Theor. Appl. G e n e t . 49 (1977) 153-156
I
9 by Springer-Verlag 1977
Estimation of Genetic Parameters in Barley (Hordeum vulgare L.) II. Partial Diallel Analysis B . D . C h a u d h a r y , S . N . K a k a r and R . K . Singh Haryana Agricultural University, H i s s a r (India) S u m m a r y . F o u r different s e t s of p a r t i a l d i a l l e l s w e r e a n a l y s e d for t h e i r r e l a t i v e e f f i c i e n c i e s for e s t i m a t i n g the g e n e t i c p a r a m e t e r s in b a r l e y : (1) p a r t i a l d i a l l e l with 12 p a r e n t s , each i n v o l v e d in only 5 c r o s s e s ; (2) p a r t i a l d i a l l e l with 12 p a r e n t s , each i n v o l v e d i n only 3 c r o s s e s ; (3) p a r t i a l d i a l l e l with 8 p a r e n t s , each i n v o l v e d i n only 5 c r o s s e s ; and (4) p a r t i a l diallel with 8 p a r e n t s , each i n v o l v e d in only 3 c r o s s e s . In p a r t i a l d i a l l e l e x p e r i m e n t s , the e s t i m a t e s of gca effects w e r e h i g h e r than in t h o s e of full d i a l l e l . Ranking p a t t e r n of the p a r e n t s on the b a s i s of gca effects i n p a r t i a l d i a l l e l s d e v i a t e d c o n s i d e r a b l y f r o m the r a n k i n g i n full d i a l l e l . With d e c r e a s i n g 's' p e r p a r e n t , the d e v i a t i o n i n r a n k i n g was also m o r e . This c l e a r l y s u g g e s t s the u n s u i t a b i l i t y of p a r t i a l d i a l l e l a n a l y s i s for s c r e e n i n g high g e n e r a l c o m b i n e r s . S e l e c t i o n of best c r o s s c o m b i n a t i o n s is also not p o s s i b l e b e c a u s e only a s a m p l e of c r o s s e s (s out of n) i s a n a l y s e d u n d e r p a r t i a l d i a l l e l so that t h e r e is e v e r y p o s s i b i l i t y of the best c r o s s being e x c l u d e d f r o m the s a m p l e . In g e n e r a l , o v e r d o m i n a n c e was exhibited, i n d i c a t i n g that t h e r e is a m p l e s c o p e for h e t e r o s i s b r e e d i n g i n b a r l e y . D i a l l e l c r o s s a n a l y s i s i n v o l v i n g all p o s s i b l e c o m b i n a t i o n s in a set of n i n b r e d s b e c o m e s u n m a n a g e a b l e as the n u m b e r of l i n e s (n) i n c r e a s e s . On the o t h e r hand, if only a s m a l l n u m b e r of i n b r e d s is t e s t e d , the e s t i m a t e s of c o m b i n i n g a b i l i t y t e n d to have a l a r g e s a m p l i n g e r r o r . These d i f f i c u l t i e s have led to the dev e l o p m e n t of the concept of s a m p l i n g of c r o s s e s p r o duced by a l a r g e r n u m b e r of i n b r e d s without affecting the e f f i c i e n c y of diallel t e c h n i q u e . To a c h i e v e this goal different a p p r o a c h e s have b e e n followed by v a r i o u s w o r k e r s ( K e m p t h o r n e and C u r n o w 1961; H i n k e l m a n n
following four s e t s of p a r t i a l diallel c r o s s e s (PD) w e r e produced: 1. PD I : 12 p a r e n t s , each i n v o l v e d in 5 c r o s s e s 2. PD II : 12 p a r e n t s , each i n v o l v e d in 3 c r o s s e s 3. PD I I I : 8 p a r e n t s , each~involved i n 5 c r o s s e s 4. PD IV : 8 p a r e n t s , each i n v o l v e d in 3 c r o s s e s . The K e m p t h o r n e and C u r n o w (1961 ) s a m p l i n g p r o c e s s was adopted. The c r o s s e s , t o g e t h e r with t h e i r p a r e n t s , w e r e t e s t e d i n a r a n d o m i s e d block d e s i g n w i t h four r e p l i c a t i o n s . In each c a s e , five p l a n t s p e r plot were selected randomly andobservations were recorded on (i) plant height, (ii) n u m b e r of effective t i l l e r s , ( i i i ) e a r length, (iv) n u m b e r of g r a i n s p e r e a r , (v) 1 0 0 - s e e d weight and (vi) g r a i n y i e l d p e r plant. The f o l lowing s t a t i s t i c a l model was u s e d for the a n a l y s i s of p a r t i a l diallel :
and S t e r n 1960; Fyfe and G i l b e r t 1963; H i n k e l m a n n 1968). In the p r e s e n t i n v e s t i g a t i o n the model p r o p o s e d
Yijl = m + r 1 + gi + sij + eijl
by K e m p t h o r n e and C u r n o w (1961) for p a r t i a l diallel was u s e d . Its r e l a t i v e e f f i c i e n c y in c o n t r a s t to f u l l d i a l l e l was t e s t e d in e s t i m a t i n g the g e n e t i c p a r a m e t e r s in b a r l e y , c o n s i d e r i n g (i) two s e t s of p a r e n t s , the one with 12 and the o t h e r with 8 p a r e n t s , and (ii) the two s i z e s of the s a m p l e d c r o s s e s p e r l i n e . The i n f o r m a tion c o l l e c t e d on the n a t u r e and m a g n i t u d e of g e n e t i c p a r a m e t e r s would help i n f o r m u l a t i n g a s u i t a b l e b r e e d ing policy in b a r l e y . M a t e r i a l and M e t h o d Six exotic ( A B - 1 2 / 5 9 , E b - 1 5 5 6 , PTS-57, A - 5 9 , N u m e r and E C - 2 4 8 8 2 ) and six i n d i g e n o u s ( B G - 1 , K - 5 7 2 / 1 0 , I B - 2 2 6 , C - 1 6 4 , RD-42 and B P - 3 ) v a r i e t i e s of b a r l e y w e r e s e l e c t e d , k e e p i n g i n view t h e i r d i v e r s i t y , and the
where, Yijl = the phenotypic v a l u e of ijth c r o s s i n lth r e p l i cation m = general mean r 1 = effect of lth r e p l i c a t i o n gi
= g e n e r a l c o m b i n i n g a b i l i t y (gca) effect of ith parent s.. = s p e c i f i c c o m b i n i n g a b i l i t y ( s c a ) effect of the 1l i • jth c r o s s eij 1 = e r r o r effect.
The g e n e r a l and s p e c i f i c c o m b i n i n g a b i l i t y e f f e c t s and v a r i a n c e s w e r e e s t i m a t e d ; t h e s e v a r i a n c e s w e r e t r a n s l a t e d into c o m p o n e n t s of g e n e t i c v a r i a n c e s (i. e. a~ and a~ ) following the model of G r i f f i n g ( 1 9 5 6 ) . The additive g e n e t i c v a r i a n c e ( ~ ) and the v a r i a n c e s due to d o m i n a n c e d e v i a t i o n s ( a~ ) w e r e u s e d to e s t i m a t e the a v e r a g e d e g r e e of d o m i n a n c e .
154
T h e o r . Appl. G e n e t . 49 (1977) Table 1. C o m b i n i n g a b i li ty a n a l y s i s in full and p a r t i a l d i a l l e l e x p e r i m e n t s with the d e g r e e of dominance Type of d i a l l e l S o u r c e experiment
F.D
PD-I
D.F.
gca sca error 2 2 aD/aA_
7 28 189
gca sca error 2 2 -/CA
11 18 87
gca sca error 2 2 _/oA
11 6 51
gca sca error 2 2 CD/aA_
7 12 57
gca sca error 2 2 _/r A
7 4 33
~D
PD-II
OD
PD-III
PD-IV
~D
Mean su m of s q u a r e s ~ Plant height (cm)
Ear length (cm)
N u m b e r of effective tillers
151.50 8 2 . 68 11.12
2.05 1.78 0.98
58.07 140.95 8.72
4.59
12.58
185.07 140.85 19.76
Grain yield (gm)
lO0-graln weight (gm)
Number of g r a i n s per ear
543.64 787.87 2 1 .3 5
0.33 0.15 0.11
206.89 108.66 3.97
7.37
14.92
1.16
4.70
6.56 3.19 0.25
558.47 355.58 2 1 .6 3
4025.57 1750.00 124.38
0.68 0.51 0.01
213.06 275.15 2.74
6.22
1.98
3.74
1.62
7.11
9.98
82.41 43.09 20.08
5.74 2.54 0.25
385.25 358.73 18.26
3865.49 1623.74 106.93
0.58 0.70 0.01
130.00 275.21 2.15
0.79
0.98
17.51
0.92
7.96
2.56
449.83 111.53 19.33
5.10 6.19 0.27
341.28 314.14 17.10
1702.63 1770.16 104.32
0.28 0.31 0.01
173.62 232.10 3.59
0.58
11.48
23.83
52.86
5.50
8.30
311.86 164.53 21.43
4.98 11.02 0.32
478.11 227.90 16.90
3029.85 944.23 100.65
0.37 0.52 0.01
215.62 340.21 4.05
1.25
1.99
1.09
0.52
4.30
3.47
All m e a n s u m of s q u a r e s w e r e s i g n i f i c a n t at 5 ~ l e v e l
P D - i , II and III f o r g r a i n y i e l d and 100 g r a i n w e i g h t .
Results C o m b i n i n g a b i l i t y a n a l y s i s s h o w e d that v a r i a n c e s due to g e n e r a l and s p e c i f i c c o m b i n i n g a b i l i t y w e r e s i g n i ficant f o r all the c h a r a c t e r s u n d e r e a c h of t h e f o u r s e t s of p a r t i a l d i a l l e l (Table 1 ) . The s i g n i f i c a n c e of both t h e s e c o m p o n e n t s i n d i c a t e d the o c c u r r e n c e of both a d d i t i v e and n o n - a d d i t i v e t y p e s of g e n e e f f e c t in the p r e s e n t m a t e r i a l . The r e l a t i v e m a g n i t u d e of a d d i t i v e to n o n - a d d i t i v e type of g e n e a c t i o n was m e a s u r e d 2 2 as a r a t i o of aD/aA , i . e . a v e r a g e d e g r e e of d o m i n a n c e . In g e n e r a l , t h e d o m i n a n c e type of g e n e a c t i o n s e e m e d to p r e d o m i n a t e . F o r n u m b e r of e f f e c t i v e t i l l e r s and n u m b e r of g r a i n s p e r e a r , o v e r - d o m i n a n c e was e x h i b i t e d u n d e r all the f o u r s e t s of p a r t i a l d i a l l e l . F o r e a r l e n g t h , the v a l u e s u n d e r th e t h r e e p a r t i a l d i a l lels, i.e.
P D - I , P D - I I I and P D - I V , w e r e in the r a n g e
F o r plant h e i g h t , h o w e v e r , t h e o v e r - d o m i n a n c e v a l u e s w e r e o b t a i n e d only u n d e r P D - I and IV, w h e r e a s t he o t h e r two d e s i g n s g a v e an i n d i c a t i o n of p a r t i a l d o m i n a n c e . A n o t h e r o b s e r v a t i o n was that t h e v a l u e f o r a v e r age d e g r e e o f d o m i n a n c e was l o w e r in P . D . -II than in P. D. I, e x c e p t f o r e f f e c t i v e t i l l e r s . S i m i l a r l y , t h e s e e s t i m a t e s w e r e l o w e r in PD IV than in PD III, e x c e p t f o r plant h ei g h t . The full d i a l l e l which was c o m p a r a b l e with PD III and IV p r o v i d e d an e s t i m a t e of d e g r e e of d o m i n a n c e which was l e s s t h a n t h a t of PD III, but m o r e t h a n PD IV, e x c e p t i n t h e c a s e of plant h e i g h t . The m e a n s u m s of s q u a r e s due to g c a and s o a w e r e g e n e r a l l y g r e a t e r in p a r t i a l d i a l l e l s than in full d i a l l e l . An a n a l y s i s of the g c a e f f e c t s ( T a b l e 2 ) o b t a i n e d u n d e r f o u r d i f f e r e n t p a r t i a l d i a l l e l s i n d i c a t e d that the
of o v e r d o m i n a n c e , but in P D - I I c o m p l e t e d o m i n a n c e
r a n k i n g p a t t e r n of t h e p a r e n t s with r e g a r d to g c a e f f e c t
w a s shown. O v e r d o m i n a n c e was a l s o e v i d e n t u n d e r
u n d e r P D - I was s i m i l a r to that u n d e r P D - I I ; a l s o , r a n -
B.D.
Chaudhary,
S.N.
Kakar
and R.K.
Singh: Estimation
T a b l e 2. G e neral
combining
Characters
Types of diallel experiment
AB-12/59
FD PD-I PD-II PD-III PD-IV
-
Plant height (cm)
Ear length (cm)
Effective tillers
Grainyield (gm)
100-grain weight (gin)
Number of grains per ear
king under groups, other.
0.49 - 0.32 0.48 - 0.20 0.75 0.27 0.50 - 0.85 1.391.40
0.06 0.97 1.69 0.06 0.50
- 0.21 0.60 0.79 - 0.37 0.08
0.69 1.56 1.38 0.44 1.39
-
1.00 5.50 4.21 - 1.21 1.73
0.64 - 6.06 - 5.52 - 6.30 -13.37
2.38 4.62 8.68 2.94 9.83
- 1,95 - 5.67 - 0,54 - 4,71 -11,55
FD PD-I PD-II PD-III PD-IV
- 0.06 -15.74 -30.24 9.75 24.60
0.47 -18.53 -21.94 3.67 13.16
9.03 19.90 32.77 15.09 40.03
- 3.44 1.20 21.18 - 3.58 -15.34
2.33 23.72 26.98 5.03 5.21
- 1,94 - 7,00 - 2,47 -12.91 -37.61
7.24 20.45 26.84 - 4.25 -13.98
- 9.10 -16.68 - 9.88 -12.63 -16.07
FD PD-I PD-II PD-III PD-IV
-
-
0.28 0.41 0.02 0.23 0.40
- 0.04 0.17 0.50 - 0.03 - 0.22
0.04 - 0.07 0.13 - 0.02 - 0.19
0.06 0.41 0.88 0.09 0.09
0.09 0.21 0.47 0.07 0.05
0.09 0.18 0.10 0.11 0.45
0.12 0.34 - 0.03 0.19 0.21
FD PD-I PD-II PD-III PD-IV
2.08 0.15 - 1.53 3.69 7.30
6.93 5.52 - 0.68 2.53 7.10
1.39 - 0.47 2.51 - 2.69 - 0.02
-
1.14 1.09 - 1.44 3.45 0.31
- 2.10 1.05 - 0.79 0.83 - 4.23
- 0.33 3.03 4.84 - 0.20 - 2.39
0.16 0.30 0.29 0.17 0.01
to PD-IV.
gca
These from
under
For
combining
number
For
ear
A-59
of effective tillers
ability.
was compared
the parents
were ranked
effects under full diallel and with the ranking
PD I was more
-
1.52 0.42 6.30 - 3.12 - 0.02
-
PD II. Similarly, were alike. ranking
the rankings
However,
similar
-
1.26 3.46 3.61 4.16
4.67 1.40 1.33 5.58
7.04
8.25
-
0.02 0.17 0.67 0.18 0,44
5.30 7.81 5.05 4.48 0.95
for PD III and PD IV
in none of these cases
to t h a t of full d i a l l e l .
was the
With the help of
T a b l e 3. R a n k i n g o f p a r e n t s b a s e d o n t h e i r full and partial diallel
gca effects in
Parents
Full diallel
PD-I
PD-II
PD-III
PD-IV
Pooled PD
AB-12/59 EB-1556 BG-1 PTS-57 A-59 K-572/10 IB-226 C-164
4 3 2 8 6 5
8 6 3 5 1 4
8 6 3 4 1 5
1.5 1.5 4 8 3 7
1 2 3 7.5 5 7.5
4 5 7 1 8 3
high combi-
BG-1 exhibited exceptionally
comparison,
1.41 1.06 3.80 0.01 2.05
-
proved to be
for plant height.
showing consistently
two each
effects
and C-164
of gca effects under partial
under
1.85 - 0.76 2.63 - 0.71 - 1.63
-
diallels
1
2
2
5
6
6
7
7
7
6
4
2
done on separa-
t e l y ( T a b l e 3 ) . A g a i n , it w a s e v i d e n t t h a t t h e r a n k i n g pattern
- 0.71 2.42 7.30 - 5.00 - 6.55
-
C-164
3.24 7.88 5.28 9.64 21.32
on the basis of their gca
the basis
- 2.91 - 4.92 0.76 - 7.47 - 9.46
3.60 3.22 5.41 - 1.44 0.76
IB-226
- 1.32 - 7.56 - 9.53 2.79 5.07
and grain yield per plant,
this ranking
K-572/10
- 0.59 - 5.09 -11.37 2.74 4.58
for grain yield per plant
a better
A-59
FD PD-I PD-II PD-III PD-IV
was also a good combiner
For
PTS-57
-
A-59 and AB-15/59.
high general
BG-1
0.13 - 0.07 0.01 0.65 0.02
EB-1556
weight.
diallel experiments
0.16 0.02 0.48 0.74 0.35
ning ability were IB-226,
and 100-grain
155
FD PD-I PD-II PD-III PD-IV
combiners
the parents
II.
-
On the basis of the data on
the best general
EB-1556
in Barley.
3.77 6.28 3.84 9.38 10.73
differed considerably
these four diallels,
length,
ability effects in full and partial
Parameters
1.81 1.66 3.55 3.82 4.94
PD-III was similar
however,
of Genetic
or less the same as under
Full Full Full Full
diallel: cliallel: diallel: diallel:
PD-I PD-II PD-III PD-IV
(rs) (rs) (rs) (rs)
= : = =
0.26 0.19 0.54 0.36
156
Theor. Appl. G e n e t . 49 (1977)
S p e a r m a n ' s r a n k c o r r e l a t i o n ( S n e d e c o r 1946 ), the
the o v e r a l l t r e n d of gene a c t i o n i n v o l v e d i n the i n h e r i -
ranking patternunder each partial diallel was compared
t a n c e of q u a n t i t a t i v e c h a r a c t e r s . The p r e s e n t study
with that of full diallel. The correlations
has i n d i c a t e d that both gca and s c a v a r i a n c e s w e r e
0.26, 0.19, 0.54 and0.36 for PDI,
(r s) were
PDII, P D Ill and
s i g n i f i c a n t in all the four s e t s of p a r t i a l d i a l l e l . How-
P D IV, respectively. All these correlations were low
e v e r , i n PD II and IV, w h e r e ' s '
was low ( 3 ) , the
and non-significant, indicating that none of these modi-
m a g n i t u d e s of gca and s c a m e a n s u m of s q u a r e s w e r e
fications could p r e d i c t the c o r r e c t o r d e r of p a r e n t s for
also low c o m p a r e d with t h o s e of PD I and III, w h e r e
their combining ability.
's' was high ( 5 ) . S i m i l a r o b s e r v a t i o n s could be m a d e for gca effects a l s o . K e a r s e y (1965) and Anand et al. (1969) have also r e p o r t e d that a d e c r e a s e i n 's' r e -
Discussion
s u l t s i n d e c r e a s e d s i g n i f i c a n c e of gca and s c a v a r i The g e n e r a l c o m b i n i n g a b i l i t y of a l i n e is defined as the a v e r a g e p e r f o r m a n c e of that l i n e o v e r n c r o s s e s , if n is the n u m b e r of l i n e s i n v o l v e d i n the d i a l l e l . Thus, the a v e r a g e p e r f o r m a n c e of a l i n e when c r o s s e d only to a
a n c e s . The a v e r a g e d e g r e e of d o m i n a n c e , m e a s u r e d 2 2 as the ratio of c D / r A , gave an o v e r a l l p i c t u r e of o v e r d o m i n a n c e . Thus, the gene action i n the m a t e r i a l i n d i c a t e s a m p l e scope for h e t e r o s i s b r e e d i n g .
s e l e c t e d l i n e ( s ) f r o m a g i v e n set of p a r e n t s ( n ) , as in the p a r t i a l d i a l l e l , m a y not be the s a m e as i t s a v e r a g e p e r f o r m a n c e in full d i a l l e l . The r a n k i n g p a t t e r n of the p a r e n t s with r e s p e c t to gca effects will, t h e r e f o r e , depend on the p e r c e n t a g e of the total c r o s s e s being s a n a l y s e d in a p a r t i c u l a r p a r t i a l diallel i . e . (~ • 100). The r e s u l t s o b t a i n e d in the p r e s e n t i n v e s t i g a t i o n have v e r y c l e a r l y i n d i c a t e d that with s m a l l e r
's' in p a r t i a l
diallel the r a n k i n g of the p a r e n t s d e v i a t e s m o r e f r o m the r a n k i n g b a s e d on full d i a l l e l . The c o r r e l a t i o n b e t ween the r a n k i n g s of p a r e n t s , b a s e d on full diallel i n f o r m a t i o n on one hand and the p a r t i a l d i a l l e l on t h e o t h e r , w e r e 0 . 2 6 , 0 . 1 9 , 0 . 5 4 and 0.36 for PD I, PD II, PD III and PD IV, r e s p e c t i v e l y . C o n s i d e r i n g the v a l u e of ( ~ •
being 127' , 25 7', 63 7, and 38 7' for
PD I, II, III and IV, r e s p e c t i v e l y , the above c o r r e l a t i o n v a l u e s a r e well j u s t i f i e d . High c o r r e l a t i o n , though n o n - s i g n i f i c a n t , i n the c a s e of PD-III is due to its l a r g e s t p r o p o r t i o n in s a m p l e d c r o s s e s . C l e a r l y the
Literature Anand, I . J . ; Murty, B . R . : S e r i a l a n a l y s i s of c o m b i ning a b i l i t y i n diallel and f r a c t i o n a l d i a l l e l c r o s s e s of l i n s e e d . Theor. Appl. Genet. 39, 88-94 (1966) F y f e , J . L . ; G i l b e r t , N. : P a r t i a l d i a l l e l c r o s s e s . B i o m e t r i c s I_~9, 278-286 (1963) G r i t t i n g , B. : C o n c e p t s of g e n e r a l and s p e c i f i c c o m bining a b i l i t y i n r e l a t i o n to diallel c r o s s i n g s y s t e m s . Aust. J . Biol. Sci. 9, 463-493 (1956) H i n k e l m a n n , K. : M i s s i n g v a l u e s in p a r t i a l diallel c r o s s e x p e r i m e n t s . B i o m e t r i c s 2_44, 903-913 (1968) H i n k e l m a n n , K. ; S t e r n , K. : KreuzungspHine z u r Selektionsz(iehtung bei ~Valdb~iumen. Silvae G e n e t i c a 9, 121-133 (1960) K e a r s e y , M . J . : B i o m e t r i c a l a n a l y s i s of a r a n d o m m a t i n g population: A c o m p a r i s o n of five e x p e r i m e n tal d e s i g n s . H e r e d i t y 2.__00, 205-235 (1965) K e m p t h o r n e , O. ; C u r n o w , R . N . : The p a r t i a l diallel c r o s s . B i o m e t r i c s 17, 229-250 (1961) Murty, B . R . ; A r u n a c h a l a m , V. ; Anand, I . J . : Diallel and p a r t i a l diallel a n a l y s i s of s o m e y i e l d f a c t o r s in Linum usitatissim~m. H e r e d i t y 2...22, 35-41 (1966) S n e d e c o r , G . W . : Rank c o r r e l a t i o n s . In: S t a t i s t i c a l methods 164-167. A m e s , Iowa: Iowa State C o l l e g e P r e s s 1946
efficiency of a p a r t i a l diallel will depend on the s i z e of the s a m p l e d c r o s s e s and just any r a n d o m n u m b e r of c r o s s e s t a k e n for a p a r t i a l diallel will not give r e l i a b l e e s t i m a t e s . Murty, A r u n a c h a l a m and A n a n d (1966) have r i g h t l y s u g g e s t e d that b i a s i n the e s t i m a -
R e c e i v e d July 3, 1976 C o m m u n i c a t e d by B . R . Murty
t e s is m o r e c o m m o n when 's' is l e s s than n / 2 . Of the four p a r t i a l d i a l l e l s s t u d i e d in the p r e s e n t i n v e s t i gation, this s i t u a t i o n was m e t only in P D - I I I . S i m i l a r l y , the p u r p o s e of diallel a n a l y s i s , to s e l e c t the best c r o s s c o m b i n a t i o n s , i s not fulfilled by the p a r t i a l d i a l l e l s b e c a u s e only a s a m p l e of the total c r o s s e s i s a n a l y s e d and the p r o b a b i l i t y of the best c r o s s being not i n c l u d e d i n the s a m p l e i s always t h e r e . The p u r pose of p a r t i a l d i a l l e l is only to give i n f o r m a t i o n on
B.D. Chaudhary Pool Officer, D e p a r t m e n t of G e n e t i c s . S.N. K a k a r Dean C o l l e g e of B asic Scs. & Hum. R . K . Singh P r o f e s s o r of G e n e t i c s Haryana Agric. University H i s s a r ( H a r y a n a ) 125004 ( I n d i a )
I
9 by Springer-Verlag 1977
Estimation of Genetic Parameters in Barley (Hordeum vulgare L.) II. Partial Diallel Analysis B . D . C h a u d h a r y , S . N . K a k a r and R . K . Singh Haryana Agricultural University, H i s s a r (India) S u m m a r y . F o u r different s e t s of p a r t i a l d i a l l e l s w e r e a n a l y s e d for t h e i r r e l a t i v e e f f i c i e n c i e s for e s t i m a t i n g the g e n e t i c p a r a m e t e r s in b a r l e y : (1) p a r t i a l d i a l l e l with 12 p a r e n t s , each i n v o l v e d in only 5 c r o s s e s ; (2) p a r t i a l d i a l l e l with 12 p a r e n t s , each i n v o l v e d i n only 3 c r o s s e s ; (3) p a r t i a l d i a l l e l with 8 p a r e n t s , each i n v o l v e d i n only 5 c r o s s e s ; and (4) p a r t i a l diallel with 8 p a r e n t s , each i n v o l v e d in only 3 c r o s s e s . In p a r t i a l d i a l l e l e x p e r i m e n t s , the e s t i m a t e s of gca effects w e r e h i g h e r than in t h o s e of full d i a l l e l . Ranking p a t t e r n of the p a r e n t s on the b a s i s of gca effects i n p a r t i a l d i a l l e l s d e v i a t e d c o n s i d e r a b l y f r o m the r a n k i n g i n full d i a l l e l . With d e c r e a s i n g 's' p e r p a r e n t , the d e v i a t i o n i n r a n k i n g was also m o r e . This c l e a r l y s u g g e s t s the u n s u i t a b i l i t y of p a r t i a l d i a l l e l a n a l y s i s for s c r e e n i n g high g e n e r a l c o m b i n e r s . S e l e c t i o n of best c r o s s c o m b i n a t i o n s is also not p o s s i b l e b e c a u s e only a s a m p l e of c r o s s e s (s out of n) i s a n a l y s e d u n d e r p a r t i a l d i a l l e l so that t h e r e is e v e r y p o s s i b i l i t y of the best c r o s s being e x c l u d e d f r o m the s a m p l e . In g e n e r a l , o v e r d o m i n a n c e was exhibited, i n d i c a t i n g that t h e r e is a m p l e s c o p e for h e t e r o s i s b r e e d i n g i n b a r l e y . D i a l l e l c r o s s a n a l y s i s i n v o l v i n g all p o s s i b l e c o m b i n a t i o n s in a set of n i n b r e d s b e c o m e s u n m a n a g e a b l e as the n u m b e r of l i n e s (n) i n c r e a s e s . On the o t h e r hand, if only a s m a l l n u m b e r of i n b r e d s is t e s t e d , the e s t i m a t e s of c o m b i n i n g a b i l i t y t e n d to have a l a r g e s a m p l i n g e r r o r . These d i f f i c u l t i e s have led to the dev e l o p m e n t of the concept of s a m p l i n g of c r o s s e s p r o duced by a l a r g e r n u m b e r of i n b r e d s without affecting the e f f i c i e n c y of diallel t e c h n i q u e . To a c h i e v e this goal different a p p r o a c h e s have b e e n followed by v a r i o u s w o r k e r s ( K e m p t h o r n e and C u r n o w 1961; H i n k e l m a n n
following four s e t s of p a r t i a l diallel c r o s s e s (PD) w e r e produced: 1. PD I : 12 p a r e n t s , each i n v o l v e d in 5 c r o s s e s 2. PD II : 12 p a r e n t s , each i n v o l v e d in 3 c r o s s e s 3. PD I I I : 8 p a r e n t s , each~involved i n 5 c r o s s e s 4. PD IV : 8 p a r e n t s , each i n v o l v e d in 3 c r o s s e s . The K e m p t h o r n e and C u r n o w (1961 ) s a m p l i n g p r o c e s s was adopted. The c r o s s e s , t o g e t h e r with t h e i r p a r e n t s , w e r e t e s t e d i n a r a n d o m i s e d block d e s i g n w i t h four r e p l i c a t i o n s . In each c a s e , five p l a n t s p e r plot were selected randomly andobservations were recorded on (i) plant height, (ii) n u m b e r of effective t i l l e r s , ( i i i ) e a r length, (iv) n u m b e r of g r a i n s p e r e a r , (v) 1 0 0 - s e e d weight and (vi) g r a i n y i e l d p e r plant. The f o l lowing s t a t i s t i c a l model was u s e d for the a n a l y s i s of p a r t i a l diallel :
and S t e r n 1960; Fyfe and G i l b e r t 1963; H i n k e l m a n n 1968). In the p r e s e n t i n v e s t i g a t i o n the model p r o p o s e d
Yijl = m + r 1 + gi + sij + eijl
by K e m p t h o r n e and C u r n o w (1961) for p a r t i a l diallel was u s e d . Its r e l a t i v e e f f i c i e n c y in c o n t r a s t to f u l l d i a l l e l was t e s t e d in e s t i m a t i n g the g e n e t i c p a r a m e t e r s in b a r l e y , c o n s i d e r i n g (i) two s e t s of p a r e n t s , the one with 12 and the o t h e r with 8 p a r e n t s , and (ii) the two s i z e s of the s a m p l e d c r o s s e s p e r l i n e . The i n f o r m a tion c o l l e c t e d on the n a t u r e and m a g n i t u d e of g e n e t i c p a r a m e t e r s would help i n f o r m u l a t i n g a s u i t a b l e b r e e d ing policy in b a r l e y . M a t e r i a l and M e t h o d Six exotic ( A B - 1 2 / 5 9 , E b - 1 5 5 6 , PTS-57, A - 5 9 , N u m e r and E C - 2 4 8 8 2 ) and six i n d i g e n o u s ( B G - 1 , K - 5 7 2 / 1 0 , I B - 2 2 6 , C - 1 6 4 , RD-42 and B P - 3 ) v a r i e t i e s of b a r l e y w e r e s e l e c t e d , k e e p i n g i n view t h e i r d i v e r s i t y , and the
where, Yijl = the phenotypic v a l u e of ijth c r o s s i n lth r e p l i cation m = general mean r 1 = effect of lth r e p l i c a t i o n gi
= g e n e r a l c o m b i n i n g a b i l i t y (gca) effect of ith parent s.. = s p e c i f i c c o m b i n i n g a b i l i t y ( s c a ) effect of the 1l i • jth c r o s s eij 1 = e r r o r effect.
The g e n e r a l and s p e c i f i c c o m b i n i n g a b i l i t y e f f e c t s and v a r i a n c e s w e r e e s t i m a t e d ; t h e s e v a r i a n c e s w e r e t r a n s l a t e d into c o m p o n e n t s of g e n e t i c v a r i a n c e s (i. e. a~ and a~ ) following the model of G r i f f i n g ( 1 9 5 6 ) . The additive g e n e t i c v a r i a n c e ( ~ ) and the v a r i a n c e s due to d o m i n a n c e d e v i a t i o n s ( a~ ) w e r e u s e d to e s t i m a t e the a v e r a g e d e g r e e of d o m i n a n c e .
154
T h e o r . Appl. G e n e t . 49 (1977) Table 1. C o m b i n i n g a b i li ty a n a l y s i s in full and p a r t i a l d i a l l e l e x p e r i m e n t s with the d e g r e e of dominance Type of d i a l l e l S o u r c e experiment
F.D
PD-I
D.F.
gca sca error 2 2 aD/aA_
7 28 189
gca sca error 2 2 -/CA
11 18 87
gca sca error 2 2 _/oA
11 6 51
gca sca error 2 2 CD/aA_
7 12 57
gca sca error 2 2 _/r A
7 4 33
~D
PD-II
OD
PD-III
PD-IV
~D
Mean su m of s q u a r e s ~ Plant height (cm)
Ear length (cm)
N u m b e r of effective tillers
151.50 8 2 . 68 11.12
2.05 1.78 0.98
58.07 140.95 8.72
4.59
12.58
185.07 140.85 19.76
Grain yield (gm)
lO0-graln weight (gm)
Number of g r a i n s per ear
543.64 787.87 2 1 .3 5
0.33 0.15 0.11
206.89 108.66 3.97
7.37
14.92
1.16
4.70
6.56 3.19 0.25
558.47 355.58 2 1 .6 3
4025.57 1750.00 124.38
0.68 0.51 0.01
213.06 275.15 2.74
6.22
1.98
3.74
1.62
7.11
9.98
82.41 43.09 20.08
5.74 2.54 0.25
385.25 358.73 18.26
3865.49 1623.74 106.93
0.58 0.70 0.01
130.00 275.21 2.15
0.79
0.98
17.51
0.92
7.96
2.56
449.83 111.53 19.33
5.10 6.19 0.27
341.28 314.14 17.10
1702.63 1770.16 104.32
0.28 0.31 0.01
173.62 232.10 3.59
0.58
11.48
23.83
52.86
5.50
8.30
311.86 164.53 21.43
4.98 11.02 0.32
478.11 227.90 16.90
3029.85 944.23 100.65
0.37 0.52 0.01
215.62 340.21 4.05
1.25
1.99
1.09
0.52
4.30
3.47
All m e a n s u m of s q u a r e s w e r e s i g n i f i c a n t at 5 ~ l e v e l
P D - i , II and III f o r g r a i n y i e l d and 100 g r a i n w e i g h t .
Results C o m b i n i n g a b i l i t y a n a l y s i s s h o w e d that v a r i a n c e s due to g e n e r a l and s p e c i f i c c o m b i n i n g a b i l i t y w e r e s i g n i ficant f o r all the c h a r a c t e r s u n d e r e a c h of t h e f o u r s e t s of p a r t i a l d i a l l e l (Table 1 ) . The s i g n i f i c a n c e of both t h e s e c o m p o n e n t s i n d i c a t e d the o c c u r r e n c e of both a d d i t i v e and n o n - a d d i t i v e t y p e s of g e n e e f f e c t in the p r e s e n t m a t e r i a l . The r e l a t i v e m a g n i t u d e of a d d i t i v e to n o n - a d d i t i v e type of g e n e a c t i o n was m e a s u r e d 2 2 as a r a t i o of aD/aA , i . e . a v e r a g e d e g r e e of d o m i n a n c e . In g e n e r a l , t h e d o m i n a n c e type of g e n e a c t i o n s e e m e d to p r e d o m i n a t e . F o r n u m b e r of e f f e c t i v e t i l l e r s and n u m b e r of g r a i n s p e r e a r , o v e r - d o m i n a n c e was e x h i b i t e d u n d e r all the f o u r s e t s of p a r t i a l d i a l l e l . F o r e a r l e n g t h , the v a l u e s u n d e r th e t h r e e p a r t i a l d i a l lels, i.e.
P D - I , P D - I I I and P D - I V , w e r e in the r a n g e
F o r plant h e i g h t , h o w e v e r , t h e o v e r - d o m i n a n c e v a l u e s w e r e o b t a i n e d only u n d e r P D - I and IV, w h e r e a s t he o t h e r two d e s i g n s g a v e an i n d i c a t i o n of p a r t i a l d o m i n a n c e . A n o t h e r o b s e r v a t i o n was that t h e v a l u e f o r a v e r age d e g r e e o f d o m i n a n c e was l o w e r in P . D . -II than in P. D. I, e x c e p t f o r e f f e c t i v e t i l l e r s . S i m i l a r l y , t h e s e e s t i m a t e s w e r e l o w e r in PD IV than in PD III, e x c e p t f o r plant h ei g h t . The full d i a l l e l which was c o m p a r a b l e with PD III and IV p r o v i d e d an e s t i m a t e of d e g r e e of d o m i n a n c e which was l e s s t h a n t h a t of PD III, but m o r e t h a n PD IV, e x c e p t i n t h e c a s e of plant h e i g h t . The m e a n s u m s of s q u a r e s due to g c a and s o a w e r e g e n e r a l l y g r e a t e r in p a r t i a l d i a l l e l s than in full d i a l l e l . An a n a l y s i s of the g c a e f f e c t s ( T a b l e 2 ) o b t a i n e d u n d e r f o u r d i f f e r e n t p a r t i a l d i a l l e l s i n d i c a t e d that the
of o v e r d o m i n a n c e , but in P D - I I c o m p l e t e d o m i n a n c e
r a n k i n g p a t t e r n of t h e p a r e n t s with r e g a r d to g c a e f f e c t
w a s shown. O v e r d o m i n a n c e was a l s o e v i d e n t u n d e r
u n d e r P D - I was s i m i l a r to that u n d e r P D - I I ; a l s o , r a n -
B.D.
Chaudhary,
S.N.
Kakar
and R.K.
Singh: Estimation
T a b l e 2. G e neral
combining
Characters
Types of diallel experiment
AB-12/59
FD PD-I PD-II PD-III PD-IV
-
Plant height (cm)
Ear length (cm)
Effective tillers
Grainyield (gm)
100-grain weight (gin)
Number of grains per ear
king under groups, other.
0.49 - 0.32 0.48 - 0.20 0.75 0.27 0.50 - 0.85 1.391.40
0.06 0.97 1.69 0.06 0.50
- 0.21 0.60 0.79 - 0.37 0.08
0.69 1.56 1.38 0.44 1.39
-
1.00 5.50 4.21 - 1.21 1.73
0.64 - 6.06 - 5.52 - 6.30 -13.37
2.38 4.62 8.68 2.94 9.83
- 1,95 - 5.67 - 0,54 - 4,71 -11,55
FD PD-I PD-II PD-III PD-IV
- 0.06 -15.74 -30.24 9.75 24.60
0.47 -18.53 -21.94 3.67 13.16
9.03 19.90 32.77 15.09 40.03
- 3.44 1.20 21.18 - 3.58 -15.34
2.33 23.72 26.98 5.03 5.21
- 1,94 - 7,00 - 2,47 -12.91 -37.61
7.24 20.45 26.84 - 4.25 -13.98
- 9.10 -16.68 - 9.88 -12.63 -16.07
FD PD-I PD-II PD-III PD-IV
-
-
0.28 0.41 0.02 0.23 0.40
- 0.04 0.17 0.50 - 0.03 - 0.22
0.04 - 0.07 0.13 - 0.02 - 0.19
0.06 0.41 0.88 0.09 0.09
0.09 0.21 0.47 0.07 0.05
0.09 0.18 0.10 0.11 0.45
0.12 0.34 - 0.03 0.19 0.21
FD PD-I PD-II PD-III PD-IV
2.08 0.15 - 1.53 3.69 7.30
6.93 5.52 - 0.68 2.53 7.10
1.39 - 0.47 2.51 - 2.69 - 0.02
-
1.14 1.09 - 1.44 3.45 0.31
- 2.10 1.05 - 0.79 0.83 - 4.23
- 0.33 3.03 4.84 - 0.20 - 2.39
0.16 0.30 0.29 0.17 0.01
to PD-IV.
gca
These from
under
For
combining
number
For
ear
A-59
of effective tillers
ability.
was compared
the parents
were ranked
effects under full diallel and with the ranking
PD I was more
-
1.52 0.42 6.30 - 3.12 - 0.02
-
PD II. Similarly, were alike. ranking
the rankings
However,
similar
-
1.26 3.46 3.61 4.16
4.67 1.40 1.33 5.58
7.04
8.25
-
0.02 0.17 0.67 0.18 0,44
5.30 7.81 5.05 4.48 0.95
for PD III and PD IV
in none of these cases
to t h a t of full d i a l l e l .
was the
With the help of
T a b l e 3. R a n k i n g o f p a r e n t s b a s e d o n t h e i r full and partial diallel
gca effects in
Parents
Full diallel
PD-I
PD-II
PD-III
PD-IV
Pooled PD
AB-12/59 EB-1556 BG-1 PTS-57 A-59 K-572/10 IB-226 C-164
4 3 2 8 6 5
8 6 3 5 1 4
8 6 3 4 1 5
1.5 1.5 4 8 3 7
1 2 3 7.5 5 7.5
4 5 7 1 8 3
high combi-
BG-1 exhibited exceptionally
comparison,
1.41 1.06 3.80 0.01 2.05
-
proved to be
for plant height.
showing consistently
two each
effects
and C-164
of gca effects under partial
under
1.85 - 0.76 2.63 - 0.71 - 1.63
-
diallels
1
2
2
5
6
6
7
7
7
6
4
2
done on separa-
t e l y ( T a b l e 3 ) . A g a i n , it w a s e v i d e n t t h a t t h e r a n k i n g pattern
- 0.71 2.42 7.30 - 5.00 - 6.55
-
C-164
3.24 7.88 5.28 9.64 21.32
on the basis of their gca
the basis
- 2.91 - 4.92 0.76 - 7.47 - 9.46
3.60 3.22 5.41 - 1.44 0.76
IB-226
- 1.32 - 7.56 - 9.53 2.79 5.07
and grain yield per plant,
this ranking
K-572/10
- 0.59 - 5.09 -11.37 2.74 4.58
for grain yield per plant
a better
A-59
FD PD-I PD-II PD-III PD-IV
was also a good combiner
For
PTS-57
-
A-59 and AB-15/59.
high general
BG-1
0.13 - 0.07 0.01 0.65 0.02
EB-1556
weight.
diallel experiments
0.16 0.02 0.48 0.74 0.35
ning ability were IB-226,
and 100-grain
155
FD PD-I PD-II PD-III PD-IV
combiners
the parents
II.
-
On the basis of the data on
the best general
EB-1556
in Barley.
3.77 6.28 3.84 9.38 10.73
differed considerably
these four diallels,
length,
ability effects in full and partial
Parameters
1.81 1.66 3.55 3.82 4.94
PD-III was similar
however,
of Genetic
or less the same as under
Full Full Full Full
diallel: cliallel: diallel: diallel:
PD-I PD-II PD-III PD-IV
(rs) (rs) (rs) (rs)
= : = =
0.26 0.19 0.54 0.36
156
Theor. Appl. G e n e t . 49 (1977)
S p e a r m a n ' s r a n k c o r r e l a t i o n ( S n e d e c o r 1946 ), the
the o v e r a l l t r e n d of gene a c t i o n i n v o l v e d i n the i n h e r i -
ranking patternunder each partial diallel was compared
t a n c e of q u a n t i t a t i v e c h a r a c t e r s . The p r e s e n t study
with that of full diallel. The correlations
has i n d i c a t e d that both gca and s c a v a r i a n c e s w e r e
0.26, 0.19, 0.54 and0.36 for PDI,
(r s) were
PDII, P D Ill and
s i g n i f i c a n t in all the four s e t s of p a r t i a l d i a l l e l . How-
P D IV, respectively. All these correlations were low
e v e r , i n PD II and IV, w h e r e ' s '
was low ( 3 ) , the
and non-significant, indicating that none of these modi-
m a g n i t u d e s of gca and s c a m e a n s u m of s q u a r e s w e r e
fications could p r e d i c t the c o r r e c t o r d e r of p a r e n t s for
also low c o m p a r e d with t h o s e of PD I and III, w h e r e
their combining ability.
's' was high ( 5 ) . S i m i l a r o b s e r v a t i o n s could be m a d e for gca effects a l s o . K e a r s e y (1965) and Anand et al. (1969) have also r e p o r t e d that a d e c r e a s e i n 's' r e -
Discussion
s u l t s i n d e c r e a s e d s i g n i f i c a n c e of gca and s c a v a r i The g e n e r a l c o m b i n i n g a b i l i t y of a l i n e is defined as the a v e r a g e p e r f o r m a n c e of that l i n e o v e r n c r o s s e s , if n is the n u m b e r of l i n e s i n v o l v e d i n the d i a l l e l . Thus, the a v e r a g e p e r f o r m a n c e of a l i n e when c r o s s e d only to a
a n c e s . The a v e r a g e d e g r e e of d o m i n a n c e , m e a s u r e d 2 2 as the ratio of c D / r A , gave an o v e r a l l p i c t u r e of o v e r d o m i n a n c e . Thus, the gene action i n the m a t e r i a l i n d i c a t e s a m p l e scope for h e t e r o s i s b r e e d i n g .
s e l e c t e d l i n e ( s ) f r o m a g i v e n set of p a r e n t s ( n ) , as in the p a r t i a l d i a l l e l , m a y not be the s a m e as i t s a v e r a g e p e r f o r m a n c e in full d i a l l e l . The r a n k i n g p a t t e r n of the p a r e n t s with r e s p e c t to gca effects will, t h e r e f o r e , depend on the p e r c e n t a g e of the total c r o s s e s being s a n a l y s e d in a p a r t i c u l a r p a r t i a l diallel i . e . (~ • 100). The r e s u l t s o b t a i n e d in the p r e s e n t i n v e s t i g a t i o n have v e r y c l e a r l y i n d i c a t e d that with s m a l l e r
's' in p a r t i a l
diallel the r a n k i n g of the p a r e n t s d e v i a t e s m o r e f r o m the r a n k i n g b a s e d on full d i a l l e l . The c o r r e l a t i o n b e t ween the r a n k i n g s of p a r e n t s , b a s e d on full diallel i n f o r m a t i o n on one hand and the p a r t i a l d i a l l e l on t h e o t h e r , w e r e 0 . 2 6 , 0 . 1 9 , 0 . 5 4 and 0.36 for PD I, PD II, PD III and PD IV, r e s p e c t i v e l y . C o n s i d e r i n g the v a l u e of ( ~ •
being 127' , 25 7', 63 7, and 38 7' for
PD I, II, III and IV, r e s p e c t i v e l y , the above c o r r e l a t i o n v a l u e s a r e well j u s t i f i e d . High c o r r e l a t i o n , though n o n - s i g n i f i c a n t , i n the c a s e of PD-III is due to its l a r g e s t p r o p o r t i o n in s a m p l e d c r o s s e s . C l e a r l y the
Literature Anand, I . J . ; Murty, B . R . : S e r i a l a n a l y s i s of c o m b i ning a b i l i t y i n diallel and f r a c t i o n a l d i a l l e l c r o s s e s of l i n s e e d . Theor. Appl. Genet. 39, 88-94 (1966) F y f e , J . L . ; G i l b e r t , N. : P a r t i a l d i a l l e l c r o s s e s . B i o m e t r i c s I_~9, 278-286 (1963) G r i t t i n g , B. : C o n c e p t s of g e n e r a l and s p e c i f i c c o m bining a b i l i t y i n r e l a t i o n to diallel c r o s s i n g s y s t e m s . Aust. J . Biol. Sci. 9, 463-493 (1956) H i n k e l m a n n , K. : M i s s i n g v a l u e s in p a r t i a l diallel c r o s s e x p e r i m e n t s . B i o m e t r i c s 2_44, 903-913 (1968) H i n k e l m a n n , K. ; S t e r n , K. : KreuzungspHine z u r Selektionsz(iehtung bei ~Valdb~iumen. Silvae G e n e t i c a 9, 121-133 (1960) K e a r s e y , M . J . : B i o m e t r i c a l a n a l y s i s of a r a n d o m m a t i n g population: A c o m p a r i s o n of five e x p e r i m e n tal d e s i g n s . H e r e d i t y 2.__00, 205-235 (1965) K e m p t h o r n e , O. ; C u r n o w , R . N . : The p a r t i a l diallel c r o s s . B i o m e t r i c s 17, 229-250 (1961) Murty, B . R . ; A r u n a c h a l a m , V. ; Anand, I . J . : Diallel and p a r t i a l diallel a n a l y s i s of s o m e y i e l d f a c t o r s in Linum usitatissim~m. H e r e d i t y 2...22, 35-41 (1966) S n e d e c o r , G . W . : Rank c o r r e l a t i o n s . In: S t a t i s t i c a l methods 164-167. A m e s , Iowa: Iowa State C o l l e g e P r e s s 1946
efficiency of a p a r t i a l diallel will depend on the s i z e of the s a m p l e d c r o s s e s and just any r a n d o m n u m b e r of c r o s s e s t a k e n for a p a r t i a l diallel will not give r e l i a b l e e s t i m a t e s . Murty, A r u n a c h a l a m and A n a n d (1966) have r i g h t l y s u g g e s t e d that b i a s i n the e s t i m a -
R e c e i v e d July 3, 1976 C o m m u n i c a t e d by B . R . Murty
t e s is m o r e c o m m o n when 's' is l e s s than n / 2 . Of the four p a r t i a l d i a l l e l s s t u d i e d in the p r e s e n t i n v e s t i gation, this s i t u a t i o n was m e t only in P D - I I I . S i m i l a r l y , the p u r p o s e of diallel a n a l y s i s , to s e l e c t the best c r o s s c o m b i n a t i o n s , i s not fulfilled by the p a r t i a l d i a l l e l s b e c a u s e only a s a m p l e of the total c r o s s e s i s a n a l y s e d and the p r o b a b i l i t y of the best c r o s s being not i n c l u d e d i n the s a m p l e i s always t h e r e . The p u r pose of p a r t i a l d i a l l e l is only to give i n f o r m a t i o n on
B.D. Chaudhary Pool Officer, D e p a r t m e n t of G e n e t i c s . S.N. K a k a r Dean C o l l e g e of B asic Scs. & Hum. R . K . Singh P r o f e s s o r of G e n e t i c s Haryana Agric. University H i s s a r ( H a r y a n a ) 125004 ( I n d i a )
