T h e o r . Appl
G e n e t , 49 (1977) 53-61
.....' ~ . ~
9 by Springer-Verlag 1977
The Significance of 2N Gametes in Potato Breeding A . O . M e n d i b u r u and S . J . P e l o q u i n D e p a r t m e n t of P l a n t P r o d u c t i o n , E E R A , INTA, B a l c a r c e ( A r g e n t i n a ) and D e p a r t m e n t s of G e n e t i c s and H o r t i c u l t u r e , U n i v e r s i t y of W i s c o n s i n , Madison, W i s c o n s i n (USA) S u m m a r y . Phureja-haploid Tuberosum h y b r i d s , which p r o d u c e 2n g a m e t e s in addition to n g a m e t e s , w e r e u s e d to obtain d i p l o i d p r o g e n i e s in 2x - 2x rantings, and t e t r a p l o i d p r o g e n y in 4x - 2x m a t i n g s . S e v e n of t h e s e d i p l o i d c l o n e s w e r e i n t e r m a t e d in a m o d i f i e d d i a l l e l d e s i g n , and a l s o c r o s s e d to s e v e n c u l t i v a r s , to obtain 21, 1 6 - c l o n e d i p l o i d ; and 49 (35, 2x x 4x and 14, 4x • 2x) 2 4 - c l o n e t e t r a p l o i d f a m i l i e s , r e s p e c t i v e l y . T h e s e p r o g e n i e s w e r e i n c l u d e d t o g e t h e r with the 14 p a r e n t a l c l o n e s , in a t u b e r y i e l d t r i a l c o n d u c t e d in two l o c a t i o n s in W i s c o n s i n . - H e t e r o t i c r e s p o n s e s w e r e s t r i k i n g in 4x x 2x p r o g e n i e s . T h r e e of t h e s e e n t r i e s had m e a n y i e l d s of 5.0, 5.0 and 5.2 l b s / h i l l , f o r 24 u n s e l e c t e d c l o n e s , thus o u t y i e l d l n g not only the m i d - p a r e n t but a l s o the b e s t t e t r a p l o i d e u l t i v a r s in the e x p e r i m e n t , which a r e highly s e l e c t e d ; Wis 643 ( 4 . 8 l b s / h i l l ) , and K e n n e b e c ( 4 . 8 l b s / h i l l ) . As a g r o u p , the 14, 4x x 2x f a m i l i e s a v e r a g e d 4 . 4 l b s / h i l l , while the m e a n of all s e v e n c u l t i v a r s was 4 . 0 l b s / h i l l , and the m i d - p a r e n t was at 3 . 4 l b s / h i l l . This u n u s u aY!y high m e a n p e r f o r m a n c e of 336 u n s e l e c t e d c l o n e s r e p r e s e n t e d in the 14, 4x x 2x p r o g e n i e s , is i n t e r p r e t e d as a m a n i f e s t a t i o n of the c a p a c i t y of 2n p o l l e n , f o r m e d by f i r s t m e i o t i c d i v i s i o n r e s t i t u t i o n ( F D R ) , to p a s s onto the p r o g e n y the a l r e a d y h e t e r o t i c diploid genotype in a l a r g e l y i n t a c t a r r a y . B e n e f i c i a l i n t r a and i n t e r - l o c u s i n t e r a c t i o n s a r e p r e s u m a b l y c o m p o u n d e d upon s y n g a m y with an u n r e l a t e d n egg f r o m the t e t r a p l o i d p a r e n t . - The p e r f o r m a n c e of 2x X 4x p r o g e n i e s was at o r b e l o w that of the m i d p a r e n t . The f a i l u r e of t h e s e f a m i l i e s to p e r f o r m as well as 4x X 2x f a m i l i e s m a y be a r e f l e c t i o n of the i n c a p a c i t y of 2n m e g a s p o r o g e n e s i s to a v o i d m e i o t i c r e a s s o r t m e n t as e f f i c i e n t l y as F D R d o e s , which would r e s u l t in i n b r e d 2n g a m e t e s . H o w e v e r , the m e t h o d of 2n m e g a s p o r o g e n e s i s is not known. H e r e d i t a r y v a r i a n c e s w e r e l a r g e , both within and a m o n g f a m i l i e s , and i n d i c a t e d c o n s i d e r a b l e n o n a d d i t i v i t y in the a c t i o n of g e n e s a f f e c t i n g t u b e r y i e l d at both l e v e l s of p l o i d y . I n b r e e d i n g was s t r o n g l y d e p r e s s i n g at both ploidy l e v e l s .
p o s s i b l e a l t e r n a t i v e to the s t i m u l a t i n g a n a l y t i c b r e e d -
Introduction The c o m m o n potato b e h a v e s as a t e t r a s o m i c (Lunden 1937; C a d m a n 1942) t e t r a p l o i d (2n = 4x = 4 8 ) . P o t a t o h a p l o i d s (2n = 2x = 24) have b e e n a c c u m u l a t e d in l a r g e n u m b e r s as a r e s u l t of the s t u d i e s of Hougas
ing s c h e m e which had been put f o r w a r d by C h a s e
(1963). The fact that diploid c l o n e s had been i n d i v i d u a l i z e d which f o r m e d both n and 2n g a m e t e s s u g g e s t e d the
and P e l o q u i n , and t h e i r a s s o c i a t e s f r o m 1957 to 1964
f e a s i b i l i t y of studying t h e i r c o m b i n i n g a b i l i t i e s s i m u l -
( P e l o q u i n , Hougas and G a b e r t 1966). T h e s e m a t e r i a l s
t a n e o u s l y . A g i v e n diploid c l o n e would be m a t e d to
furnish excellent opportunities for breeding, genetic
o t h e r d i p l o i d s and to t e t r a p l o i d s . The f o r m e r s e r i e s
and e v o l u t i o n a r y i n v e s t i g a t i o n s , p a r t i c u l a r l y b e c a u s e
of m a t i n g s g i v e r i s e to diploid p r o g e n i e s whose p e r -
s o m e t w o - t h i r d s of r e l a t e d t u b e r o u s Solariums a r e
f o r m a n c e e v a l u a t e s the b r e e d i n g v a l u e of the n g a m -
diploid (2n = 2x = 2 4 ) . M a t i n g s of h a p l o i d s with o t h e r
e t e s p r o d u c e d by that diploid p a r e n t . The l a t t S r s e r i e s
wild and c u l t i v a t e d d i p l o i d s r e s u l t in v i g o r o u s h y b r i d s
of m a t i n g s y i e l d t e t r a p l o i d p r o g e n i e s w h i c h , upon e v a l -
(Hougas and P e l o q u i n 1959; P e l o q u i n and Hougas
uation of t h e i r p e r f o r m a n c e , a r e e x p e c t e d to p r o v i d e
1961; P e l o q u i n eV a / . 1966). H a n n e m a n n and P e l o -
i n f o r m a t i o n on the b r e e d i n g v a l u e of the 2n g a m e t e s
quin (1967; 1968) d e m o n s t r a t e d that s o m e of t h e s e
p r o d u c e d by the s a m e diploid p a r e n t . The q u e s t i o n to
h y b r i d s f o r m g a m e t e s with the u n r e d u c e d n u m b e r of
be a n s w e r e d would then b e : Do t h e s e two e s t i m a t i o n s
chromosomes, i.e.,
of c o m b i n i n g a b i l i t y f o r t u b e r y i e l d , which have been
2n g a m e t e s , s i n c e they g i v e
r i s e to t e t r a p l o i d s in 4x - 2x m a t i n g s . Many t e t r a p l o i d f a m i l i e s p r o d u c e d f r o m 4x - 2x c r o s s e s w h e r e
m a d e in the s a m e c l o n e , c o i n c i d e ? T h e r e is a t h i r d s e r i e s of m e a s u r e m e n t s that can
the d i p l o i d p a r e n t was a Phureja-haploid Zuberosum
be m a d e , s i n c e the clonal p e r f o r m a n c e i t s e l f m a y be
h y b r i d w e r e highly v i g o r o u s and m a n i f e s t e d s t r i k i n g
e s t i m a t e d in r e p l i c a t e d y i e l d t r i a l s . T h e s e m e a s u r e -
h e t e r o t i c r e s p o n s e s in t e r m s of t u b e r y i e l d ( H a n n e -
m e n t s c o u l d p e r h a p s be u t i l i z e d as p r e d i c t o r s of the
m a n and P e l o q u i n 1969). T h e s e findings s u g g e s t e d a
p e r f o r m a n c e of t e t r a p l o i d p r o g e n y r e s u l t i n g f r o m
54
A . O . M e n d i b u r u a n d S . J . P e l o q u i n : The S i g n i f i c a n c e of 2n G a m e t e s in P o t a t o B r e e d i n g
4x - 2x m a t i n g s . A r e l a t i o n s h i p m i g h t be e x p e c t e d in v i e w of t h e f a c t t h a t t h e r e is no c h a n g e in p l o i d y l e v e l
T a b l e 1. P a r e n t a g e a n d s e e d s e t in 4x - 2x c r o s s e s of s e v e n d i p l o i d p a r e n t a l c l o n e s
a s s o c i a t e d w i t h t h e s e q u e n c e of e v e n t s : d i p l o i d s p o r o -
Female*
Male*
Designation
Seeds/ fruit
Seeds/ fruit
Parentage
c l o s e l y p r e d i c t t h a t of i t s t e t r a p l o i d p r o g e n y t h a n t h e
W1268.8 W5285.5 W5293.3 W5295.7 W5302.1 W5337.3
12.8 8.6 13.8 6.7 4.2 0.6
0.8 1.5 9.9 48.8 0.8 30.1
p e r f o r m a n c e of i t s d i p l o i d p r o g e n y , p a r t i c u l a r l y b e -
W6128.2
6.8
**phu 4XWl (Kat) phu 9 . 1 0 X W l phu16.2 xWl phu 2 0 . 2 X W l **stn 2.3 xWl phu 1 3 . 1 • (Chippewa) (W25 ( K a t ) • 3) • (phu4 xWl)
phyte-modified meiosis-2n gamete. A question sugg e s t s i t s e l f : How g r e a t a m o d i f i c a t i o n of t h e g e n o t y p ic c o n s t i t u t i o n of t h e p a r e n t a l d i p l o i d g e n o t y p e d o e s t h i s s e q u e n c e of e v e n t s e n t a i l ? If t h e r e i s but a s l i g h t m o d i f i c a t i o n of t h e p a r e n t a l d i p l o i d g e n o t y p i c c o n s t i tution, then, the clonal p e r f o r m a n c e
should more
c a u s e the p a r e n t a l d i p l o i d c l o n e s u t i l i z e d w e r e h i g h l y heterozygous. The a v a i l a b l e m a t e r i a l f o r c e d t h e s u p p o s i t i o n of
sterile
* Data f r o m H a n n e m a n and Peloquin (1967). ** C l o n a l s e l e c t i o n s f r o m G r o u p Phza,eja a n d G r o u p Stenotomum.
no r e c i p r o c a l d i f f e r e n c e s in 4x - 2x m a t i n g s , s i n c e s o m e c l o n e s f o r m e d only f e m a l e o r m a l e 2n g a m e t e s . This a s s u m p t i o n i s g e n e r a l l y a c c e p t a b l e in h i g h e r p l a n t s , e s p e c i a l l y with r e f e r e n c e to s t u d i e s c o n n e c t e d with quantitatively i n h e r i t e d t r a i t s . During the c o u r s e of t h e s e i n v e s t i g a t i o n s , h o w e v e r , it w a s r e a l i z e d t h a t t h e a s s u m p t i o n of no r e c i p r o c a l d i f f e r e n c e s in 4x - 2x c r o s s e s c o u l d be w r o n g e v e n if e x t r a c h r o m o s o m a l d i f f e r e n c e s w e r e a b s e n t . R e c i p r o c a l d i f f e r e n c e s in t h e s e m a t e r i a l s m a y r e f l e c t d i f f e r e n c e s in t h e m e t h o d of 2n s p o r o g e n e s i s in t h e two s e x e s ( K i d a n e - M a r i a m , P e l o q u i n a n d M e n d i b u r u 1971; K i d a n e - M a r i a m and Peloquin 1972). The i n t e r d i p l o i d c r o s s e s w e r e to p r o v i d e i n f o r m a t i o n on t h e t y p e s of g e n e t i c v a r i a n c e a n d g e n e a c t i o n i n v o l v e d in t h e d e t e r m i n a t i o n of t u b e r y i e l d of d i p l o i d c u l t i v a t e d S o l a n u m s . The r e s u l t s w e r e to be c o n f r o n t ed with P r o f e s s o r S e w a l l W r i g h t ' s h y p o t h e s i s ( W r i g h t 1956) c o n c e r n i n g t y p e s of g e n e a c t i o n e x p e c t e d to p r e v a i l in a s e x u a l l y p r o p a g a t e d o r g a n i s m s
(see also
W r i g h t 1 9 6 7 ) . I n f o r m a t i o n of g e n e a c t i v i t i e s g a i n e d f r o m t e t r a p l o i d f a m i l i e s c o u l d be c o n t r a s t e d with t h a t o b t a i n e d at t h e d i p l o i d l e v e l .
Materials and Methods Two g r o u p s of p a r e n t a l c l o n e s w e r e s e l e c t e d . The d i p l o i d g r o u p i n c l u d e d s e v e n h y b r i d (Phureja-haploid Taberosum) c l o n e s w h i c h h a d b e e n d e m o n s t r a t e d to r o d u c e 2n g a m e t e s by H a n n e m a n a n d P e l o q u i n 1 9 6 8 ) . The t e t r a p l o i d g r o u p a l s o c o m p r i s e s s e v e n clones: Four cultivars (Katahdin, Kennebec, Merrim a c k and Platte), and three Wisconsin advanced breeding selections (Wis 231, Wis 639, and W is 643). Tuber yield w a s not a criterion of selection in the diploid group, since these clones w e r e chosen because they produce 2n gametes. However, they are m o r e likely to overestimate than to underestimate the aver-
~
a g e y i e l d i n g a b i l i t y of a l a r g e p o p u l a t i o n of c o m p a r able hybrids. The p a r e n t a g e a n d s e e d s e t in 4x - 2x c r o s s e s of t h e d i p l o i d p a r e n t a l c l o n e s a r e l i s t e d in T a b l e 1. One m a y n o t e t h a t WI, a h a p l o i d r e p r e s e n t e d in t h e p e d i g r e e of m o s t of t h e d i p l o i d c l o n e s u s e d , w a s e x t r a c t ed f r o m K a t a h d i n ( H o u g a s a n d P e l o q u i n 1 9 5 7 ) . T h e r e fore, tetraploid progenies originated from Katahdind i p l o i d m a t i n g s will be m o r e i n b r e d , on t h e a v e r a g e , t h a n t h o s e i n v o l v i n g o t h e r t e t r a p l o i d p a r e n t . The s e v e n d i p l o i d c l o n e s w e r e i n t e r m a t e d in all p o s s i b l e c o m b i n a t i o n s without r e g a r d to s e x . T w e n t y - o n e f a m i l i e s w e r e t h u s o b t a i n e d . A s a m p l e of s i x t e e n c l o n e s p e r f a m i l y w a s i n c l u d e d in t h e t u b e r y i e l d t r i a l s . The s a m e s e v e n diploid clones were m a t e d with the s e v e n t e t r a p l o i d s to o b t a i n 49 f a m i l i e s . All c r o s s e s were performed utilizing the cut-stem technique ( M c L e a n a n d S t e v e n s o n 1952; P e l o q u i n a n d H o u g a s 1959). The t u b e r y i e l d t r i a l s w e r e c o n d u c t e d at two l o c a t i o n s : U n i v e r s i t y of W i s c o n s i n P o t a t o R e s e a r c h F a r m , R h i n e l a n d e r ( R h i n e l a n d e r ) a n d U n i v e r s i t y of W i s c o n s i n E x p e r i m e n t a l F a r m , H a n c o c k ( H a n c o c k ) . The e x p e r i m e n t a l m a t e r i a l c o m p r i s e d the seven diploid p a r e n t s , t h e 21 i n t e r d i p l o i d c o m b i n a t i o n s , a n d t h e 49 d i p l o i d - t e t r a p l o i d f a m i l i e s to m a k e a t o t a l of 84 e n t r i e s . T h e s e w e r e a r r a n g e d in 9 X 9 s i m p l e l a t t i c e d e s i g n with f o u r r e p l i c a t i o n s , two i n e a c h of t h e two l o c a t i o n s . The t h r e e e n t r i e s t h a t c o u l d not be a c c o m m o d a t e d in t h e d e s i g n w e r e i n t e r c a l a t e d at t h e e n d of the incomplete blocks. These three extra entries were 2x x 4x f a m i l i e s f o r w h i c h it h a d not b e e n p o s s i b l e to o b t a i n t h e r e q u i r e d n u m b e r of p r o g e n y . T h e r e w e r e 16 a n d 24 c l o n e s p e r d i p l o i d a n d t e t r a p l o i d f a m i l y , r e s p e c t i v e l y . The 14 p a r e n t a l c l o n e s w e r e r e p r e s e n t ed by 16 h i l l s p e r r e p l i c a t i o n . C l o n e s in f a m i l i e s w e r e i n d i v i d u a l i z e d t h r o u g h o u t t h e e x p e r i m e n t in a n e f f o r t to e s t i m a t e t h e w i t h i n f a m i l y v a r i a n c e s . Thus, c l o n e s in f a m i l i e s w e r e a s s i g n e d a n u m b e r f r o m 1 to 16 f o r t h e 2 x - 2x, a n d f r o m 1 to 24 f o r t h e 4x - 2x c o m b i n a t i o n s . The two l o c a tions represent quite different environments. Rhinelander, located farther North, has a shorter growing s e a s o n t h a n H a n c o c k ( a b o u t 105 a n d 140 d a y s , respectively). The c o m p l e t e t r i a l c o n s i s t e d of 6 , 6 5 6 s i n g l e h i l l s , not c o u n t i n g t h e t h r e e e x t r a e n t r i e s . H i l l s w e r e h a r -
A.O.
Mendiburu and S.J.
Peloquin:
T h e S i g n i f i c a n c e o f 2n G a m e t e s
vested individually in separate bags. The yield was e x p r e s s e d i n p o u n d s p e r h i l l , r o u n d i n g to t h e n e a r est quarter pound.
in Potato Breeding
55
The most striking point emerging presented
from the results
in Table 3 is the verification of genuine bet-
e r o t i c r e s p o n s e s a s s o c i a t e d w i t h 2n g a m e t e s p r o d u c e d Results and Discussion
by highly heterozygous 4x - 2x c r o s s e s
Certain general
from the analyses
of variance
results emerging
of tuber yield trials for Rhinelander, a n d c o m b i n e d o v e r t h e two l o c a t i o n s a r e
presented
i n T a b l e 2.
randomized
to Rhinelander.
complete block design,
lander results.
i t w a s d e c i d e d to
means when dealing with Rhine-
Adjusted treatment
used for those comparisons results
On the basis of
o f t h e s i m p l e l a t t i c e i n r e l a t i o n to a
use actural treatment
h e r e do p o s s e s s
of the type
a unique potential in po-
Another feature illustrated responses
by these data is that
are almost exclusively re-
s t r i c t e d to 4x • 2x f a m i l i e s .
High yields being the
exception rather than the rule when the crosses
flects much more favorable growing conditions at
the accuracy
considered
the heterotic
T h e l a r g e d i f f e r e n c e in m e a n y i e l d s c l e a r l y r e -
compared
The c o n c l u s i o n s e e m s
tato improvement.
Hancock,
Hancock,
parents.
d i f f i c u l t to a v o i d t h a t i n t e r p l o i d c r o s s e s
T u b e r y i e l d s o f 4x p r o g e n y f r o m
made in the reverse
direction.
t e m p t e d to d e d u c e t h a t r e c i p r o c a l
differences
very important
in the determination
these families.
This inference seems
involving Hancock and
cytoplasm
are
of tuber yield in
it i s r e a l i z e d t h a t 4x • 2x p r o g e n i e s
means will be
are
One should be at once
w h i l e 2x • 4x p r o g e n i e s
reinforced when are in T~erosw~
have their cyto-
combined over the two locations.
The results
T a b l e 2. S o m e s t a t i s t i c s o b t a i n e d f r o m t h e a n a l y s e s o f v a r i a n c e f o r t u b e r y i e l d s i n two l o c a t i o n s
i n v o l v i n g t h e 49 4x - 2x p r o g e n y
m e a n s a r e g i v e n i n T a b l e 3. T h e c l o n a l m e a n t u b e r y i e l d s o f t h e 14 p a r e n t s cross
and the direction
are indicated along the margins
Parental
missing.
32 h i l l s p e r l o c a t i o n ,
the precision
Location
C.V.
(lbs/hill)
(g)
(7o)
0.45
14.8
107.0
0.36 0.29
8.3 10.4
122.0 128.9
when no hills were
Since the stand was very high throughout
the experiment,
St. Dev.
(lbs/hill)
of the table.
m e a n s a r e b a s e d o n 16 h i l l s p e r r e p l i c a -
tion, i.e.,
Mean
Accuracy of simple lattice in respect to RCB design
of the
i s v e r y c l o s e to t h e
ideal of no missing hills. T a b l e 3. C o m p a r i s o n o f 4x - 2x f a m i l y m e a n s figure) combined over the two locations
Rhine2.95 lander Hancock 4.33 Combined 3.64
(upper figure,
in Ibs/hill,
adjusted)
with mid-parent
(lower
2x parent
W1268.8
W5285.5
f
W5295.7
m
W5337.3
3.7
3.8
3.7
1.9
3.3
W i s 231 3.7
3.2 3.9
3.7 4.3
3.5 3.7
5.0 ~ 3.7
3.7 3.7
4.4 ~ 2.8
3.4 3.4
Wis 3.9
639
2.9 4.0
3.5 4.4
3.9 3.8
4.3 ~ 3.8
3.6 3.8
3.8 ~ 2.9
4.4 ~ 3.6
Wis 4.8
643
4.4 4.4
4.4 4.8
4.3 4.3
5.0~ 4.3
4.6 4.3
4.5 ~ 3.4
3.8 4.1
Katahdin 4.2
3.4 4.1
3.2 4.5
3.5 4.0
3.9 4.0
3.4 3.9
3.4 3.1
3.7 3.7
Kennebec 4.8
3.6 4.4
4.5 4.8
4.1 4.3
4.1 4.3
3.3 4.2
4.2 ~ 3.4
4.1 4.0
Merrimack 3.1
3.0 3.6
3.6 4.0
4.1 ~ 3.4
4.8 ~ 3.4
3.8 3.4
3.7 ~ 2.5
3.7 ~ 3.2
Platte 3.9
3.1
4.5
4.2
5.2 ~
4.0
4.7 ~
3.8
3.9
4.3
3.8
3.8
3.8
2.9
3.6
at the .05 level of probability.
f
W6128.2
4.8
~* S i g n i f i c a n t l y h i g h e r t h a n t h e m i d - p a r e n t lbid. at the .01 level of probability.
f
W5302.1
4.0
~
f
W5293.3
4x parent
m
f
56
A . O . M e n d i b u r u and S . J . P e l o q u i n : The S i g n i f i c a n c e of 2n G a m e t e s in P o t a t o B r e e d i n g
Table 4. Mean s ( l b s / h i l l ) of r e l e v a n t g r o u p s of 4x p a r e n t s , 2x p a r e n t s , and p r o g e n i e s ( R h i n e l a n d e r , actual; other means, adjusted) Mean of Location
All 4x parents
Rhinelander Hancock Combined
3.7 4.5 4.0
plasm
from
All 2x parents 2.7 4.5 3.6
Phureja. Even
Group
nized that the results at hand quivocal
decision
to emphasize are more
our view
terms
formation
associated sociated
effects
(specific combining
(general
2.2 3.6 2.8
2.9 4.1 3.4
3.5 5.1 4.4
2.9 4.9 3.9
3.3 4. ? 4.0
3.1 4.4 3.8
be m o r e c l e a r l y i l l u s t r a t e d by p r e s e n t i n g , as is done in Table 4, the m e a n s of the m a i n g r o u p s i n v o l v e d ,
an une-
abilities).
The estimate
in each,
from
of the lattice design,
of
differences.
analysis
main
involves
genies compares very favorably not only with their mid-parent, but also with the performance of the
effects as-
cultivars. This is particularly remarkable when one
analyses
were
variance
The data p e r t a i n i n g to 2x • 4x f a m i l i e s a r e a l s o i l l u m i n a t i n g in r e l a t i o n to n o n a d d i t i v e gene a c t i o n .
all treatments
Th ese p r o g e n i e s not only fail to m a n i f e s t h y b r i d v i g o r
differences
are established
among
abilities of the diploid parents,
among
combining
parents,
significant
Specific combining
in either location,
the analysis
combined
cating that small from
over
location to location.
have
performing from
very
knowledge
abilities of the parents, One
should
perhaps
perhaps
been
Statistically,
results fit an additive model progenies
particularly close
to what
of the general
indi-
then, these well. The would
be
combining
to add that this statistito be equated
gene
force in the determination
of tuber yield in these materials. indicates,
rather,
with additive
The table just pre-
that entire groups
lies with one parent
in common
sistently high,
or intermediate.
low,
diploid p a r e n t s . Its p r o g e n i e s a r e g e n e r a l l y i n f e r i o r in
consistent
cal additivity is in no way
sented
h a v i o r of the c u l t i v a r Katahdin in c r o s s e s with the
with very little interaction.
hasten
action as a principal
tation a p p e a r s r e i n f o r c e d when one o b s e r v e s the b e -
abilities are not
but they are detected
of fami-
tend to be either conThis point may
but they, on the whole, b e h a v e quite as they would in the p r e s e n c e of i n b r e e d i n g d e p r e s s i o n . This i n t e r p r e -
and in the com-
locations,
differences
predicted
genand
abilities of the tetraploid
in each of the two locations
bined analysis.
en c u l t i v a r s , being R h i n e l a n d e r s e l e c t i o n s , a r e e x p e c t e d to be unduly f a v o r e d in t h i s l o c a t i o n .
was
analysis
eral combining general
considers the results obtained at Hancock. These provide a fairer comparison, since three of the sev-
in the experiment. Significant
A model based on additive gene action can hardly
abilities)
the corresponding
which
f a m i l i e s , and the c o r r e -
4x • 2x progenies. The performance of these pro-
in
that the effects involved of the error
4 x x 2x and 2 x x 4 x
explain the unusually high performance of the 14,
and interactions
These
i.e.,
sponding parental means.
observed
due to mode
combining
parents,
on the assumption
are random.
2x x 4x progeny
it is recog-
to further
with the diploid parents;
obtained,
2x X 4x midparent
in each location and combined
with the tetraploid
performed
Female 2x parents
do not warrant
than cytoplasmic
are amenable
of main
4x x 2x progeny
that the differences
The results obtained locations
4x • 2x midparent
on this point, an effort will be made
likely to reflect inequalities
2n gamete
over
though
Male 2x parents
in t u b e r y i e l d i n g a b i l i t y c o m p a r e d to all o t h e r s (Table 3 ) . This co u l d be i n t e r p r e t e d as m e a n i n g that Katahdin, in s p i t e of its r e l a t i v e l y high y i e l d i n g c a p a c i t y , is the p o o r e s t c o m b i n i n g p a r e n t . H o w e v e r , knowing that the haploid W l , which is in the p e d i g r e e of 6 of the 7 d i p l o i d p a r e n t s , was e x t r a c t e d f r o m Katahdin, it a p p e a r s l o g i c a l to c o n c l u d e that the low c o m b i n i n g a b i l i t y of this c u l t i v a r is an a r t e f a c t c r e a t e d by t he i n b r e e d i n g d e p r e s s i o n m a n i f e s t e d in i t s p r o g e n i e s . The s e v e n t h diploid p a r e n t , W5337.3, was e x t r a c t e d f r o m the c u l t i v a r Chippewa, which is a f u l l - s i b of K a t a hdi n. T h e r e f o r e , the p r o g e n i e s i n v o l v i n g W5337.3 a r e a l s o additionally inbred for this r e a s o n .
One m a y a l s o
note that t h i s e f f e c t o c c u r r e d i r r e s p e c t i v e l y of the d i r e c t i o n of the c r o s s , t h e r e b y r e n d e r i n g any e x p l a -
A . O . M e n d i b u r u and S . J . P e l o q u i n : The S i g n i f i c a n c e of 2n G a m e t e s in P o t a t o B r e e d i n g
57
nat i o n s b a s e d on d i f f e r e n c e s in c y t o p l a s m s i m p r o b -
Inbreeding coefficients
able.
The approximate value of the coefficients of inbreed-
The good fit to a s t a t i s t i c a l l y a d d i t i v e m o del which has been g o t t e n in s p i t e of the r e l a t i v e l y s m a l l f a m i l i e s s t u d i e d , i n d i c a t e s that p r o g e n y t e s t i n g is an e f f i c i e n t tool to e v a l u a t e the b r e e d i n g v a l u e f o r t u b e r y i e l d of both t e t r a p l o i d and diploid p a r e n t s in 4x - 2x c r o s s e s of the type dealt with h e r e . We do not wish to i m p l y that all five f e m a l e diploid
ing of the t e t r a p l o i d p r o g e n i e s can be c a l c u l a t e d if one knows the m o d e of 2n g a m e t e f o r m a t i o n in the d i p l o i d . The c o e f f i c i e n t of double r e d u c t i o n m a y be r e g a r d e d to be z e r o . This s e e m s a r e a s o n a b l e a s s u m p t i o n f o r a c h a r a c t e r depending on a l a r g e n u m b e r of gene loci such as t u b e r y i e l d . M u l t i v a l e n t f o r m a t i o n is low enough ( H o w a r d 1970) that double r e -
p a r e n t s p r o d u c e 2n g a m e t e s by the s a m e m e t h o d . In
duction would p r e s u m a b l y affect only t h o s e l o c i l o -
f act , the r e s u l t s s u g g e s t that they m a y c o n s t i t u t e two
c a t e d in the d i s t a l p o r t i o n of the l o n g e s t c h r o m o -
d i f f e r e n t g r o u p s in this r e g a r d . The e v i d e n c e at hand,
s o m e s . The c o e f f i c i e n t f m ay be e x p r e s s e d in t e r m s
h o w e v e r , c o m e s f a r s h o r t f r o m s e t t l i n g t h i s point,
of p, the f r e q u e n c y of s i n g l e e x c h a n g e t e t r a d s c h a r -
p a r t i c u l a r l y in the a b s e n c e of c y t o l o g i c a l s t u d i e s of
a c t e r i s t i c of the l o c u s in q u e s t i o n . The c o e f f i c i e n t of
megasporogenesis.
i n b r e e d i n g of the t e t r a p l o i d i s d ef i n ed as the p r o b a b i l -
F o r t u n a t e l y , the c y t o l o g i c a l p r o c e s s w h e r e b y
ity that two a l l e l e s taken at r a n d o m f r o m a m o n g f o u r ,
d i p l a n d r o u s g a m e t e s a r e f r o m e d has been c l a r i f i e d
at a s p e c i f i e d l o c u s , a r e i d e n t i c a l by d e s c e n t ( K e m p -
in the two m a l e diploid p a r e n t s , W5295.7 and
t h o r n e 1957). F o r u n r e l a t e d m a t e s the p h y l o t y p e s
W5337.3 (Wang, P e l o q u i n and M e n d ib u r u 1971; Mok
( C o t t e r m a n 1940; s e e a l s o C r o w and K i m u r a 1970)
and P e l o q u i n 1975). It was d e m o n s t r a t e d that f i r s t
a r e of the f o r m A1A2A3A 4 - A5A 6. With no double
m e i o t i c d i v i s i o n r e s t i t u t i o n ( F D R ) is r e s p o n s i b l e f o r
r e d u c t i o n , a u t o z y g o s i t y m a y only o r i g i n a t e f o r g e n e s
the f o r m a t i o n of d i p l a n d r o u s g a m e t e s in t h e s e two
t r a c i n g back to the diploid p a r e n t , and the p r o b a b i l i -
c l o n e s . This i m m e d i a t e l y s u g g e s t s an e x p l a n a t i o n f o r
ty of picking just two out of four is 1 / 6 , so , f o r t e -
the h e t e r o t i c r e s p o n s e s o b s e r v e d . An F D R m e t h o d
trasomic-FDR,
of s p o r o g e n e s i s is c a p a b l e of c a p t u r i n g h e t e r o z y g o s i ty and c o m p l e x e p i s t a t i c c o m b i n a t i o n s , if they a r e p r e -
f4x = 6"
P
= "~ p
sent in the p a r e n t a l g e n o t y p e , without d e s t r o y i n g t h e m to a s i g n i f i c a n t d e g r e e . All gene l o c i not a f f e c t e d by
so that 0~