Estimate of Space Occupied Proposed as a
152 A M E R I C A N S O C I E T Y O F SUGAR B E E T T E C H N O L O G I S T S
t h a t t h e effect of r o w w i d t h on yield of s u g a r beets was essentially i n d e - p e n d e n t o f t h e n u m b e r o f p l a n t s i n t h e r o w . T h e r e f o r e , t h e s p a c i n g be- tween rows m a y be safely i g n o r e d a n d t h e e s t i m a t e of space o c c u p i e d can b e based o n t h e d i s t r i b u t i o n o f sugar b e e t p l a n t s w i t h i n t h e r o w . C o o n s
(1) has r e v i e w e d E u r o p e a n a n d A m e r i c a n l i t e r a t u r e r e p o r t i n g t h e effect of space r e l a t i o n s h i p s o n t h e sugar b e e t c r o p .
T h e r e is g e n e r a l a g r e e m e n t t h a t w h e n space is fully o c c u p i e d it m a k e s little difference h o w m a n y p l a n t s a r e p r e s e n t , p r o v i d e d e a c h o f t h e m h a s sufficient r o o m to p r o d u c e a b e e t of m a r k e t a b l e size. In g e n e r a l , t h e crops from thick s t a n d s h a v e slightly h i g h e r sucrose c o n t e n t t h a n those from t h i n stands. T h i s t e n d s to c o m p e n s a t e for small losses from beets of u n m a r k e t - able size w h e n t h e u p p e r limits o f p l a n t p o p u l a t i o n s h a v e n o t b e e n seriously exceeded. T h e r e f o r e , in a r r i v i n g at an e s t i m a t e of space o c c u p i e d we may assume t h a t t h e o n l y l i m i t o n t h e total n u m b e r o f p l a n t s i n a given l e n g t h of r o w is t h a t most of t h e m m u s t h a v e sufficient space to d e v e l o p a r o o t of m a r k e t a b l e size. If m o r e t h a n this n u m b e r of p l a n t s is p r e s e n t in an a p - p r e c i a b l e p o r t i o n of t h e field it is o n l y e v i d e n c e of a p o o r j o b of t h i n n i n g . Such a c o n d i t i o n is of i n f r e q u e n t o c c u r r e n c e a n d as growers gain e x p e r i e n c e in m a c h i n e t h i n n i n g it will be even less likely to occur.
I t r e m a i n s t o define t h e m a x i m u m space b e t w e e n hills i n t h e r o w a t which t h e b e e t p l a n t s will p r e s u m a b l y fully use the p l a n t food, m o i s t u r e a n d r o o m at t h a t l o c a t i o n . A m e r i c a n growers of s u g a r beets m o r e or less agree t h a t 12 inches b e t w e e n hills in t h e r o w is an o p t i m u m s p a c i n g . T h e r e is less g e n e r a l a g r e e m e n t on a permissible m a x i m u m s p a c i n g . T o l m a n (5) r e p o r t e d t h a t u n d e r some c o n d i t i o n s yield c o u l d b e m a i n t a i n e d a s s p a c i n g in t h e r o w was i n c r e a s e d to 15 i n c h e s b e t w e e n hills a n d t h a t "Yields b e g i n to d e c l i n e as spacing w i t h i n t h e r o w is i n c r e a s e d to 20 i n c h e s . " D e m i n g ( 3 ) , r e p o r t i n g o n e x p e r i m e n t s a t F o r t Collins, C o l o r a d o , states t h a t w h e n ap- p r o x i m a t e l y full s t a n d s w e r e m a i n t a i n e d t h e differences in yield from 8, 12- a n d 16-inch spacings in t h e row w e r e n e g l i g i b l e . Spacings used by sugar beet growers i n t h e C o l o r a d o - N e b r a s k a - W y o m i n g area h a v e v a r i e d a p p r e c i - ably a n d m a n y e x c e l l e n t yields h a v e b e e n h a r v e s t e d from s t a n d s w i t h r o w s p a c i n g in excess of t h e a s s u m e d o p t i m u m of 12 inches.
On t h e basis of this e v i d e n c e it is t e n t a t i v e l y a s s u m e d t h a t s u g a r b e e t p l a n t s will fully occupy t h e space w i t h i n t h e r o w w h e n t h e m a x i m u m space b e t w e e n hills a p p r o x i m a t e s 16 inches. H o w e v e r , as a m a t t e r of c o n v e n i e n c e , in t h e a c t u a l m e a s u r e m e n t of spaces u n d e r t a k e n in 1953 a n d r e p o r t e d in T a b l e 1 no " L o s t s p a c e " was r e c o r d e d unless t h e space b e t w e e n hills was 18 inches o r m o r e . T h u s , all spaces b e t w e e n hills u p t o a n d i n c l u d i n g 17.5 inches were i g n o r e d in c o l l e c t i n g t h e d a t a . All spaces of 18 inches or m o r e were n o t e d , 1 6 i n c h e s s u b t r a c t e d a n d t h e r e m a i n d e r r e c o r d e d a s u n o c c u p i e d space. T h e total of inches of u n o c c u p i e d space in each p l o t was s u b t r a c t e d from t h e t o t a l inches of r o w for t h e p l o t to o b t a i n t h e t o t a l inches of r o w o c c u p i e d by b e e t p l a n t s a n d from this v a l u e p e r c e n t of o c c u p i e d space was c a l c u l a t e d .
After t h i n n i n g t h e e x p e r i m e n t a l s u g a r b e e t p l o t s o n t h e A g r o n o m y F a r m at F o r t Collins, C o l o r a d o , in 1953, t h e spaces b e t w e e n hills of t h e inside (for harvest) rows of t w o variety tests w e r e m e a s u r e d a n d u n o c c u p i e d
PROCEEDINGS—EIGHTH GENERAL MEETING 153 space for all plots recorded. Counts of hills in the same plots were also
made. From these records percentage of space occupied and hills per 100 ieet of row were calculated as estimates of the thinned stands. These esti- mates of stand for the agronomic evaluation test of leaf spot and black root-resistant varieties were statistically analyzed by the analysis of variance for a Latin square. A summary of these data is given in Table 1.
T h e plots in this 8 x 8 Latin square were 30 feet in length and 8 rows in width. T h e initial stands were good and fairly uniform. A moderately weedy condition extended across the field rows of the test at about "Row 4"
of the summary table. T h e test was thinned by four laborers who worked one row at a time in pairs or singly on various portions of the experiment.
No record was made of the rows worked by different individuals, though it was noted at the time that the spacings being used by the laborers varied from about 8-10 inches by two teenagers to approximately II inches by the two experienced older workers. T h e subsequent count of hills showed that full stands varied from about 31-33 hills to well over 40 hills per 30-foot plot row. It is known that the two teenagers worked more of the plots represented in "Columns 6-8" of the table than they did of the balance of the experiment.
When hills per 100 feet of row were used as the estimate of stands in this test the F value for columns, rows and varieties each exceed the one percent point for probable significance. Conversion of the estimates of stand to space occupied materially reduced the variability in this test. In the case of columns Ve exceeded Vc and the F values for rows and varieties, while still exceeding the one percent point and the five percent point, respectively, are less than half as great as when hills were used as the measure of stand.
Since stands in this test were relatively good, as evidenced by the variety means and the general mean, some further comment may be warranted. As
154 A M E R I C A N S O C I E T Y O F SUGAR B E E T T E C H N O L O G I S T S
t h e n u m b e r of hills in a g i v e n l e n g t h of r o w w o u l d be i n f l u e n c e d by t h e basic spacings u s e d by t h e different l a b o r e r s t h e differences, if any, w o u l d be f o u n d in t h e c o l u m n m e a n s of t h e t a b l e . T h e F v a l u e for c o l u m n s in- dicates t h a t h i g h l y significant differences for hills d i d exist. H o w e v e r , w h e n space o c c u p i e d was u s e d as t h e e s t i m a t e of s t a n d s no significant differences b e t w e e n c o l u m n m e a n s w e r e f o u n d .
T h e e s t i m a t e of space o c c u p i e d w o u l d p r o b a b l y be of t h e m o s t v a l u e as a m e a s u r e of s t a n d s o b t a i n e d by m a c h i n e t h i n n i n g . U s u a l l y an a p p r e c i - a b l e p o r t i o n o f t h e hills i n m a c h i n e - t h i n n e d sugar b e e t s c o n t a i n s m o r e t h a n o n e p l a n t a n d t h e r e is less u n i f o r m i t y of t h e space b e t w e e n hills t h a n w i t h h a n d - t h i n n e d s t a n d s . B o t h of these factors t e n d to m a k e estimates of s t a n d based on c o u n t s of p l a n t s or hills m o r e or less u n r e a l i s t i c . U n f o r t u n a t e l y d a t a on t h e s t a n d of a m a c h i n e - t h i n n e d field of sugar b e e t s by all t h r e e m e t h o d s o f e s t i m a t i n g s t a n d w e r e n o t o b t a i n e d . I t s e e m e d possible t h a t some o f t h e p o p u l a t i o n s s t u d i e s c o n d u c t e d a t F o r t C o l l i n s i n p r e v i o u s years h a d some of t h e characteristics of a m a c h i n e - t h i n n e d s t a n d . It was f o u n d t h a t s t a n d s for all p l o t s of t h e p o p u l a t i o n s study c o n d u c t e d in 1949 h a d b e e n r e c o r d e d as t h e c o n d i t i o n of each hill, i.e., 1, 2- or 3-plant hill or b l a n k hill, in s e q u e n c e for e a c h r o w of t h e plots. Since 8- a n d 12-inch spacings a n d v a r i o u s c o m b i n a t i o n s of b l a n k s , 1-, 2- a n d 3-plant hills w e r e used in this e x p e r i m e n t p a r t of t h e v a r i a b l e s to be e x p e c t e d in m a c h i n e - t h i n n e d s t a n d s w e r e p r o b a b l y r e p r e s e n t e d i n these p l o t s . H o w e v e r , 8 inches was t h e m i n i m u m s p a c i n g o f a n y t r e a t m e n t i n this e x p e r i m e n t a n d t h u s t h e r e were n o n e of t h e very close spaced hills often p r e s e n t in m a c h i n e - t h i n n e d s t a n d s .
O b v i o u s l y it was n o w i m p o s s i b l e to m e a s u r e t h e spaces w h i c h were b e t w e e n t h e hills of these p l o t s a n d it was, t h e r e f o r e , necessary to assume t h a t t h e p l a n n e d spacings, 8 - o r 12-inch respectively, h a d b e e n a t t a i n e d . U s i n g this a s s u m p t i o n a n d t h e definition o f u n u s e d space p r e v i o u s l y given t h e t o t a l hills, t o t a l p l a n t s a n d o c c u p i e d space for each p l o t w e r e c a l c u l a t e d . T h i s s t u d y was o f e i g h t t r e a t m e n t s g r o w n i n six r a n d o m i z e d blocks. T h e plots were 60 feet in l e n g t h a n d 8 rows in w i d t h . All d a t a a r e from t h e six inside rows of e a c h p l o t . Since, by d e f i n i t i o n , all space is o c c u p i e d unless t h e d i s t a n c e b e t w e e n hills exceeds 16 inches single skips in 8-inch s t a n d s w e r e i g n o r e d ; t w o a d j a c e n t skips c h a r g e d w i t h 8 inches of u n u s e d space, etc.
In t h e case of 12-inch spacings single skips w e r e c h a r g e d w i t h 8 inches of u n u s e d space, two a d j a c e n t skips c h a r g e d w i t h 20 inches, etc. D a t a for s t a n d s a s hills, p l a n t s o r o c c u p i e d space for this e x p e r i m e n t a r e p r e s e n t e d i n T a b l e 2 . T h e r e c o r d e d yields o f r o o t s a r e a d d e d i n t h e last c o l u m n o f this t a b l e as of possible i n t e r e s t .
As Ve exceeds Vb for all t h r e e estimates of s t a n d a n d t h e block m e a n s h a v e b e e n o m i t t e d as of no p r o b a b l e i n t e r e s t . Since t h e t r e a t m e n t s in this test were d e s i g n e d to o b t a i n large s t a n d differences t h e F values for t h e t h r e e e s t i m a t e s of s t a n d , w h i l e very g r e a t , are p r o b a b l y of little i m p o r t a n c e . In this case t h e c o n v e n t i o n a l analysis of v a r i a n c e for a r a n d o m b l o c k test gave l i t t l e i n f o r m a t i o n o n t h e t h r e e estimates o f s t a n d , e x c e p t t h a t t h e space
P R O C E E D I N G S — E I G H T H G E N E R A L M E E T I N G 155 Table 2-—Thinned Stands and Acre Yields of Roots, Populations Study, Fort Collins,
Colo., 1949. Stands Expressed as: (1) Hills Per 100 Feet of Row, (2) Plants per 100 Feet of Row, (3) Percent of Row Length Occupied by Sugar Beet Plants. Data Given as 6-Plot Averages.
o c c u p i e d e s t i m a t e r e s u l t e d ix\ t h e l o w e s t s t a n d a r d e r r o r v a l u e a n d a l o w e r difference l o r p r o b a b l e significance t h a n e i t h e r o f t h e o t h e r m e t h o d s o l e s t i m a t i n g s t a n d s .
H o w e v e r , e x a m i n a t i o n o f t h e t r e a t m e n t m e a n s o f t h e s t a n d e s t i m a t e s s h o w s s o m e i n t e r e s t i n g c o m p a r i s o n s . T a k i n g f i r s t t h e 8 - a n d 12-inch full s t a n d s o f s i n g l e - p l a n t h i l l s , t h e p l a n t o r h i l l c o u n t e s t i m a t e i n d i c a t e d t h a t t h e
12-inch s p a c i n g fell o n l y s i x - t e n t h s of a p e r c e n t s h o r t of a v e r a g i n g a "perfect s t a n d w h i l e t h e s a m e e s t i m a t e i n d i c a t e d t h a t t h e 8-inch s p a c i n g was 9 p e r c e n t s h o r t o f a p e r f e c t s t a n d . W h e n o c c u p i e d s p a c e was u s e d a s t h e m e a s u r e o f s t a n d s for t h e s e t w o t r e a t m e n t s e q u a l i t y o f t h e s t a n d s was i n d i - c a t e d . I n c i d e n t a l l y , t h e yields o f r o o t s w e r e also a p p r o x i m a t e l y t h e s a m e for b o t h . P r e s u m a b l y m o s t o f t h e s k i p s i n t h e 8-inch s t a n d w e r e o n e - h i l l skips a n d d i d n o t effect t h e e s t i m a t e o f o c c u p i e d s p a c e a n d also p r o b a b l y h a d l i t t l e effect o n t h e y i e l d .
A n o t h e r case i s t h a t o f t h e 8-inch s t a n d i n w h i c h o n e - t h i r d o f t h e hills w e r e s k i p s a n d t w o fifths o f t h e r e m a i n i n g h i l l s c o n t a i n e d 2 o r 3 p l a n t s e a c h . I n t h i s case t h e e s t i m a t e o f s t a n d b y hills i n d i c a t e d s l i g h t l y m o r e t h a n a full s t a n d by t h e c o n v e n t i o n a l s t a n d a r d of 100 hills p e r 100 feet of r o w a n d i f t h e e s t i m a t e b a s e d o n t o t a l p l a n t s i s u s e d a t h i c k s t a n d was i n d i c a t e d . H o w e v e r , w h e n s p a c e o c c u p i e d was u s e d a s t h e e s t i m a t e o f s t a n d for t h i s t r e a t m e n t i t b e c a m e o b v i o u s t h a t i t was n o t a full s t a n d a n d t h a t o n l y a b o u t n i n e - t e n t h s o f t h e a r e a was a c t u a l l y u s e d t o p r o d u c e t h e c r o p w h i l e t h e o t h e r t e n t h w a s u n p r o d u c t i v e . T h e y i e l d o f r o o t s was also signifi- c a n t l y l o w e r t h a n t h e y i e l d s from full s t a n d s ; a n a d d e d i n d i c a t i o n t h a t s p a c e was n o t fully u s e d b y t h e s u g a r b e e t p l a n t s .
I n t h e case o f t h e last f o u r t r e a t m e n t s g i v e n i n t h e t a b l e , all 12-inch s p a c i n g , b u t w i t h d i f f e r e n t p r o p o r t i o n s of b l a n k hills a n d w i t h 1, 2 or 3
156 A M E R I C A N S O C I E T Y O F SUGAR B E E T T E C H N O L O G I S T S
p l a n t s i n e a c h b e e t - c o n t a i n i n g h i l l , i t i s o b v i o u s t h a t t h e s t a n d e s t i m a t e s based o n t o t a l p l a n t s , w h i l e c o m p a r a b l e a m o n g themselves, are q u i t e mis- l e a d i n g . T h e s t a n d estimates b a s e d o n t o t a l hills a r e a l s o c o m p a r a b l e a m o n g themselves a n d since t h e basic s p a c i n g for all hills was t h e s a m e they a r e fairly g o o d estimates of t h e a c t u a l s t a n d s . H o w e v e r , t h e e s t i m a t e s of space o c c u p i e d by t h e s t a n d s of these four t r e a t m e n t s are p r o b a b l y j u s t as a c c u r a t e a s those b a s e d o n t o t a l hills a n d show t h a t t h e a c t u a l s t a n d s w e r e slightly b e t t e r t h a n i n d i c a t e d b y t h e l a t t e r m e t h o d .
C o n c l u s i o n
T h e p r o p o s a l t o use a n e s t i m a t e o f t h e space o c c u p i e d b y t h e p l a n t s a s a m e a s u r e of t h i n n e d s t a n d s of sugar beets is a d v a n c e d . Some of t h e a s s u m p - t i o n s t h a t m u s t b e m a d e t o o b t a i n such a n e s t i m a t e a r e discussed. E x a m p l e s are g i v e n t o i n d i c a t e t h a t t h e m e t h o d i s m o r e a c c u r a t e t h a n estimates o f s t a n d b a s e d on e i t h e r t h e t o t a l p l a n t s or total hills in a g i v e n l e n g t h of r o w . T h i s e s t i m a t e of space o c c u p i e d will p r o b a b l y be m o s t useful as a m e a s u r e of s t a n d s of m a c h i n e - t h i n n e d sugar beets. M o r e e v i d e n c e is n e e d e d on this p o i n t .
L i t e r a t u r e C i t e d (1) C O O N S , G. H.
1948. Space r e l a t i o n s h i p s as affecting yield a n d q u a l i t y of sugar beets.
P r o c . A m e r . Soc. S u g a r B e e t T e c h . 1948: p. 252-268.
(2) D E M I N G , G . W .
1948. T h e effect o f v a r i a t i o n s i n r o w w i d t h a n d p l a n t p o p u l a t i o n s o n r o o t yields a n d sucrose p e r c e n t a g e of s u g a r beets at F o r t Col- lins, C o l o . P r o c . A m e r . Soc. S u g a r B e e t T e c h . 1948: p. 280-281.
(3) D E M I N G , G . W .
1942. R e l a t i v e yields of r e d u c e d s t a n d s of sugar beets p l a n t e d at a n o r m a l d a t e a n d o f r e p l a n t e d s u g a r beets. Proc. A m e r . Soc.
S u g a r B e e t T e c h . 1942: p. 197-202.
(4) T O L M A N , B I O N ; J O H N S O N , R O N A L D ; B I G L E R , J . A .
1948. R o w w i d t h s a n d s u g a r b e e t p r o d u c t i o n . P r o c . A m e r . Soc. S u g a r B e e t T e c h . 1948: p . 282-286.
(5) T O L M A N , B I O N .
1946. P o p u l a t i o n a n d d i s t r i b u t i o n studies w i t h sugar beets. P r o c . A m e r . Soc. S u g a r B e e t T e c h . 1946: p. 177-184.