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~