134 J O U R N A L OF T H E A. S. S. B. T.
D e t e r m i n a t i o n of raffinose is given as p e r c e n t on dry substance in the beet juice a n d assumes a constant marc. Calculations are on o b t a i n e d data w i t h o u t transformation.
Variability of Population
T h e variances of the p a r e n t a l a n d F1 p o p u l a t i o n s may be used to m e a s u r e e n v i r o n m e n t a l variability if the p a r e n t s are homozygous for the genetic factors u n d e r consideration. T h e total variance of the segregating generations is the sum of the genetic a n d e n v i r o n m e n t a l variability. In this study, the variances p r o v i d e an estimate of the homozygosity of the parents.
I n a s m u c h as the m e a n squares of the two p a r e n t s a n d the F1 ( T a b l e 1) do n o t differ significantly as m e a s u r e d by the s t a n d a r d errors of the variance as described by Fisher ( 5 ) , it may be assumed t h a t the p a r e n t s are homo- zygous for genes c o n d i t i o n i n g raflinose p r o d u c t i o n .
Table 1.—Variances and Their Standard Error for Percent Raffinose on Dry Substance for Six Populations Derived from Two Inbred Lines of Sugar Beets.
Population Means
T h e o b t a i n e d means of the various p o p u l a t i o n s differ significantly in all comparisons except F1 a n d F2 as shown in T a b l e 2. T h e m e a n s of the F1 a n d F2 p o p u l a t i o n s are statistically equal a n d are e q u a l to the average of the m e a n s of the p a r e n t a l p o p u l a t i o n s . T h e m e a n s of the backcross popu- lations are also e q u a l to the average of the m e a n s of the F1 a n d their respec- tive p a r e n t s . T h e s e relationships can exist only in the absence of measurable d o m i n a n c e a n d / o r genic interactions or linkage. C o m p a r i s o n of obtained p o p u l a t i o n m e a n s with calculated theoretical m e a n s on the arithmetic scale gives a good fit by b o t h s t a n d a r d e r r o r a n d X2 tests. T h e X2 value for comparison o b t a i n e d with geometric m e a n s eliminates the possibility t h a t gene action in this case can be following the geometric scale. The scale thus can be considered as additive a n d n o t multiplicative.
Table 2-—Obtained Arithmetic and Theoretical Arithmetic Means Compared with Geometric Means for Percent Raffinose in Sugar Beets Based on Dry Substance.
Table 3.—Frequency Distributions as Percent for Six Populations for Percent Raffinose on Dry Substance.
136 J O U R N A L OF T H E A. S. S. B. T.
PERCENT RAFFINOSE
F i g u r e 1.—Frequency d i s t r i b u t i o n for six p o p u l a t i o n s . Genetic Analysis
Both Table 3 a n d Figure 1 indicate t h a t the frequency distributions for the P2 a n d B1 to P2 p o p u l a t i o n s do n o t reach zero on the scale, indicat- ing P2 carries some genes for raffmose p r o d u c t i o n .
T h e o r e t i c a l values for the ratios of the e x t r e m e genotypes each popu- lation has in c o m m o n are given in T a b l e 4. T h i s table has been calculated from the e x p a n s i o n of the b i n o m i a l for the backcross a n d F2 populations, as d e m o n s t r a t e d by Powers ( 2 ) ; the ratios are d e v e l o p e d assuming no d o m i n a n c e , linkage, or gene interactions; a n d t h a t effective factor pairs for the p r o d u c t i o n of raffmose are e q u a l in m a g n i t u d e , a n d t h a t o n e effective factor p a i r is non-isodirectional (or in o t h e r words, o n e effective factor p a i r for raffinose p r o d u c t i o n enters the cross from the low raffmose parent).
O n e premise in the use of g e n o t y p i c ratios for d e t e r m i n a t i o n of effective factor pairs is that the frequency d i s t r i b u t i o n s should n o t be inhibited at the e n d of the curve from which the ratios are d e t e r m i n e d . It was indicated above ( T a b l e 3 a n d Figure 1) t h a t b o t h the P2 a n d to a lesser extent the B1 to P2 p o p u l a t i o n s , a p p e a r to be i n h i b i t e d at the lower e n d of the popu- lation curve. T h e lower classes of the P2 a n d B1P2, however, are probably a c c u m u l a t e d r a t h e r t h a n i n h i b i t e d . In the chemical analysis used it is necessary to a c c u m u l a t e n u m b e r s in the lower classes d u e to t h e lack of refinement in m e a s u r i n g m i n i m a l values. Since a r i t h m e t i c accumulation is involved in the d e t e r m i n a t i o n of t h e ratios of the extremes of the popula- tions, this analytical a c c u m u l a t i o n should n o t influence the o b t a i n e d ratios unless there is a c c u m u l a t i o n b e y o n d the classes which involve t h e genotypes u n d e r consideration. Assuming this to be an a c c u m u l a t i o n , r a t h e r than an i n h i b i t i o n , it is possible to utilize b o t h extremes of the frequency distribu- tions in estimating genotypic ratios.
V O L . IX, No. 2, J U L Y 1956 137 T a b l e 4.—Theoretical Genetic Model for Number of Factor Pairs. One Effective Factor
Pair Non-isodirectional but All of Equal Magniture in Effect.
T a b l e 5.—Ratios, as Percentages, Between Frequency Distribution Classes for Specified Populations Percent Raffinose on Dry Substance.
T h e obtained ratios for the various comparisons are listed in T a b l e 5.
T h e following n u m b e r of factor differences between the two parents were estimated when the obtained values are compared to the theoretical values for different numbers of factor pairs ( T a b l e 4 ) .
T h i s information indicates that the two parents differ by about 5 effec- tive factor pairs for raffinose production, one of which is non-isodirectional.
Inheritance in Relation to Results of Previous Mass Selection It was reported by Wood (4) that progeny of one mass selection for low raffinose content had about 25 percent lower raffinose than the p a r e n t variety. T h i s reduction is in line with the findings of this inheritance study.
Assume the parental variety from which the selection was made had t h e same genetic characteristics as the F2 population studied. 10 beets were
Table 5A.—Indicated Number of Factor Pairs for Each of Eight Genotypic Ratios.
138 J O U R N A L OF T H E A. S. S. B. T.
chosen from 150 in the selection. If these r e p r e s e n t e d the lower 1/15 of the genotypic d i s t r i b u t i o n , assuming 5 effective factor pairs of equal magni- t u d e in effect, additive, a n d in e q u i l i b r i u m , the theoretical r e d u c t i o n in raffinose should have b e e n 60 p e r c e n t ; the result of a r e d u c t i o n in gene frequency from 50 p e r c e n t to 20 p e r c e n t . However, with genetic a n d en- v i r o n m e n t a l variability confounded, it m i g h t be assumed t h a t the roots selected h a d genotypes falling in the lower half of the genotypic distribution.
On this basis the frequency in raffinose genes would be r e d u c e d from 50 p e r c e n t to 37.7 p e r c e n t , resulting in a r e d u c t i o n in raffinose of only 25 percent.
Summary
1. The i n b r e d lines of sugar beets used as p a r e n t a l m a t e r i a l for this study were a p p a r e n t l y homozygous for the factors each carried for production of raffinose in the beet.
2. Quantitatively, the factors for raffinose p r o d u c t i o n in the two par- ents followed an a r i t h m e t i c scale a n d consequently are additive.
3. T h e n u m b e r of effective factor pairs for p r o d u c t i o n of raffinose between the two p a r e n t s is a b o u t five a n d at least o n e is non-isodirectional a n d all are e q u a l i n m a g n i t u d e .
4. N e i t h e r d o m i n a n c e , heterosis, n o r linkage a p p e a r e d to be involved in the cross studied.
References
(1) B R O W N , R. J. 1952. Analytical Chemistry 24:384.
(2) POWERS, L E R O Y . 1955. C o m p o n e n t s of variance m e t h o d a n d partition- ing m e t h o d of genetic analysis a p p l i e d to weight p e r fruit of tomato h y b r i d a n d p a r e n t a l p o p u l a t i o n s . T e c h . Bulletin N o . 1131, U. S. Dept.
of A g r i c u l t u r e .
(3) BREWBAKER, H. E. a n d DOXTATOR, C. W. 1954. Cooperative testing of i n b r e d s — t h r e e years results. Proc. Amer. Society Sugar Beet Tech.
8 (2) : 75-78.
(4) W O O D , R. R. 1954. B r e e d i n g for i m p r o v e m e n t of processing character- istics of sugar beet varieties. Proc. Amer. Soc. Sugar Beet Tech.
8 (2) : 125-133.
(5) F I S H E R , R. A. 1934. Statistical m e t h o d s for research workers, p. 78.
Oliver a n d Boyd, E d i n b u r g h a n d L o n d o n .