Differences in milk production and in age at first calving among Indian and crossbred dairy cattle in India

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DIFESBEaCSS IE MDZ PBOBtJCSIQa iED JS MSS AS ?IHS3? CiLTISB m m moms

mb

ceossbeed daiex castes m

jsbia

Uar

Oa&h Behari Tandon

A Dissertation Submitted to the xtiTtiLuxsi.vc ^ctuLui-Ugjr au ircuTo xcu. .uuxixxxaiouu vj.

She Sequirements for the Degree of BOOTOS 0]? PHILOS0?HT Major Subjects: Animal Breeding Genetics

Approved:

•(a J.

Giiarge of Major Work k / . < £ C alvings 1 0 .3 9 .1

8 .9

8 .2

7 .5 7 .2

7 .0

1 .8

7 .2

7 .0 9 .1

1 0 .8

Under th e n u l l h y p o th e s is t h a t th e m onthly d i s t r i b u t i o n o f th e c a lv in g s i s uniform a

was computed.

S ig n if ic a n t ly more c a lv in g s o c c u rre d

betw een November and F e b ru a ry ( th e w in te r months) th a n betw een May and September ( th e summer m o n th s).

Mo s i g n i f i c a n t d if f e r e n c e s among

th e months o f c a lv in g were found i n m ilk y i e l d p e r l a c t a t i o n , i n c a lv in g i n t e r v a l o r i n d ry p e r io d . More p u re b re d S ah iw als and S a h iw a l-H o lste in c ro s s e s c a lv e d betw een Ja n u a ry and A p r il th a n betw een J u ly and Septem ber a c c o rd in g to Sikka (1931) .

2he l a c t a t i o n y i e l d s w ere more v a r ia b le fo r th e cows c a lv in g

betw een Septem ber and November th a n f o r th o se c a lv in g i n any o th e r m onth.

He a ls o found e r r a t i c v a r i a t io n s i n m ilk y i e l d from one c a lv in g

month to a n o th e r . s ig n if ic a n t.

£he l a t t e r d if f e r e n c e s w ere n o t s t a t i s t i c a l l y

On t h i s b a s i s Sikka concluded th a t no la r g e e f f e c t o f

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-19season. on m ilk y i e l d e x is te d .

The d iff e r e n c e s "between th e means o f

th e d i f f e r e n t m onths were e x p la in e d by th e u n eq u al m onthly d i s t r i b u ­ t i o n o f cows o f d i f f e r e n t l e v e l s o f p ro d u c tio n . Age when th e r e c o r d s were made

A ccording to Gowen (192*0 and many o th e rs th e m ilk y i e l d i n E uropean cows r i s e s a t an ev e r d ecre a sin g r a t e a s th e age o f th e cow ad v an ces, u n t i l th e age o f maximum p r o d u c tiv ity i s re a c h e d . i t d e c lin e s a t a n e v e r in c r e a s in g r a t e a s age in c r e a s e s .

T h e re a fte r

T his

phenomenon can be c o n s id e re d a s an ex p ressio n o f grow th and sen escen ce. Jo sep h and Dave (1931^ p re s e n te d th e fo llo w in g ev idence re g a rd in g th e e f f e c t o f age on th e m ilk p ro d u c tio n o f S a h iv a l cows: L a c ta tio n number 1 2 3 b 5 6 7 8

Average y i e l d 2975 lt> s. 3^13 * *1018 “ k2J5 « H3S6 " 3851 " **076 H *0.36 w

P e rc e n ta g e o f h ig h e s t l a c t a t i o n y i e ld 68 7S 91 97 100 88 93 9k

M ilk y i e l d in c r e a s e d about fo rty - s e v e n p e r c e n t from f i r s t c a lv in g to m a tu r ity a t th e f i f t h l a c t a t i o n .

A fte r m a tu rity o n ly a s lig h t

d e c lin e was n o tic e d . S ikka (1931) summarized th e re c o rd s o f Sahiw al cows from s e v e ra l h e rd s a s fo llow s*

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-20L a c ta tio n number

Kean y i e l d (from th e raw lumped l a c t a t i o n s * )

1 2 3 b 5 6 7 8 S 10 11

3763 l b s U033 ■ h0 9 8 * U216 " H0 6 5 " H1 2 H » U331 " U1 0 5 ■ 3755 8 U6 b7 "

Even though th e f i r s t p e a k was rea c h e d a t th e f o u r t h l a c t a t i o n , an I r r e g u l a r i t y i s e v id e n t i n su b seq u en t l a c t a t i o n s .

S e le c tio n may have

been r e s p o n s ib le f o r th e h ig h re c o rd s o f t h e l a s t two l a c t a t i o n s . T hese, o f c o u rse , w ere made by o nly th o s e cows w hich rem ained i n th e h e rd a f t e r th e p o o r ones w ere c u lle d .

Chance and sm all number o f

r e c o r d s , i n a d d itio n to s e l e c t io n , a r e o th e r f a c t o r s l i k e l y to have b e e n re s p o n s ib le f o r t h i s i r r e g u l a r i t y . To r e f i n e h i s e s tim a te s o f th e e f f e c t s o f age on m ilk p ro d u c tio n S ik k a u se d th e "Composite curve m ethod".

T h is method i s becoming

more g e n e r a lly c a lle d now th e " p a ire d l a c t a t i o n m ethod*.

I t c o n s is ts

o f com puting means f o r th e f i r s t and second l a c t a t i o n s o f cows th a t had r e c o rd s i n b o th p e r io d s .

By s e t t i n g th e mean o f th e f i r s t l a c t a ­

t i o n eq u al to 100 a co rresp o n d in g v a lu e f o r th e mean o f th e second l a c t a t i o n i s found.

L e t t h i s be caL led X.

Kean y i e l d s a r e th e n

c a lc u la te d f o r cows t h a t had b o th second an d t h i r d l a c t a t i o n s .

The e f f e c t o f s e le c t io n was n o t c o n s id e re d .

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By

-21s e t t i n g th e mean o f th e second l a c t a t i o n y i e l d s o f th e s e cows equal to X a co rresp o n d in g v alu e f o r th e mean o f t h e i r t h i r d l a c t a t i o n s i s found and so on.

The f ig u r e s f o r th e p u re b re d S ahiw als o b ta in e d

th u s by Sikka a re a s fo llo w s? L a c ta tio n number 1 2 3 4

Com parative y i e l d ( c o r r e c te d f o r s e r v ic e p e r io d ) 100.00 108.SO 109.5S

5

1 1 1 .0 9 1 0 6 .8 9

6 7

103.S 3 102.72

s

9 3 .5 1

9 10

Sk.65 77.86

He f i t t e d a lo g a rith m ic cu rve o f th e form y c a + b x + cx

p

+ d lo g x

w here y was th e com parative y i e l d and x th e number o f th e l a c t a t i o n . On f i t t i n g t h i s smooth curve th e fo llo w in g p e rc e n ta g e y i e l d s were c a lc u la te d : L a c ta tio n number 1 2 3 5 6 7 8 9 10

P e rc e n t y i e l d from th e smoothed curve P u reb red S ahiw als C ro ssb red s 100.88 108.05 IIO .36 1 1 0 . If5 108.65 1 0 5 .2 4 IOO.36 9 4.81 86.50 77.50

9 8 .5 4 106.58 115.95 124.59 131.85 137.42 141.17 143.01 14^5.10 138.68

The maximum y i e l d f o r th e cu rve f o r th e p u re b re d Sahiw als o c c u rre d a t 3 .5 2 l a c t a t i o n s and f o r th e c ro s s b re d s a t 8 .4 3 l a c t a t i o n s .

Sikka

drew th e fo llo w in g c o n c lu sio n s re g a rd in g th e r e l a tio n s h ip betw een age

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. 3. a -JT" ~ 1*« 1 •0 • i •. The above e q u a lity would, th e r e f o r e , he tr u e o n ly when th e a ’ s and th e 3*‘s a r e o rth o g o n a l i . e . when th e r e a r e p r o p o r tio n a te s u b c la ss num bers.

The e x p e c ta tio n o f th e mean sq u are o b ta in e d b y th e method

o f th e l e a s t sq u ares can be shown (even i n d is p r o p o r tio n a te d a ta ) to be a l i n e a r f u n c tio n o f t r u e v a ria n c e s o f th e e f f e c t s o r o f th e v a ria n c e s and th e q u a d ra tic f u n c tio n s o f th e e f f e c t s (Eem pthorne, 1950)*

However,

i n d is p r o p o r tio n a te d a ta , th e mean sq u a re s o b ta in e d by th e s o - c a lle d c o n v e n tio n a l method can be sh o rn to be b ia s e d e s tim a te s o f th e same. Under th e n u l l h y p o th e s is t h a t th e p a ra m e te rs o r th e c o n s ta n ts i n any s e t a re zero,. th e e x p e c ta tio n of th e mean s q u a re s f o r t h a t s e t o b ta in e d by th e method o f th e l e a s t s q u a re s ca n be shown to be th e same a s th e e x p e c ta tio n o f th e mean sq u ares a s s o c ia te d w ith th e a p p ro p ria te e r r o r a g a in s t which th e mean sq u a re s a s s o c ia te d w ith th e s e t un d er c o n s id e ra tio n would be t e s t e d .

The e x p e c ta tio n o f th e mean sq u ares

o b ta in e d f o r th e same s e t by th e s o - c a lle d c o n v e n tio n a l method, how ever, would be d i f f e r e n t from t h e e x p e c ta tio n o f th e a p p r o p ria te e r r o r mean sq u a re s i f th e d a ta a r e d is p r o p o r tio n a te .

I n such d a ta , un d er th e n u l l

h y p o th e sis t h a t th e c o n s ta n ts i n any s e t a r e z e ro , th e sum o f sq u ares a s s o c ia te d w ith th a t s e t and th e sum o f th e sq u a re s a s s o c ia te d w ith th e a p p r o p ria te e r r o r te rm , ijfoen th e two a r e o b ta in e d by th e s o - c a lle d c o n v e n tio n a l method, would n o t be d i s t r i b u t e d in d e p e n d e n tly a s X2

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A stim e s t h e e x p e c ta tio n o f th e a p p r o p ria te e r r o r mean s q u a re .

Hence

u se o f th e 3? t e s t f o r t e s t i n g h y p o th e sis shout th e c o n s ta n ts in th e s e t u n d er c o n s id e ra tio n would he in p ro p e r and th e sta te m e n ts ahout th e t e s t s o f s ig n if ic a n c e would he in a c c u r a te . I t m ight he emphasized here t h a t th e a d d itio n theorem o f th e sum o f th e s q u a re s does not h o ld good i n c a s e s o f d is p r o p o r tio n a te d a ta ; i . e . E (p . a , p) would n o t and should n o t he ex p ected to he eq u al to E (a) . + E(£5) + E(u) 0 . po pa ttp

Here th e s u b s c r ip ts to th e n a re n th e s e s ~

in d ic a te th e s e t s o f th e p aram eters w h ic h were e lim in a te d b e fo re th e re d u c tio n s f o r each s e t o f th e p a ra m e te rs in c lu d e d w ith in th e p a r e n th e s is were o b ta in e d .

But E (p, a , 8) would e q u a l B (a) 4- E(S) + S (p) _ where *“ CO CLfj

th e same system o f n o ta tio n a s used above i s fo llo w e d .

(The d isc re p a n c y

betw een th e two sta te m e n ts i s e a s i l y e x p lic a b le by th e f a c t t h a t S (a ) 4 E (a) a . and R (s) 4 E (s) . (Jbp (J/X Ot shown.

The f i r s t i n e a u a lity has a lr e a d y been

The second can a ls o he shown s i m i l a r l y .

A ll th e s e c o n s id e ra tio n s can be ex ten d ed to case s o f more th a n two s e ts o f p a ra m e te rs . fl S hort Cut Method o f E s tim a tin g S ed u ctio n s 'ilhsn many c o n sta n ts o r p aram eters have to he f i t t e d i t i s convenient to ab so rb o r e lim in a te th e l a r g e s t s e t .

T his tech n iq u e red u ces th e

number o f l e a s t sq u ares e q u atio n s to be s o lv e d .

A f te r ab so rb in g a

s e t thb new ly o b tain e d e q u a tio n s a r e s o lv e d f o r th e rem aining unknowns. The v a lu e s o f th e se unknowns, a f t e r th e y a re found, a re s u b s t itu t e d The s t a t i s t i c a l methods g iv en i n t h i s s e c tio n and th o se g iv e n on p a e H6 a r e w e ll known. They a re in c lu d e d i n t h i s t h e s i s on ly f o r com pleteness o f th e p r e s e n ta tio n .

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in. th e e q u a tio n s o f th e p a ra m e te rs th a t w ere a b so rb ed to o b ta in th e e s tim a te s f o r th e ab so rb ed p a ra m e te rs .

The e s tim a te o f each p a ra m e te r

i s m u l t i p l ie d by th e r ig h th a n d s id e o f th e e q u a tio n w hich was o b ta in e d by p a r t i a l l y d i f f e r e n t i a t i n g th e sum o f th e sq u a re d e r r o r s w ith r e s p e c t to t h i s p a ra m e te r.

A ll such p ro d u c ts a r e summed to g iv e th e r e d a c tio n

i n sum o f th e sq u are s o f th e dependent v a r ia b le due to f i t t i n g th e s e t s o f p a ra m e te rs co n cern ed . In o rd e r to o b ta in th e a d d itio n a l sum o f th e sq u a re s a t t r i b u t a b l e to any one s e t , say ® , th e e q u a tio n s f o r t h a t s e t a r e l e f t o u t and new s o lu tio n s to rem aining unknowns a r e found.

I f th e s e t i n q u e s tio n i s

n o t th e one t h a t was ab so rb e d , th e n th e e q u a tio n s o b ta in e d a f t e r ab so rb in g a r e so lv ed f o r a l l th e unknowns e x c e p t th e a , s.

The v a lu e s

o b ta in e d a r e a g a in s u b s t i t u t e d i n th e e q u a tio n s o f th e absorbed s e t , s o lu tio n s f o r which a r e o b ta in e d .

A new r e d u c tio n i s o b ta in e d a g a in

by m u ltip ly in g th e new s o lu tio n s by th e a p p r o p r ia te rig h th a n d s id e , and summing o v e r a l l th e p r o d u c ts . Thus e a ch tim e a s e t o f p a ra m e te rs i s l e f t o u t, s u b s t i t u t i o n o f th e new s o lu tio n s in th e e q u a tio n s fo r th e ab so rb e d s e t h as to be made and th o se e q u a tio n s so lv e d .

When th e r e a r e many s e t s o f p ara m e te rs

and many p a ra m e te rs i n th e ab so rb ed s e t , t h i s work takes a long tim e. I t a ls o in c r e a s e s th e p o s s i b i l i t i e s o f c o m p u tatio n al e r r o r s .

F u rth e r­

m ore, a s th e rig h th a n d s id e s o f th e o r i g i n a l l e a s t sq u a re s e q u a tio n s a r e l a r g e i n most c a s e s, t h i s m ethod n e c e s s i t a t e s f in d in g s o lu tio n s o f th e unknowns a c c u ra te to fo u r o r more p la c e s a f t e r th e decim al so th a t i n th e r e d u c tio n th e e r r o r s due to ro u n d in g a r e s m a ll.

The

number o f th e d i g i t s to w hich th e s o lu tio n s would have to be a c c u r a te

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depends upon th e m agnitude o f th e r ig h th a n d s id e s and th e accu racy d e s ir e d i n th e r e d a c tio n s .

The l a r g e r th e r i g h t hand s id e s o r th e

g r e a t e r th e accu racy i n th e r e d a c tio n s r e q u ir e d , the more d i g i t s m ust he c a r r ie d i n th e s o lu tio n s .

A ll th e s e o p e ra tio n s r e q u ir e tim e;

hence some s h o rtc u t method was sought to save tim e and red u ce th e p o s s i b i l i t i e s o f co m p u tatio n al e r r o r s . A model th a t h a s £ , a th e fo re g o in g d is c u s s io n .

,

£ , V a n d £ p aram eters w i l l i l l u s t r a t e

For s im p lify in g th e d is c u s s io n , ? and Y

p a ra m e te rs a r e r e p re s e n te d to g e th e r by 'X .

Thus th e model becomes!

and th e l e a s t sq u a re s e q u a tio n s!

S u b s titu tin g t h i s in th e Ol. e q u a tio n s th e fo llo w in g i s o b ta in e d !

F or any p a r t i c u l a r

^ s a y

the

, ,, th e eq u a tio n would be!

A

S o lu tio n o f th e e q u a tio n f o r each o f th e X ^ s g iv e s th e " T- i ' s which v

when s u b s t i t u t e d in tn th n ^ + ® a

J

■paluss ppsstilt i n

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2?he re d u c tio n H( !* , a » ^ ) th e n becomes T [ —2 - (v - T n .. t , ) ] ^ Ln^ ^ i. • . ij • 3 -*

"

i1 1

[l»s X* r •^

Y,

“ i 3Jj

+

8

? ej ^

T, . «.a,T) « H( ^ , a

Hence i n term s o f th e n o ta tio n s u sed can b e w r i t t e n :

a ) + S (p , Y ) p ,,a .

) can be o b ta in e d a c c u r a te to any d eg ree d e s ir e d w ith o u t much

e x tra c a lc u la tio n . e lim in a tin g ^

E( ^

and a .

\ )jL ,a i s th e re d u c tio n due to ^

S in ce th e rig h th a n d s id e s o f th e

t h a t a r e o b ta in e d a f t e r ab so rbing!!

and Y a f t e r

X - e q u a tio n s

and a- ^ would alw ays b e s m a lle r

th a n th e rig h th a n d s id e s o f th e o r i g i n a l e q u a tio n s , g e t t i n g th e same a c c u ra c y i n th e r e d u c tio n would n o t r e q u ir e th e s o lu tio n s o f th e X j ' s to be a c c u r a te to a s many decim al p la c e s when u s in g th e s h o r t- c u t m ethod a s when u s in g th e lo n g m ethod.

I t can a ls o be shown, by u s in g

th e above tech n iq u e^ t h a t R(P

,a

) = R( P-

,a

) + S ( 2 ^

and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-

e( n ,

52-

* ) = S ( V' O. ) + E( y

Of "both o f th e s e th e R{ M1 , a

) p a r t h a s a lr e a d y been found o n ce.

In

each c a s e , th e r e f o r e , o n ly th e s o lu tio n s o f th e P 's and th e Y *s have to he found from and m u ltip lie d by th e r ig h th a n d s id e s o f th e e q u a tio n s in to which P* and a were ab so rb ed . The a d d itio n a l sum o f sq u a re s f o r th e th r e e s e t s o f th e p a ra m e te rs i n th e above example would th e n be computed as»

E( a £ p x «= E( y. , a , 2(

P

tf = B.( y* , Qt t

X ) - B( p. , P, If ). P

) —h( |x ,

cl f

Y }«

y i,a,g = S( H , a f P, J' ) - R( y- , a , ,8 ). These sums o f th e sq u a re s a re c a l l e d " a d d itio n a l" because th e y r e p r e s e n t o n ly th e e x tr a v a r i a t i o n in tro d u c e d i n th e dependent v a r ia b le b y in tro d u c in g each o f th e s e s e ts o f cau ses when a l l th e o th e r s e ts a r e h e ld c o n s ta n t. i n R(

P,

Bolding P and ^ c o n s ta n t w i l l a lr e a d y have in c lu d e d

Y ) a n th e v a r ia t io n i n th e dependent caused j o i n t l y

by P and a and by ^ and

a , a s w e ll a s t h a t

caused d i r e c t l y b y a

but

g o in g i n to S (

P , ^ ) because h o ld in g P and V c o n s ta n t a ls o re d u c e s

th e v a r i a t io n i n

a i f th ey a r e c o r r e la te d w ith a .

due to a i s o n ly

th a t caused by th a t p a r t o f a w hich i s n o t c o r r e la te d

Hence th e " a d d itio n a l"

w ith P o r )T and th e r e fo r e n o t i n any way i n d i c a te d by them.

These

" a d d itio n a ls " do not form a sound b a s is f o r comparing th e r e l a t i v e im p o rtance o f

a , P and ^ a s causes o f v a r i a t i o n i n Y, b u t o n ly answer

th e q u e s tio n o f how much more s t a t i s t i c a l c o n s id e rin g each

c o n tr o l o v er Y i s a c h iev ed by

o f th e s e when th e o th e r s have a lr e a d y b een c o n s id e re d .

I n g e n e r a l i f th e c o r r e la tio n s among th e s e t s a r e p o s itiv e th e " a d d itio n a l"

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-53mean s q u a re s , th e mean s q u a re s o b ta in e d on d iv id in g th e a d d itio n a l stan o f th e sq u ares by p ro p e r d eg rees o f freedom , would "be s m a lle r th a n th e "direct** e f f e c t s o f each s e t o f th e c a u s e s , th e term d i r e c t h e re b e in g u se d i n th e sen se i n w hich W right ( I 9 2 l) u sed

i t . But t h a t

need

n o t h o ld i f some o f th e c o r r e l a t i o n s a r e n e g a tiv e . O ther p r in c ip l e s and t h e th e o ry o f th e method o f th e l e a s t sq u ares have been d isc u s s e d by B ra n d t (1933)# Ya t e s (193^0 and H enderson (lP h g ) . They a r e , t h e r e f o r e , n o t g iv e n h e r e .

Models Hsed F o r th e p u rp o se o f t h i s stu d y , on th e b a s is o f a 'p r io r i b io lo g ic a l in fo rm a tio n a v a i l a b l e , th e fo llo w in g m odels were u se d : 1 . -Age a t th e f i r s t c a lv in g : y . . . . ■ * + H. + H + (HH) , + P + T + « 4xjklm i j ij jk 1 ijk lm w here

d e n o te s t h e age a t th e f i r s t c a lv in g o f th e mth i n d iv id u a l h av in g th e i t h p r o p o r tio n o f H o ls te in b lo o d , p ro d u ced by c ro s s in g o f th e .1t h n a tiv e b re e d , r a i s e d i n th e .ikth h e rd and who c a lv e d i n th e 1th sea so n .

a

s ta n d s f o r th e e f f e c t common to e ach in d iv id u a l o f th e p o p u la tio n o f w hich th e d a ta s tu d ie d a r e o nly a sam ple.

3?he a r ith m e tic mean o f a p o p u la tio n having

la r g e and equal numbers o f in d iv id u a ls in each sub­ c la s s w ould approach t h i s v a lu e .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

i s an e f f e c t common to a l l th e cows h av in g th e 1t h p r o p o rtio n o f H o ls te in "blood.

I t m easures th e

c h a r a c t e r i s t i c in flu e n c e o f th e genes f o r each p ro p o rtio n o f th e 2q1 s t e i n b lo o d . H" J

i s an e f f e c t common to a l l th e cows produced from th e c ro s s in g o f th e .i t h n a tiv e breed w ith th e Hoi s t e i n s .

I t m easures th e in flu e n c e o f th e g en es

which a re c h a r a c t e r i s t i c o f each n a tiv e b re e d . (HST).

i s an e f f e c t common to a l l th e cows th a t belong to th e i t h p r o p o r tio n o f H o ls te in blood and th e .1t h n a tiv e b re e d .

I t m easures th e d ep artu re o f th e

J o in t e f f e c t s o f th e g en es o f the two so u rces from th e l i n e a r com bination o f t h e i r e f f e c ts when th o s e a r e m easured in d e p e n d e n tly . i s an e f f e c t common to a l l th e cows th a t have th e j t h n a tiv e b re e d i n t h e i r a n c e s try and who were k e p t i n th e k th h e rd .

I t m easures th e e f f e c t s

o f th e management a s f a r a s t h a t d i f f e r s from h e rd to h e rd . i s an e f f e c t common to a l l th e cows th a t calv ed f o r th e f i r s t tim e i n th e 1t h season.

I t m easures

th e se a so n a l in flu e n c e on th e age a t th e f i r s t c a lv in g .

with permission of the copyright owner. Further reproduction prohibited without permission.

-55e

ijk lm

i s th e e r r o r p e c u l i a r to th e ijk lm th cow.

I t is

assumed to be u n c o r r e la te d w ith o th e r e r r o r s . I t in c lu d e s th e e f f e c t s o f chance i n M endeliaa sam pling, d isc re p a n c y betw een th e m ath e m a tic a l model and th e a c t u a l b io lo g ic a l r e l a t i o n s h i p and a l l o th e r f a c t o r s w hich were n o t s p e c i f i e d . As th e c ro ss b re d s o f th e two n a tiv e b re e d s were k e p t i n d i f f e r e n t s e t s o f h e rd s , a m o d ified f o r a o f th e above model w ith in e a c h n a tiv e b re e d was u sed f o r e s tim a tin g and c o r r e c tin g f o r t h e h e rd e f f e c t s . T h is w as: ^fcLn =

“+

Hi

+

+ T1 + m s

where a l l th e term s a r e d e fin e d a s ab o v e. 2 . K ilk y i e l d p e r la c ta tio n * y w here

, e ^ + 1 + 5 + (HBT), . + P ., + T , + B + L + ijk lian o i j ij jk 1 a a

Y4 j y i mT»n

€ ijklm no

d en o tes th e m ilk p ro d u c tio n i n th e o t h r e c o r d o f a cow h a v in g th e i t h p r o p o r tio n o f H o ls te in b lo o d , produced by c ro s s in g th e .i t h n a tiv e b r e e d , k ep t i n th e .ik th h e rd , who c a lv e d i n th e 1 t h season o f th e mth c a le n d a r y e a r and had th e l a c t a t i o n o f th e n th c la s s o f l a c t a t i o n l e n g th s .

** H » ® ' i 3

. and P ., a r e d e fin e d th e same way a s th e y w ere f o r Jk th e model f o r th e age a t f i r s t c a lv in g , except th a t th e y m easure th e e f f e c t s o f th e s e f a c t o r s on m ilk p ro d u c tio n p e r l a c t a t i o n i n s t e a d o f t h e i r e f f e c t on age a t th e f i r s t c a lv in g .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-56T 1

i s an e f f e c t common to a l l th e re c o rd s th a t were made "by th e cows c a lv in g i n th e 1 th seaso n .

It

m easures th e in flu e n c e o f c a lv in g in th a t season on th e m ilk p ro d u c tio n . S SI

i s an e f f e c t common to a l l th e cows t h a t calved i n th e mth c a le n d a r y e a r .

I t m easu res th e e f f e c t

o f th e management and th e h e r e d ity p e c u li a r to th a t y e a r. L n

i s an e f f e c t common to a l l th e cows t h a t had a l a c t a t i o n o f th e n th l a c t a t i o n le n g th c l a s s .

Prom

th e s e e f f e c t s one can c o r r e c t f o r d if f e r e n c e s i n le n g th o f l a c t a t i o n . e e ijk lm n o

i s th e e r r o r p e c u lia r to th e ijk lm n o th re c o rd . — I t in c lu d e s th e e f f e c t s o f chance i n M endelian sam pling o f th e g e n e s t h a t a f f e c t th e m ilk produc­ t i o n and th e e f f e c t s o f any d is c r e p a n c ie s "between th e above m ath em atical m odel and th e a c tu a l b io lo g i­ c a l r e l a t io n s h i p .

I t a ls o in c lu d e s th e e f f e c ts o f

a l l th e o th e r f a c to r s w hich w ere n o t s p e c ifie d . These e r r o r s a re assumed to be u n c o r re la te d w ith each o th e r . A E io d ific a tio n i n t h i s model was a ls o n e c e s s a r y , to c o r r e c t th e re c o rd s f o r th e h erd e f f e c t s , f o r th e same re a s o n s a s m entioned above. The m o d ifie d model fo r th e a n a ly s is w ith in e a c h n a tiv e b re e d was:

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-57TiklmttO = * + Ei * Pk + T1 + \

+ Ln + € iklmno

A ll th e s e term s a re d e fin e d a s above.

Grouping o f th e D ata 1 . Age a t th e f i r s t c a lv in g fh.e changes i n th e age a t f i r s t c a lv in g a s s o c ia te d w ith v a ry in g p ro p o rtio n s o f H o ls te in b lo o d c o u ld have been s tu d ie d by f i t t i n g a l i n e a r r e g re s s io n o f th e fo rm er on th e l a t t e r .

Thus the slo p e

o f th e s t r a i g h t l i n e w hich b e s t f i t t e d th e o b s e rv a tio n s would have been found.

I f th e t r u e r e l a t i o n s h i p betw een the two v a r ia b le s were

n o t l i n e a r , th e b e s t f i t t i n g s t r a i g h t l i n e w ould n o t have g iv e n as good a s o lu tio n to th e above q u e s tio n a s f i t t i n g o f th e c o n s ta n ts . H e ith e r would i t have d e s c rib e d th e r e l a t i o n s h i p a s c o r r e c tly nor w ould i t have p ro v id e d a s dependable a b a s is f o r p r e d ic tin g th e age a t f i r s t c a lv in g from th e p r o p o r tio n o f H o ls te in blood i n an in d iv id u a l a s would th e f i t t i n g o f c o n s ta n ts f o r d i s c r e t e c l a s s e s .

Hot knowing

th e n a tu r e o f th e r e l a t io n s h i p among th e two v a r ia b le s e x a c tly , but a f t e r o b se rv in g th e a r ith m e tic means o f th e c la s s e s w ith d if f e r e n t p r o p o r tio n s o f H o ls te in b l o o d ,i t was d e c id e d to f i t a c o n s ta n t fo r each c l a s s .

I t was th u s e x p ected t h a t th e n a tu r e o f th e r e la tio n s h ip

and th e most p ro b a b le v a lu e s fo r each c l a s s would be e s tim a te d . A n th e re c o rd s were c l a s s i f i e d i n t o th e fo llo w in g c l a s s e s : Hq , and H^.

H ere th e s u b s c r ip ts d en o te i n u n i t s o f one e ig h th

th e p r o p o rtio n o f H o ls te in b lo o d .

As o n ly 28 re c o rd s w ere a v a ila b le

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-

58-

from th e l / S H o ls te in - 7 /3 Sahiwal c la s s and. no re c o rd s a t a l l from the l / S H b ls te in -7 /8 S in d h i, th e se r e c o rd s w ere combined w ith th e re c o rd s from th e 2 /8 H o ls te in - 6/S n a tiv e c l a s s .

Thus Hg r e p r e s e n ts th e c la s s

o f cows h av in g l / S and 2 /8 H o ls te in b lo o d .

The w hole p a t t e r n o f th e

b re e d in g to o b ta in th e d i f f e r e n t c la s s e s i s shown d ia g ra m m a tic a lly in F ig u re 2. Two n a tiv e breeds* th e Sahiw al (H^) and th e S indhi (B^) were u s e d f o r c ro s s b re e d in g .

Hence th e an im als were grouped in to th e two

c l a s s e s depending upon th e n a tiv e b re e d c ro ss e d w ith th e H o ls te in to p ro d u ce them. The b a s i s o f th e se a so n a l c l a s s i f i c a t i o n was th e same f o r age a t c a lv in g a s f o r m ilk p ro d u c tio n and w i l l be e x p la in e d l a t e r . 2. M ilk p ro d u c tio n p e r l a c t a t i o n : These re c o rd s were grouped in to th e H and th e Hf. c la s s e s on * th e same b a s is a s j u s t d is c u s s e d . The s e a so n a l in flu e n c e on any c h a r a c te r can be d i r e c t o r i n d i r e c t . The d i r e c t way in v o lv e s th e in flu e n c e o f t h e a tm o sp h e ric te m p e ra tu re s , h u m id ity , le n g th o f th e day, e t c . th a t a r e c h a r a c t e r i s t i c o f any season. Tho i n d i r e c t in flu e n c e s would be th o s e th a t come about th ro u g h chang es i n th e fe e d su p p ly o f t h e a n im a ls.

A t d i f f e r e n t tim e s o f th e y e a r ,

d i f f e r e n t q u a n t i t i e s an d q u a l i t i e s o f fe e d s a r e n o rm a lly a v a i l a b l e . D uring some seaso n s th e fo d d er i s abundant and g re e n w h ile a t o th e r tim e s very l i t t l e g re e n fo d d er i s a v a i l a b l e . As in d ic a te d e a r l i e r , a tte m p ts were made i n a l l th e h e rd s to c o n tr o l, a s f a r a s p r a c t i c a b l e th e fe e d su p p ly , b o th q u a n t i t a t i v e l y and q u a l i t a ­ tiv e ly .

Hence th e i n d i r e c t in flu e n c e o f th e seaso n s would b e l e s s

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

CO

cO

CO

Diap.rriinmatic Ronrepent.ntion of the Breed 1ri

p la c e d over

th e symbol f o r t h a t p aram e ter.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

TE3 PSSS227T IFTBSTI&AiTI OH

Age a t F i r s t C alving Age a t f i r s t c a lv in g w i l l be p r e s e n te d f i r s t . 1 . Sahiwal and H o ls te in c r o s s e s : Using th e m o d ifie d model d e s c rib e d e a r l i e r th e l e a s t sq u a re s e q u a tio n s were o b ta in e d and so lv e d i t e r a t i v e l y .

Then th e fo llo w in g

re d u c tio n s were c a lc u la te d : B(S> *

I

2

Y iklm iklm

= b-51S.39

a f Rf ,

E„

P)

w ith 5hJ d . f .

*

^ 39.^7 w ith

lh d .f .

*

IA39.23 w ith 12

d .f.

From t h i s in fo rm a tio n th e fo llo w in g a n a ly s is o f v a ria n c e was o b ta in e d : Source o f v a r i a t io n Seasons Rem ainder

d .f.

S .S .

2

4 0 .2 6

533

78-92

M .S. j. 0 .1 3

2? A l.lp -

0 .1 5

The p r o b a b i l i t y i s f a i r l y la r g e o f o b ta in in g d if f e r e n c e s among th e se a so n a l in flu e n c e s a s l a r g e o r l a r g e r th a n e x i s t i n th e p r e s e n t data* due to f lu c tu a ti o n s i n random sam pling a lo n e .

The above ev id en ce

in d i c a t e s t h a t season h as no r e a l e f f e c t on th e age a t f i r s t c a lv in g o r a t l e a s t none w hich was u n c o r r e la te d w ith e i t h e r H o r P .

By

o m ittin g T from th e model th e fo llo w in g r e d u c tio n s w ere c a lc u la te d :

_

I n t h i s in v e s t i g a t i o n F v a lu e s were o b ta in e d i n each case on d iv id in g th e l a r g e r mean sq u are by th e s m a lle r o n e.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-67a(P-

,E )

= HU3 6 .5 3 w ith 6 d . f .

,p )

«= h h a . u

w ith 7 d . f .

These le a d to th e fo llo w in g a n a ly s is o f v a r ia n c e .

d .f.

s .s .

M .S.

p

H erds

6

2 .7 0

0 .4 5

3 . 0 0 **

P ro p o rtio n s o f H o ls te in blood

5

1S .1 2

3 .6 2

2 4 . 1 3 **

535

7 9 .1 6

.1 5

Source o f v a r ia tio n

Eem ainder

W ithin the S a h iw a l-H o ls te in c r o s s e s th e p r o b a b i l i t i e s a re v ery sm all th a t the d if f e r e n c e s among th e herd e f f e c t s and th e d if f e r e n c e s among th e e f f e c t s dae to v a r y in g p r o p o r tio n s o f S o l s t e in b lo o d on age a t f i r s t c a lv in g a re o n ly sam pling e r r o r s .

Most l i k e l y th e h erd

e f f e c t s in age o f th e cows a t f i r s t c a lv in g were b ecau se o f th e en v iro n ­ m ental d if fe r e n c e s among h erd s ( s e e page 1 0 0 .

T hese environm ental

d if f e r e n c e s are n o t p e r tin e n t to th e g e n e t i c q u e s tio n s under c o n sid ­ e r a t io n .

Hence i t became n e c e s s a r y to make c o r r e c t io n s fo r them

b e fo r e p roceed in g w ith th e n e x t a n a l y s is .

Herd e f f e c t s w ere c o r r e c te d

by s u b tr a c tin g th e c o n s ta n ts f o r h erd s from th e a g e a t c a lv in g o f th e cows i n th o se h e r d s .

I n d ic a te s th e p r o b a b ilit y l e s s than .0 1 .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-68S a b le UMean a g e s a t f i r s t c a lv in g i n th e herds where Sahiw als and Sahiw al-H ol s t e i n c r o s s e s w ere kept

Herd

Mean age in y e a r s

P1

2 .7 5 2 .8 ? 2 .9 2 3 .0 9 2 .8 1 2 .8 k rs * or«» £♦©5

p3

P6 P7

'

2 . Sindhi and H o ls te in c r o s s e s : U sing the same model and th e same tech n iq u e a s above th e fo llo w in g r e d u c tio n s and the a n a ly s is o f v a r ia n c e were o b ta in ed : * iklm Yiklm E(P5(1*

,H ,? )

Source o f v a r ia t io n Seasons Eemainder

= 3 1 8 6 .9 1

w ith 35 H d . f .

= 3 1 1 2 .1 3

w ith

12 d .f .

= 3 1 1 2 .0 6

w ith

10 d .f .

d .f .

S .S .

M.S.

I*

2

.0 7

.o k

5 .5 0

Jk2

7k . 78

.2 2

She d if f e r e n c e s among th e se a so n a l e f f e c t s on th e age a t f i r s t c a lv in g o f th e S in d h i-H o ls te in c r o s s e s a r e p ro b a b ly o n ly sam pling e r r o r s; h en ce

T

was l e f t o u t o f th e model and th e fo llo w in g r e d u c tio n s

and a n a ly s is o f v arian ce were o b ta in e d to t e s t th e h y p o th e ses regard­ in g th e h erd d if fe r e n c e s and th e d if f e r e n c e s among th e e f f e c t s o f va ry in g p r o p o r tio n s o f H o ls te in b lo o d :

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-69R( M- ,H)

= 3I I I .55 w ith 6 d . f .

R( * ,? )

= 3076.97 w ith 5 d . f .

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

d .f.

S .S .

M.S.

H erds

k

.51

.13

P r o p o rtio n s o f H o ls te in b lo o d

5

35.09

7^2

7^*85

.2 2

Remainder

3^

F I .69 35-51* * *

E nvironm ental d if f e r e n c e s among th e h e rd s where S in d h i-H o ls te in c r o s s e s were k e p t were n o t la r g e .

Small h e rd d if f e r e n c e s th a t w ere

o b serv ed w ere p ro b a b ly sam pling e r r o r s .

Hence no c o r r e c tio n s were made

f o r them. I n o r d e r to g e t th e in fo rm a tio n re g a rd in g th e d if f e r e n c e s among th e two n a tiv e b re e d s , th e d i f f e r e n t p ro p o rtio n s o f H o ls te in blood and th e i n t e r a c t i o n among th e tw o, th e c o r re c te d v a lu e s from th e

S ahiw al-

Hol s t e i n c ro s s e s w ere combined w ith th e re c o rd s o f th e S in d h i-H b ls te in cro sses.

By f i t t i n g th e model! * “♦ h *

+

*

£u i

th e l e a s t sq u are s e q u a tio n s were o b ta in e d . i n T able 5«

These e q u a tio n s a r e shown

®ie r e d u c tio n s and a n a ly s is o f v a r ia n c e shown i n T ab les

6 and 7 were o b ta in e d from th e s e e q u a tio n s .

I n d ic a te s th e p r o b a b i l i t y l e s s than .0 1 .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Ta

L east sq a u res e q u a tio n s £

A m

E> * ™ 2

j a r H4

^ S5

^ E 6

h

H2

“ < a ^ 0 2 H^ 2 1 ^ 2 2

67

50

67

84

28

201

151

72

34

107

86

41

16

25

547

112 552

^ H 4:

106

ju » E .. s

5

193

S

i 67

84

201

72

107

16

H

: 50

28

151

34

86

25

HH

s 67

^

™ 21* m 2S:

m i2 , 2 8 51* ® 52*

HK

62

:

H »n « ^72*

50

151

34 10 7

86

86 16 25

28 201

72

*Z3C A V

28

84

131 72

201

50

201

107

ol

84

28 201

m iV

201

84

28

28

67 50

84

84

354

02* 50

50

67

67

TTT.r 41

16 25

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-

70-

T able 5 e q u a tio n s f o r th e age a t f i r s t c a lv in g

31 ^ 2 2

= * «

^ 4 2

“

51 M S2 ™ 6 1 ^ 6 2

EVl ^

2

*

• •

4 0 0 .9 7 23

3 3 8 .2 3 201

151

9 1 0 .2 2 72

54

2 9 5 .3 9 107

86

5 5 2 .0 9 16

201 28

72 131

107

25

16

34

86

1 0 9 .7 3

1 5 4 2 .3 2 25

1 0 4 2 .9 1

2 1 2 .8 7 1 8 8 .1 0 2 5 7 .8 2 28

8 0 .4 1 201

5 4 2 .4 1 131

3 6 7 .8 1 72

1 9 7 .3 5 34

3 6 .6 4 107

2 9 0 .4 0 86

2 4 1 .6 9 16

4 1 .4 7 25

6 8 .2 6

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

-71Table 6 S ed u c tio n i n th e sub o f th e sq u a re s o f age a t f i r s t c a lv in g due to f i t t i n g d i f f e r e n t s e ta o f p a ra m e te rs

E t!)

■ ifx

« 76UU.71 w ith 901 d . f .

YU 1

r(

* 7*481.00 w ith

E(

= 7h73.SU w ith

2(

* 7*480.05 w ith

11 d . f .

E(

« 7^ 23.07 w ith

7 d .f.

12 d . f . 7f

A U.O

#•

T able 7 A n a ly s is o f v a ria n c e f o r age a t f i r s t c a lv in g Source o f v a r i a t io n N a tiv e s

d .f.

S .S.

M .S .

F 135 days

Average le n g th o f dry p e rio d i n days

.10

.13

.13

•13

.07

.bb

156

II

.lb

.13

• lb

.lb

.08

• 37

138

III

.18

.20

.23

.15

.06

.18

105

IV

.16

.19

.18

.13

.07

.27

12b

V

.10

.08

.12

.13

.10

.b 6

137

V ia

.16

.12

.21

.10

.11

.31

12b

Vlb

.15

•19

.20

.20

•09

.16

102

VI1

.13

.15

•23

.20

.11

.18

109

“

I

56

C lass

55-7^ days

O lasses o f d ry p e rio d s 9 5 - llh days 75-9 b days 115-13'! days

“

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

fable 19

-9 6 a s to f in d w hether th e d i s t r i b u t i o n o f dry p e r io d s w ith in each o f th e e ig h t p e d ig re e c l a s s e s was o r was n ot s im ila r to th e d i s t r i b u t i o n w ith in th e o th e r seven p e d ig re e c la s s e s .

On o b s e rv a tio n o f 5?a tie 19

i t ap p eared th a t th e p u re b re d In d ia n b re e d s te n d to have lo n g e r dry p e r io d s th a n th e c ro s s b re d s .

E xcept f o r t h i s th e d i s t r i b u t i o n o f

th e dry p e r io d s w ith in th e e ig h t p e d ig re e c l a s s e s ap p eared s im il a r . She com parison among th e av erag e d r y p e r io d s o f th e cows o f d i f f e r e n t p e d ig re e c la s s e s gave f u r t h e r ev id en ce on th e n a tu r e o f th e d if f e r e n c e s among th e p u re b re d and th e c ro ss b re d c a t t l e i n th e le n g th o f d ry p e r io d .

The p u re b re d d a ir y c a t t l e o f any one o f th e

two In d ia n b reed s i . e . th e Sahiw al and th e S in d h i, have lo n g e r d ry p e r io d than, th e H o ls te in c ro ss b re d s produced by u s in g th e same In d ia n b re e d (T able 19)*

M oreover, among th e f o u r p e d ig re e c la s s e s in v o lv in g

each o f th e n a tiv e b re e d s th e tyS H o ls te in c la s s e s have th e s h o r te s t a v era g e d ry p e r io d s .

She av erag e dry p e r io d d e c re a se s w ith th e

in c r e a s e i n th e p ro p o rtio n o f H o ls te in b lo o d up to th e

H o ls te in

b lo o d l e v e l . In o rd e r to examine th e n a tu r e o f th e changes i n t h i s co n n e c tio n , a s th e p r o p o rtio n o f th e H o ls te in b lood i n th e an im als in c r e a s e s o v e r f i f t y p e r c e n t, th e f o u r th and th e e ig h th p e d ig r e e c la s s e s o f T ab les IS and 19 w ere s p l i t in to t h e i r component c la s s e s .

The r e s u l t s

a r e g iv en i n T ables 20 and 21. The dry p e r io d s betw een 55 and 11 If days long were c o n s id e re d a s m ost d e s ir a b le f o r th e fo llo w in g r e a s o n s i

( l ) A d ry p e r io d o f about

e ig h t weeks was found to g iv e th e b e s t annual y i e l d f o r h ig h p ro d u cin g cows c a lv in g a t a tw elv e m onth i n t e r v a l (K le in an d Woodward, 19^3)*

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Table 20 D istribution o f the dry periods o f tho oows with U/8 or more H olstein blood

Class o f cows ___

Classes o f dry period________

Total days > 135 dmra________

U/8 3olatein-U /8 Sahiwal lUo

153

180

112

U9

13U

771

5/8

"

- 3/«

H

28

32

39

23

10

38

170

6 /8

»

-2 /8

«

36

Uo

32

27

17

59

211

7/8

«

-1 /8

»

1

3

2

2

2

11

21

U/8 H olstein-U /8 Sindhi

71

9*+

102

96

U3

80

>*86

5/8

"

- 3/8

11

11

lU

33

28

22

26

I 3U

6/8

«

-2 /8

»

36

39

U5

lf)+

21

3U

219

7/8

»

-1 /8

"

U

6

lU

8

3

13

U8

-5 8 -

c la s s in each

CU oI— 1

i-i*

VO CS r*

KV H rl

r-l

K".

60

ri

rt

H

60

H

CU CU •

*0 CVi

r-4 IfN

VO o

VO

o•

to oe

r l*

ir\

•St

K\ H •

o H•

oc\j

CU CU

8

o

oCU

ur\

©

o H

60

CU rl

60

O

vO H

60

a

s

s

60

60

60

K\ 1

CU I

H i

a

z

=

60

•

t*'*

60 H r-f

o

H

O

o

CU or-l

ir\

o

60 CU

A.

cr\ O

VO O

VO

0

F ractions

of the dry periods

which

are

o

©

r-3

•

K\ CU

Kl CU •

tT\

ocu

O'. r-i •

© 60 P^S.

O

oI—I

CU rl

0> l“"\ OI f

VO

ir \

rH

to

r-


o KV

r!

(— 1 ir\

60

P

P

cu

r- l

60

O

H

f—I

cu

I— i

I—I

60

cu

LTV CU •

"cu •

cu

tO

r—J

r-l

© CJ Si ■8 £ fl4

©