Cunningham e Henderson 1965.pdf

8/11/2019 Cunningham e Henderson 1965.pdf

1/7

E. P. Cunningham and C. R. HendersonTraits in Beef Cattle

Estimation of Genetic and Phenotypic Parameters of Weaning

1965, 24:182-187.J ANIM SCI

http://www.journalofanimalscience.org/content/24/1/182services, is located on the World Wide Web at:

The online version of this article, along with updated information and

www.asas.org

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2/7

E S T I M A T I O N O F G E N E T I C A N D P H E N O T Y P I C P A R A M E T E R S

O F W E A N I N G T R A I T S I N B E E F C A T T L E 1

E P

C U N N I N G H A I V s ~ A N D C R H E N D E R S O N

C o r n el l U n i v e r si ty I t h a c a N e w Y o r k

R E W E A N I N G p e r fo r m a n c e is re c og n iz e d

a s o n e o f t h e m o s t i m p o r t a n t f a c t o r s i n

d e t e r m i n i n g t h e e c o n o m i c r e t u r n s f r o m b e e f

c a t t le , a n d i n g e n e t ic im p r o v e m e n t o f t h e

b e e f c a t t l e p o p u l a t i o n f o r o v e r al l p r o d u c t i v i t y .

G en e t i c r e s p o n s e t o s e l ec t i o n i n s u ch a p o p u l a -

t i o n d ep en d s o n t h e i n t en s i t y o f s e l ec t i o n , t h e

g e n e t i c v a r i a b i l i t y o f t h e t r a i t s c o n c e r n e d ,

t h e r e l a t i o n a m o n g t h e m , a n d t h e a c c u r a c y

w i t h w h i c h w e c a n i d e n t i f y t h e i n d i v i d u a l s

i n t h e p o p u l a t i o n w i t h t h e i r g e n o t y p e s . E f f o r t s

to m a x i m i z e t h i s r e s p o n se f o r p r e w e a n i n g p e r -

f o r m a n c e r e q u i r e a k n o w l e d g e o f t h e g e n e t i c

a n d p h e n o t y p i c p a r a m e t e r s o f t h e c o m p o n e n t s

o f t h i s t r a i t . A n u m b er o f e s t i m a t e s o f t h e s e

p a r a m e t e r s h a v e b e e n d e r i v e d f r o m r e c o r d s i n

e x p e r i m e n t s t a t i o n h e r d s . T h e p r e s e n t p a p e r

r e p o r t s o n t h e e s t i m a t i o n o f e n v i r o n m e n t a l

e f fec t s, v a r i an ce co m p o n en t s , h e r i t ab i l it i e s an d

co r r e l a t i o n s f o r w ean i n g t r a i t s i n a l a r g e p o p u -

l a t i o n o f co m m er c i a l h e r d s .

M a t e r i a l s a n d M e t h o d s

T h e d a t a a v a i l a b l e 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 o n 8 3 f a r m s i n N e w Y o r k o v e r t h e

y ea r s 1 9 4 6 t o 1 9 6 0 , an d co m p r i s ed 7 ,9 7 1 r e -

c o r d s o f th e A n g u s , H e r e f o r d a n d S h o r t h o r n

b r e e d s . T h e b r e e d i n g p a t t e r n o f t h e s e h e r d s

in N 'ew York i s l a rge ly s easonal , i . e . , t he cows

c a Iv ~ i n M a r c h , A p r i l a n d M a y a n d t h e c a l v es

a r e w e a n e d i n O c t o b e r , N o v e m b e r a n d D e -

c e m b e r . T h e y a r e u s u a l l y s o l d a t w e a n i n g

as f e ed e r c a l v e s. E ac h r eco r d co n s i s t ed o f a

w e i g h t a n d t y p e s c o r e o n a w e a n l i n g c a l f w i th

i n f o r m a t i o n o n t h e i d en t i t y o f t h e ca l f , s i r e ,

d a m a n d h e r d , a n d o n t h e b r e e d , s e x, y e a r

a n d d a t e o f b i r t h , d a t e o f w e i g h in g a n d c r e e p -

f eed s t a t u s o f t h e ca l f . B ecau s e o f d e f i c i en c i e s

o f V a ri o u s k i n d s i n t h e d a t a an d t h e r e s t r i c -

t i o n s i m p o s ed f o r t h e p u r p o s e s o f t h e an a l y s i s ,

3 , 1 3 3 , o r 3 9 o f t h e s e r e co r d s w e r e d i s ca r d ed .

T h i s r e d u c t i o n e l i m i n a t e d d a t a f o r t h e f i r s t

x Based in p art on a thesis subm itted by the senior autho r

to the Graduate School Cornell Univ ersity in partial fulfillment

of the requirements for the Ph.D. degree.

Present address: Animal Breeding and Genetics Depart ment

The Agricultural Inst itute Castleknock Co. Dublin Ireland.

3 y e a r s o f t h e p r o g r a m f ro m t h e S h o r t h o r n

b r e e d a n d f r o m 2 8 h e r d s , m o s t o f w h i c h h a d

v e r y s m a l l n u m b e r s o f c o w s .

T r a i t s S t u d i e d . P r e w e a n i n g p e r f o r m a n c e

m a y b e e v a l u a t e d b y m e a n s o f r e c o r d s o n

w e i g h t a t w e a n i n g ( W W ) , a v e r a g e d a il y ga i n

f r o m b i r t h t o w e a n i n g ( A D G ) a n d , t o a l e ss e r

e x t e n t , b y t h e t y p e s c o r e o r g r a d e o f t h e c a l f

a t w e a n i ng ( T S ) . A D G is a f u n c t io n o f W W ,

d a y s o f a g e ( D A ) a n d b i r th w e i g ht ( B W ) .

I f g r o w t h i s l i n e a r w i t h a g e o f c a lf , th e n A D G

W W - B W

m a y b e e x p r e s s e d a s D A . I n t h e p r e -

s e n t d a t a b i r t h w e i g h t w a s n o t a v a i l a b l e , a n d

w a s t a k e n a s a c o n s t a n t f o r e a c h b r e e d ( 6 0 lb .

f o r A n g u s a n d 7 0 l b . f o r H e r e f o r d ) . I n t h is

c a se W W s t a n d a rd i z e d f o r a g e o f c a l f m a y b e

co n s i d e r ed t h e s am e t r a i t a s A D G , d i f f e r i n g

f r o m i t o n l y b ecau s e o f a s ca l in g f ac t o r . T h i s

i s co n f i r m ed b y t h e v a l u e s o f 0 . 9 8 an d 0 . 9 3

o b t a i n e d f o r t h e g e n e t i c c o r r e l a t i o n o f A D G

a n d W W b y K o c h a n d C la r k ( 1 9 5 5 a ) a n d

L e h m a n n et al . ( 1 9 6 1 ) , a l t h o u g h i n b o t h o f

t h e s e s t u d i e s a c t u a l b i r t h w e i g h t s w e r e u s e d .

T h e a s s u m p t i o n o f l i n e a r i t y o f g r o w t h w i t h

a g e w a s e x a m i n e d b y d i v i d i n g t h e a g e o f c a l f

i n t o 1 0 - d a y i n t e r v a l s f r o m 1 2 0 t o 2 5 0 d a y s

a n d p l o t t i n g t h e u n a d j u s t e d m e a n s o f t h e

r e c o r d s f o r e a c h i n t e r v a l . T h i s w a s d o n e

s e p a r a t e l y f o r e a c h b r e e d , a n d t h e r e s p o n s e

a p p e a r e d t o b e c l o s e l y l in e a r . I n a d d i t i o n ,

t e s t s o f t h e s i g n i f i c an ce o f l i n ea r r eg r e s s i o n

w e r e c o m p u t e d , u s in g u n a d j u s t e d w e a n i n g

w e i g h t s a n d s i n g le - d a y a g e in t e r v a l s f r o m

1 2 0 t o 2 5 0 d a y s . T h e s e a r e p r e s e n t e d i n t a b l e

1 . T h e v a l u e s o f t h e r eg r e s s i o n co e f f ic i en t w e r e

1 .6 7 f o r t h e A n g u s an d 1 .4 9 f o r t h e H e r e f o r d s .

A l l W W r e c o r d s w e r e c o n v e r t e d t o A D G

f ig u r e s, a n d t h e t r a i ts A D G a n d T S w e r e

t h e n t a k e n a s a m e a s u r e o f p r e w e a n i n g p r e -

f o r m a n c e . T S w a s b a s e d o n t h e s t a n d a r d

f e e d e r c a l f g r a d e s , w i t h e a c h g r a d e b e i n g

d i v i d e d i n t o p l u s , a v e r a g e a n d m i n u s . N u -

m e r i c a l v a l u e s w e r e t h e n a s s i g n e d t o t h e

v a r i o u s g r a d e s, r a n g i n g f r o m 4 ( C o m m o n ) t o

1 7 ( F a n c y + ) . A l m o s t a ll o f t h e c a l v e s i n

t h e p r o g r a m w e r e g r a d e d b y o n e m a n .

182

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3/7

E S T I M A T I N G W E A N I N G T R A I T S I N C A T T L E i 3 3

T A B L E 1 . A N A L Y S I S O F V A R I A N C E ] ?O R L I N E A R R E G R E S S I O N O F

W E A N I N G W E I G H T O N D A Y S O F A G E ~

A n g u s H e r e f o r d

S o u r c e d . f . M S f d . f . M S f

L i n e a r r e g r e s s i o n 1 7 7 3 6 2 7 6 . 0 1 8 6 1 . 8 * * 1 2 9 8 2 5 7 2 . 0 4 8 0 . 5 * *

D e v i a t i o n s f r o m

l i n e a r r e g r e s s i o n 1 2 8 4 1 5 5 . 3 1 . 3 1 2 4 6 2 0 7 . 3 1 . 2

E r r o r 3 2 7 9 3 1 6 2 . 8 9 1 7 32 5 1 1 6 . 2 . .

a I nc ludes 427 r ecords w hich were d i s carded in the l a t e r ana lys es fo r l ack o f age-of -dam in fo rmat ion .

~ p ~ . 0 1 .

G e n e r a l i n f o r m a t i o n r e l a t i n g t o t h e d a t a i s

s u m m ar i zed i n t ab l e 2 .

Method o f Analys i s

E a c h A D G a n d T S

r eco r d w as c l a ss i fi ed b y b r eed , s ex , ag e o f d am ,

y e a r , s i re , h e r d , c r e e p - f e e d s t a t u s a n d m o n t h

o f b i r t h . S e p a r a t e a n a l y s e s w e r e c a r r i e d o u t

f o r t h e t w o b r e e d s . M e a n v a l u e s f o r b o t h

t r a i t s v a r i e d l i tt l e w i t h m o n t h o f b i r t h , a n d

th i s c l as s i f i ca t ion was ignored . S i r es were

n e s t e d w i t h i n h e r d s a n d h e r d s w i t h i n c r e e p -

f eed i n g c l a s s e s . C l a s s i f i c a t i o n b y d am s w as

n o t c o n s i d e r e d , a n d t h e d a m c o n t r i b u t i o n t o

v a r i a t i o n w a s t a k e n t o b e a r a n d o m v a r i a b l e .

T h e f o l l o w i n g m o d e l w a s c o n s t r u c t e d f r o m

the f ive c l as s i f i ca t ions , s ex , age of dam, year ,

s i r e , h e r d , an d t h e i r i n t e r ac t i o n s , f o r p u r p o s e s

o f l o ca t i n g an d t e s t i n g t h e p r i n c i p a l s o u r ce s

o f v a r i a t i o n :

Xijk lm q=/~ + SI- -~Aj+Yk-~- SAIj-~-S Y l k + P l m

- ~ - e i j k l m q

w h e r e

X ijk lm q i s t h e s i n g l e o b s e r v ed A D G o r T S

i s t h e p o p u l a t i o n m e a n

Si i s the e f f ec t o f the

i th

sex

A j i s t h e e f f ec t o f t h e j t h ag e o f d am

Yk i s the e f f ec t o f the k t h y e a r

P lm i s the e f f ec t o f the

l m t h

s i r e - h e r d

c las s

eijklmq iS a r an do m e rro r specif ic to this

o b s e r v a t i o n .

T h e r e w e r e t h r ee s ex es : b u l l , h e i f e r an d s t e e r .

A g e o f d am w as g r o u p ed i n t o s ev en c l a s s e s

as fo l lows : 2 , 3 , 4 , 5 , 6 , 7 to 10 and over 10

y e a r s o f a g e . T h e s e g r o u p i n g s w e r e s e t u p

f r o m t h e o b s e r v e d d i s t r i b u t i o n o f t h e m e a n

T A B L E 2 . M E A N S A N D S I R E A N D H E R D

N U M B E R S A N D N U M B E R O F C A L V E S

F O R E A C H B R E E D

N 0 . N o . N o . M e a n M e a n M e a n a g e

of o f o f AD G, type o f ca l f

B reed ca lves herds s i r es l b . /d ay s corea days

Angus 3190 39 121 1 . 829 11 . 626 195 . 86

Hereford 1648 16 55 1 . 812 11 . 534 199 . 37

a Faney--[ -~-17, F an cy m l6 , Fancy--~---15, etc.

A D G f o r d i f f e r e n t a g e s o f t h e d a m f r o m 2

t o 2 0 y ea r s .

V a r i o u s a p p r o x i m a t e t e s t s o f t w o - a n d

t h r e e - w a y i n t e r a c t i o n s h a v e b e e n p r o p o s e d

( S n ed eco r an d C o x , 1 9 3 5 ; S w i g e r , 1 9 6 1 ) . A s

a p r e l i m i n a r y s t e p , t h e t w o - a n d t h r e e - w a y

i n t e r a c t i o n s a m o n g t h e s e x , a g e o f d a m a n d

y e a r c l a s s e s w e r e p l o t t e d a n d e x a m i n e d . T h e y

i n d i ca t e d n o l a r g e i n t e r ac t i o n e f f ec t s . A n a n -

a l y s i s o f v a r i a n c e w a s t h e n c o m p u t e d f o r t h e

m o d e l g i v e n . T h e n o n o r t h o g o n a l n a t u r e o f

t h e d a t a r e q u i r e d t h e 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 , w h i c h a m o u n t e d t o a s e t o f

1 9 9 eq u a t i o n s i n t h e A n g u s b r eed . T h e s i z e o f

t h e co m p u t e r , t h e r e f o r e , s e t a l i m i t t o t h e s i z e

o f t h e m o d e l w h i c h c o u l d b e d e a l t w it h . T h e s e

e q u a t i o n s w e r e s o l v e d b y p a r t i t i o n i n g a n d a b -

s o r p t i o n . A n a l y s i s o f v a r i a n c e f o r b o t h b r e e d s

f o r A D G i s g i v en i n t ab l e 3 .

A l l f o u r c l a s s e s o f m a i n e f f ec t s w e r e h i g h l y

s i g n i f i c an t s o u r ce s o f v a r i a t i o n . T h e s ex b y

a g e - o f - d a m i n t e r a c t i o n w a s n o n s i g n i f i c a n t ,

a n d t h e s e x b y y e a r i n t e r a c t i o n b o r d e r e d o n

s i g n i fi c an ce a t t h e 5 % l ev e l . B o t h o f t h e s e

i n t e r a c t i o n c l a s s e s w e r e t h e r e f o r e d r o p p e d

f r o m t h e m o d e l . T h e r e m a i n d e r s u m o f

s q u a r e s , w h i ch w as o b t a i n ed a s a d i f f e r en ce

b e t w e e n t h e s u m o f sq u a r e s d u e t o t h e u l t i m a t e

s e x b y a g e - o f - d a m b y y e a r b y h e r d - s i r e s u b -

c l a s s e s an d t h a t d u e t o t h e f u l l m o d e l , w as

u s ed t o t e s t a l l i n t e r ac t i o n s n o t s p ec i f i ed i n

t h e m o d e l . T h i s p r o v e d s i g n i f i c a n t , w h i c h i s

n o t s u r p r i s i n g , c o n s i d e r i n g t h e n u m b e r o f

d e g r e e s o f f r e e d o m i n v o l v e d . H o w e v e r , t h e

s m a l l s iz e o f t h e r e m a i n d e r m e a n s q u a r e s

s u g g e s t e d t h a t t h e m o d e l w a s a r e a s o n a b l e

o n e , a n d t h e a n a l y s i s w a s p u r s u e d w i t h t h e

m o d e l g i v en , w i t h t h e i n t e r ac t i o n c l a s s e s o m i t -

t ed an d t h e h e r d - s i r e c l a s s i f i c a t i o n b r o k en

d o w n i n t o h e r d s a n d s i re s - w i th i n - h er d s .

T h e m e t h o d o f a n a ly s i s u s e d w a s b a s e d o n

M e t h o d I I o f H e n d e r s o n ( 1 9 5 3 ) . T h i s is a

t w o - s t a g e p r o c e d u r e f o r t h e e s t i m a t i o n o f

v a r i a n c e c o m p o n e n t s i n m i x e d m o d e l s i t u a -

t i o n s , i n w h i ch t h e f i r s t s t ag e i s t h e l e a s t



4/7

184

C U N N I N G H A M A N D H E N D E R S O N

T A B L E 3 . A N A L Y S I S O F V A R I A N C E F O R A V E R A G E D A I L Y G A I N

A n g u s

Sum of

Mean

S o u r c e d . f . s q u a r e s s q u a r e

H e r e f o r d

S u m o f M e a n

d . f. s q u a r e s s q u a r e

T o t a l 3 1 9 0 1 0 9 4 6 . 5 3

S e x 2 2 2 . 9 7 1 1 . 4 8 *

A g e o f d a m 6 1 2 . 6 0 2 . 1 0 *

Y e a r 1 1 1 . 8 7 0 . 1 7 *

S e x x a g e o f d a m 1 2 0 . 6 7 0 . 0 5

S e x x y e a r 2 2 1 . 6 0 0 . 0 7 *

H e r d - s i r e 1 20 8 9 . 3 3 0 . 7 4 * *

F u l l m o d e l 1 7 4 1 0 8 0 7 . 9 4 . .

U l t i m a t e s u b c l a s s e s 1 6 05 1 0 8 8 2 . 5 2

R e m a i n d e r 1 4 31 7 4 . 5 8 0 . ' 0 5 *

E c r o r 1 58 5 6 4 . 0 0 0 . 0 4

1 6 4 8 5 6 0 5 . 9 7

2 1 1 . 5 7 5 . 7 ; * *

6 4 . 8 7 0 . 8 1 *

1 1 4 . 5 3 0 . 4 1 *

1 2 0 . 6 9 0 . 0 5

2 2 2 . 6 3 0 . 1 1

5 4 5 9 . 5 0 1 . 1 0 *

1 0 8 5 5 0 0 . 7 8 . .

6 0 7 5 5 3 8 . 6 8

4 9 9 3 7 . 8 9 0 . 0 7 *

1 0 41 6 7 . 2 8 0 . 0 6

P < . 0 5 .

P < . O I .

s q u a r e s e s t i m a t i o n o f t h e f i x ed e f f e c ts a n d t h e

c o r r e c t io n o f t h e d a t a b y s u b t r a c t i n g f r o m

e a c h o b s e r v a t i o n a n a p p r o p r i a t e l i n e a r f u n c -

t i o n o f t h e s e e s t i m a t e s .

U n d e r c e r t a i n c o n d i t i o n s t h e l e a s t s q u a r e s

e s t i m a t e s o f t h e f i x e d e f fe c t s c a n b e i m p r o v e d .

T h i s p o s s i b i l i t y a r i s e s w h e n t h e f i x e d c l a s s e s

a r e u n e q u a l l y s p r e a d o v e r t h e r a n d o m c l a s s e s ,

s i n c e t h e d i f f e r e n c e b e t w e e n t h e c l a s s t o t a l s

f o r t h e l a t t e r w i l l t h e n c o n t a i n i n f o r m a t i o n

o n t h e f o r m e r . I n t h e p r e s e n t c a s e , f o r i n s t a n c e ,

t h e d i f f e r e n t y e a r s a r e u n e q u a l l y r e p r e s e n t e d

i n a l l h e r d s , a n d , t h e r e f o r e , t h e h e r d d i f f e r e n c e s

h a v e p a r t i a ll y c o n f o u n d e d w i th t h e m i n f o r m a -

t i o n o n t h e y e a r e f f e c t s . T h i s i n f o r m a t i o n c a n

b e re c o v e r e d a n d c o m b i n e d w i t h t h e r e g u l a r

l e a s t s q u a r e s e s t i m a t e s i n a j o i n t w e i g h t e d

s e t o f e s t i m a t e s , w h i c h w i ll b e a n i m p r o v e m e n t

o n t h o s e d e r i v e d b y r e g u l a r l e a s t s q u a r e s

m e t h o d s , p r o v i d e d t h a t t h e w e i g h t s a r e k n o w n

o r c a n b e e s t i m a t e d w i t h s u f f i c i e n t a c c u r a c y

a n d p r e c is i o n . T h i s r e c o v e r y i s r e la t i v e l y

s i m p l e in b a l a n c e d d a t a . I n u n b a l a n c e d c a s es ,

s u c h a s t h e p r e s e n t o n e , i t i s u s u a l l y i m p o s -

s i b le if c o n v e n t i o n a l a n a l y s e s a r e u s e d . T h i s

d i f fi c u lt y c a n b e o v e r c o m e b y t h e a p p l i c a t io n

o f a c o m p u t a t i o n a l p r o c e d u r e f o r t h e d e r i v a -

t io n o f m a x i m u m l ik e l ih o o d e s t i m a t e s , w h i c h

a p p l i e s i n m i x e d m o d e l s i t u a t i o n s u n d e r v e r y

g e n e r a l c o n d i t i o n s H e n d e r s o n , 1 9 5 2 , 1 9 6 3 ;

H e n d e r s o n

e t a l .

1 9 5 9 ) . T h e s e e s t i m a t e s a r e ,

i n f a c t , a u t o m a t i c a l l y w e i g h t e d l e a s t s q u a r e s

e s t i m a t e s . T h e w e i g h t s u s e d a r e v a r i a n c e

c o m p o n e n t s .

F r o m a c o m b i n a t i o n o f t h e s e t e ch n i q u e s

a n i t e r a t i v e p r o c e d u r e w a s d e v e l o p e d in w h i c h

w e i g h t e d l e a s t s q u a r e s e s t i m a t i o n o f t h e f i x e d

e f f e c ts i n t h e m o d e l a l t e r n a t e s w i t h v a r i a n c e

c o m p o n e n t e s t i m a t i o n . T h i s p r o c e d u r e i s d e -

s c ri b e d i n d e ta il b y C u n n i n g h a m 1 9 6 2 ) .

F o r t h e e s t i m a t i o n o f c o m p o n e n t s o f c o v a r i -

a n c e b e t w e e n t h e t r a i t s A D G a n d T S , t h e

r e g u l a r c o v a r i a n c e a n a l o g u e o f M e t h o d I I

H e n d e r s o n , 1 9 5 3 ) w a s u s e d . E s t i m a t e s o f

t h e h e r i t a b i l i t y o f e a c h t r a i t w e r e c o n s t r u c t e d

u s i n g t h e v a r i a n c e c o m p o n e n t e s t i m a t e s , a n d

t h e g e n e t i c , p h e n o t y p i c a n d 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 b e t w e e n t h e t w o t r a i t s w e r e c o m -

p u t e d f r o m t h e e s t im a t e s o f th e v a r i a n c e a n d

c o v a r i a n c e c o m p o n e n t s .

R e s u l t s a n d i s c u s s i o n

F i x e d E f f e c t s . T h e e n v i r o n m e n t a l e f f e c t s f o r

w h i c h e s t i m a t e s w e r e o b t a i n e d w e r e t h e t h r e e

s e x es , s e v e n ag e s o f d a m a n d 1 2 y e a r s . I n f a c t ,

t h e s e p a r a m e t e r s w e r e n o t i n d i v i d u a l l y e s t i -

m a b l e , a n d t h e q u a n t i t i e s e s t i m a t e d w e r e t h e

d i f f e r e n c e s b e t w e e n p a r a m e t e r s w i t h i n e a c h

c l a s s i f i c a t i o n . T h e s e q u a n t i t i e s w e r e e s t i m a t e d

b y r e g u l a r l e a s t s q u a r e s , w e i g h t e d l e a s t

s q u a r e s , a n d b y t h e i t e r a t i v e e s t i m a t i o n p r o c -

e s s . T h e i t e r a t i v e p r o c e d u r e w a s c a r r i e d

t h r o u g h f o u r i t e r a t i o n s i n t h e c a s e o f t h e

A n g u s d a t a , a n d s e v e n in t h e H e r e f o r d d a t a ,

a t w h i c h p o i n t t h e e s t im a t e s a p p e a r e d t o h a v e

s t a b i l i z e d i n e a c h c a s e .

T h e r e l a t i v e e f f e c t i v e n e s s o f t h e d i f f e r e n t

s e t s o f e s t i m a t e s a s c o r r e c t i o n f a c t o r s w a s

m e a s u r e d b y u s i n g t h e m t o a d j u s t t h e d a t a

a n d t h e n c o m p a r i n g th e e q u a l i t y o f m e a n s

w i t h i n s ex , a g e o f d a m a n d y e a r c l as s e s. T h e r e

w a s l i t t l e d i f f e r e n c e b e t w e e n t h e e s t i m a t e s o b -

t a i n e d b y t h e w e i g h t e d l e a s t s q u a r e s a n d i t e r a -

t i v e p r o c e d u r e s a s m e a s u r e d b y t h e d i f f e r e n c e s

b e t w e e n t h e m e a n s w i t h i n c l a s s e s . T h e r e g u l a r



5/7

E S T I M A T I N G W E A N I N G T R A I T S I N C A T T L E

1 8 5

l e a s t s q u a r e s e s t i m a t e s w e r e l e s s e f f e c t i v e a s

c o r r e c t i o n f a c t o r s . O f t h e t h r e e m e t h o d s o f

e s t i m a t i o n , t h e i t e r a ti v e p r o c e d u r e a p p e a r s

t o g i v e t h e b e s t e s t i m a t e s f o r u s e a s c o r r e c t i o n

f a c t o r s . T h e r e w a s e v i d e n c e t h a t t h e v a r i a n c e

o f t h e i t e r a t i v e e s t i m a t e s w a s l e ss t h a n t h a t

f o r t h e r e g u l a r a n d w e i g h t e d l e a s t s q u a r e s

e s t i m a t e s .

T h e e s t i m a t e s o b t a i n e d b y t h e i te r a t i v e p r o -

c e d u r e a r e p r e s e n t e d i n t a b l e 4 . T h e s e x ef fe c ts

a r e g i v e n a s d e v i a t i o n s f r o m t h e s t e e r e f f e c t ,

t h e a g e - o f - d a m e f f e ct s a s d e v i a t i o n s f r o m t h e

7 - t o 1 0 - y e a r a g e g r o u p e f f e c t a n d t h e y e a r

e f f e c t s a s d e v i a t i o n s f r o m t h e 1 9 5 5 e f f e ct .

T h u s , t h e v a l u e s f o r se x a n d a g e o f d a m m a y

b e u s e d , w i t h s i g n s r e v e r s e d , a s c o r r e c t i o n

f a c t o r s to a d j u s t A D G a n d T S v a l u e s to a

s t a n d a r d v a l u e r ep r e s e n t e d b y t h e c a l f f r o m

a c o w a g e d 7 t o 1 0 y e a r s .

T h e p a t t e r n o f t h es e e s t i m a t e s c o n f o r m s

w i t h t h a t t o b e f o u n d i n t h e e x t e n s i v e l i t e ra -

t u r e . T h e p a r a l l e l a n a l y s e s fo r th e t w o

b r e e d s a g r e e w e l l i n t h e s e x a n d a g e - o f - d a m

e s t i m a t e s . B u l l c a l v e s g r o w f a s t e r t h a n s t e e r s ,

a n d s t e e r s fa s t e r t h a n h e i f e r s . B u l l c a l v e s a l s o

g r a d e b e t t e r t h a n s t e e r s o r h e if e r s , b u t h e i f e r s

g r a d e c o n s i d e r a b l y b e t t e r t h a n s t ee r s. T h e o b -

T A B L E 4 . E S T I M A T E S O F E N V I R O N M E N T A L

P A R A M E T E R S O B T A I N E D B Y I T E R A T I V E

E S T I M A T I O N P R O C E D U R E

Angus Here ford

I te m A D G T S A D G T S

ex

Bull 0.108 0. 634 0.113 0. 499

He ifer - - . 142 0.532 -- . 107 0.307

Steer 0.000 0.000 0. 000 0. 000

Age of dam

2 - - . 2 6 1 - - . 4 9 7 - - . 2 6 4 - - . 4 7 4

3 - - . 1 5 9 - - . 0 6 3 - - . 1 9 2 - - . 2 8 8

4 - - .0 69 0 .106 - - .0 81 0 .146

5 - - . 03 6 0 .056 - - . 027 0 .212

6 - - . 025 0 .059 - - . 01 0 0 . . 127

7-10 0 .000 0 .000 0 .000 0 .000

~ 1 0 - - . 0 2 9 - - . 5 6 5 0 .0 22 - - . 0 9 0

Y e a r

1949 0.085 1.350 0.04 6 0.491

1950 0.067 0.587 0.02 0 0.391

1951 0.082 0.674 0.003 0.91 0

1952 0.055 0.271 0.02 4 0.254

1953 0.005 0.408 -- .0 09 0.556

1954 0.013 -- .2 05 0.113 0.673

1955 0 .000 0 .000 0 .000 0 .000

1956 - - . 01 0 - - . 0 30 0 .031 0 . 728

1 95 7 - - . 0 8 8 - - . 2 4 4 - - . 2 7 0 - - . 6 2 8

1958 - - . 07 8 - - . 291 - - . 082 0 . 360

1959 - - . 051 - - . 40 8 - - . 15 7 - - 1 . 270

1 96 0 - - . 0 0 1 - - . 1 9 2 - - . 0 5 7 - - . 4 4 5

s e r v e d d i f f e re n c e s b e t w e e n b u l l s a n d s t e e r s a r e

i n p a r t a t t r i b u t a b l e t o t h e e f f ec t s o f s e l e c t io n ,

i n t h a t b r e e d e r s t e n d t o s a v e t h e h e a v i e r ,

h i g h e r g r a d i n g c a l v es a s b u l ls a n d t o c a s t r a t e

t h e r e m a i n d e r . T h e w e i g h t e d m e a n o f t h e m a l e

c a l v es f o r A D G w a s 0 .1 5 8 A n g u s ) a n d 0 . 16 0

H e r e f o r d ) h i g h e r t h a n t h e m e a n f o r f e m a l e s ,

a n d fo r T S w a s 0 . 4 5 4 A n g u s ) a n d 0. 1 53

H e r e f o r d ) b e lo w th e f em a l e m e a n . A D G i m -

p r o v e s w i t h a g e o f d a m i n a c u r v i l i n e a r f a s h i o n

t o a m a x i m u m a t 7 to 1 0 y e a r s o r o v e r . T h e

s a m e p a t t e r n h o l d s t r u e f o r T S , e x c e p t t h a t

t h e v a lu e s t e n d t o re a c h a m a x i m u m a t e a r l i e r

a g e s 4 t o 5 y e a r s ) a n d t o d e c l i n e a f t e r t h a t

a g e . T h e e f fe c t o f s e l e c t i o n a m o n g c o w s w a s

i g n o r e d in t h e c o m p u t a t i o n o f th e s e a g e -o f -

d a m e ff ec ts , w h i c h m a y b e b i a s e d u p w a r d a s

a r e s u l t L u s h a n d S h r o d e , 1 9 5 0 ) . T h e s i g n i fi -

c a n c e o f t h e s e p o s s i b l e b i a s e s i n b e e f c a t t l e

t r a i t s i s d i s c u s s ed b y K o c h a n d C l a r k 1 9 5 5 a ) .

A s l i g h t b r e e d d i f f er e n c e d o e s s h o w u p i n

t h e e s t i m a t e s o f t h e y e a r e f f e c t s . T h e A n g u s

d a t a a p p e a r t o b e le s s v a r i a b l e t h a n t h e

H e r e f o r d . T h i s i s p r o b a b l y a r e f l ec t io n o f

d i ff e re n c es i n t h e a v e r a g e h e r d e n v i r o n m e n t

f o r th e t w o b r e e d s . T h e d e c l in e in A D G o v e r

t h e p e r i o d s t u d i e d , w h i c h i s i n d i c a t e d b y t h e

e s t i m a t e s o f t h e y e a r e f f e c ts , m a y b e d u e t o

t h e g r a d u a l i n c l u s i o n i n t h e p r o g r a m i n t h e

l a t e r y e a r s o f h e r d s w i t h p o o r e r e n v i r o n m e n t

o r g e n e t i c m a t e r i a l .

Components o] Variance and Covariance

T h e e s t i m a t i o n o f c o m p o n e n t s o f v a r i a n c e f o r

b o t h t r a i t s w a s c a r r i e d o u t o n a w i t h i n - b r e e d

b a s i s, u s i n g m o d i f i c a t i o n s o f M e t h o d I I H e n -

d e r s o n , 1 9 5 3 ) . T h e d a t a w e r e fi r st c o r r e c t e d

f o r s e x , a g e - o f - d a m a n d y e a r e f f e c t s . M e a n

s q u a r e s w e r e th e n c o m p u t e d f o r h e r d s , s i re s ,

h e r d s b y y e a r s a n d e r r o r . F i n a l l y , t h e s e m e a n

s q u a r e s w e r e e q u a t e d t o t h e i r e x p e c t e d v a l u e s

a n d t h e r e s u l t i n g e q u a t i o n s w e r e s o l v e d f o r

t h e r e q u i r e d v a r ia n c e c o m p o n e n t s . T h e p r o -

p o r t i o n o f t h e v a r i a t i o n i n th e a d j u s t e d r e c o r d s

w h i c h w a s d u e t o e a c h o f t h e s e s o u r c e s i s i n -

d i c a t e d i n ta b l e 5 . T h e b r e a k d o w n o f t h e v a r i -

a t i o n i s s i m i l a r fo r b o t h t r a i t s a n d b o t h b r e e d s .

T h e f a c t t h a t a g r e a t e r p r o p o r t i o n o f t h e

v a r i a n c e f o r T S i s i n r e s i d u a l a n d l e s s i n h e r d s

m a y r e fl e ct th e s u b j e c t i v e n a t u r e o f t h e t y p e

s c o r in g p r o c e d u r e , o r p o s s i b l y t h a t h e r d e n -

v i r o n m e n t h a s a g r e a t e r e ff ec t o n A D G t h a n

o n T S .

T h e a c t u a l e s t i m a t e s o f t h e v a r i a n c e a n d

c o v a r i a n c e C o m p o n e n t s n e e d e d i n t h e c o m p u -

t a t i o n o f h e r i t a b i l i t i e s a n d c o r r e l a ti o n s a r e



6/7

186

TABLE 5. PERCENT OF VARIATION IN SEX,

AGE OF DAM AND YEAR ADJUSTED

RECORDS WHICH IS DUE TO

VARIOUS SOURCES

Angus

Source ADG TS

CUNNINGHAM AND HENDERSON

herd heritability requires, in addition, the as-

sumption that all herd-to-herd variation is

nongenetic. The values for both traits in each

breed are given in table 7.

Hereford These values fall within the range of those

ADG TS repor ted elsewhere (Warwick, 1958), but

are considerably larger than most of the esti-

15 3 mates in the literature, which indicate a value

10 11 close to 0.3 for AD G and 0.2 for TS. It seems

3 5

72 81 probable tha t the present values are overesti-

mates resulting from biases in the variance

component estimates. This is borne out by

the values of 0.48 and 0.28 obtained for the

repeatability of these traits in the same data

(Cunningham and Henderson, 1965).

Several factors may contribute to the infla-

tion of the heritability estimates. The denom-

inator may be reduced due to underestimation

of ~r2e, resulting from correlated errors. Since

a2e is the within-sire-herd-subclass variance,

TABLE 7. ESTIMATES. OF THE HERITABILITY

OF ADG AND TS

Herds 18 9

Sires 11 11

Herds x years 9 6

Residual 62 74

given in table 6. The necessary components

a r e

a2 n= her d component of variance

~2s/~i=sire-within-herd component of vari-

ance

a2e=-error component of variance

(ri2s/R= sire-within-herd component of co-

variance

alze=err or component of covariance

The values obtained separately for the two

breeds show good agreement except that the

herd component of variance is considerably

larger for the Angus than for the Hereford

data. The greater inherent variability of the

Hereford records is reflected in the larger error

components of variance and covariance for

that breed.

Heri tab i l i t i e s The heritability of each trait

was computed from the variance component

estimates on both an intra- and inter-herd

basis, using the formulas

4 0 " 2 8 / H 4 O ' 2 S / H

h 2 i n t r a - a n d h 2 1 n t e r ~

~ - b ~ ' ~ 9 ~ - t- ~

h e s e formulas require the following as-

sumptions: (1) that identifiable environmental

variation has been corrected for, (2) that

e p i s t a t i c gene action may be neglected, (3)

that there is random mating with respect to

the genes involved in this trait, (4) that the

frequencies of these g e n e s a r e stable, and

(5) that the effects of these genes, as devia-

tions from the mean, do not change from one

generation to the next. The formula for inter-

TABLE 6. ESTIMATES OF COMPONENTS OF

VARIANCE AND COVARIANCE FOR

ADG AND TS

B r e e d T r a i t ~ 2 H a ~ s / H ~ r2 e a 1 2 S / H ~ 1 2 e

A D G 0 . 0 1 2 0 0 . 0 0 7 0 0 . 0 4 0 4

A n g u s T S 0 . 2 9 4 9 0 . 3 6 9 5 2 . 3 9 6 4 0 . 0 4 6 7 0 . 0 6 2 4

A D G 0 . 0 1 3 0 0 . 0 0 9 2 0 . 0 6 4 6

H e r e f o r d T S 0 0 9 1 8 0 . 3 5 2 7 2 . 5 5 7 1 0 . 0 3 0 4 0 ' . 1 4 70

Heritability estimate

Breed Trait Intra-herd Inter-herd

Angus ADG 0. 590 0. 471

TS 0. 534 0.483

Hereford 1-)G 0.400 0.425

TS 0.485 0.410

the fact that observations within such a sub-

class may be repeated records on the same

dam, or records on closely related dams would

reduce the estimate. It could also be reduced,

and the estimate of sire variance simultan-

eously increased by any differential or assorta-

tive mating, i.e., by mating the better cows

with one sire, the poorer with another. Though

the records were corrected for age of dam,

differential mating of dam might have a similar

effect. Furthermore, the fact that sires were

partially compounded with years would have

an inflationary effect on the sire variance if

an interaction of sires with years existed and

was ignored in the analysis. All these factors

tend to bias the ratio

O- 2 ~ ,TT

O ' 2 S / H + 0 ~ e

upward. This ratio is multiplied by four to

give heritability, and hence even a moderate

bias in the variance components would result

in a large bias in the heritability.

An alternative interpretation of these high

heritability estimates is that there exists con-



7/7

E ST I MAT I NG W E ANI N G T R AI T S I N C AT T L E

187

TABLE 8. ESTIMATES OF CORRELATIONS

BETWEEN ADG AND TS

Correlation Angus Hereford

Genetic 0.61 0.36

Phenotypic 0.28 0.36

Environmental -- . 95 0.37

siderably more additive genetic variation for

these traits in New York commercial beef

herds. There may be some truth in this, be-

cause all the reports from elsewhere are based

on few and large herds, often at experiment

stations, in which selection may have reduced

the genetic variability.

Correlations. The genetic, phenotypic and

enviro nmenta l correlations between the two

traits were computed from the variance and

covariance component estimates of table 7.

The values obtained are given in table 8.

The estimates agree with some of those

reported in other studies Koch and Clark,

1955b; Lehmann e t a l . 1961). However,

the large discrepancy between the values for

the two breeds reduces the value of these

estimates. Furthermore the sampling variance

of the estimates is probably quite large, and

the possible biases affecting the heritability

estimates ma y also influence these correlations.

There appears to be a positive and fairly large

genetic relationship between these two traits.

Su m m a r y

The genetic and phenotypic parameters of

average daily gain from birth to weaning

ADG ) a nd type score at weaning TS) have

been evaluated from 4,838 records on beef

cattle in New York. The records were drawn

from 39 herds with 121 sires of the Angus

breed and from 16 herds with 55 sires of

the Hereford breed for the years 1949 to 1960

inclusive.

The data were tested for the presence of

interaction effects. Estimates were obtained

by an iterative procedure of the effects of sex,

age-of-dam and year differences on the two

traits. The records were adjusted for these

fixed effects and components of variance and

covariance were estimated for herds, sires,

herds by years, and error. These components

were used to compute estimates of the herit-

ability of each trait and of the genetic, pheno-

typic and enviro nmental correlations between

them.

L i t e r a t u r e C i t e d

Cunningham, E. P. 1962. Estimation of genetic and

phenotypic parameters in a beef cattle population.

Ph.D. Thesis. Cornell University, Ithaca, New

York.

Cunningham, E. P. and C. R. Henderson. 1965.

Repeatability of weaning traits in beef cattle. J.

Animal Sci. 24:188.

Henderson, C. R. 1952. Specific and general combin-

ing ability. In Heterosis J. W. Gowen, Editor).

Iowa State College Press, Ames, Iowa.

Henderson, C. R. 1953. Estimation of variance and

covariance components. Biometrics 9:226.

Henderson, C. R. 1963. Selection index and expected

genetic advance. Statistical genetics and plant

breeding. National Academy of Sciences--National

Research Council publication No. 982.

Henderson, C. R., O. Kempthorne, S. R. Searle and

C. M. von Krosigk. 1959. The estimation of envi-

ronmental and genetic trends from records subject

to culling. Biometrics 15:192.

Koch, R. M. and R. T. Clark. 1955a. Influence of

sex, season of birth and age of dam on economic

traits in range beef cattle. J. Animal Sci. 14:386.

Koch, R. M. and R. T. Clark. 1955b. Genetic and

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Cunningham e Henderson 1965.pdf