig th s tended t o produce c a lv e s w ith lo w er weaning w e ig h t s . This r e s u l t was p a r t i a l l y due to a n e g a t iv e env ironm enta l a s s o c i a t i o n , i . e . , n e g a t iv e v a lu e o f a EoEm. Koch (1972) s p e c u la t e s t h a t t h e e f f e c t s o f m a t e r n a l e n v ir o n m e n t f o r p r e w e a n in g g r o w th o f p r e v io u s g e n e r a t io n s ( th e fm path i n F igu re I) should have a va lu e o f - 0 .1 t o - 0 . 2 f o r t h e e n v i r o n m e n t a l c o v a r i a n c e t o s a t i s f y o b s e r v e d 30 c o r r e l a t i o n s and r e g r e s s i o n s . S i n c e th e . env iron m enta l c o var ian ce i s a l s o a f u n c t i o n o f O^Am and OAoAm, a s Koch (1 9 7 2 ) sh o w e d , th e o n ly way to d eterm in e th e r e l a t i v e c o n t r ib u t io n o f aAoAm. and oEoEm to the ph en otyp ic v a r ia n c e o f weaning w e ig h t i s to s o lv e s im u lta n e o u s ly fo r a l l th e c o v a r ia n c e s . This procedure has not been done y e t . Regarding dominance e f f e c t s on w eaning w e ig h t , Deese and Koger (1967) found a v a lu e o f z e ro f o r cr2Do w h i le i n Hohenboken and Brinks (1971a) s tu d y a 2do was 52.4 kg2, corresp on d in g to 10.3 % o f the t o t a l v a r i a t i o n . T h e ir e s t i m a t e o f oDoDm ( - 76.7 k g 2 ? - 17.8 % o f t h e v a r ia n c e ) i s the o n ly one found i n th e l i t e r a t u r e . However, s in c e the au th o rs assumed O2Dm to be z e r o i n order to s o lv e th e e q u a t io n s , the e s t i m a t e i s p o s s i b l y n o t v e r y r e l i a b l e s i n c e by t h e C au ch y-S ch w arz i n e q u a l i t y : a ^Do . O2Dm 2. <3 DoDm. 31 MATERIAL AND METHODS The d a t a f o r t h i s s t u d y w e r e c o l l e c t e d a t t h e 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 te r (NARC) l o c a t e d 13 km SW o f H avre, Montana. The g eograp h ic c o o r d in a te s o f the s t a t i o n a re: l a t i t u d e 48° 30'N, lo n g i t u d e 109° 48*W. The approxim ate a l t i t u d e i s 819 m above se a l e v e l . The area can be d e s c r i b e d a s t y p i c a l o f t h e n o r t h e r n g l a c i a t e d p l a i n s and i s b o r d e r e d on t h e s o u t h by t h e B ear Paw m o u n t a in s . The B ear Paw m o u n t a in s w e r e t h e s i t e o f t h e Rocky Boy I n d ia n R e s e r v a t i o n l e a s e l o c a t e d 48 km s o u t h o f H avre and t h i s l e a s e was u s e d a s t h e summer g r a z in g s i t e from the l a t e s 40’s to the e a r ly 70’s. Weather Weather s t a t i s t i c s a t NARC were taken by i t s own c l i m a t i c s t a t i o n f o r th e p e r i o d 1 9 5 1 -1 9 8 0 (USDC, 1 9 8 2 ) . Annual mean t e m p e r a t u r e was 6°C. A v era g e t e m p e r a t u r e f o r t h e c o l d e s t month (J a n u a r y ) and th e h o t t e s t m onth ( J u l y ) w e r e -1 0 .9 ° C and 2 0 .7 °C , r e s p e c t i v e l y . The extrem e tem p era tu res r e g i s t e r e d w ere -49.4°C (January 1953) and 42.2°C (J u n e 19 0 0 ) . Mean t e m p e r a t u r e s w e r e a p p r o x i m a t e l y 4°C l e s s a t th e Rocky Boy s u b s t a t io n during th e same per iod . Annual mean p r e c i p i t a t i o n was 297 mm a t NARC and 438 mm a t Rocky Boy. M ost o f t h e p r e c i p i t a t i o n (80%) (A n d erso n , 1966) o c c u r r e d betw een A p ril and September. Anderson (1966) comments t h a t the snow f a l l a t t h e m a in s t a t i o n i s l i g h t w i t h a maximum h e i g h t o f th e snow cover o f 15 cm during m ost o f the y e a r s . This i s a l s o r e la t e d to the 32 w arm in g e f f e c t s o f t h e C h inook w in d s w h ic h te n d t o r e d u c e t h e snow c o v e r . A l a r g e a m o u n t o f e v a p o r a t i o n i n r e l a t i o n s h i p t o t h e p r e c i p i t a t i o n o ccu rs a t NARC during the summer. The lo w e r eva p o ra tio n r a t e and g r e a t e r p r e c i p i t a t i o n a t Rocky Boy p r o d u c e d b e t t e r r a n g e c o n d i t io n s during the summer. S o i l s The NARC s o i l s were c l a s s i f i e d a s mixed a r i d i c A r g ib o r o l l s o f the s e r i e s A t te w a n , T e l s t a d and J o p l i n (USDA-SCS,19 8 2 ) . S e r i e s T e l s t a d and J o p l in have f in e - lo a m y t e x tu r e . Whereas th e Attewan t e x tu r e i s f in e - lo a m y over sandy or s a n d y - s k e le t a l . Ranee C o n d i t i o n s • The p a s tu r e s a t NARC can be d e s c r ib e d as mixed p r a ir e g r a ss la n d s . The s p e c i e s a r e n a t i v e and i n t r o d u c e d g r a s s e s l i k e c r e s t e d w h ea t ( A e r o o v r o n d e s e r t o r u m ) . n e e d l e and t h r e a d ( S t i n a c o m a t a ) and b lu e gramma (B o u te lo a e r a c i l i s ) . Anderson (1966) d e c r ib e d th e summer g r a z in g s p e c i e s a t Rocky Boy a s b a s i c a l l y g r a s s e s s u c h a s T im oth y ( Phleum p r a t e n s e ) , June g r a s s (K o e l e r i a c r i s t a t a ) . Id a h o f e s c u e (F e s tu c a i d a h o e n s i s l . Rough fe s c u e (F estu ca s c a b r e l l a ) and Mountain brome (Bromus Sp p J . Experim ental Animals B ir th and weaning w e ig h t s w ere taken on 4,423 c a l v e s from 1938 to 1983. In fo rm a tio n on the same w e ig h t s o f the cows was a l s o a v a i la b le s in c e 1928. There were t h r e e d i f f e r e n t phases o f data c o l l e c t i o n and b reed in g sy s te m s . The f i r s t one c o n s i s t s o f the an im a ls r a is e d before 1946. These c a t t l e were o r ig in a t e d a t Havre and were th e s to c k graded 33 t o t h e o l d e s t l i n e d e v e lo p e d a t t h e F o r t Keogh, L i v e s t o c k and Range Research S t a t io n , M ile s C ity , Montana i n the second phase. This l i n e was b e t t e r known a s l i n e H. The second phase i s c h a r a c te r iz e d by the c r e a t io n and developm ent o f i n b r e d l i n e s and c r o s s l i n e s o f H e r e fo r d c a t t l e . The p r o c e ss was i n i t i a t e d i n 1946 and was m ain ta in ed through 1966. I n u r e d l i n e I w as i n i t i a t e d i n I 94 6 , l i n e 2 i n 1947 and l i n e 3 i n 1 948 . L in e 4 a c t e d a s a c o n t r o l l i n e . C r o s s l i n e s c a l v e s w e r e produced by m ating cows from l i n e 4 w ith b u l l s o f l i n e s I , 2 and 3 to c r e a t e l i n e s 5 , 6 and 7 , r e s p e c t i v e l y . The f i n a l p h a s e s t a r t e d i n 1975 and i s c o n t in u in g . The fo u n d a t io n o f t h e s e l i n e 4 c a t t l e i s from in bred s t o c k purchased from F ort Keogh, L iv e s to c k and Range S t a t io n , M ile s C ity i n 1962 and 1963. These purebred c a t t l e are s e l e c t e d by the index: 1=365 d. a d ju s te d w e ig h t -3 .2 a d ju s te d b ir th w e igh t . Further d e s c r i p t io n o f managemental and s e l e c t i o n procedures has been g iv e n by Flower e t a l (1963)' and Anderson (1966). Management o f th e b reed in g herd H e i f e r s w e r e b red t o c a l v e f i r s t a s 3 - y e a r - o l d s i n t h e e a r l i e r y e a r s o f t h e p r o j e c t . A f t e r 1951 , h e i f e r s w ere b red t o c a l v e a s 2 - y e a r - o l d s . The b r e e d in g s e a s o n l a s t e d ap p rox im ate ly 60 d beg inn ing t h e f i r s t w eek o f June . N a t u r a l s e r v i c e was u s e d i n s i n g l e s i r e p a s tu r e s a t th e summer g r a z in g l e a s e . H e i f e r s and cows w ere fed during th e w in te r a t NARC s t a r t i n g i n December during most o f th e y e a r s . When n a t iv e range p a s tu r e s became an i n s u f f i c i e n t source o f food su p p ly , a r a t i o n c o n s i s t i n g o f a lm ost equal p a r ts o f c e r e a l s tr a w s and le g u m e -g r a s s hay a d - l ib i t u m was f e d t o t h e c o w s . In t h e l a t e r y e a r s , c o r n s i l a g e r e p l a c e d t h e l e g u m e - g r a s s hay. Corn s i l a g e was decreased p r io r to c a lv in g w ith hay be ing in c r e a s e d . F i r s t c a l v i n g h e i f e r s w e r e w i n t e r e d s e p a r a t e l y from t h e o l d e r cows and fe d a d i f f e r e n t r a t i o n o f g r a in and a l f a l f a hay. S in ce 1970, g r a i n h a s n o t b e e n f e d and t h e r o u g h a g e s o u r c e w as c o r n s i l a g e and a l f a l f a hay. N u t r i t i o n a f t e r c a lv in g c o n s i s t e d o f c r e s t e d w heat g r a s s p a s tu r es f o r a l l the f e m a le s from th e m iddle o f A pril through May supplem ented by d ecreased amounts o f corn s i l a g e r e p la c e d by second c u t t i n g a l f a l f a hay . Then, th e c o w s w e r e t r u c k e d t o t h e Rocky Boy s u b s t a t i o n t o be a l o t t e d i n t o t h e i r r e s p e c t iv e b reed in g herds i n e a r ly June. A fter the b r e e d in g s e a s o n , c o w s w e r e c o m b in e d i n t o on e h erd w h ic h g r a z e d t h e mountain p a s tu r e u n t i l a p p rox im ate ly November. At t h a t t im e , th e herd w as t r a i l e d back t o NARC i n o r d e r t o p a s s t h e w i n t e r p e r io d . S i n c e 1975, the purebred herd has been m a in ta in ed a t NARC during th e summer p r im a r i ly on i r r i g a t e d p a s tu r es . S e l e c t i o n and B reeding Procedures The p r o j e c t i n i t i a t e d i n 1946 was d es ign ed to measure g e n e r a l and s p e c i f i c com bining a b i l i t y o f l i n e s I , 2 and 3. In order to f u l l f i l l t h i s g o a l , a system o f s e q u e n t ia l s e l e c t i o n on th e m ale s id e was put i n t o p r a c t i c e . Female s e l e c t i o n accounted f o r a v a r ia b le but s m a l le r p o r t i o n o f t h e s e l e c t i o n d i f f e r e n t i a l s o f b i r t h w e i g h t and w e a n in g w e ig h t (F low er e t a l , 1964). A f i r s t c u l l i n g o f male c a lv e s took p la ce a t w e a n in g t im e . S low p r e w e a n in g g r o w t h , c o n f o r m a t i o n d e f e c t s , or c o lo r p a t te r n were the r e a so n s f o r c a s t r a t i n g a p p ro x im a te ly 17? o f th e b u l l c a l v e s . The r e m a i n i n g b u l l c a l v e s w e r e p u t on a 168 d 34 35 perform ance t e s t w ith in d iv id u a l f e e d in g . Therefore , mass s e l e c t i o n was a p p l ie d on the b a s i s o f growth r a t e through a year o f age. The r e c u r r e n t p h a se o f t h e s e l e c t i o n sc h e m e w as p rod u ced by m ating two h ig h - g a in in g y e a r l i n g b u l l s from each o f the th r ee purebred l i n e s t o c o w s o f t h e g r a d e t e s t e r l i n e 4 , u s i n g h e r d s o f 15 f e m a l e s per s i r e . This procedure was not a lw a y s p o s s ib l e to a c h ie v e . At the c o n c l u s i o n o f t h e p r o g e n y t e s t s , t h e s t r a i g h t l i n e b u l l s w h ich p e r fo r m e d b e s t w i t h r e s p e c t t o t h e i r c r o s s l i n e p r o g e n y w e i g h t s and g a i n s w e r e s e l e c t e d t o s i r e s t r a i g h t l i n e c a lv e s u n le s s cu rren t herd b u l l s had a t t a i n e d s u p e r i o r c r o s s l i n e p r o g e n y t e s t s . Proven b u l l s w e r e a b l e t o s i r e s t r a i g h t l i n e c a l v e s a s 3 - y e a r - o l d s . S e l e c t i o n p r e s s u r e a c h i e v e d . b y r e c u r r e n t s e l e c t i o n o f b u l l s w as n e g l i g i b l e ( F lo w e r e t a l , 1 9 6 4 ) . A p p r o x im a t e ly o n e - t h i r d o f t h e t e s t e r l i n e c o w s w e r e b red to b u l l s o f t h e i r own l i n e to p rov id e r e p la c e m e n t h e i f e r s . Some h e i f e r c u l l i n g was e x e r te d a t 18 mo based on weaning w e ig h t , 140-d g a in t e s t and 18-mo w e ig h t . The r a t i o n f o r t h e b u l l f e e d t e s t c o n s i s t e d o f r o l l e d b a r l e y , (35%), d r i e d m o l a s s e s b e e t p u lp (35%), r o l l e d o a t s (20%) and w h ea t bran (10%). A l f a l f a hay a d ^ i ib ltu m was provided as a roughage source. The h e i f e r s were g r o u p -fe d i n o u t s id e l o t s w ith good p r o t e c t io n from the weather during 140 d. The r a t i o n was made o f second c u t t in g a l f a l f a hay p lu s .90 kg d a i l y o f r o l l e d b a r ley i n l a t t e r y e a r s . K ress and B u rfen in g (1972) r e p o r te d means and standard d e v ia t io n s o f i n b r e e d i n g p e r c e n t a g e o f c o w s o f 12.6 + 7.4%, 10.7 ± 6.5% and 11.4 ±. 7.0% f o r l i n e s I , 2 and 3 , r e s p e c t i v e l y . A s a m p le o f y e a r s 1939 , 1949 and 1959 had a v a l u e o f 1.2 ± 2 .6 f o r l i n e 4 c o w s . Few c o w s had in b r e e d in g p e r c e n ta g e s g r e a te r than 24 to 28 %. S t a t i s t i c a l procedures The o r i g i n a l d a t a s e t c o n t a i n e d 5 ,1 7 3 o b s e r v a t i o n s . E d i t i n g p r o c e d u r e s w e r e b a s e d on d e l e t i n g i n c o m p l e t e r e c o r d s ( i . e . , l a c k o f one o f t h e w e i g h t s , unknown s i r e i d e n t i f i c a t i o n ) . T here w e r e 75 c a l v e s w i t h e i t h e r b i r t h w e i g h t or w e a n in g w e i g h t m i s s i n g and 660 c a lv e s w ith an unknown s i r e , a lm o s t a l l coming from th e e a r l i e r years . Abnormal v a lu e s ( i . e . , w e ig h t s below or above fou r standard d e v ia t io n s f r o m t h e m e a n ) w e r e a l s o d e l e t e d , t h o u g h t h e i r n um ber w a s c o m p a r a t iv e ly s m a l l (15 c a lv e s ) none o f which were s e l e c t s a s s i r e s . The f i n a l d a ta f i l e f o r p a te rn a l h a l f - s i b a n a l y s i s c o n s i s t e d on 4,423 o b s e r v a t io n s . The t o t a l number o f s i r e s t h a t produced progeny was 202. A ll the s i r e s r a i s e d a t NARC (1 0 5 ) had r e c o r d s a v a i l a b l e on t h e i r own b i r t h w e ig h t and w eaning w e ig h t . The rem a in in g b u l l s were r a i s e d a t M ile s C ity and, t h e r e f o r e , they w ere r a i s e d under d i f f e r e n t environm ental c o n d i t i o n s . The g r e a t number o f y e a r s o f d a t a a l l o w e d f o r a c o n s i d e r a b l e number o f r e p e a te d m atin gs . Hence, f a m i l i e s o f a t l e a s t two dams per s i r e and two or more c a lv e s per dam were s e l e c t e d and t h i s r e s u l t e d i n 976 f u l l - s i b c a l v e s from 402 f u l l - s i b f a m i l i e s . W illh am (1 9 6 3 ) h a s s u g g e s t e d t h a t t h e b e s t s e t o f r e l a t i v e s to u se to e s t i m a t e the im portance o f g e n e t i c m aternal e f f e c t s are s e t s o f m a t e r n a l c o u s i n s s i n c e t h e i r u s e r e d u c e s t h e e n v i r o n m e n t a l c o n t r i b u t i o n t o t h e m a t e r n a l v a r i a n c e . H en ce , th e c o u s i n p a t t e r n s 36 37 p r o p o s e d . by Van V le c k and H art (1 9 6 6 ) w e r e e v a l u a t e d . A ls o t h e c o v a r i a n c e o f f u l l - s i b s w h o se p a r e n t s a r e p a t e r n a l h a l f - s i b s and p a te r n a l h a l f - s i b s whose dams are p a te r n a l h a l f - s i b s were c o n s id ered . M aternal granddam -sibs (MGD) Dam I------------------------O ffspring I Granddam< -Dam 2-------:----------- : O ffspring 2 Single first cousins (SFC) Granddam — — P=-Dain T——:-----=------------ O ffspring I Grandsire ----- — ^Dam 2 — :------------------O ffspring 2 Paternal half-sibs Plus maternal half-sib dams (PHS + MHSDl •Dam I ------- :—;-----------O ffspring I Granddam S i r e < ^ -Dam 2 ------ ------ ;-------- O ffspring 2 Paternal half-sibs plus single first cousins (PHS + SFCl. Dam 1 ----------------------- O ffspring I Sire«c Dam 2 —:------------------- O ffspring 2 Full-sibs Plus paternal half-sib parents (FS + PHSPl •S ire c—----------------—r Off spring I G randsire; D a m ------:----------------O ffspring 2 38 Eateraal half-sibs plus paternal half-sib dams CPHS + PHsm Dam I O ffsp r in g I G randsire Dam 2 S ir e O ffsp r in g 2 As e x p e c te d , the c l o s e r th e r e l a t i v e r e l a t i o n s h i p i s , the s m a l le r th e number o f d e g r e es o f freedom fo r th e a n a l y s i s becomes. The reason f o r u s in g th e s e e s t i m a t e s was to i n c r e a s e the number o f eq u a t io n s f o r e s t i m a t i n g th e n ine d i r e c t and m aternal v a r ia n c e s and c o v a r ia n c e s and to p rov id e more e q u a t io n s to e s t i m a t e the dominance v a r ia n c e s and the c o v a r i a n c e b e t w e e n d o m in a n c e d i r e c t and dominance m aternal e f f e c t s . E rror t e r m s w e r e i n c l u d e d s i n c e t h e number o f d e g r e e s o f f re e d o m u s u a l ly in v o lv e d i s h ig h , which in c r e a s e s th e accuracy o f e s t im a t io n . E x p e c ta t io n s f o r the en v iron m en ta l components were o b ta in ed under the a s s u m p t i o n t h a t e r r o r s i n t h e m o d e ls i n c l u d i n g i n d i v i d u a l s r e l a t e d th r o u g h s i r e - t y p e r e l a t i o n s h i p s i n v o l v e d 2 Eo, EoEm and 2 Em s i n c e a l m o s t one f o u r t h o f t h e r e c o r d s w e r e f u l l - s i b s , w h ich h ave m aternal environm ent i n t h e ir e x p e c t a t io n s . Fam ily r e l a t i o n s h i p s w ere ana lyzed by l e a s t squares procedures as o u t l in e d by Harvey (1977). The b a s ic model used was y i jk lm = u + I 1 + a j + s k + ( a s ) j k + b X ij^ m + gi;L + BjJ klmn where Jr1JkIm = o b s e r v a t io n on th e mth b ir t h w eight and weaning w e igh t , u = g e n e r a l mean common to a l l the o b s e r v a t io n s , I 1 = e f f e c t o f t h e I th l i n e - y e a r , i = 4 - 3 8 , ....... 1 - 5 0 , 2 - 5 0 , 3 - 5 0 , 4 - 5 0 , . . , 4 -83» 39 a j = e f f e c t o f t h e j th a g e o f dam, j = 2 , 3 , 4 , 5 , 6 - 1 0 , 1 1 or more, s k = e f f e c t o f t h e k fch s e x , k = I ( h e i f e r ) , 2 ( b u l l ) , 3 ( s t e e r ) , ( a s ) j k = e f f e c t o f th e i n t e r a c t i o n betw een th e j th age o f dam and kfch se x , bXi J k lm r r e Sr e s s i 6 n o f b i r t h w e i g h t on b i r t h d a t e or w e a n in g w e ig h t on age a t w eaning, £>11 = random f a m i l y e f f e c t . T h is i s a g e n e r a l term u s e d f o r s i r e , m a t e r n a l g r a n d s i r e , p a t e r n a l gran d s i r e and m a t e r n a l g r e a t gran d s i r e n e s t e d w i t h i n t h e i th l i n e - y e a r , and ei jk lm r nandom e r r o r . The s o l u t i o n o f t h e l e a s t - s q u a r e s e q u a t i o n s i n t h e H a rv ey ’s package i s o b ta in ed by im p o s in g th e r e s t r i c t i o n s E S E E E i ^ i r J aJ = k s k = j ( a s ) j k = Jf ( a s ) j k = 0 Table 4 shows the d i s t r i b u t i o n o f r e co r d s per l i n e and per year . S in c e during th e e a r l i e r and l a t e r y e a r s l i n e four c a lv e s are th e on ly r e co r d s a v a i l a b l e , da ta was c l a s s i f i e d by l i n e - y e a r s u b c l a s s e s in s te a d o f r e co r d in g th e two f a c t o r s i n d i v i d u a l l y . Due to the s m a l l number o f o b s e r v a t io n s per s u b c la s s , the re co r d s w e r e c o r r e c t e d f o r l i n e - y e a r e f f e c t s i n som e o f t h e m o d e ls u s i n g c o n s ta n ts o b ta in e d from a f i x e d e f f e c t s model. This model in c lu d ed t h e e f f e c t s o f a g e o f dam, s e x , l i n e , y e a r and t h e r e g r e s s i o n s , o f b ir th w e ig h t on b ir th d a te and weaning w e ig h t on weaning age. UO TABLE 4 . DISTRIBUTION OF RECORDS BY LINES AND BY YEARS Year L in es I 2 3 4 5 6 7 1938 - - - 78 «** — — 1939 - - - 89 - _ ■ 1940 - - - 42 _ 1941 — - - 38 — 1942 — _ 44 — - 1943 - - - 61 - — «■ 1944 - - - 69 - - - 1945 - - - 85 - - ■ 1946 - - - 95 - - - 1947 - - - 70 - — 1948 6 - - 108 7 - — 1949 .17 - - 79 - 3 1950 14 15 5 60 I I I 1951 20 19 22 53 - 11 3 1952 20 18 22 25 16 18 14 1953 8 21 14 33 20 18 20 1954 12 25 19 21 22 21 20 1955 13 22 16 20 17 22 21 1956 10 16 13 21 19 23 22 1957 14 25 14 29 20 17 20 1958 13 19 14 20 ' 18 22 17 1959 13 20 6 20 14 20 14 1960 14 27 10 16 18 14 16 1961 22 23 11 27 17 19 10 1962 19 18 14 22 18 11 3 1963 22 20 14 25 15 26 21 1964 17 21 12 21 22 17 18 1965 27 32 15 14 24 23 25 1966 27 28 21 11 21 27 30 1967 18 17 22 28 23 21 24 1968 7 6 4 36 18 18 20 1969 8 7 5 25 22 23 19 1970 5 4 5 33 15 32 21 1971 - - - 28 - _ 1972 - - - 38 - - - (C on tin u es on th e n ext page) TABLE 4 . 1973 (C ontinued) 44 1974 - - - 52 1975 - - - 55 1976 - - - 59 1977 - - - 61 1978 - - - 63 1979 - - . - 70 1980 - - - 71 1981 - - - 79 1982 - - - 85 1983 - - - 133 U2 The dam c o m p o n e n t w as e s t i m a t e d from t h e f u l l - s i b m od el w here dams w e r e n e s t e d w i t h i n s i r e and fro m a m od el i n w h ic h dams w e r e n e s te d w i t h in m aternal granddams. The f i t t i n g c o n s t a n t s m e t h o d o r H e n d e r s o n ’ s m e t h o d I I I (Henderson, 1953) was used , a s o u t l in e d by Harvey (1977)» to e s t im a t e th e v a r ia n c e components i n a l l th e a n a ly s e s d e sc r ib e d above. The c o v a r ia n c e s betw een o f f s p r i n g and dam ( c o v ( 0 ,D ) ) , o f f s p r i n g and s i r e ( c o v ( 0 ,S > ) , o f f s p r i n g and m a t e r n a l gran d dam ( c o v ( 0 , MGD)), a u n t and n i e c e ( p a t t e r n D) (cov(A »N )) and a u n t ( f u l l s i b o f th e s i r e ) and nephew or n i e c e (c o v (N ,A )) w e r e e v a l u a t e d by s i m p l e l i n e a r r e g r e s s io n procedures a f t e r a d j u s t in g both w e ig h t s f o r a l l the f i x e d e f f e c t s . The c o v a r i a n c e b e t w e e n m a t e r n a l gran d s i r e p r o g e n y and grand o f f s p r i n g ( c o v ( S , MGS)) w as o b t a i n e d fro m a tw o -w a y random m odel w i t h o u t i n t e r a c t i o n w i t h t h e d a t a c o r r e c t e d f o r t h e f i x e d e f f e c t s . The e s t i m a t i o n procedure was R e s t r i c t e d Maximum L ik