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INHERITANCE OF LODGING RESISTANCE

IN CERTAIE OAT CROSSES

By

Donald AlSOp Wheeler

W

AN ABSTRACT

Submitted to the College of Agriculture of Michigan
State University of Agriculture and Applied
Science in partial fulfillment of the
requirements for the degree of

EASTER OF SC ENCE

Department of Farm Creps

Year 1956

Approved

 

 

 

 

INHERITANCE OF LODGING RESISTANCE

IN CERTAIN OAT caossg

Genetically weak straw is one of the common causes
of lodging in small grains. The inheritance of lodging
resistance and lodging susceptibility in oats was studied
in the hope of finding a practical method of improving
lodging resistance.

The parents used were, from strongest to weakest,
Craigs Afterlea, Clintland, Craig, and A587-lO. Host of
the possible combinations of these parents were obtained.
Only seeds of Clintland x Craig, Clintland X ASB7-lO, and
A587-10 x Craigs Afterlea survived an excessive disin-
fectant treatment. The three Fi's were grown in the green-
house. The F2's were also grown in the greenhouse. The
parents, the Fé's, and the F3's of each cross were grown
together in the field. Readings were made when the plants
were in the soft dough stage. Following the method des-
cribed by Grafius and Brown in the Agronomy Journal 46:
hlh-hlB, a chain of known weight was hung from the base of
a panicle of each plant to determine resistance of the culm
to external torque.

The distributions of the observations were skewed in

the direction of lodging susceptibility. There was no

reduction in skewness in the F3, which indicated a problem
in scaling. When natural logarithms of the data were used,
the distributions approached much more closely to a normal
distribution. Dominance relations were assessed by compar-

ing F and F3 means to the mid-parent. Lodging resistance

2
was dominant in the cross Clintland x Craig. Lodging sus-
ceptibility was dominant in the crosses Clintland X ABBY-10
and ABBY-10 x Craigs Afterlea.

Variations in the F2 and the F3 were separated, using
the method preposed by Mather in Biometrical Genetics (Dover
Publications Inc., New York, lghg), into heritable and non-
heritable portions. The heritable variation was further
divided into fixable genetic and non-fixable genetic compo-
nents. These components of variation were calculated both
from the observed numbers of links of chain supported and
from the natural logarithms of these observations. Little
fixable genetic variance could be demonstrated in the cross
Clintland x ASBY-lo. In the other two crosses the use of
legarithms increased the proportion of fixable genetic
variance. In these two crosses the fixable genetic variance
calculated from the F2 plant readings was approximately 15
per cent while that calculated from the F3 means was approx-
imately 35 per cent.

Selection for lodging resistance prior to the F3 gener-
ation seems likely to be on the basis of non-fixable differ-

ences. Selection based on means of F3 families utilized

more fixable variation and seemed to be a good start toward
isolating superior lines.

Logarithms were valuable in determining the effective-
ness of selecti-n in this study. Logarithms did not change
the order of the data; therefore selection can be on the
basis of the original measurements.

Lodging resistance was defined by Grafius and Brown
as a ratio of torque resiStance to height. When either
factor is held constant a change in the other will change
the lodging resistance. Selection for lodging resistance
should be only on plants of similar heights. The quickest
advances by hybridization would be made by crossing strong

plants of the same height.

INHERITANCE OF LODGING RESISTANCE

IN CERTAIN OAT CROSSES

By

Donald AlSOp Wheeler

A THESIS

Submitted to the College of Agriculture of Michigan
State University of Agriculture and Applied
Science in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE

Department of Farm Crops

1956

ACKNOWLEDGKEHT

The author wishes to express his sincere appreciation
to Dr. John E. Grafius for his guidance in this investiga-
tion, for his advice in the preparation of this manuscript,
and for the photographs included herein.

Acknowledgment is also given to Dr. Carter M. Harrison
for his helpful criticism of the manuscript. Thanks are
extended to Dr. Pichard L. Kiesling and to several members
of the Farm Creps Department for helpful suggestions in
the field. In addition, the author expresses his appreci-
ation to his wife, Doroth , for her aid and encouragement
in this investigation and for her assistance in the prep-

aration of this manuscript.

TABLE OF CONTENTS

INTRODUCTION
REVIEW OF L TERATURE
MA'ZRIELS AND KETHODS
THE COMPOHZUTS OF VARIATION
RESULTS
Clintland x Craig
Clintland x A587-lO
Clintland x Craigs Afterlea

Consideration of Linkage in
Clintland x A587-10

DISCUSSION
S MMARY

LITERATURE CITED

12

19
22

27
3o

36
38

M3

INTRODUCTION

Lodging of small grains is a problem of wideSpread
occurrence on soils high in fertility. Lodging often oc-
curs in low areas of a field, on fields receiving large
amounts of nitrogen fertilizer, and on much areas. The
immediate cause of lodging is generally a windstorm ac-
companied by rain which pushes the plants over. Indirect
or contributing causes include high fertility, high soil
moisture, lack of sufficient light, high temperatures,
and genetically weak straw. Grain which has lodged is
difficult to harvest and losses in harvesting are in-
creased. Often the yield and quality of the crop are
lessened. The stage of development of the plant at the
time of lodging determines the degree of damage.

Several common oat varieties have genetically weak
straw, therefore they often lodge badly when grown on rich
soil. It is desired that high-yielding varieties with
genetically strong straw be obtained. In order to accom-
plish this it is desirable to understand the inheritance
of the character. The aim of this study was to determine

the method of inher tance of lodging susceptibility versus

3

lodging resistance in cats. A further pureose was to
ascertain whether lodging resistance could be improved
by the ordinary oat breeding method of crossing and se-

lecting within the segregating generations.

PO

REVIEW or LITJRELTUELE

Pendleton (8)* found that 90 degree lodging at head—
ing time caused reduction in yield to 63 per cent of that
of erect plants and a reduction in test weight to 79 per
cent. The yield was reduced to about 85 per cent by as
degree lodging at heading time or by 90 deg°ee lodging
20 days after heading. Thus the time when lodging oc-
curred determined its effect on yield.

Several methods have been preposed for measuring dif-
ferences between strains in respect to lodging or lodging
resistance. The standard method is to observe a nursery
where lodging has occurred and to make notes of the per-
centage of plants not standing erect in each plot and to
note the approximate number of degrees by which they de-
part from the vertical. This method can be used only on
plots where lodging has already occurred.

The breaking strength of the straw has been used as
a measure of lodging resistance. Several machines have
been developed to measure breaking strength of straw.

One type of machine was that described by Helmick (6).

"o
I

Numbers in parentheses refer to the "Literature Cited."

b.

In this device a bucket was suspended from the straw and
shot we added to the bucket until the total weight was
enough to break the straw. The instrument described by
Salmon (10) measured the pressure required to break the
straw. In this case the pressure was applied from above;
but the results of the machines were comparable. Atkins
(2) stated that while lodging was not significantly cor-
related with breaking strength of straw at one station in
one year, the two were highly correlated when considered
over several stations in several years. Atkins (2) also
found a high correlation coefficient between breaking
strength of straw and weight per unit length of culm at
the base of the plant. He advocated use of the latter
measurement as being quicker.

Breaking strength of straw was only one factor con-
tributing to lodging resistance. In View of this fact
there have been recent attempts to find a more inclusive
method of measuring lodging resistance. Hamilton (5)
gave a lodging index based on a discriminate function
whereby the relative value of root type, diameter of culm,
and height were assessed. This function was approximately
the sum of ten times the diameter of the calm in the sec-
ond internode above the ground, less five times the root
type on a scale of one to ten as given, less the height of

the plant in inches.

S

Grafius and Brown (+) gave the definition of lodging
as the extent of resnonse to torque caused by external
force. In order to determine this response, they hooked
a chain to the base of the panicle and observed how many
links of the chain were supported when the culm bent to
an equilibrium.point. They derived a formula for lodging
resistance: ch '*§’ where F, the force applied, was the
grams of chain supported, b was the height of the plant to
the base of the panicle, and c was a preportionality con—
stant to convert b into a force, based on the assumption
that external force would be roughly proportional to plant
height.

Inheritance of lodging resistance in small grains
was governed by many genetic factors in most cases. Ramiah
and Dharmalingham (9) reported one case of single-factor
inheritance of lodging versus non-lodging in rice, with
the lodging factor dominant. Atkins (1), found that the
character of weight per unit length was transmitted from
a parent to its progeny. He cited correlation coeffi-
cients of .609 between F2 and means of its F3 progeny lines

'1 / o 9
and of .023 between F3 and means of its F) progeny lines.

L

HATSRIALS hHD XSTHODS

Four parents were chosen for this study on the basis
of past lodging history. Two were commercial oat varie-
ties, Clintland and Craig. Of these, Clintland was more
resistant to lodging. A third parent was the experimental
strain A587le which was very susceptible to lodging.

The fourth parent was the variety Craigs Afterlea, a very
strong eat from Scotland.

Crossing was done in the field in the summer of lgSh.
Crosses were attempted among the four parents in all comp
binations. Several seeds were obtained as the result of
crossing; however, most of them were killed by an over-

dose of fungicide and consequently only three F plants

1
were obtained. These three plants were from the follow-
ing crosses: Clintland x Craig, Clintland x ABBY-lo,
and ABBY—10 x Craigs Afterlea.

T‘

11

(D

three Fl seedlings were started in three-inch
pots and then were transplanted into ten-inch pots filled
with soil. These plants continued to grow in the green-
house throughout the fall and winter of IQSh-SS. The
pots were watered daily and were supplied with a complete

nutrient solution at about ten-day intervals. Incandescent

lights were used to maintain a day length of at least
twelve hours throughout the winter and also for supple-
mentary light on cloudy days. Under these treatments the
F1 plants continued to tiller from.October until Harch.
Each plant produced 25 to 50 culms. As each head ripened,
it was cut from.the plant. In early February all the
seeds which had ripened thus far were planted in rows on
the greenhouse bench in a mixture of sand and soil. Water
and nutrient solution were agplied as to the F1 plants.
This planting was made a little later than desirable, so,
in order to mature seeds quickly, the F2 plants were sup-
plied with continuous illumination. The seeds borne later
by the F1 plants; that is, F2 seeds and the seeds borne

by the F2 plants; that is, F3 seeds were harvested for
planting in the field.

The F2's, the F3's, and the parental varieties were
planted in the field in the spring of 1955. The rows were
two feet apart with plants three inches apart in the row.
The three crosses were planted in separate, adjoining
areas. The progeny of each F2 plant was planted together.
These F3 families averaged about eight members. The F2
seeds were divided into groups of ten and these were ran-

domized among the F3 families w th a restriction of one F2

group to each three to six F3 families, depending on the
ratio of seed available of the particular cross. The
parents, in groups of eight, were planted with the pro-
geny at eight row intervals. Clintland was planted as a
uniform check variety throughout the area. Each other
parent was planted, in alternate cheek rows, in the area
with its progeny.

Locging resistance readingrwere made when the plants
were in the soft dough stage. The method used was that
described by Grafius and Brown (4). The culms to be used
were visually selected to be at the same stage of maturity.
Some plants from seed which germinated slowly were so badly
affected by red leaf that they produced only one culm;
these were not studied. Neither were readings made on the
few plants which had previously lodged. One culm.of each
plant was selected for study. The height to the base of
the panicle was measured. A chain was attached to the
base of the panicle by means of a hook. The weight of the
chain caused the culm to bend over and the excess links
of chain piled up on the ground. Then the culm ceased
bending the number of links of chain still being supported

was determined. Figures 1 to 3 illustrate

Q

-1.

she differences

that were shown by this method. In Figur l, the chain

attached to Craigs Afterlea caused it to bend only slightly
from the vertical. The opposite extreme is illustrated in
Figure 2. Here the plant has lodged from the base and is

supporting very little weight. The most common reaction

was between these extremes, as exemplified by Figure 3.

 

 

 

 

Figure 1. Chain attached to lodging resistant plant.

 

 

 

Figure 2. Chain attached to lodging susceptible plant.

 

 

Figure 3. Chain attached to plant
showing typical lodging reaction.

11

l2

TIE: C EIPOITZBUTS OF ‘33 .‘LTIOI‘I

Variation in a biometrical experiment, according to
Mather (7), can be partitioned into three components. The
first is non-heritable variation resulting from.the action
of environmental factors. The second portion of variation
is due to differences in character expression between home-
zygotes for each gene pair involved. Heritable variation
between true breeding strains is of this kind and in this
sense such variation may be described as fixable. The
third component of variation is comprised of differences
between the expression ofiaimtzygotes and the average of
the corrCSponding homozygotes. Such variation may be des-
cribed as unfixable in that it cannot be utilized in the
selection of true breedine strains.

Fisher, Inner, and Tedin (3) developed a method of
determining the contributions of each gene to the fixable
and unfixable components of variation. Following the
designation of these authors, let the average effects on

the character in question due to the three genotypes for

13

\l
5

gene A—a” be:

AA = da BB = db
Aa = ha , for B-b: Bb = hb , and so on.
£13. 3 ~da bb = -db

Aa

 

 

 

 

 

 

K
\
4
i

m-—-

a 0 AA

Figure A. The d and h increments of
the gene A-a. (after Mather)
Figure n represents the d and h increments of the gene pair
Aa. The zero point is chosen mid-way between the homozy-
gotes. Then d represents an increment in a constant direc-
tion along the scale of moas rements, while h may be an
increment in either direction.

The variation of the measurements of true breeding
parents and of their F1 is exclusively non-heritable.
Therefore the variances of these measurements give esti-
mates of the non-heritable portion of the variances of

the F2 and later generations. The heritable portion of

r The A—a designation of allelomorphs here does not carry
the conventional implication of dominance.

1h

the variance of one of the later generations is the sum
of the contributions due to the individual gene pairs
providing that there is no linkage and no interaction of
non-allelic genes.

In respect to any one segregating gene pair A-a, the
F2 is: 2AA; %aa; iaa. The mean measurement of F2, ex-
pressed as a deviation from.the mid-parenn.for this locus,
is ida - iha - %(”da) I kha. The contribution of A-a to
the sum of squares of deviations from.the mid-parent is
,

EdaZ - %ha2 - %(-da)2. Then the contribution to the sums

of squares of deviations from the F2 mean is
.1. 2 .1: 2 1 1 1
2da - zfla -(£ha)2 or gdaz - ghaz. Summing over all
genes contributing to the character being considered,
total heritable variance in F is -=1-s(d 2) ism 2)
“- l 2 23 a " t‘; a o
The F3 families derived from F2 individuals of the
genotypes AA and aa contribute da and -da respectively to
the F3 means. One-half of the F3 families are from F2
individuals of the genotype Aa and in these families se-
gregation is occurring in the same ratio as in the F2,
_. . .1- _1_ ;L_( .1“ 1
giving contributions of Qda - Bha - 4 "da) = aha to tne
mean.. Thus taking frequencies into account, the mean of

F3 means is iha from the mid-parent. The variance of F3

- 2 " '1
means is ida - %(%lia)2 _ a‘(-da)2- (flag or gdae _ haz

15

and, summing, the total heritable variance of F3 means is
esmaz) +-};;S(ha2).

The variance of F3 families can be represented by
i0 + %(%daa + Thaz) + £0 ' idag +'%ha2 since only the fami—
lies derived from.A—a individuals are segregating. Summing,
the mean variance of F3 families is %S(da2) + §S(ha2).

In each case, these formulae contain a part S(da2)
due to fixable variation and a part S(ha2) contributed by
non fixable variation. Denoting these by D and H respec-
tively, and remembering that observed variances also con-
tain a non-heritable portion, we have the equations given

in Table 1.

Table 1: Components of Variation in F2 and F

3

F2 F2 variance 1/2 D + 1/h H * 31
vii; Variance of means of 1/2 D + 1/16 H * E2
F3 families
VFB Mean variance of F3 1/3 D + 1/8 H * E1
families

Number of plants

10

   
 

Clintland

 

M1

Craig

 

30

‘ M‘d'Pore nt
35.5

10 1

2O

15

10

 

 

16

 

 

   

 

MeEn‘»
h2
fanfllos: I Weakest ' strum"?

30 55
15 25 35 *5 55 65

Numbers of links of chain supported.

‘3

Figure 5. Frequency distribution based on number of links of

chain supported for parents, F2, and F of Clintland x Craig

cross. 3

Number of plants

10

 
 

l7

 
 

 

 

 

 

 

 

 

 

 

 

 

 

5 Clhnland
0
M1
5
A 587-l O
O -—’ l l - —::==__.
23
[Mid-parent
32
10
5 F2
0 ___I; -
31

20

PS
15
10 K Sta ard

deviation
5
0 an __

29
psfamilies: I Weakest I Strongest
17 h2
10 20 3o l+0 so 60

Numbers of links of chain supported.

Figure 6. Frequency distribution based on number of links of
chain supported for parents, F2, and F3 of Clintland X A587-10
cross.

Number of plants

10 18

 

 

 

 

5
Craig: Aficrleo
O c-3n;::r-wr*""al eLr *'-===
72
5
A587-ib
o ——1”’T"“T-——
23
lMid'pare nt
h7.5

10

5

O A

36

       
   

 

20
15
10
5 Stan ard
"‘“5661 tion I
0‘ Me n l g
33
[Weakest ' 'Strongefl fF?’ families
15 N7
15 30 M5 60 75 90

Numbers of links of chain supported.

~Figure 7. Frequency distribution based on number of links of
chain supported for parents, F2, and F3 of A 587-10 x Craigs
Afterlea cross.

19

Figures 5, 6, and 7 show the means, standard devia-
tions, ranges, and approximate distributions of the ob-
served values for the number of liics supported in these
three crosses. Host of the original curves appear to be
skewed toward the low side. In order to eliminate this
condition a transformation of the data might be useful.
The taking of logarithms would tend to shorten the upper
end of the scale; therefore this would be a good trans-
formation. In accordance with these considerations, nat-
ural logarithms of the data were taken and several sta-
tistics were computed from.both the original data and the
data transformed to logarithms. Table 2 presents the num~
ber of plants and also the means and standard deviation
for each generation of each cross. The transformation to
logarithms has reduced the coefficient of variability
(the standard deviation expressed as a percentage of the
mean) for each of the generations.

In order to find the components of variation several

variances were required. Variances were computed for the
F2, means of F3 families, and mean variance of F3 families

in each segregating population. Each of these variances

apnea»
IQHQWP
mo pcoflo
naeaeeo e

pepACLQSan
ac mg:wflam

mafiacmoan paw mezeama pow

)
(q
i
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\n .0 \Jo \ \. H\. \W‘ .0 t\ . \. d.:_. A- 1.‘ ti
an o e; n u.mH n.no : w e a meawoeeq «Lawto
1‘ \JIIIIII l,\(|
r Nave
mmao Hmem Gama mama :.~ mm mm «seahopwd mwmm&o
smfiififi<
ea.“ am.m m.s a.mm a.» an a :oan ,u a eeei .eao
n1\ \ \) . W J N 1 o 1 4 .< ) -111.
ro.© anam <.; view a.. ma h .oauwwmd x pcma+cero
\
\ ill. ‘Iqu \ LI i. O 4 6 \ .1 Jq 1.. I.. w 4 .Ju
eds; ream 3 ea eaa; lfl\ Hm D ..Haao : raaa+awro
E u .1 \\ a l. .‘w I! W 4 N i O .i., .I .1 1‘
K). {am 0.: (3.; Get 5. a {$9.0 ._. Em p53
ma.o no.3 0.3H 9.0H W.He .m Amv eeaeeeaa mimeeo
adoo moem c.9m H.m -Hamm c.w m oalwmm
eo.c mm.m «.lm H.m wamm mew ; eflmno
Hw.o mm.m no.3w mew .HQHJ mew Hm pnmapgflao
\v i i_
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omeenpt: mo nacho deflpmw>om No; min: .mewaflimm
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.o: swam we .0: coflpmaocem so heefiamb

fifrH $0 60L

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msowpmfl>em Usersmpm tum amuse: ampsmaa mo panama

21

contained a non—heritable component. Since the parental
groups, F2 groups, and F3 groups were of approximately the
same sizes, the variance within parental groups can be
taken as an approximation of the non-heritable component
in F2 and F3 variances. The non-heritable component of
the variance of F3 means can be estimated from the vari-
ance of parental group means.

Many of the F3 families contained only a few plants.
In order to obtain a fairly good sample of the potential
of a particular family, only families consisting of five
or more members were considered in calculating F3 variances.
It would be desirable to have larger families, but, if a
larger number had been required, the Clintland x Craig
cross would have been eliminated from.the study. This same
requirement of five members per group was applied to the
parents in determining the estimates of error variances.
Since the parental variety Craigs Afterlea was badly damp
aged by red leaf disease, only two groups were usable.
This was too few, so Craigs Afterlea was not considered in
determining the error variances. In its place, a pooling
of the variances of the other three parents was used. In
the crosses involving Clintland the estimates of error

were obtained by pooling the variances of the two parents.

22

Clintland X Craig
The variances calculated from.the original data on
the number of links supported in the segregating cross,

Clintland x Craig, ~re as given in the following five

equations.
VF2 - 1/2 D + l/h H + El a 121.9
VF; . 1/2 D + 1/16 H + 32 = A3.6
. V 1 0 Ta - }
F3 = 1/4 D . 1/0 H + 51 - 93.1
V within parental groups = El - h7.7
V parental group means = E2 = 22.0

The first step in obtaining the least squares estimates
of the four components of variation was to multiply through
each equation by the coefficient of D whichit contained.
The new equations thus obtained were summed. Where D did
not appear the equation was omitted. Thus the following

equations were obtained.

 

l/h D + 1/8 H + 1/2 El = 60.95

1/4 D + 1/32 H .1/2 32 = 21.8

1/16 D + 1/32 H . 1/i E1 . 23.35
(1) 9/16 D + 3/16 H + 3/4 El + 1/2 32 = 106.1

23

Similarly multiplying through the original equations by the
coefficients of H, 31, and E2 and summing the following

were ootained.

(2) 3/16 D + 21/256 H + 3/8 31 + 1/16 32 = 1;.u.8
(3) 3/h D + 3/8 H + 3 31 = 2 3.2
(a) 1/2 D + 1/16 H + 2 32 = 63.6

The solution of these four simultaneous equations gave es-
timates of D, H, El, and Ba. Mather (7) presented a method
for solving these equations using a matrix of multipliers.
For the purpose of this studv, these equations were solved

by the standard method of solving

LJ

simultaneous linear equa-
tions in more than ore unIInown. That is, each equation was
added to or subtracted from each of the other three in or-
der to eliminate one unknown. The remaining three equations
in three unlwnozns were compared and another unkiown was
eliminated. This process was repeated until a solution was
obtained for one rhnown. Then the other equations were
solved by substituting known values.

Solution of these equat ens gave the following values

for the components of variar ce 1n the cross Clintland x Craig.

D a 10.7
H = 27105
£1 = 51.1

21.6

F
a)
l

21+

Upon substituting these values in the original equations

he expected values given in Table 3 were obtained.

Table 3: Variances of number of links supported
in Clintland x Craig cross

Components Variances computed from
number of links

observed xpected deviation

V —-.

F2 1/2 D + 1/4 H + 11 121.9 124.3 -2.4
V—— / i
F3 1/2 D + 1/16 H + mg 43.6 44.0 -0.4
'Va -1
.333 1/14. D + 1/8 H 4' 11:1 9301:}. 8707 507
V within parental groups - El 47.7 51.1 -3.h
V parental group means - E2 22.0 21.6 0.4

Components Variances computed from
logarithms
observed expected deviation
V .

F2 1/2 D + 1/4 H + El .066 .064 .002
VF; 1/2 D + 1/16 H + E2 .025 .026 -.001
vF3 l/Ji D + 1/8 H + El .052 .052 .000
V within parental groups = El .039 .041 -.002

V parental group means E2 .Olh .013 .001

23

Q

The variances calculated from the natural logarithms
of the number of links are as giveL in the "observed" col-
umn of Table 3. Least squares estimates of the four com-
ponents of variation were obtained by the same procedure
used previously. It should be noted that the left sidesof
equations (1) to (4) on pages 22 and 23 remain constant
for all experiments of the same design. Thus only the

right sides were calculated, and these equations became

(1a) 9/16 D + 3/16 H + 3/4 E1 + 1/2 22 = .058
(2a) 3/16 D + 21/256 H + 3/8 El + 1/16 32 = .024
(3a) 3/4 D + 3/8 H + 3 E1 = .157
(4a) 1/2 D + 1/16 H + 2 E2 = .039 .

Solution of these simultaneous equations gave the
following values for the components of variance in the

cross Clintland x Craig.

D = .020
H = .051
E1 = .041
22 = .013

‘

Taking tne logarithms of the data has greatly reduced the
relative value of H and has increased the relative value
of D in relation to the values for these components com-

puted from the original data.

An estimate of the fixable genetic variation

26

1*

n the

F2 generation was obtained by dividing the portion of to-

tal variation due to D by the total expected variation;

that is, using the

__ 1/2D
expected

Similarly,

1/2 D . 1/4 H
expected

__1/2 D
expected

1/2 D + 1/16 H
expected

 

origi

--43315 x 100

12”... 3

’D
.1322: x 100

1214-0 3

nal data

.4 . o
4.3” fixable genetic var-
iation in F2.

59% total genetic vari-
ation in F2.

'—r5*15 x 100 a 12% fixable genetic var-

L44- 0

L,

iation in F3 means.

fifing x 100 51$ total genetic vari-

ation in F3 means.

Using he components of variation computed from.the

logarithms of the data,

1/2 D :

expected

1/2D.1/4H
expebted

1/2 D _

expected

1/2D.1/16H_

expected

.OlO

.' ‘
00!.
O \’ ~1-

these values become

15.6% fixable genetic varia-

3S.9$ total genetic variation
in F2.

1 w . .
38.5» fixaole genetic varia-
tion in F3 means.

=7 . . .
50p total genetic variation in
F3 means.

27

Clintland x ASBZle
For convenience the calculations for both the original
data and the logarithmic transformation were carried through
at the same time. The variances calculated from.the segre-

gating cross Clintland x A587-10 were as follows:

using no. using log-
of links arithms
VF2 . 1/2 D + 1/4 H + 31 = 74.1 .094
VF; . 1/2 D + 1/16 H + 32 = 27.7 .035
VF3 = 1/4 D + 1/8 H + El = 70.4 .091
V within parental groups :31 = 44,6 .036
V parental group mean =- $2 = 20.8 .018

Least squares estimates of the components of variance
were obtained by the same method used in the previous cross.
Thus were obtained equations similar to (l) to (4) on pages

using no. using log-
of links arithms

(lb) 9/16 D + 3/16 H + 3/4 31 + 1/2 E2 = 68.5 .087
(2b) 3/16 D 4 211256 H + 3/8 E1 +1/16 E2 = 29.1 .037
(3b) 3/4 D + 3/8 H + 3 El = 189.1 .222
(4b) 1/2 D + 1/16 H + 2 22 = 48.5 .053

28

Solution of these simultaneous equations gave the fol—
lowing values for the components of variance in the cross

Clintland x A587-10.

Using no. of links Using logarithms
D = -1.6 .006
H = 121.2 .208
El = 48.3 .0h6
E2 = 20.9 .018

Since D is a sum of squares, it cannot be negative. How-
ever, the small negative value obtained for D cannot be
considered as different from zero nor from.the small pos-
itive value obtained for D using logarithms. As the data
stand it is not possible to demonstrate any fixable genetic
variance in this cross. In this cross, logarithms in-

creased rather than decreased the relative value of H.

F3

able 4 shows the observed and expected values for the sev-

O

eral variances using the components as given above.

Table 4:

in Clintland x A587-10 cross

Components

F2 1/2 D + 1/4 H . El
1/2 D + 1/16 H . 22
VF 1/4 D + 1/8 H + H1

V within parental groups

V parental group means

Components

V1212 1/2 D35- 1/4

VF; 1/2 D . 1/16

a:

4.

F3
N

VF3 1/4 D + 1/8 H . El

V within parental groups

V parental group means

29

Variances of number of links supported

Variances computed

from no. of link

observed expected deviation
74.1 77.8 -3.7
27.7 27.7 0
70.1.}. 6301 703
= El 44.6 48.3 -3.7
3 E2 20.8 20.9 -0.1

Variances computed
from logarithms

observed expected deviation
.094 .101 —.007
.035 00314- .001
.091 .074 .017
= El .036 .046 -.010
'3 E2 0018 0018 0000

4§§1¢10 x Craigs Afterlea

The variances calculated from the

O
segregatin

2587—10 x Craigs Afterlea were as follows:

V within parental

I

1/2 D + 1/4 H + H1

1/2 D 4 1/16 H

1/4 D + 1/8 H + El
groups = El

V parental group means

11

Using no.
of links

172.1

CI’OS

.137

.041

.018

The least squares estimates of the four components

30

8

Using log-
arithms

were obtained from.the following equations which were de-

rived in the same manner as those used in the precedin.

two crosses.

(1c)
(2c)
(30)
(he)

following

9/16
3/16

"fv'he n

D . 3/16
D + 21/256
D 4‘ 3/8

D + l/l6

these simultaneous equations were solved,

H
H

H
H

+ 3/4
+ 3/8

El 11/2 32

Using no. Using log-

El +1/16 E2 =

E

l

+

2

E

’3
L

1

of links

50.0

64.9

367.3

74.3

arithms

.129
.055
.317
.070

the

values were obtained for the components of variance.

31

Using no. of links Using logarithms
D = 6.2 .020
H . @87.2 - .BMQ
E1 = 60.0 .057
E2 = 20.4 .019

The expected values given in Table 5 were obtained by
substituting these values for D, H, El, and E2 in the o-
riginal equations. It should be noticed that the devia-
tions between the observed and the expected values were
quite large due chiefly to a difference in the values of
D and H between the VF2 and VF3. Such a difference might
have resulted from the effects of linkage.

In the case of linkage, the heritable portion of var—
iance was no longer simply the sum of the contributions due
to the ihdividual gone pairs but also involved a factor
derived from the recombination or crossover values. Kather
(7) derived certain formulae for D and H when linkage was
present. With linkage, the values for D and H in the F2

differed from those for D and H

I-h

n the F3. To test for the
presence of linkage, then, it must be determined whether
this difference in D and H between F2 and F3 existed.

In the exteriments here being reported, D and H of the

F2 generation were estimated from VFZ and “F“ while D and H

H.212.
r)...
1..
.(f. .
.1.1.
4.!(9
.U.\I J‘
C.-.(
7 .0
CILDK

muChO

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....L (C
1.an 15..
_r MI...
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. . ..\ \
, n. U
--. : J.

F Ctr

. . H1

.rLC.+.P\/%rs. I
....I4. 4.. l
a. .r. prrvrw.
ODFLOQ

mcaao+wa m..

La.

. 1

. ,\ .... .. 4'...
k,‘ -.. \x 1: r
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rt. rxa

.. 4 . -. . A 1? 4
L ....ww.r.L CF (11%.“
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_.
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, .1 1. c t 1.- I
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.7“. 1 II -.... .0 . - I
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1!.

o ‘14. ...4 ( _ I.. . 4 .. I.
T . .

....AIO‘ r} .I pa » L. ..M f}:r.r\ a?.o 1!.
.... -... .... o .1.1.. -.-c
H_”rk anuw \rrH/l.L..1 F“.W,Hnfiasuuuvl)
r-- . , .-o
4.1.4.. r
p{, r! I! + *5 w.“\ r +
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, x . O C v + .l‘ ...-1 *-
1 . s . .
01, L. T x -\ r
. -- 0 P... .r« ..- .-..
Fr. .f u + D» (x F! +
be mocaaahw:
x. 01 . ..3 Ln) - i
.. CO H» H Ukud! CLCLL _.

rmnmhxcs; Hupsosmo

1.. 6

r w;

......)_- . .UJ1 Mich: .
. \ . o.-(kr

... ...! 1 .\ .1 . J. .4.‘ 1 a 1 I IV a... 1 .. I . _ .y I D l.‘\
.irmerflJ -2 QH‘rwpxtsnw CW. "x. Wrectxéupmw VuMpfiFHr no PC." ..ZCP CC UCDACA...»G§. .L

a...
L ._ - . .
-w£+w: r
a“
..- ”1...: r.
...r C. F .-
.\
r... -
... ‘.~ I "ll
.-r C\ A: by
0
.... ... .4. r....
C C\ r. Fv
4
\U_

w+awp b

nt/xp

E...

mflrmh

33

of the F3 generation were estimated from VFB. If DF3 and
HF3 differed from DF2 and HFZ resuectively, a perfect fit
could have been obtained for F3 by adjustment of D and H.
is a result of this perfect fit in?F , the sum.of squares
of the observed variances from their expectation would
have been reduced by this adjustment of D and H. The es-
timation of D and H from the complete data for the cross
ASGY-lo x Craigs Afterlea has previously been done. The
next step was to estimate D and H from VF and Vfi‘, assum-
2 3
ing the perfect fit in'VF . The variances required are:

Using no. Using log-
of links arithms

VF2 = 1/2 D . 1/i H . El . 172.1 .137
VF; . 1/2 D + 1/16 H + 32 a 53.8 .052
31 = 17.1 .Ohl

E2 I 20.5 .018

Equations for least squares estimates of the four com-
ponents of variance were obtained by a method analogous to
that used previously. Each equation was multiplied through
by the coefficient of D which it contained and the result-

ing equations were summed, and so on for H, El: and 32, This

31.

gave the following equations:

Using no. Usi.1 log-
of links arithms

(5) 1/2 D + 5/32 H + 1/2 El + 1/2 32 = 112.95 .094
(6) 5/32 D + 17/256 H + 1/H El +1/16 32 = H6.39 .037
(7) 1/2 D + l/h H + 2 E1 . 219.2 .178
(8) 1/2 D + 1/16 H + 2 32 = 7H.3 .070

Solving these simultaneous equations the following
estimates were obtained for the components of variance in

the cross A587-10 x Craigs Afterlea.

Using no. of links Using logarithms
D - 5.H .038
H = h89.3 .293
El ' @736 .Oh3
E2 = 20.5 .017

The expected values given under the headings "corrected”

in Table 5 were obtained by substituting these values for
D, H, E1, and E2 in the original equa ions. It was ob-
served that the relative values of D and H had been changed
when VF was omitted, which gave strong evidence that link-
age was involved in this cross. However, there was no more
recovery of parental types than expected. This indicated

the presence of several linkage groups on different

35

chromosomes with rand m combinations between groups. In
a wide cross such as this it was eszoected that there would

be linkage of factors fro on each of ti 1e diverse parent

m

.
Estimates of fi: {able gen etic variation obtain ed from

the original data, uncorrected and corrected for linktge,

were about the same. However, the percentage of fixable

q,

genetic variation was increased by using the logarithms of
the data and was further increased by the correction for
linkage. The bronortion of variation due to heredity is

presented in Table 6.

Table 6: Genetic variation expressed
percent of total variation in A587-lO
x Craigs Afterlea cross

Using no. of links Using logarithms
uncorrected corrected uncorrected corrected
for ling- for link-
age age
Fixable genetic 1.7% 1.6% 6.hfi 1h.l$
variation in F2
Total genetic
variation in F2 68 72 63 68
Mi able genetic
_ . /
Vafla atiOn in F3 5.0 5.0 19.6 35.0
means
Total gene ic
variation in F, 59 63 63 69
J

mo c’ll’lS

Consideration of Linkage
in Clintland X A587-10

Consideration of linkage in the calculations from the
cross ASST-10 x Craigs Afterlea was shown to increase the
‘proportion of fixable genetic variation in relation to to-
tal variation. The deviation of observed from expected

n the cross Clintland X

H.

variances was also fairiv high

A587-10, especially when logarithms were taken. Therefore
a test should also be made for linkage in Clintland x

A587-10, using logarithms. Least squares estimates of the

3

components of var ance were obtained by the same method

used previously. The left sides of equations (5) to (8)
/ . . u . 0

on page 20 apply in this case. when the right Sides of

the equations were computed, the following equations were

obtained.
(5a) 1/2 D + 5/32 H + 1/2 El + 1/2 32 = .065
(6a) 5/32 D + 17/250 a + 1/h El +1/16 32 = .026
(7a) 1/2 D + 1/i H + 2 E1 = .130
(8a) 1/2 D + 1/16 H + 2 Ba . .053

The following estimates for the components of variance

were obtained When these simultaneous equations were solved.

D I . 003;.
H . .23h
El a .035
E2 = .018

37

These values are only slightly changed from.those obtained
by using the mean variance of F3 families. Therefore

evidence of linkage is lacking.

Lo
03

DISCUSSION

Mather (7) gave a method for calculating the standard
errors of D, L, El, and E2 from.the sum of squares of devia-
tions of observed from expected values of the several vari-
ances. This method involved use of multipliers which were
not calculated in the present stud“. Lacking these stand-
ard errors, there was no reliable way of telling whether
the values observed were significant or not. It seemed that
the high values of H in the three crosses indicated domi-
nance. Changing the data to logarithms changed the value of
H in the cross Clintland x Craig enough that, lacking its
standard error, the preceding statement was not certain.

Dominance relations could also be assessed by compar-
ing the Pl and its derivatives to the mid-parent value.

No Fl's were grown in the field, so the F2 and the F3 were
utilized in determining dominance. The following obser-

'V

vations were based on the data presented in Figures 5, 6,

L)

w

and 7. In the cross Clintland x Craig tnere was domi-

nance of the factors favoring lodging resistance. In the cross
A587-10 X Craigs Afterlea there was dominance of the

factors favoring lodging susceptibility. In the cross

Clintland x A587-10 there was douinance,to a lesser ex-

tent,of factors favoring lodging susceptibility. This

reduction in degree of dominance was probably due to a
balancing of some dominant susceptibility factors from
A587-1O by dominant resistance factors from Clintland.

In plant breeding work it is desired that individuals
selected for any trait be able to traismit the trait to
their progeny. Selection is accomplished on the basis of
individual readings or on the basis of family means. These
individual readings or means are subject to variation and
this variation will be composed of D, H, and E portions.
In order to increase the heritability or ability to trans-
mit the trait to progeny, it is desired to increase the
preportion of the variance due to difference between home-
zygotes represented by D. The best way to increase the
proportion of D is to decrease the proportion of H.and E.

In self -pollinated crops the D component of means re-
mains constant while the H component decreases by one-half
in each generation. Thus Selection in later generations
becomes more and more effective. Economy of time suggests
making selections in as early a generation as possible.
The D component which was calculated for the cross Clint-
land x A587-10 was very small. The greatest proportion of

fixable genetic variation Was nine per cent fixable genetic

110

variation in F3 means. This low value indicated that se-
lection might not be successful in this cross. In the
other two crosses, Clintland x Craig and A587-10 X Craigs
Afterlea corrected for linkage, the proportion of fixable
genetic variation to total variation was about 15 per cent
in the F2 and about 35 per cent in the F3 means. This 15
per cent of ariation due to fixable genetic differences
in the F2 was low enough that selection might be ineffi-
cient. However, by the F3 generation, the figure for fix-
able genetic variation had risen and selection might be
more effective. Furthermore, this incr ase in fixable
genetic variation increased the probability of retaining
the best progeny. The statistics utilized were not sen-
sitive in determining tne size of population to save.

Another way to increase the preportion of variation
due to D would be to reduce the proportion due to E. In
these calculations values of 30 to 60 per cent of the to—
tal variation have been found for non-heritable variation.
Replication would have helped greatly in removing or ac-
counting for much of the non-heritable variation encoun-
tered in the experiment.

In the formula, ch -Ԥ, given by Grafius and Brown

(h) lodging reS1stance was a function of both the weight

supported and the height. The weight supported, but not

n

the height, has been considered in this study. Height of
the plant is inherited separately from.the factors deter-
mining torque resistance. When either height or torque re-
sistance is held constant, a change in the other factor will
cause a change in lodging resistance. Selection for lodg-
ing resistance should, on a practical basis, be made only
hts. Similarly, if it were de-
sired te improve lodainq resistance by hybridization, the
quickest advances would be made by crossing strong plants

of the same height. Crossing of strong plants of consid-
erably different heights would give a wide“ range of heights
compounded on the range of torque resistance. Then the
desired combination may not be found in a small sample.

Conversion of the data by taking logarithms changed

the proportion of fixable genetic variance. The original
H figure might have included a part due to interaction of

genes due to imprOper scaling. The order of the original

p—l.

data was no: affected by logarithms; therefore selection

(a
H
o.
6
:3
:2
$3
"3’
9
o
:3
(F
m
.
H
H)

should be done on the basis of the fi
under selection, it would be necessary to consider whether

he original scale was adequate. The logarithmic trans-
formation used in this paper was, in effect, equal to hano-
ing a heavy chain on strong plants and progressively li hter
chains on the weaker plants so that all plants might bend to

the same distance above the ground.

SUUMARY

Inheritance of lodging resistance versus lodging sus-
ceptibility was studied in three oat crosses involving
the parents Clintland, Craig, A587-10, and Craigs Afterlea.
Crosses were obtained for most of the possible combina-
tions of these parents but several seeds were killed by
excessive disinfectant treatment. The parents, the Fg's,
and the F3's for each cross were grown together in the
field. A chain of known weight was used to determine
resistance of each plant to external torque.

Lodging resistance was found to be dominant in the
cross Clintland x Craig and was found to be recessive in
the crosses Clintland x A587-IO and A587-10 x Craigs
Afterlea.

Variations in the F2 and the F3 were separated into
heritable and non—heritable portions. The heritable vari-
ation was further divided into fixable genetic and non-
fixable genetic components according to the method pro-
posed by Mather (7). The distributions of the original
observations were skewed toward the low side. There was
no reduction in skewness in the F3, which indicated that

the problem.was in scaling. When natural logarithms of

’43

Q

the data were used, the distributions approached much more
closely to a normal distribution. Conversion of the data
had an important effect in increasing the proportion of
fixable genetic variance in the calculations on the crosses
Clintland X Craig and A587-10 x Craigs Afterlea.

The fixable genetic variance, in the two crosses
where it could be calculated, was approximately 15 per
cent when the F2 plant readilgs were used and 35 per cent
when the F3 means were used. Selection for lodging resist-
ance prior to the F3 generation seems likely to be on the
basis of non-fixable differences. Selection on the basis
of means of F3 families seemed to give a good start toward
isolating superior lines. Logarithms were valuable in
this study in determining the effectiveness of selection

but were not necessary for selection as they did not change

the ranking of plants.

l.

2.

3.

LITERATURE CITED

Atkins, J. M. Inheritance of weight per unit length
of culm and other characters in Kanred x Coppei wheat.

Jour. Agr. Res. 76: 53-72. leB.

Atkins, J. M. Relation of certain plant characters to
strength of straw and lodging in Winter wheat. Jour.

Agr. Res. 56: 99—120. 1938.

Fisher, R. A., Immer, F. R., and Tedin, O. The genet-
ieal interpretation of statistics of the third degree
in the study of quantitative inheritance. Genetics

17: 107-12i. 1932.

Grafius, J. E. and Brown, H. M. Lodging resistance in

oats. Agron. Jour. A6: hid-@18- 195M.

Hamilton, D. G. Culm, crown, and root development in
oats as related to lodging. Sci. Agr. 31: 286-315.
1951.

45

6. Helmick, B. C. A method for testing the breaking
strength of straw. Jour. Am. Soc. Agron. 7: 118-

120. 1915.

7. Rather K. Biometrical Genetics. Dover Publications,
.9

Inc. New York. 19kg.

8. Pendleton, J. W. The effect of lodging on Spring oat
yields and test weight. Agron. Jour. i6: 265—266.
1954.

9. Ramiah, K. and Dharmalingham, S. Lodging of straw and
its inheritance in rice. Ind. Jour. of Agr. Sci. #2

880-89a. 193A.

10. Salmon, 3. C. An instrument for determining the break-
ing strength of straw and a preliminary report on the
relation between breaking strength and lodging. Jour.

Agr. Res. A3: 73—82. 1931.

l _.__h_-

 

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