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HETEROSIS m YIELD AND YIELD
COMPGNENTS or BARLEY
(HORDEUM VULGARE, L. EMEND. LAM.) _ *

Thesis'for the Degree of Ph; D‘
MICHIGAN STATE UNIVERSITY
LAUD B, OKOLI
19 69

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This is to certify that the

thesis entitled

Heterosis in Yield and Yield Components of
Barley (Hordeum vulgare, L. Emend. Lam.)

 

presented by

Laud B. Okoli

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in grog $91 ence

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ABSTRACT

HETEROSIS IN YIELD AND YIELD COMPONENTS OF BARLEY

(HORDEUM VULGARE, L. EMEND. LAM.).

 

BY

Laud B. Okoli

In an 8 x 8 diallel cross of barley varieties, the
genetic mechanisms influencing the F1 and heterotic res-
ponses in yield and yield components were examined.

Trait dominance was found to be inversely related
to the performance of parental lines. Both trait dominance
and additivity were shown to influence the performance of
the components of yield in the progeny, but the geometric
configuration of these components in the parents was most

important in determining grain yield in the F A prediction

1’

equation using geometric configuration and yield both computed

from general combining ability estimates on the parents' yield

components gave a 64% determination of the F1 grain yield.

A method of computing geometric configuration was presented.
The base angle measuring the degree of relationship

between parents was not related to F performance except

1

as it relates to the components of yield in their expression

in geometric configuration of the F1 yield.

 

 

 

 

 

Laud B. Okoli

The ontogenetic sequence of development of the yield
components was found to exert an influence on grain yield

by influencing the components of yield.

 

HETEROSIS IN YIELD AND YIELD COMPONENTS OF BARLEY

(HORDEUM VULGARE, L. EMEND. LAM.)

BY

7 ,. L .12 :v' ,r _.L

Laud BS Okoli]

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of CrOp Science

1969

 

 

 

ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation
to Dr. J. E. Grafius for his help and guidance throughout
this study.

Thanks are also due to Doctors R. Thomas and C. M.
Harrison for their critical appraisal of the manuscript.

The author also wishes to acknowledge the assistance
of the U. S. Agency for International Development in pro-
viding the funds for his scholarship at Michigan State
University. The many hours spent by the author's wife,
Chioma, in the preparation of the manuscript are greatly

appreciated.

ii

 

TABLE OF CONTENTS

Page
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1
LITERATURE REVIEW. . . . . . . . . . . . . . . . . . .

Definitions of Heterosis . . . . . . . . . .
The Occurrence of Heterosis. . . . . . .
Kinds of gene action involved in Heterosis .

Dominance hypothesis. . . . . . . . . .

Heterozygosity and Heterosis. . . . . .
Geometric interpretation . . . . . . . . . .
Heterosis and environment. . . . . . . . . .
Heterosis in barley. . . . . . . . . . . . . . . .

\DwflU'lUlkww

MATERIALS AND METHODS. . . . . . . . . . . . . . . . . 11

A) Procedure . . . . . . . . . . . . . . . . . 111
Measurements taken. . . . . . . . . . . . . . 12
B) Genetic concepts investigated . . . . . . . . . l3
Heterosis . . . . . . . . . . . . . . . . . . l3
Trait dominance . . . . . . . . . . . . . . . l3
Additivity. . . . . . . . . . . . . . . . . . 13
Base Angle. . . . . . . . . . . . . . . . . l4
Geometric configuration . . . . . . . . . l4
Sequential effect of development. . . . . . . 17

RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . 19
Suggested genetic factors in F1 performance. . . . 21

a) Trait dominance. . . . . . . . . . . . . . 21

b) Additivity I I I I I I I I I I I I I I I I 26

C) Base Angle I I I I I I I I I I I I I I I I 28

d) Sequential effects . . . . . . . . . . . . 29

e) Geometric configuration. . . . . . . . . . 32

GENERAL DISCUSSION . . . . . . . . . . . . . . . . . . 46
SUMMARY AND CONCLUSIONS. . . . . . . . . . . . . . . . 49
LITEMTURE CITED I I I I I I I I I I I I I I I I I I I 51

APPENDIX I I I I I I I I I I I I I I I I I I I I I I I 56

 

 

 

10.

ll.

12.

'41
. . H HI 4""?" ‘;“

 

LIST OF TABLES

Page
Heterosis in yield and the yield components 3
expressed as a percent of the midparent . . . 20 L
Deviations from parental values used in :
computing trait dominance in yield and :
components of yield . . . . . . . . . . . . . 26 I
Multiple regression statistics for heterosis @
in the number of heads per plant (heterosis
as percent of midparent). . . . . . . . . . . 27

Multiple regression statistics for the number

of seeds per head in the F1 . . . . . . . . . 27

Multiple regression statistics for heterosis
(percent of midparent) in seed weight . . . . 28

Correlation coefficients between parents
based on seventeen traits . . . . . . . . . . 29

Multiple regression statistics for the

number of heads per plant in the F1 . . . . . 31
Multiple regression statistics for heterosis
(percent of midparent) in the number of seeds
per head in a plant . . . . . . . . .7. . . . 31

Multiple regression statistics for average
seed weight in the F1 plants. . . . . . . . . 32

Multiple regression statistics for yield in
grams per plant in the F1 . . . . . . . . . . 34

Multiple regression statistics for heterosis
(percent of midparent) in grain yield per
plant I I I I I I I I I I I I I I I I I . I I I 36

Multiple regression statistics for heterosis

(percent of Better parent) in grain yield
per plant I I I I I I I I I I I I I I I I I I 36

iv

 

 

Table

l3.

14.

15.

Page

Analysis of variance of 8 varieties and
their 28 crosses in grain yield per plant
(Eberhart and Gardner's Analysis II). . . . . 40

Simple regression statistics for F progeny

grain yield as the dependent variaDle and

geometric configuration and yield predictions

each used as the independent variable . . . . 42

Multiple regression statistics for F progeny

grain yield as the dependent variabl and

geometric configuration and yield as the
independent variables . . . . . . . . . . . . 45

 

—— A--. ,

 

 

Figure

1.

LIST OF FIGURES

Trait dominance in yield. Yield in gram

of a parent subtracted from the average

of the yield of all crosses with that

parent plotted against the yield of the

parent. . . . . . . . . . . . . . . . . . . . .

Trait dominance in the number of heads per
plant. Performance of a parent subtracted
from the average of its performance in all
crosses and plotted against the parent's
performance . . . . . . . . . . . . . . . . . .

Trait dominance in the number of seeds per
head. Performance of a parent subtracted

from the average of its performance in all
crosses and plotted against the parent's
performance . . . . . . . . . . . . . . . . . .

Trait dominance in seed weight. Performance
of a parent subtracted from the average of

its performance in all crosses and plotted
against the parent's performance. . . . . . . .

Geometric configuration and F grain yield.
Configuration estimated as thé ratio of the
product to the sum of the F components each
expressed as a percent of that of the highest
yielding cross. . . . . . . . . . . . . . . . .

Geometric configuration and heterosis. Con-
figuration estimated as the ratio of the '
product to the sum of the midparental com-
ponents each expressed as a percent of the
highest yielding cross. . . . . . . . . . . . .

-.

Geometric configuration and F grain yield in
gram per plant. Average effeét of the parents
in the crosses was used as the parental values
and midparental values scaled using the com-
ponents of the highest yielding cross . . . . .

vi

Page

22

23

24

25

33

36

38

 

 

Yifif'

 

 

 

Figure

8. Observed yield and yield predicted from
the average effect of yield in parents
(Av. of all crosses with a parent used as
the parental effect; estimate of general
combining ability). . . . . . . . . . . .

Page

43

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LIST OF APPENDIX TABLES

Table Page

I. Analysis of variance of raw data in yield
and yield components. F values and
significance levels . . . . . . . . . . . . . . 51

II. Average F and parental performance for yield
in seed wéight in grams per plant, and in the
Components Of Yield I I I I I I I I I I I I I I 57—60

III. Analysis of grain yield data using Eberhart
and Gardner's general model for genetic effects.
Table of genetic constants. . . . . . . . . . . 61

IV. Average parental performance for yield and
components of yield . . . . . . . . . . . . . . 62

viii

 

 

 

 

 

 

 

LIST OF APPENDIX FIGURES

Figure Page

I. Eberhart and Gardner's genetic constants and
geometric configuration. Configuration h

computed from estimates of general combining :1

ability of the components of yield . . . . . . 63 E
II. Yield and geometric configuration estimated ‘4

from observed midparental values . . . . . . . 64 l

ix

 

 

 

 

INTRODUCTION

The successful utilization of hybrid vigor, first
in corn and later in other crops, has stimulated a great
deal of interest in the general area of heterosis. The
prospects of a hybrid barley in commercial production make

the search for the causes of heterosis in this crop par-

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ticularly important.

In plant and animal breeding, the economically
desirable heterotic effects are often associated with yield.
Yield in most cases is a complex trait with a complicated
inheritance pattern where a large part of the variation is
caused by genotype-environment interaction. Extensive
programs for the evaluation of lines that will combine to
give heterosis have been undertaken, and many breeding
techniques evolved from them. These systems do a creditable
job of isolating additive effects but are helpless in pre-
dicting specific combining ability a priori without first
making the cross. Success in the later category awaits a
better understanding of the real basis for specific com-
bining ability effects. The present study was undertaken
to find ways of increasing the precision of F1 yield

prediction.

 

 

 

   

 

‘We will consider such things as:

l) the effect of sequential ontogenetic development
of the components of yield in F1 yield performance;
2) the effect of the "geometric configuration" of the
components of yield in the parental lines on the
F1 yield and on heterosis;
3) The degree of relationship between putative parents
(base angle) and the F1 performance and the amount

of heterosis to be expected.

 

 

   

 

LITERATURE REVIEW

 

Definitions of Heterosis

 

Shull 1952 suggested that the concept of heterosis
be applied to "the interpretation of increased vigor, size, ' l
fruitfulness, speed of develOpment, resistance to disease

and to insect pests, or to climatic rigors of any kind,

wars-wr-

manifested by crossbred organisms as compared with corres—
ponding inbreds...." As currently used the term heterosis
refers to either an increase in performance over the better
parent or more commonly to an increase over the average per—
formance of both parents in a cross.

This dual meaning for the same term may be confusing.
Consequently, the term "heterobeltiosis" was coined by
Patterson and Bitzer (1966) to designate the improvement of
the heterozygote over the better parent in the cross. It
therefore seems that "heterosis" should be reserved for an
increase in performance over the mid-parental value, the

definition used in this study.

The Occurrence of Heterosis

 

As.a result of some of the earlier work with maize
(East and Hayes 1912, East 1936, Hayes and Johnson 1939,
Johnson and Hayes 1940, Wu 1939) it is commonly accepted that

crosses of more distantly related parents show greater

 

 

 

     

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'heterosis than those more closely related. This conclusion
may not hold absolutely for the entire range of genetic di-
versity encountered in the species. From a more recent work
on combining ability analyses in sorghum crosses, Niehaus
SE if (1966) concluded that genetic diversity could be the
key to obtaining hybrid vigor. In this report, crosses
involving geographically and presumably genetically diverse

parents produced high yielding hybrids. Similar work done

.‘OAJ-.. ‘hh -?-_ F—

in corn by Kinman and Sprague (1945) led them to suggest
that the range in combining ability among the inbred parents 3
would determine the efficiency of including those parents
in a synthetic variety. Also in maize, Moll 32 El (1965)
noted that the degree of genetic diversity among the parental
pOpulations led to increased heterosis within a restricted
range but that extremely divergent crosses resulted in a
decrease.
In a survey of many self pollinated crOps, Ashton
(1946) showed some evidence that greater heterosis was
exhibited from interspecific than intraspecific crosses.
Shull (1952) concluded that heterosis in a cross was the
result of unlikeness in the constitutions of the uniting
parental gametes.«

Kinds of gene action involved
in‘fleterosis

 

Though many theories have been offered to explain the

mechanism of heterosis, it is quite possible that different

 

 

 

 

mechanisms operate in different organisms. The success of

hybrid vigor utilization first in corn, and later in many
other crops stimulated some interest in the search for the

genetic basis of heterosis.

Dominance hypothesis

 

Considerations of dominance and heterozygosity have
been of primary interest to workers attempting to explain
the genetic mechanism of heterosis. Jones (1917) proposed

that heterosis arises as a result of the dominance of linked

Wit 5.7 r—

factors. Dobzhansky (1941) and others have recorded that,
along the course of evolution, deleterious recessive genes
accumulate in many species, thereby reducing the efficiency
of the organism. When the genes are in the heterozygous
state on the other hand, the deleterious (efficiency re—
ducing) effect is masked by their dominant alleles.

Crow (1952) suggests that inbreeding depression and
recovery on crossing are mainly the result of loci at which
the favorable allele is dominant and the recessives are at

low frequency.

Heterozygosity.andtHeterosis

Much of the early work on heterosis was with maize,
a cross-pollinated crop. In most cases, crosses involving
inbred lines resulted in heterosis. It was natural there-
fore, to associate heterosis with heterozygosis and thus

arose the overdominance theory of heterosis. This theory

 

 

 

 

states that heterozygosity per se is necessary for the full

expression of heterosis. Shull (1908) stated that hybridity
itself has a stimulating effect on the physiological acti-
vities of the organism. This conclusion probably has no
basis in fact. Explanations must therefore revolve around
the characteristics of the heterozygote and how they differ 1
from homozygotes. For instance, East (1936) attaches to '
heterozygotes a versatility of develOpment that is expressed
in terms of alternate metabolic pathways not available in
homozygotes. On the other hand, Mather (1956) argues that i
the genetic advantage of heterozygosity lies in providing
flexibility and greater stability while Robertson and Reeve
(1952), and Haldane (1954) hold the view that heterosis
results from the physiological advantages of heterozygotes.

With heterozygosity being associated as a likely cause
of heterosis, interest arose as to the nature of the heter-
otic loci. Green and Green (1940) in studies of pseudoal-
lelism showed that the unit of specific physiological action
may not be one locus in the classical sense but a complex of
tightly linked loci. It is now commonly held by many investi-
gators that these heterotic complex loci produce the specific
effects of heterosis.

Much of the evidence concerning over-dominance has
been reviewed by Lerner (1954) and he concludes that over—
dominance with respect to characters closely connected with

fitness is widespread and very important. Mather (1955) on

 

 

 

 

 

the other hand believes that much of what appears to be over-

dominance with respect to certain characters in plants can
be attributed to epistasis. It seems that the most plaus-
ible explanation for heterosis, at least in some traits, is

offered by a geometric interpretation.

Geometric interpretation k
We define for the purposes of this discussion a com-
plex trait as one whose components are known (Grafius 1965).

For example, yield in barley is a complex trait having as

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its components the number of heads per plant, the number of
seeds per head, and the average seed weight.

The so-called overdominance effects at least in the
complex traits, are due to the multiplicative action of the
components. Adams and Duarte (1961) found the complex
trait, total leaf area in the field bean (Phaseolus vulgare
L.) had exhibited heterosis as a result of the multipli-
cative relationship that prevails between the two components
——1eaf area and leaflet number. The component traits were
influenced by an additive and a dominant gene system
respectively.

Grafius (1959) concluded that yield in small grains
is an artifact and that there probably is no series of quanti-
tative genes for yield as such, but perhaps only genes for
the components. This would imply that such genic effects

as dominance and additive gene action only refer to the

 

 

 

 

components, that hybrid vigor in small grains is due to
epistasis associated with the geometry of the complex trait.
Jinks (1955) associated non-allelic interaction with
overdominance-like effects in several crops. It is interest-
ing to note that he found these effects only in complex
traits such as yield and height. Reasoning that epistasis
results from the product of the sum of inter-locus effects
(additive-geometric model éAi :IBl , where A and B are loci,
and n is the number of loci) Grafius (1965) postulates that
this model along with relatively small amounts of dominance
for the component traits offers the most plausible explan-
ation of the large heterotic effects seen in many complex

traits.

Heterosis and environment

 

Any phenotype is a product of the genotype and the
environment. The expression of traits is therefore in-
fluenced by the environment. Pfahler (1966) found that
heterosis was dependent on the interrelation of environment
and genotype, and that the environments affected the magni-
tude and direction of heterosis in crosses of rye, Secale
cereale. Similar phenomena have been observed in maize by
Sprague (1952) and in DrOSOphila by Gowen (1952).

Most experiments evaluating heterosis in crosses of
plant species have been with spaced planting. It is not

likely that similar amounts of heterosis may be displayed

 

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‘under more conventional planting methods. Santiago 33 31
(1968) showed that heterobeltiosis (increase over the better
parent in a cross) was higher in hill than drill plantings
for winter wheat. They suggested that the advantages of

hybrids may be overestimated to some extent from hill data.

Heterosis in barley

 

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I

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Gowen (1952) has reviewed many different aspects of
this subject. In all, yield seems to be the trait of great-

est interest. Pawlisch and Van Dijk (1965), using distinctly

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different varieties, reported heterosis for both forage and
grain yield in 4 Fl barley hybrids. Immer (1941) and

Suneson (1962) have reported that grain yields of some barley
varieties exceed their respective better yielding parents.
Rasmusson 32 El (1966) reported heterosis in certain malting
quality characters in F1 hybrids of 8 barley crosses. Murphy
(1966) and Upadhyaya and Rasmusson (1967) showed heterotic
responses in yield and yield components of oats and barley
respectively.

It is unlikely that only one kind of gene action is
universally responsible for heterosis. It could well be that
many kinds of gene action may Operate simultaneously in
determining heterosis. Hutchinson gt El (1938) concluded
that epistasis or interallelic gene interaction along with
dominance might be involved in heterosis. Similarly, Morley

Jones (1958) concluded that heterosis is a complex genetical

 

 

phenomena depending on
and epistasis, as well
noted further that the
type of gene action or

cative qf the presence

10

the balance of additivity, dominance
as on the gene distribution. He
presence or absence of any particular
interaction is not in itself indi—

or absence of heterosis: heterosis

can result from a whole range of combinations of gene

effects.

The evidence seems strong at least for the complex
traits, that heterosis results from the multiplicative

action of the components which themselves are affected by

 

dominance and additivity.

 

 

MATERIALS AND METHODS

 

A. Procedures

Eight parental barley (Hordeum vulgare L. Emend.,
Lam.) lines (hereinafter called varieties) were crossed l
in a diallel arrangement (without reciprocals). Seven of I A
the varieties were second cycle selections from Liberty x
Kindred crosses made in 1960 at East Lansing, Michigan. The
other variety was Traill. Liberty was derived from a Titan
x (Lion-Manchuria Chevron) cross and Traill from Titan x
Kindred cross (Grafius, personal communication).

Each of the 8 varieties was planted in 6 pots of sand
at the rate of 4 seeds per pot in the greenhouse at East
Lansing, Michigan in the fall of 1966. The cultures were
watered using Hoagland's solution. Fl seeds from the
crosses and selfed seeds from parental lines were harvested
and planted at the Crop Science Farm at East Lansing, in
.May 1967. There were 16 plants on the average of each
cross or parent per row. Spacing was 6 inches within and
12 inches between the rows. Row allocation was randomized
within each block and two replications were used. There
were two border rows of Betzies (a 2-row barley variety) on
each end of the plot.

The plots were dusted regularly with sulfur against

mildew.
11

 

 

 

 

   

 

12

Measurements Taken

Notes were taken on heading dates estimated as the
date on which 75% of the heads were out of the boot. At
maturity, each plant was pulled, loosely tied together and
dried in a warm chamber at 105F for 3 days. The height of
each plant was measured. The number of head bearing tillers I
on each plant was recorded and the heads removed, threshed
separately and the grain yield of each plant recorded. A

3.0 gram portion of seed from each plant was counted using

 

an electronic seed counter, and the average seed weight g
recorded. The average number of seeds per head was obtained
by dividing the entire weight of seeds per plant by the pro-
duct of seed weight and tiller number.

Protein content was determined on each sample using
a Udy colorimeter. Diastatic power was estimated using
'Clinitest Reagent Tablets' to estimate the amount of sugar
in the seed samples. Test weight measurements were taken on
bulked variety seeds.

The following vegetative characters were measured on
the parent varieties; average length and width of the flag
leaf; average length of the glume and glume awn. The antho—
cyanin content of the awn on the lemma was scored visually.
The density of (a) barbs on the awns; (b) lemma teeth were
microsc0pically examined and scored on a l to 4 scale:

1 being none, and 4 several or most.

 

 

 

 

 

13

B. (Senetic Concepts Investigated

An analysis of variance of the F1 and parental lines
data showed no significant differences between the repli-
cations (See Appendix Table I). Therefore the average of
both replications for each measurement was used in all sub-

sequent analysis. I

Heterosis

 

Heterosis in a trait was estimated as the deviation

 

from the midparental value. This deviation expressed as a g
percent of the midparental value was called 'percent

heterosis'. Heterobeltiosis in a trait is defined according

to Patterson and Bitzer (1966) to be the excess in perform-

ance over the higher parent. This excess expressed as a

percent of the higher parent is called 'percent heterobelt-

iosis'.

Trait Dominance

 

For any one character, the dominance effect of each
parental line is termed the trait dominance. It was esti-
mated by regressing the deviation of a parent from the
average performance of that parent in all the crosses involving

it against that parent.

Additivity

 

The additive estimate for the F1 was taken to be the

parental contribution to their offspring, that is, the

 

 

s-r gels-um

, awn—qr

 

 

 

 

 

14

theorxatical midparent value. This of course assumes inde-

pendent and additive action of the genes responsible for the

trait.

Base Angle

When two varieties are represented as vectors using
many traits (Grafius, 1965), it is possible to determine
the simple correlation coefficient r, between such vectors.
The angle having the same cosine-value as r, is the base

angle between the two-varieties. Seventeen traits were-

kam'bm
. "'1”

used to form the vectors from whicthhe baSe angle for

each pair of parents Was determined.

Geometric Configuration

Yield in barley is a product and can be visualized
to have a geometry. The 3 components—-number of heads per
plant, é, number of seeds per head, Y, and the average seed

weight, E, constitute the edges of a parallelepiped.

 

 

|><

 

 

IX

 

 

 

IN

 

 

 

It is obvious that the shape and volume of this
parallelepiped will be determined by the relative amounts

of the three yield components.

 

 

 

15

The geometric configuration for each cross was esti—
mated as the ratio of the product to the sum of its yield
components (ratio of volume to perimeter) each expressed as
a percent of that of the highest yielding parent. The
rationale for this is discussed below.

Since a cube has the maximum volume for a parellele-
piped of a given perimeter, and since yield in barley is a
volume, it is postulated that the variety having the con-
figuration of a cube (optimum configuration) will have the
highest yield. The next variety having a configuration
closest to that of a cube will have the next highest yield,
and so on.

Since the geometric configuration is also dependent
on the scale of each of the edges, we assume that the high—
est yielding variety has a configuration approaching a cube
and adjust its values of 5, Y, and E to a scale where
X'=Y'=§'=l.00. Under this constraint, this outstanding

variety becomes a cube with a ratio of X' . Y' . Z' = l/3
x' +Y'+Z'

 

as a maximum configuration value. Deviations from the hypo-
thetical cube by other varieties will show up as differences
from the maximum ratio of 1/3.

It is evident that configuration as used here has two
components--volume and shape. The validity of this mathemat-
ical concept may be illustrated by examining the relationship

between different shapes and volumes and the configuration

 

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"‘3‘" r

 

16

conmnrted as a ratio of the product to the sum of the edges.
Consider the parallelepipeds of a constant volume but with
varying shapes:
Case I.
Let the ratio of the edges be 1 : 1 : 1. Then

the confi uration i l x l x 1
g sl—+1—+—1°r 1/3-
Case II.
Let the ratio of the components be 0.8 : l : 1.2.

Then the configuration is 0.32.

 

Case III.
For a component ratio of 0.6 : 0.8 : 1.6, the
configuration is 0.256.
Case IV.
For a component ratio of 0.4 : 0.5 : 2.1, the
configuration is 0.14.
Consider parallelepipeds of a constant shape but vary-
ing volumes:
Case I.
Let the ratio of the edges be 1 : 1 : 1. As
in case I above, the configuration is 1/3.
Case II.
Let the ratio be 0.8 : 0.8 : 0.8; then the
configuration is 0.213.
Case III.
For a component ratio of 0.5: 0.5 : 0.5, the

configuration is 0.08.

 

17

Thus it is seen that both shape and size affect the
configuration of the parallelepiped, deviations from the
optimum due to either or both,'1eading to a low configuration
value. By hypothesis, this should lead to a low yield. It is to
be noted that by construction, the Optimum configuration
cannot be exceeded.

Geometric configuration for the prediction of F1 grain
yield was computed by using the effect of each parental line
(an estimate of the general combining ability) as the parental

value. Midparental values in each of the components were

 

calculated for each cross, and then expressed as a percent
of the equivalent component in the highest yielding variety.
The rationale here is that any variety with the highest
average effect is biologically the most efficient form.
Hence, the components are scaled to be a cube which is the
most efficient shape mathematically. Atvthis point, some-

thing new has_beenhadded to the geometric approach. Hereto-
kuwmmmu-wJ, - 1-MW_WW _‘

. . MA I
a mg" 5'” C, u... .. 1. .1...“ x... M_~.W.a-K'A~b——Afnaa.w\w*‘4i W

foremmhavemusedmthe.-.pr..Iela’<:—.i9r1..,meana,._.1;9.. $831.9 With - A
comparison will be made between the efficiency of yield
prediction using this geometric configuration approach and

the conventional method using general combining ability

estimates.

Sequential Effect of Deve10pment
It is known that grain yield in barley proceeds by a
sequence of events. The simplest of such sequence may be

listed as: formation of tillers on which the heads form on

 

   

18

whitfli the seeds are formed. It is known that the amount of
iflua'previous incident affects the amount of the one following
it. For example, in inbred lines, seed weight may influence
the surface area of the crown primordia on which the tillers
are formed; the number of tillers may influence the number

of seeds per head; and the total number of seeds may in-

 

fluence the amount of carbohydrates to be stored in each
seed since this would be synthesized from a given photosyn-

thetic surface. An effective weighting system will be

 

introduced later by which the effect of such sequential ‘fl
develOpment is accounted for in estimating the contributions
of the other genetic factors.
The variance of the grain yield data for the eight
varieties and their 28 variety crosses were analyzed using

Eberhart and Gardner's general model for genetic effects.

 

   

RESULTS AND DISCUSSION. ..

 

The mean heterotic response calculated as a percent
of the midparental performance for yield and yield com-
ponents is presented in Table 1. In grain yield per plant, Fa
11 of the 28 F1 hybrids exceeded their midparental average 1
for the cross and significantly exceeded the entire F

1
population average as shown by Duncan's multiple range test 1

 

(See Appendix Table II). Eight of these 11 heterotic lines I
also exceeded their higher yielding parents (heterobeltiosis).

In number of tillers per plant, E, 8 of the 28 F 's exceeded

1
their midparental values and 5 of these exceeded their

higher parents. Twenty of the 28 Fl's exceeded their mid-
parental values for the number of seeds per head; sixteen
exceeded their higher parents. In seed weight (weight of

1000 seeds) 13 of the 28 F 's exceeded their midparental

1
values; only 4 exceeded their higher parents. For the three
components of yield, the most heterosis was exhibited in the
number of seeds per head and the least in seed weight.

The data seem to be in line with what is usually found
in the literature. For instance, Upadhyaya (1967) observed
that out of 28 F1 hybrids in barley, the number that signif-
icantly exceeded the corresponding midparental values for yield,

kernel weight, kernels per head and heads per plant were 14,

7, 11, and 5 respectively.
19

 

20

 

 

 

'Table 1. Heterosis in yield and the yield components
expressed as a percent of the midparent.
Fl - M.P. x 100
M. P.
No. of seeds

Cross Yield Tiller No. Ayper head Seed wt.
1 x 2 10.79 0.53 7.67 1.90
1 x 3 7.96 1.66 4.27 0.93
1 x 4 -7.01 -5.13 -1.30 1.77
1 x 5 10.41 4.57 16.34 -7.29
1 x 6 -2.54 -1.38 -3.82 1.75
1 x 7 -7.14 -12.82 -0.24 6.88
1 x 8 38.39 23.42 19.86 7.35
2 x 3 13.09 1.82 5.26 4.39
2 x 4 -16.52 -19.49 2.99 -2.76
2 x 5 -10.75 -7.89 4.96 -8.48
2 x 6 -9.97 -15.83 8.01 -1.82
2 x 7 2.71 -8.93 2.54 10.52
2 x 8 6.19 -12.78 9.90 -2.70
3 x 4 -25.04 -14.39 -3.19 8.18
3 x 5 -8.23 -6.59 -1.36 -0.44
3 x 6 -11.62 -9.16 0.76 3.57
3 x 7 3.66 1.39 -0.03 1.88
3 x 8 -2.77 -6.88 0.95 2.21
4 x 5 -21.45 -14.24 -0.78 -7.94
4 x 6 -4.00 -12.15 9.23 0.00
4 x 7 -21.83 -21.04 0.19 -2.22
4 x 8 -17.33 -23.75 5.38 1.68
5 x 6 -20.81 -22.06 2.59 -1.65
5 x 7 -20.03 -17.50 0.12 -3.02
5 x 8 2.76 -15.35 20.28 -13.85
6 x 7 -13.53 -1l.98 -0.50 -1.75
6 x 8 13.73 16.63 9.09 -10.78
7 x 8 21.60 7.95 16.48 -4.34

 

IWm-‘n-‘n-L )- -u

 

«Ina

{€-

 

21

Suggested Genetic Factors in
El Performance

 

 

a) Trait Dominance

Figures 1-4 show the relationship between trait
dominance and the parental values for yield and yield com-
ponents (See Table 2). A negative slope of the regression
lines indicates a decreasing rate of dominance effects as
the midparental value increases. In the case of X, the
number of seeds per head, however, one point (involving
Traill) was inexplicably off the line (Fig. 3). Since
Traill was the least related to any other in the set, this
divergence could be an indication of genetic diversity. It
could also be a chance happening. Since it is an isolated
incident, no positive explanation can be offered. However,
this aberrant point was ignored in calculating the regression
line for dominance in seed number.

All the regression coefficient values (b's) are sig-
nificant suggesting that dominance is important in deter-
mining the F1 values in both yield and the yield components.
There is an apparent negative relationship between midparent
and the amount of dominance expressed. This seems to be a
natural law for traits: that the effect of a variety in its
crosses is inverse1y related to the magnitude of the per-
formance of the variety. It follows then that higher per-
forming parents can be expected to make a prOportionately
lower contribution to their offspring than their lower

performing relatives.

1'_ .. -1; ‘ 7-LCI..¢»¥‘—”zr‘
l‘1. 21a;- v

 

 

22

Av. of Crosses - Par.

‘ 2. To .. .77:

  
 
 

-2.2342W+ 25.46

2
ll

 

4.01**

 

 

9 10 11 12 13 ' 14 " 15

Yield of parents gm/plant

Figure 1. Trait Dominance in Yield. Yield in gm of seed
of a parent-subtracted from the average of the
yield of all crosses with that parent plotted
against the yield of the parent.

4'! I...

‘ JP" " Vi“! '4..x-‘;c:al. ‘ AS a: 5:15 w tr" .. '53,

 

23

 

    

 

 

Cross Av. - Par.
21
XD D
1-
o- n
i h
E
'11 'w
*1
-2 -
XD= r0.9470X + 11.39
-3 L,
t = S.11**
_4 A. I I 1 l A?
10 11 12. 13 14 " 15

Parents

Figure 2. Trait Dominance in the Number of Heads per Plant.
Performance of a parent subtracted from the
average of its performance in all crosses and
plotted against the parents' performance.

 

24

4‘.

Cross Av. - Par.

  

 

 

]_ ..
0 Y5: -o.5542y + 24.44
t = 3.07**
-1,
n l I 1 l 1 g
36 37 33 39 4o 41 42 43

Parents

Figure 3. Trait Dominance in the Number of Seeds per Head.
Performance of the parent subtracted from the
average of its performance in all crosses with
it plotted against the performance of the parent.
Point (43,3) was ignored in calculating this
regression. (See Page 21)

 

 

 

L
201-
Cross Av.
A
10-
2D

-10 _

-20 -

 

    

25

l1~V:=,. ‘

 

1'.

-0.95Z + 211.34

 

-30 L
= l0.0l**
-40 l l J L I}
200 210 220 230 240 250 260 270

Figure 4.

Parents seed wt. gm/1000

Trait Dominance in Seed Weight. Seed weight of
a parent subtracted from the average seed weight
of all the crosses with that parent plotted
against the seed weight of that parent.

 

26

'Table 2. Deviations from parental values ([31) used in
computing trait dominance in yield and components
of yield. Performance of a parent subtracted
from the average of its performance in all crosses
involving it.

Variety AW V AX A'Y AZ

 

 

 

 

l 1.31 0.40 3.28 0.21
2 0.00 -1.67 2.40 1.43
3 -0.59 -l.02 -0.77 1.46
4 -3.33 -3.01 -0.58 -0.39
5 -l.81 -l.25 2.72 -2.70
6 -0.41 -0.39 1.98 -1.36
7 —0.16 -1.66 3.29 0.73
8 1.13 1.46 2.94 -4.00

 

b) Additivity

The effect of additivity was estimated using the mid-
parental effect in a multiple regression analysis (Tables
3, 4, and 5). Additivity accounts for about 17% (0.43 - 0.26
in the R2 deletes column, Table 3) of the heterosis observed
in the number of tillers per plant; 14% of the F1 performance
observed in the number of seeds per head (Table 4); and 6%

of the heterosis observed in seed weight (Table 5). In all

cases, additivity was significant at the 5% level.

 

27

Table 3. Multiple regression statistics for heterosis
in the number of heads per plant (heterosis
as percent of midparent) as the dependent
variable and base angle, trait dominance,
additivity (midparent value) and the chrono-
logical sequence gf development as independent
variables. The R deletes indicate the degree
of determination without the indicated variable.
(R = 0.66; R = 0.43).

 

 

 

. Beta Sig. Partial corr. 2
Variable weights level coeff1Cients R deletes
Base angle 0.07 0.71 0.08 0.43
Trait dom. 0.12 0.52 0.13 0.42
Additivity -O.45 0.01 -0.48 0.26
Seq. effect 2-0.48 0.01 -0.51 0.23

 

Table 4. Multiple regression statistics for the number of
seeds per head in the F as the dependent variable
and base angle, trait dominance» additivity (mid-
parent value) and the chronological sequencezof
development as independent variables. The R
deletes indicate the degree of determinatign with—

 

 

 

out the designated variable. (R = 0.66; R = 0.43)
Beta Sig?” Partial corr.
Variable weights -1eve1 coefficients R deletes
Base angle -0.08 0.62 -o.10 0.43
Trait dom. -0.08 0.73 -0.07 0.43
Additivity 0.57 0.03 0.45 0.29

Seq. effect 0.25 0.13 0.31 0.37

 

t :. w w‘mi‘nenn Lflfin‘f->-._'VT
‘ r;
w
.

d .
Lu

     

28

'Eablxe 5. Multiple regression statistics for Heterosis

(% M.P.) in seed weight as the dependent

variable and base angle, trait dominance,
additivity (mid-parent value) and chronological
sequeace of development as independent variables.
The R deletes indicate the degree of determination
without the designated variable. (R = 0.81;

R

 

 

 

 

= 0.66).
Beta Sig. Partial corr.
Variable weights level coefficients R deletes
Base angle 0.21 0.11 0.33 0.62 F}
Trait dom. 0.18 0.48 0.15 0.65 1 "
Additivity —0.52 0.05 -0.39 0.60
Seq. effect -0.38 0.005 -0.54 0.52 '
i
-r’

 

c) Base Angle

Correlation coefficients estimated using 17 traits
are presented in Table 6. Base angle as estimated indicates
a wide range of differences between parental lines. For
example, crosses with variety 8 show: a range in correlation
coefficients from -0.91 to 0.90 which is about the extreme.
The base angle however, did not show any significant re-
lationship to either the F1 performance or heterosis. This
result was entirely unexpected. Since the magnitude of the
correlation coefficient could be considered a measure of the
number of genes which parental lines have in common, one
would expect the more widely different types to show more
heterosis. This was not the case. In a way, the results
are confirmed by Hanson (1967) in his work with soybeans. If

this is really true, it would indicate that relatedness with

 

 

29

rEspect to genes in common is important only with respect
to the components themselves and here, as will be seen
later, only with respect to how the genes affect the con-

figuration of the yield parallelepiped.

Table 6. Correlation coefficients between parents
based on 17 traits.

 

 

 

Var. 1 2 3 4 5 6 7
2 0.28
3 -0.14 0.86
4 0 47 0.99 0.81
5 -0.12 -0.96 -0.97 -0.94
6 -0.50 -0.99 -0.79 -0.10 0.92
7 0.97 0.15 -0.36 0.25 0.11 -0.28

 

d) Sequential Effects

In estimating the relative contributions of additivity,
trait dominance, and base angle to F1 performance in the yield
components, the chronological order of development of these
components was taken into account. Since the number of seeds
per head would depend in part on the number of heads é, formed,
it (number of heads- formed) was used as one of the inde-

pendent variables in a multiple regression analysis with Y,

.-

wfi—fipr-m-mu— at. Q...

in. 1.
‘v_—I-'

 

i

 

 

30

the Ixumber of seeds per head, as the dependent variable.
Similarly, the product of E and 3 (total number of seeds)
was used as an independent variable in the analysis for seed
weight 5 as the dependent variable.

The size of a seed may determine the size of the
crown primordia where tillers are formed. Thomas (1966)
has reviewed the available information on the relationship
between parents and their progeny in seed weight. He con-
cludes that the maternal seed weight in the Gramineae
exerts an influence on seedling vigor and development of
the progeny. The seed weight in the F1 was therefore used
as one of the independent variables in the analysis for g,
the number of heads per plant.

The multiple regression statistics for the number
of heads per plant, §,in the F1 (See Table 3) and for
heterosis are presented in Table 7. Seed weight seems to
determine about 24% (0.25 - 0.01 in the R2 deletes column,
Table 7) of the heads number in the F1 as indicated by
'Sequential effects', and about 20% of the heterosis in the
number of heads per plant (Table 3).

The number of heads formed on the other hand seems
to determine about 6% of the number of seeds per head in the
F1 (See Table 4) and about 10% of the heterosis in Y, again
listed as 'Sequential effects' (Table 8). The values of
6% and 10% are however, not significant at the 5% level

and probably are not real.

 

 

31

 

 

 

 

 

Table 7. Multiple regression statistics for number of
heads per plant in the F as the dependent
variable and base angle, trait dominance and
additivity (midparent value) and the chrono-
logical sequence gf development as independent
variables. The R deletes indicate the degree
of determinaEion without the designated variable.
(R = 0.50; R = 0.25).

Beta Sig. Partial corr. 2
Variable weights level coefficients R deletes
Base angle 0.04 0.84 0.04 0.25
Trait dom. 0.12 0.57 0.12 0.24
Additivity 0.12 0.56 0.12 0.24
Seq. effect -0.52 0.01 —0.49 0.01
Table 8. Multiple regression statistics for heterosis

(% M.P.) in the number of seeds per head in

a plant as the dependent variable, and base
angle, trait dominance, additivity (midparent
value) and the chronological sequence of
development as independent variables. The R
deletes indicate the degree of determination
without the indicated variable. (R = 0.36;

R

 

 

 

= 0.13).

Beta Sig. Partial corr. 2
Variable weights level coefficients R deletes
Base angle -0.10 0.63 -0.10 0.13
Trait dom. —0.09 0.76 -0.07 0.12
Additivity 0.08 0.78 0.06 0.13
Seq. effect 0.32 0.12 0.32 0.03

 

 

32

The total number of seeds on a plant may determine
about 26% of the seed weight (Table 9) and about 14% of the
heterosis observed in seed weight (See Table 5). This is
understandable since the entire seeds are filled with carbo-
hydrates from a given surface area of leaves, awns and culms;
the more the seed number, the less the seed weight--as shown
by the negative correlation coefficient between seed number [R

and seed weight.

Table 9. Multiple regression statistics for average seed
weight in the F plants as the dependent variable, .4
and base angle, trait dominance, additivity (mid-
parent value) and the chronological sequencezof
development as independent variables. The R
deletes indicate the degree of determinatian with—
out the designated variable. (R = 0.65; R = 0.42).

 

 

 

. Beta Sig. Partial corr. 2
Variable weights level coefficients R deletes
Base angle 0.24 0.16 0.29 0.37
Trait dom. 0.28 0.41 0.17 0.41
Additivity 0.40 0.24 0.24 0.39
Seq. effect -0.52 0.004 -0.56 0.16

 

e) Geometric Configuration

Figure 5 shows the relationship between the geometric
configuration of the yield components and yield. Yield may
be considered a volume determined in barley by the product
of the number of seeds per head, number of heads per plant
and the average seed weight. As postulated above in the

section on "concepts investigated," an optimum configuration

 

 

33

    

 

 

15
Fl=58.90G-4.72
13.
F=310.96** EM1
3,1
F
11‘ t‘
9 l 1 L l n I 1 I 1 1 .
v230 -250 -270 .290 5310 7330

X' . Y' . Z'
X' + Y' +7r (G)

 

Figure 5. Geometric configuration and yield. Configu-
ration estimated as the ratio of the product
to the sum of the F components each expressed
as a percent of that of the highest yielding
cross (1x8).

 

34

WOUJ11 approach a cube. It is likely that the configuration
for any population will differ for biological reasons in
different environments, but whatever the environment, the
optimum configuration will give the highest yield in that
population; similarly, the next best configuration will
give the next highest yield, and so on, with the lowest
yielding having the poorest configuration.

The above postulate was found to hold for the data
being analyzed; the regression coefficient between yield

and configuration being highly significant. Also, geometric

FV""—

configuration determines about 84% of the F1 yield (Table 13).

Table 10. Multiple regression statistics for yield in gm
per plant in the F as the dependent variable
and base angle, trait dominance, additivity
(midparent value) and the geometric config—
uration of the F yield compoaents as the
independent variébles. the R deletes indicate
the degree of determination without the desig-

 

 

 

nated variable. (R = 0.97; R = 0.94).

_ Beta Sig. Partial’corr. 2
Variable weight level coefficients R deletes
Base angle -0.09 0.08 —0.35 0.93
Trait dom. 0.28 0.97 0.01 0.94
Additivity -0.04 0.94 0.02 0.94

Geometric
configuration 0.94 0.0005 0.97 0.10

 

. 431"

 

35

Figure 6 shows the relationship between heterosis
and geometric configuration. Table 11 shows the proportion
of heterosis accounted for by geometric configuration. The
highly significant relationship between heterosis and geo-
metric configuration is to be expected since high yields
associated with the 'right' configuration would in most
cases result in increases above the midparental value. For
similar reasons, geometric configuration determines about
47% of the excess yield over the better parent (heterobelt-
iosis) as shown in Table 12.

For prediction purposes, geometric configuration may
be estimated from the average effect of parents in crosses
involving them. Figure 7 shows the relationship between
geometric configuration computed this way and F1 grain
yield. Supposing that the highest yielding variety has the
(optimum) configuration of a cube, the components in the
other crosses are scaled, based on the respective values for
the highest yielding variety and the geometric configuration
determined as described above.

The regression coefficient is highly significant and

indicates the importance of shape with regard to yield.

 

 

   

'F

1 Midparents 36

       

4 r (heterosis)

Fl=573.30G-159.05 .

‘L

 

1"";
kg.-

 

L I

.310 830

l

«290

.270

230 .250

X' . Y' . Z'
XT+Y' +Z' (G)

 

Figure 6. Geometric configuration and heterosis.
Configuration estimated as the ratio
of the product to the sum of the mid-
parental components each expressed as
a percent of the highest yielding
cross (1x8).

 

37

 

 

 

 

 

'Takile 11. Multiple regression statistics for heterosis
(as a percent of the midparent) in grain yield
per plant as the dependent variable and base
angle, trait dominance, additivity (midparent
value) and the geometric configuration of the
F yigld components as the independent variables.
The R deletes indicate the degree of deter-
mination without the designated variable.
(R = 0.98; R = 0.96).
Beta Sig. Partial corr. 2
Variable weights level coefficients R deletes
Base angle —0.06 0.17 -0.28 0.96
Trait dom. -0.04 0.94 -0.02 0.96
Additivity —0.46 0.39 -0.18 0.96
Geometric
configuration 0.79 0.0005 0.97 0.37
Table 12. Multiple regression statistics for heterosis

(as a percent of the better parent) in grain
yield per plant as the dependent variable and
base angle, trait dominance, additivity (mid-
parent value) and geometric configuration of

the F yield comp nents as the independent
variagles. The R deletes indicate the degree
of determinaEion without the designated variable.
(R = 0.95; R = 0.98.

 

 

 

Beta Sig. Partial corr. 2
Variable weights level coefficient R deletes
Base angle -0.01 0.88 —0.03 0.95
Trait dom. -0.11 0.84 —0.04 0.95
Additivity -0.64 0.26 -0.23 0.95
Geometric

configuration 0.70 0.0005 0.96 0.48

 

 

F1 Yie d/plant

 

38

  
   

 

15
Fl=40'34G + 0.07
fF=35.09**
13.
ll-
)—
' O
9 I l L l l
-270 .290 .310
X' . Y' . ZJ
W' (G)
Figure 7. Geometric configuration and F grain yield

in gm per plant. Average effect of the
parents in the crosses was used as the
parental values and midparental values
scaled using the components of the highest
yielding cross.

 

39

The estimates of genetic constants (Eberhart and
Gardner's general model) from yield data are presented in

Appendix Table III. It may be seen that the crosses with

positive specific heterotic effects showed the most heterosis.

An analysis of variance of the grain yield data, however,
failed to show significant specific heterotic effect (Table
13). A comparison of the specific heterotic effect of the
crosses as determined by the Eberhart and Gardner's method
and the geometric configuration for these crosses (Appendix
Figure I) exhibits some interesting points. Apparently, a
cross with a low specific heterotic effect may have a good
configuration, but a cross with a high specific heterotic
effect does not have a poor configuration. This would seem
reasonable if it is remembered that while configuration may
have a good relationship with yield, that it (configuration)
might result either from additive or specific heterotic
effects of the edges of the yield figure. Thus the ideo-
graphs in Figure A below representing the parents and their
Fl offspring show complementation in 1 x 8, and additivity

in l x 3. Both offspring show good configuration and high

yield.

_
I
v

 

 

'Tablxe 13. Analysis of variance of 8 varieties

 

40

 

and their

 

 

 

28 crosses in grain yield per plant (Eberhart
and Gardner's Analysis II).
Source d.f. M.S.
Reps. 1
Entries 35 1.78 N.S.
Varieties 7 1.72 N.S. .‘1
Heterosis 28 1.96* .u
Av. het. 1 1.64 N.S.
Var. het. 7 3.20 N.S. 1
Specific het. 20 1.54 N.S. iii
Error 35 1.02

 

 

* Significant at the 95% level
N.S. Not significant at the 95% level

d. 4.: _.

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41

 

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42

The conventional method of using the average effect
Of gnxrents as a prediction of the performance of their pro-
geny (Figure 8) was shown to be less efficient for this
data than a prediction based on geometric configuration
(Figure 7). However, computing yield by using the average
effect of parents in the components was not significantly
different from the conventional method of using average yield
obtained from estimates of general combining ability. There
was no correlation between the observed yield and the mid-

parental values (Table 14).

 

Table 14. Simple regression statistics for F grain yield
as the dependent variable and geom tric con-
figuration, midparental values and yield pre-
dictions from general combining ability estimates,
each used as the independent variable.

 

 

 

Significant Corr. ' 2
Variable -level .- coefficient R
Av. effect of
yield in parents 0.0005 0.6553 0.4294
Geometric
configuration 0.0005 0.7579 0.5744

Fl midparental
values 0.1210 0.3000 0.0900

 

 

43

 

 

 

Observed Fl yield
15-
Fl=2.35W—15.20
F=l9.57**
l3.
_ O
11.
I
O
9 ' '
10 ll 12

Av. effect of parents
in yield (W)

Figure 8. Observed yield and yield predicted from
the average effect of yield in parents
(Av. of all.crosses with a parent used
as the parental effect).

'0

h

ray
5.»-

 

44

A significant increase in the accuracy of F1 yield
prediction was obtained by using geometric configuration and
yield both computed from general combining ability estimates
of the components of yield as independent variables and yield
in the F1 as the dependent variable in a multiple regression
analysis (Table 15). Both of the independent variables were
significant at the 15% level, and both combined determine 64%
of the F1 progeny grain yield; a significant increase on 57%
determination by geometric configuration alone and 42% by
general combining ability estimates of yield alone.

A prediction equation is as follows:

Fl = 30.56G + 1.06Y - 9.31
where,

F1 is the predicted progeny grain yield;

G is the geometric configuration factor; and

Y is the yield.

Both G and Y are computed from general combining

ability estimates of the components of yield.

 

45

 

 

 

Tabli: 15. Multiple regression statistics for F progeny
grain yield as the dependent variable and
geometric configuration and yield both computed
using general combining ability (g.c.a.) estimates
of components 9f yield as the independent variables.
(R = 0.8021; R = 0.6433.
Significant Partial corr. 2

Variable level coefficient R deletes

Geometric

configuration 0.001 0.6187 0.4221

Yield computed
from g.c.a.
estimates 0.037 0.4024 0.5744

 

 

 

 

 

 

 

GENERAL DISCUSSION

 

The study showed that there was no relationship in
yield and the yield components between genetic diversity as
measured by the base angle (correlation of traits) between
putative parents and the performance of F1 progeny. This
was unexpected. Apparently, the degree of genetic diversity
between parents is influential in heterosis only when it
affects the components of yield which in turn determine the
geometric configuration. It is postulated that the increased
heterosis occasionally found in wide crosses is the result
of the chance selection of parents which differ in their
effects on configuration. This inference arises from an
observation of the data of this study. The variety Traill
is the most unrelated to any other line in the set. Crosses
involving Traill account for 5 of the 11 hybrids exceeding
the mean of their parents. Traill has a long edge in Y, the
number of seeds per head. Crosses involving Traill and parents
with short edges in Y (1, 6, and 7) showed the highest heter-
otic reSponses. Apparently component complementation operates
by adjusting the geometric configuration to the optimum for
that environment.

The close relationship between the shape and volume of

a parallelepiped, a purely mathematical concept on the one hand,

46

 

 

 

 

 

 

 

47

and the components of yield and yield on the other is striking
and may offer another tool in plant breeding techniques.
Selection for high yield in such crop plants as barley or
wheat may then be made in relatively small plots or even in
the greenhouse using data as simple as may be obtained in
these limited spaces. By using geometric configurations com-
puted from the average effect of varieties to predict Fl grain
yields, it may even be possible to reduce the number of
crosses that should have been made in order to determine high
yielding matings and hence parents with high specific com-
bining ability.

A prediction of F1 progeny yield based on the average
effect of their parents in crosses (estimate of general com-
bining ability) was not as efficient as a prediction based on
the geometric configuration of the F1 progeny estimated from
the average effect of the parents on the components of yield,
and yield computed from general combining ability estimates
of the components of yield. Similarly, a prediction of F1
grain yield based on the actual midparental values (Table 15)
either directly or expressed as geometric configuration was
not significant (Appendix Fig. II). The accuracy of the F1
progeny yield prediction is significantly increased by using
both the geometric configuration and yield both computed from

the general combining ability estimates in the components.

 

 

48

Information on the general combining ability of lines
or varieties is readily obtainable from top-crosses. Rather
than make crosses of all the lines in all possible combinations

in order to determine the ones that will "nick, a prediction
using this information and their geometric configuration might
suffice.

The F data in the number of seeds per head and in

1
seed weight indicate appreciable amounts of additivity. Trait
dominance also has a strong influence on the three yield
components.

It is interesting to note that there was no effect of
the chronological sequence of development on the number of
seeds per head. It is not expected that this will always be
true, but in this case it is reasonable as practically no
correlation exists in the present data between the number of
heads and the number of seeds per head. On the other hand,
the size of the seed showed a marked positive influence on
the number of heads formed; also, the number of seeds on a
head showed a strong negative influence on the average seed
weight. Both results would be expected since the 'size' of
the crown primordia would generally affect the number of heads
formed. If so, the gain in using the largest seeds for plant-
ing can be substantial.

The number of seeds per head would determine the quantity

of carbohydrates and other food materials synthesized from a

 

 

 

 

49

given surface area and available raw materials that would be
sored in each seed.

In all, a judicious selection of parents for a cross
may result in efficient utilization of additive and dominance
gene action to give components whose geometric configuration

will approach the Optimum for the particular environment.

,tl' .

 

 

fifvu 3‘ on“?

1~z..;:i._- . ..
i

 

 

 

S UMMARY AND CONCLUS IONS

Eight barley lines crossed in all possible combinations
(without the reciprocals) were used in a study of the genetic
and other mechanisms influencing the F1 and heterotic responses
in yield and yield components.

The performance of the F1 and parental lines in grain
yield and yield components along with estimates of heterosis
and the relationship between heterosis and the suggested
genetic factors responsible for heterosis in yield and
yield components are presented. Simple and multiple regres-
sion statistics obtained from analyses of F1 yield and yield
components and the proportionate contribution of each genetic
factor are given. It is assumed that the same genetic factors
as determine the F1 performance in yield and yield components
also determine the amount of heterosis obtained.

Dominance and additivity were shown to influence the
F1 yield component values and the heterotic responses in the
yield components, but the geometric configuration of the
yield components largely determined the F1 yield and heter-
osis in yield.

The base angle measuring the degree of relationship

between parents was not related to F1 performance except as

50

 

 

 

 

 

51

it relates to the components of yield in their expression in
geometric configuration.
A method of computing geometric configuration for the

prediction of F grain yield was presented and the possibili—

l
ties of such a technique in breeding programs discussed. A
prediction equation for the F1 progeny yield was presented.
The effect of sequential ontogenetic development of
the components of yield on grain yield was of significance.

The size of the seed was found to affect the number of heads,

§, formed; also, the number of seeds on a head was found to

 

affect the seed weight, 5. The number of heads formed, how-
ever, had no effect on the number of seeds formed on a head.
Though the genetics of yield and yield component
inheritance were carefully considered, the geometrics of the
yield configuration is thought to have the greatest predictive

value.

 

 

_—-'v .y—ww

F"

 

10.

11.

12.

 

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APPENDIX

 

 

57

'Tablxa I. Analysis of variance of raw data in yield and
yield pomponents. F value and significance
level.

 

 

 

Grain Head Seed: wt.

Source d.f. yield/pl. number/ Seeds/ gm. 1000
plant head seeds

Reps. l 0.32 N.S. 0.73 N.S. 0.38 N.S. 0.95 N.S.
Varieties 35 1.79 * 2.25 ** 2.60 ** 1.91 *

 

1*significant at 5% level
**significant at 1% level

N.S.not significant at 5% level

 

 

 

 

 

 

 

 

5i3

 

 

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66.. ~..n. 6«.66. «a... 6«.66 66... ««.66. 6.... 6.. 69.6. .«.66.. .6.~. -«.66.. 66... .
u«.66.. .6... 6« 66.. -«.66.. 6.... .«.66.. on... 6«.66 6..6. 6«.66.. 6.... 6
.66.. «6... u«.66.. 6.... ««.66.. 6.... 6«.66.. 6n.~. .66.. 6.... 6
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66.. 6.... 6.. .6... .66.. .6... n
6.. «6.6. .66.. on... a
«.66.. a..~. .
6 . 6 6 6 6 ~ . ...6....>
6.... .9..- ..a.6.a. 3888 «o .2... an .5 a.
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p 0.325

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«oveno oo.H~ H
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5
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«even nn.~¢ «oveno -.ne «oven H¢.~c n
«ove n¢.o¢ «oven n~.~¢ N
«ov Ho.on H
.-1. . o n n n e n N H oOHueHuo>

 

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TABLE III .

60

Analysis of grain yield data using Eberhart

and Gardner's general model for genetic effects.
(Yij = kl(Vi+vj) + k2(Hi+3j)+Sij).

Table of genetic constants.

 

 

Varieties Varietal effect Varietal Specific
and K heterotic heterotic
Crosses 1 effect K2 effects Sij
l -0.89 1.58
2 -0.53 0.29
3 0.26 0.13
4 2.22 -1.91
5 1.05 -0.77
6 -0.69 -0.61
7 -0.78 -0.06
8 -0.66 2.93
l x 2 -0.13
1 x 3 -0.25
l x 4 0.01
l x 5 0.96
l x 6 -0.69
l x 7' -l.73
l x 8 1.83
2 x 3 1.66
2 x 4 0.10
2 x 5 -0.26
2 x 6 —0.23
2 x 7 0.63
2 x 8 -l.77
3 x 4 -0.93
3 x 5 0.17
3 x 6 -0.30
3 x 7 0.90
3 x 8 —l.25
4 x 5 0.36
4 x 6 1.73
4 x 7 -0.20
4 x 8 -l.06
5 x 6 -0.55
5 x 7 -0.99
5 x 8 0.30
6 x 7 -0.26
6 x 8 0.30
7 x 8

 

 

61

 

 

 

TABLE IV. Average parental performance for yield and
components of yield.
Yield/p1. Heads/ Seeds/ Wt. of 1000
Variety (gm.) plant head seeds gm.
206-205 (1) 10.85 12.79 39.01 21.9
206-258 (2) 11.21 13.82 40.45 20.1
208-319 (3) 12.00 13.70 42.33 20.8
208-324 (4) 13.96 14.50 51.61 23.2
210-350 (5) 12.79 13.02 40.05 24.6
210-353 (6) 11.05 11.81 39.39 23.9
210-360 (7) 10.96 13.72 36.71 21.7
Traill (8) 11.08 43.76 24.3

10.42

 

 

lHereinafter, the varieties will be designated by
the numbers in parenthesis. '

In." ..I .—

 

 

 

62

 

Genetic
constants
2r
9'. '
1L . .
. O O
o-
O O .
I 1.
O
O
_16- . '
O
' I
-2 1 1. 1 1 L i.
270 290 310 330

Figure I.

xl .Y' .Z'
XT+Y' + z'

 

Eberhart and Gardner's genetic
constants and geometric con-
figuration. Configuration computed
from estimates of general combining
ability of the components of yield.
(See text).

 

 

 

 

ll

 

F1 yield/plant 63

 

 

gm
15 ‘
l3_ ' .
o . ’
. o
' o
p
11.
o o
O I
. o
, I
.. o
O ' .
9. I 41 l I l
260 280 300

x' . Y' . Z'
x' + Y' + Z' (G)

Figure II. F yield and geometric configuration.
Observed midparental values used in
the estimation of geometric configuration.
Highest yielding variety taken to have
the "best configuration.

 

 

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