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Rodrigo A. Duarte

1966

Thesis @01- We

FHESls

LIBRARY

Michigan State
University

       

This is to certify that the

thesis entitled

RESPONSES IN YIELD AND YIELD COMPONENTS FROM RECURRENT
SELECTION PRACTICBD IN A BEAN HYBRID POPULATION 1
AT THREE LOCATIONS IN NORTH AND SOUTH AMERICA

presented by

Rodrigo A. Duarte i

has been accepted towards fulfillment
of the requirements for .

_Bh...ll.__degree in.CI‘.Qp..S.£i£nce

 

Major professor t

Date February 18. 1966

' ”Ht

0-169

 

ABSTRACT

RESPONSES IN YIELD AND YIELD COMPONENTS FROM RECURRENT
SELECTION PRACTICED IN.A BEAN HYBRID POPULATION
AT THREE LOCATIONS IN NORTH AND SOUTH AMERICA
By Rodrigo A. Duarte

The population studied originated from an intra-specific
cross of Phaseolu§_vulgaris variety Algarrobo by variety
Michelite. Algarrobo is a kidney bean variety native to Colombia,
South America and Michelite is a navy bean variety from Michigan.
These two varieties possess contrasting characteristics not only
in leaf area components namely, number of leaflets per plant (N)
and size of the leaflets (S), but also in yield (W) components,
namely number of pods per plant (X), number of seeds per pod
(Y), and seed weight (Z).

Recurrent selections methods were applied to this popula-
tion with the aim of producing sets of lines with high Levels
(A) of each component, intermediate (M) levels, and low (B)
levels. Results from two cycles of selection are reported in
this thesis.

The experiments were conducted at three locations, two of
them Palmira and Medellin in Colombia, S.A., and the third one
East Lansing in Michigan, U.S.A. These locations differ in cli-
matic conditions such as temperature, rainfall,etc.

Selection in Colombia was practiced independently for N, S,
X, Y, and Z. In Michigan, selections were made for each of X, Y,

Z and also W. Identical selection criteria were used at all

locations.

Rodrigo A. Duarte

The results show clearly that great progress due to selection
was made for each one of the components of the complex traits under
study. The rate of progress for each particular component at either
the high or low level of expression was not the same at each
location. Genotypic ~wenvironmental interactions at the three
different locations are inferred. There was a tendency toward
preferential recovery of the Algarrobo type in the selected families
in Colombia, and of the Michelite type in Michigan.

Comparing the average values of yield in grams per plant
when selections were made independently for X, Y, Z and N at high
and low levels, it was observed that all values at each level
were practically the same. Progress for yield itself was not
really made. Progress of individual components was obtained but
the progress in one component was at the expense of another or
other components, giving through the multiplicative interaction
(comparable seed yields. Although yield is modified by environ-
mental forcea, it shows homeostatic stability to offset the force
of component selection in any direction, high or low.

The unselected components present a similar pattern of

variation at all locations during the two cycles of selection.

Rodrigo.A. Duarte

They exhibited negative relationships with the selected ones,

the magnitude of the association depending upon the response to

selection. Due to the fact that in the second cycle more pro-

gress was made in the selected components, the negative associations

with the unselected ones were more pronounced; however, if one of

the unselected characters shifted too far in a direction opposite

to the selected one the third component shifted in the same direction

as the selected, stabilizing in this manner the final product: yield.

This pattern of relational symmetry and reversion toward the modal

class for the non-selected components was typical of all locations.
The idea of negative associations among components was

supported by the correlation coefficients obtained; however, the

sign of these correlations changed from one cycle of selection to

the next, suggesting that the effect of selection and/or environ-

ment can change the degree of relationship among components.

These findings are in good agreement with results obtained

bywother authors ; jand strongly suggest that these correlations

are not truly genetic. It also furnishes evidence indicating that

mainly independent genetic systems are controlling each one of the

yield components in beans.

Rodrigo A. Duarte

Two hypotheses are presented to explain the negative associa-
tions, both based on the idea that the yield components share a
common pool of resources for their development. Bothfhypotheses
assign an important role to the manner of distribution 6: resources
to the developing components. In one hypothesis the distribution
of resources would depend on the interaction between the genotype
of each component and resource-producing genes. These interactions,
which take the form of de-repression or 'turningon' processes,
occur prior to floral development. ' .

fundamental to the second hypothesis is the fact that yield
components follow a sequential pattern of development, each having
its own genetic system. If a proportionately greater share of the
resources were used in producing highfix, a proportionately lesser
amount would be available to produce high'Y values or possibly 2
values which follow I in the time sequence of development. Selecting
for a component such as Z its high.expression.would depend on
plentiful resources which implies genotypes of low levels of ex-
pression for Y and 2.

Path coefficient analyses were made in order to obtain infor-
mation of the direct and indirect effects of N and 8 upon the
yield components I, Y, and Z, and the effect of the latter components
upon yield (W). The high value of the positive correlation between

N and X is made up mostly of direct effects indicating the great

Rodrigo A. Duarte

influence that N has in determining X. The main direct effect of
S is upon Z; X exerts the greatest influence upon seed yield;
followed by Y, then by Z. The magnitude of the direct effects of
each one of the components was enhanced by recurrent selection.
The fact that N has a large direct effect upon the determination
of X, and S upon Z gives support to the hypothesis of the "turning

on" of genes before floral development.

RESPONSES IN YIELD AND YIELD COMPONENTS FROM RECURRENT
SELECTION PRACTICED IN A BEAN HYBRID POPULATION
AT THREE IDCATIONS IN NORTH AND SOUTH AMERICA

B , !e\
yw

Rodrigo Ai’Duarte

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirement
for the degree of

DOCTOR OF PHILOSOPHY

Department of Crop Science

1966

ADKNOWLEDGEMENTS

The author wishes to express his sincere gratitude to
Dr. M.‘W. Adams.for his guidance, valuable advice and helpful
suggestions throughout the course of this study and in the
‘preparation of the manuscript. Appreciation is extended to
Dr. J. E. Grafius for constructive discussion of certain
portions of this thesis.

Indebtedness is acknowledgeiand appreciation extended to
Ingenieros Agronomos S. H. Orozco and J. I..Alvarez and to
Dr. L. H. Camacho for their help in the selection programs
carried out in Colombia. Without their help this study would
not have been possible.

A special note of gratitude is expressed to my wife Ligia
not only for her moral support and encouragement but also for
her valuable help in the greenhouse and in the field. Also to
our children Stella,{Pilar, Clara and Jehn for their c00peration,
patience and devotion during the last two and one-half years.

Finally the author expresses his acknowledgements to the
Rockefeller Foundation for the fellowship granted to undertake

I

this investigation.

11

TABLE OF CONTENTS

INTRODUCTION . o . . . . . . . . e . .
REVIEW OF LITERATURE . . . . . . . . .
MATERIALS AND METHODS. . . . . . . . .

EXPERIMENTAL RESULTS AND DISCUSSION. .

I. Response to Selection . . .1. . . . .

II. Compensation Among Yield Components.

III. Path Coefficients Analyses . . . . .

SUMMARY AND CONCLUSIONS. . . . . . . . . .

LITERATURECITEIWH

iii

Table

1.1

1.2

2.1

2.2

3.1

3.2

h.l

LIST OF TABLES

Page

t-tests, and mean values of families selected for

high number of leaflets per plant (NA), in two

cycles of recurrent selection at Palmira and

Medellin. Data are expressed as percentage of the
nodalclass.....o............oo13

t-tests and mean values of families selected for

low number of leaflets per plant (NB), in two

cycles of recurrent selection at Palmira and Medellin.
Data are expressed as percentage of the modal class 1h

t-test and mean values of families selected for

high size of leaflets per plant (SA), in two cycles

of recurrent selection at Palmira and Medellin.

Data are expressed as percentage of the modal

Class O O O O O O O O C O O C O O I O O O O O O O O 16

t-tests and mean values of families selected for

low size of leaflets per plant (SD) in two cycles

of recurrent selection at Palmira and.Hbdellin.

Data are expressed as percentage of the modal class . l6

t-tests and mean values of families selected for

high number of pods per plant (XA), in two cycles

of recurrent selection at Palmira, Mbdellin and

East Lansing. Data are expressed as percentage of

the "wal- c1883 0 O O O O O 0 O O O O O O O O O O O 19

t-tests and mean values of families selected for

low number of pods per plant (X3) in two cycles

of recurrent selection at Palmira, hdellin and

East Lansing. Data are expressed as percentage
OfthenOdBICIGBBeeeeeeaeeeeeeeeeee20

t-tests and mean values of families selected for

high number of seeds per pod (IA), in two cycles

of recurrent selection at Palmira, Medellin and

East Lansing. Data are expressed as percentage
ortmmalcusae‘eeeeeeeeeeeeeeee023

1V

Table

h.2

5.1

5.2

10

t-tests and mean values of families selected

for low number of seeds per pod (Is), in two
cycles of recurrent selection at Palmira,
Medellin and East Lansing. Data are expressed
as percentage of the modal class. . . . . . . . .

t-tests and mean values of families selected

for high seed weight (ZA), in two cycles of re-
current selection at Palmira, Medellin and

East Lansing. Data are expressed as percentage
OfthemOdach-aasesesesesssoeesee

t-tests and mean values of families selected for
low seed weight (23), in two cycles of recurrent
selection, at Palmira, Medellin and East Lansing.
Data are expressed as percentage of the modal

Chase..oeeseeeeeeeeeeeesee

t-tests, and mean values of families selected
for high (WA) and low (NB) seed yield, in two
cycles of recurrent selection at East Lansing.
Data are expressed as percentage of the modal

€1.53.oeooeeeesssesessseses

Average seed yield in grams per plant, for X,

I, Z and w. Selected families at the end of the

2nd cycle of recurrent selection, in two levels,

high and low, at East Lansingva‘. . . . . . . . .

Simple correlation coefficients of families
selected for yield and its components, in the
first cycle of recurrent selection, at Palmira,
hdellinandnaflthn'mSeeeOeeeeseee

Simple correlation coefficients of families
selected for yield and its components, in the
second cycle of recurrent selection at Palmira,
Medellin and East Lansing . . . . . . . . . . . .

Simple correlation coefficients for yield and
its components, for 768 unselected and 36 selected
families during the second cycle of recurrent

‘seieetion, at Medellin. . . . . . . . . . . . . .

Page

2h

27

28

31

38

“9

56

vi

Table

11 Simple correlation coefficients for yield and its

l2

13

1h

15

16

17

18

19

components, in families selected for X, Y and Z at
high, intermediate and low level of expression, at
Palmira, Medellin and East Lansing during the first
cycle of recurrent selection. . . . . . . . . . . . .

Simple correlation coefficients for yield and its
components in families selected for X, Y, and Z

at high, intermediate and low level of expression
at Palmira, Medellin and East Lansing. . . . . . . .

Simple correlation coefficients for N and S, yield
and its components, in families selected for N and
S at high, intermediate and low level of expression,
at Palmira and Medellin during the first cycle of
recurrent selection. . . . . . . . . . . . . . . . .

Path coefficient analysis of the influence of X, Y
and Z upon yield (W), in families selected for X

at all levels, A, M, and B at Palmira, Medellin

and East Lansing in the first cycle of selection . .

Path coefficient analysis of the influence of X,

Y and Z upon yield (W), in families selected for

Y at all levels, A, M, and B, at Palmira, Medellin
and East Lansing in the first cycle of selection . .

Path coefficient analysis of the influence of X,

Y and Z upon yield (W) in families selected for Z
at all levels, A, M, and B, at Palmira, Medellin
and East Lansing in the first cycle of selection . .

Path coefficient analysis of the influence of X,

Y and Z upon yield (W) in families selected for

X at all levels, A, M, and B, at Palmira, Medellin
and East Lansing in the second cycle of selection. .

Path coefficient analysis of the influence of X,

Y and Z upon yield (W), in the families selected
for Y at all levels, A, M, and B, at Palmira,
Medellin and East Lansing in the second cycle of
selection. . . . . . . . . . . . . . . . . . . . . .

Path coefficient analysis of the influence of X,

Y and Z upon yield (W), in families selected for Z
at all levels, A, M, B, at Palmira, Medellin and
East Lansing in the second cycle of selection. . . .

Page

65

66

66

69

7O

71

72

73

71.

vii

Table Page

20 Path coefficient analysis of the influence of X,
Y, and Z upon yield (W), and the influence of N
and S upon yield components, in families selected
for N at all levels, A, M, and B at Palmira and
Medellin in the first cycle of selection . . . . . . 78

21 Path coefficient analysis of the influence of X,
Y, and Z upon yield (W), and the influence of N
and S upon yield components, in families selected
for S at all levels, A, M, and B at Palmira and
Medellin in the first cycle of selection . . . . . . 80

LIST OF FIGURES

Figure Page

1 Response to two cycles of recurrent selection
for high (A) and low (B) level of expression
of number of leaflets per plant (N), at Palmira
and Medellin. Data are expressed as percentage
0fth£m0dalc1888sseeeeeeeeeeeeeeo15

2 Response to two cycles of recurrent selection for
high (A) and low (B) level of expression of size
of leaflets (s), at Palmira and Medellin. Data
are expressed as percentage of the modal class. . . 17

3 Response to two cycles of recurrent selection
for high (A) and low (B) level of expression
of number of pods per plant (X), at Palmira,
Medellin and East Lansing. Data are expressed as
percentage of the modal class. . . . . . . . . . . . 21

h Response to two cycles of recurrent selection for
high (A) and low level of expression of number
of seeds per pod (r), at Palmira, Medellin and
East Lansing. Data are expressed as percentage
of the modal class . . . . . . . . . . . . . . . . . 25

5 Response to two cycles of recurrent selection for
high (A) and low (B)levels of expression of seed
weight (2), at Palmira, Medellin and East Lansing.
Data are expressed as percentage of the modal class. 29

6 Response to two cycles of recurrent selection for
high (A), and low (B) levels of expression of X,
Y, Z and W at East Lansing, expressed as percentage
OfthCMOdBlClasaeeeessseoseeeeeoe32

7 Effects of selection for either X, Y or Z
individually upon relative values of the other two
components. Data are obtained from lst cycle of
selection at Palmira and expressed in percentages
onthemOdaICIaBBeesesseseeeseeeeeMI].

8 Effects of selection for either X, Y or Z indi-
vidually upon relative values of the other two
components. Data are obtained from lst cycle of
selection at Medellin and expressed in percentages
on the modal class . . . . . . . . . . . . . . . . . M3

viii

"Figure

10

11

12

13

1h

ix

Effects of selection for either X, Y or Z
individually upon relative values of the other two
components. Data are obtained from 1st cycle of
selection at East Lansing and expressed in per-
centages on the modal class. . . . . . . . . . . . .

Effects of selection for either X, Y or Z
individually upon relative values of the other two
components. Data are obtained from 2nd cycle

of selection at Palmira and expressed in percentages
anthemOdBICIEBBesseseeseooeeseee

Effects of selection for either X, Y and Z
individually upon relative values of the other two
components. Data are obtained from the 2nd cycle
of selection at Medellin and expressed in
percentages on the modal class . . . . . . . . . . .

Effects of selection for either X, Y and Z
individually upon relative values of the other

two components. Data are obtained from 2nd cycle
of selection at East Lansing and expressed in
percentages on the modal c1883 0 e e e s e s s s e a

Direct effects and associations of components
determiningyield....o.....o......o

Direct effects and associations of components of
yield and factors influencing the components . . . .

P888

uh

hS

A6

“7

63

INTRODUCTION

Progress has been made in crop yield improvement without
clearecut genetic information on the inheritance qf grain
yielding ability. It has been expected that as new genetic
information.was obtained, it would lead to greatly increased
efficiency in selection programs, that in turn would lead toward
greatlyeincreased upper yield levels.

During recent years plant breeders have devoted more
attention to the study of the individual components of com-
plex traits such as yield with the purpose of gaining a greater
understanding of the genetic mechanisms that control these traits.

Tomdatesit«has been clearly demonstrated that certain.com;~
plex traits often may be viewed as artifacts made up by the
multiplicative interactions of their components. Moreover the
heritability of the complex characters has been shown frequently
to be low, and the heritability of the components to be, in
general, higher.

Seed yield in beans is a complex trait made up by number of
pods per plant (X), number of seeds per pod (Y) and average
seed weight (Z). 80 is total leaf area which is comprised of number
of leaflets per plant (N) and average leaflet size (8).

With the purpose of producing by means of selection sets of
lines with the individual components represented at different
levels of expression, high, intermediate, and low, recurrent see

lection methods were used. It is well known that recurrent

selection is a powerful tool to increase the frequency of desirable
genes and gene combinations in a plant population, although it has
not been used extensively in self-fertilizing species.

Environmental conditions interacting with the genetic make
up of the components of complex traits, can produce different
phenotypic effects. In view of such interations and in order to
see if results of selection at one location bore any similarity
to results obtained at another location, this study was conducted
at two places in Colombia, South America and in East Lansing,
Michigan. Moreover, one of the parents of the hybrid population
under study originated in Michigan and the other is of Colombian
origin.

The purpose of this thesis was to obtain a fuller knowledge
with respect to the response to selection, in quite different
environments, of each one of the components of the complex traits;
of equal importance was the desire to obtain a better understanding
of the relationships between the selected and non-selected com-
ponents, relationships of great concern for they fix the final
product - yield.

Of greater importance to the plant breeder is to get more
knowledge about the direct and indirect contributions of each one
of the cOmponents in determining the complex trait. To contribute
to this knowledge, path coefficients analyses were made to determine
the direct and indirect influence, of X, Y and Z upon W, and also

the effects that N and 8 could have upon the yield components.

REVIEW OF LITERATURE

Yield in oats has been interpreted by Grafius (h) as the
volume of a rectangular parallelepiped, whose edges are the yield
components: the number of panicles per unit area X, the average
number of kernels per panicle Y, and the average kernel weight Z.
It was pointed out that the edge most subject to change would
be the longest and that changes in the components or edges would
tend to counterbalance.

Working with cotton, Hutchinson (6) partitioned yield into
bolls per plant, seed cotton per boll, seeds per boll, and lint
per seed. Environmental variations seemed to affect some
characters more greatly than others, and selection was found to
be more effective for certain components. This work was the
first to show clearly in a selection eXperiment the compensatory
variation that develops among components; that is, the intensi-
fication of one character that can only be obtained at the expense
of the others because of ”physiological incompatibilities".

Whitehouse gt a]; (12) reported upon yield components-of
wheat using as the components: weight per grain, grains per
spikelet, spikelets per ear, and ears per plant. Correlation
analysis between components were made, and it was found they were
completely independent of each other. Yield predictions by means
of diallel crosses, in which the best varieties for yield com-

ponents were chosen, was also mentioned.

Camacho st 31 (2) studied genotypic and phenotypic correlations
of components of yield in kidney beans. The authors found that all
correlations between yield components were negative but that yield was
positively correlated with its components. From the genotypic correla-
tions they concluded that an increase in pod number caused a decrease
in number of beans per pod, and that an increase in the latter com-
ponent was reflected in a reduction of bean size.

Response to selection for yield in cotton was analyzed by
Manning (7) using the yield components designated by Hutchinson. He
found considerable genetic variability in the material after seven
generations of self-fertilization. Of particular interest was the
improvement of the modal-class bulk (intended as a stable pOpulation
from which to measure selection gains) which suggests that natural
selection favors the breeder whenever the number of seeds produced
is intimately related to yield.

According to Olsson (9), no correlation would be demonstrated
between the seed yield of an individual plant and the yield of a
progeny plot in Brassica and Sinapis. In regard to number of seeds per
pod and seed size however an evident correlation between mother and
progeny was found, suggesting adaptive modifications of pod number
between parental plants and their progeny in plots. The author also
reported the tendency toward a decrease in seed weight when number of
seeds per pod were increased and that selection for low number of seeds

resulted in a decrease in fertility.

In a two-year study of corn yield and its components-ear number;
number of kernel rows, kernels per row and kernel weight-Hoen
and Andrew (5) found significant positive correlations between
yield and its components. Ear number showed no correlation with
kernels per row or kernel weight. No correlation between kernel
rows with kernels per row or kernel weight was observed; however,
a significant negative correlation was detected between kernels per
row and kernel weight during one year out of two.

Archibong (1) studied the influence of spacing and inter-
strain competition in navy beans. He found that the stress of
competition caused significant changes in the pattern of relation-

ships among the yield components of the several genotypes.

MATERIALS AND METHODS

Intra-specific crosses of Phaseolus vulgaris variety Algarrobo

 

by variety Michelite were produced. These two varieties possess

contrasting characteristics, which can be summarized as follows:

 

.gharacteristics Algarrobo
Origin Colombia, S.A.
Type of seed Mottled kidney bean

Type of growth

 

Determinate (bush)

Number of leaflets per plant (N) Few

Size of the leaflets (5) Large

Number of pods per plant (X) Few

Number of seeds per pod (Y) Few

Seed weight (2) Heavy
Characteristics Michelite
Origin Michigan,U.S.A.
Type of seed Navy bean

Type of growth Indeterminate (vine)
Number of leaflets per plant (N) Many

Size of the leaflets (S) Small

Number of pods per plant (X) Many

Number of seeds per pod (Y) Many

Seed weight (2) Light

Crosses were made under greenhouse conditions in l959-60“and

F1 and F2 progenies were grown in that environment in order to
produce F2 and F3 generations for planting in the field. Seed
coming from the F3 generation was divided in three parts to be
planted on land of the Agricultural Experiment Stations at Palmira.
and Medellin (Colombia, S.A.) and at the Michigan Agricultural
Experiment Station in East Lansing, respectively. Palmira is
located at 1,000 mts. over sea level, with an average temperature

of 25°C. and rainfall of 1,000 m.m. per year; Medellin with an

average temperature of 21°C. and rainfall of 1,300 m.m. is situated
at 1,500 mts. over sea level.

One hundred and twenty one Fh families were planted in February
1962 at Palmira and Medellin and during the summer of the same year
at East Lansing. Each family was planted in an individual row,
with 3 replications, using 20 plants per replication with a 6-inch
spacing between plants within rows.

Selections in Colombia were practiced for components of Total
Leaf Area (T), namely, number of leaves per plant (N) and size of
the leaves (S), and for yield (W) components, namely, number of pods
per plant (X), number of seeds per pod (Y), and average seed
weight (Z). In East Lansing, selection was practiced independently
for each of X, Y, Z and W.

Selections were made at three levels of expression for each of
the characters under study. The levels were: high (A), inter-
mediate (M), and low (B).

Four families were selected for each character, at each level,
giving a total of 60 families in Palmira, 60 in Medellin and #8 in
East Lansing. For the high (A) and low (B) selections the extremes
were taken, i.e., the h highest and the h lowest in the pOpulation
for any component. The intermediate or modal-class selections
were restricted to families within one (1) standard deviation centered
on the mean.

Leaf area (S) measurements and leaf counts (N) were made two
weeks after the onset of flowering, taking two plants at random per

family per replication. At maturity number of pods per plant (X),

and number of seeds per pod (Y), were recorded in a 3-foot
section of the row. In order to obtain the average weight of
a seed (Z), a sample of 100 seeds was taken.

With the aim to produce by recurrent selection methods sets
of lines with high levels of each component, with intermediate
levels of each component, and with low levels of each component,
crosses were made among components at each level. That is, con-
sidering yield components, plants in families with high number
of pods per plant (XA) were crossed with plants in families having
high number of seeds per pod (YA) and with plants in families
having high seed weight (ZA), doing the same thing with YA and ZA.
To illustrate this point, calling XA-l, XA-2, XA-3, XA-h the four
selected families for high number of pods, and YA-l... YA-h, ZA-l...
ZA-h the four selected families for high number of seeds per pod
and high seed weight, respectively, the following kinds of crosses

were performed.

YA-l YA-l
XA-l YA-2 XA-3 YA-2
YA-3 YA-3
YA-h YA-h
YA-l YA-l
XA-2 YA-E XA-h YA-2
YA-3 YA-3
YA-h YA-h
ZAal ZA-l
XA-l ZA~2 - XA-3 ZA-2
ZA-3 ZA-3
ZA-h ZA-h
ZA-l ZA-l
XA-2 ZA-2 XA-h ZA-2
za-3 ZA-3
za-h ZA-h
ZA-l ZA-l
YA—l ZA-2 YA-3 ZA-2
ZA-3 ZA-3
ZA-h ZA-u
ZA-l ZA-l
YA-2 ZA-2 YA-h ZA-2
ZA—3 ZA-3
ZA-h ZA-h

In the same manner, crosses for intermediate expressions of
yieldcomponents, namely, XM, YM, ZM, and for low expressions
XB. YB, ZB, were made.

In addition, in Palmira and Medellin, crosses were per-
formed between families with high number of leaves per plant,
NA-l...NA-h, and families with large size of leaves SA-l..SA-h,
and similarly for families with intermediate and low levels of
expression, namely: NM-l...NM-h, SM-l...SM-h and NB-l ... NB-h,
SBel ... SB-h. Seeds resulting from the one hundred and ninety

two possible combinations of crosses made were planted in the

10

field in the two locations in Colombia. An average of seven
F1 plants were grown per each combination, coming from 2 or 3
artificially pollinated pods.

in East Lansing, selections on the basis of yield (V) itself
were made, besides the selections for yield components X, Y, and
Z. Crosses of yield-component selections were performed following
the same program described above. Families selected for W'were
intercrossed among themselves, but not with.X, Y and Z.

One hundred and sixty two possible combinations were obtained
and from 3 to h F1 plants were grown in the greenhouse, per each
combination.

The F2 generation produced in preparation for the second
cycle of selection was grown under field conditions. In Palmira
and Medellin 192 F2 plots were planted with an average of 30
plants per plot.

0n visual criteria, but not with actual measurements, h
plants per each of the F2 plots, were chosen in order to give
rise to the F3 generation. In some cases it was not possible
to get h plants so 1, 2 or 3 were selected. These selections
were based on 3 levels of expression (A,#\MI- B) and the
characters under consideration (N, S, X, Y, Z and W). The first
third of the F2 population was made up of families with high level
of expression (A), the second third of families with intermediate

levels (M) and the third part of families with low Levels (B).

11

Seven hundred and sixty eight F3 families were grown in
Medellin; 532 in Palmira and th in East Lansing. Planting
methods, selection procedures and selection pressures were the
same as in the first cycle of selection, already discussed.

Since in Colombia there are two growing seasons per year
in contrast to Michigan that has only one, the schedule of
crossing and selection events in the two places was arranged
somewhat differently. The final selections of the 2nd cycle
were made during the fall of l96h in Colombia, and during the
summer of 1965 in East Lansing.

For the purpose of this thesis two cycles of recurrent
selection are considered. However, this study will continue
until the 3rd or hth cycle. At the end of this time all re-
sulting lines from all cycles will be grown at all locations
for one year to see what has been accomplished by the different

levels of selection.

EXPERIMENTAL RESULTS AND DISCUSSION

I. Response to Selection

A. Number of Leaflets for Plant (N)

Tables 1.1 and 1.2 contain t-test comparisons of gains between
the first and second cycle of recurrent selection, for high (NA)
and low (NB) number of leaflets per plant respectively, at Palmira
and Medellin. For these tables and for the following ones, the
mean values of the selected families are expressed on a percentage
basis with the mean of the modal class selections being taken as
100 percent in each one of the cycles. In this way, changes in
means due to variation in environmental conditions prevailing
during each cycle of selection are minimized.

Figure 1 shows graphically the response to selection from
the first to the second cycle of recurrent selection for high (NA)
and low (NB) levels of expression of number of leaflets per plant,
at Palmira and Medellin as compared to the modal class on the
percentage basis.

Highly significant differences between cycles for NA were
observed at Palmira as well as at Medellin. Ninety nine and thirty
three relative units of progress were obtained at Medellin and
Palmira respectively (Figure 1). For the purpose of this thesis
the difference between the average percentage in the first and
the second cycle is called relative units of progress.

Selections for a lower number of leaflets per plant show highly

significant differences at Palmira. Progress toward a lower number

12

of leaflets was made at Medellin, but the difference was not signi-

ficant by the t-test.

In these two locations twenty two and

twelve relative units of progress toward the lower level were ob-

tained.

Table 1.1 - t-tests, and mean values of families selected for-high

Values of A selected families

number of leaflets per plant (NA), in two cycles of
recurrent selection at Palmira and Medellin. Data are
expressed as percentage of the modal class.

 

 

 

 

Locations 1st cycle 2nd cycle t-values fi_
lh3.05 182.37
Palmira 1hh.9h 181.51
159.06 180.65
w_ 1hh.00 177.20
Average 147.76 18o.h3 8.21§*
Madellin 151.9h 230.53
_151.0h 230.53
150.90 256-99
___ 132s92_ 264-55 _.
_Average lh6.h9 g§5.6§ Q.8h**

 

**P (.01

1%

Table 1.2- t-tests, and mean values of families selected for low
number of leaflets per plant (NB), in two cycles of
recurrent selection at Palmira and Medellin. Data
are expressed as percentage of the modal class.

 

Values of h selected families

 

 

 

 

 

Locations lst cycle 2nd cycle t-valuesg_
67.76 39.57
Palmira 68.71 hh.73
6h.9u hl.29
6h.9h 52.57
Average 66.Sg__r hh.52 7.08**
Medellin 53.h0 5h.80
59.27 h8.19
59-73 39-68
61.68 h1.57
Average 58.§2 h6.06 1.h5
**P‘< .01

B. Leaflet Size (3)

Mean values of the selected families and t-tests, for the two
cycles of recurrent selection, at Palmira and Medellin for large
(SA) and small leaflet size (SB) are shown in Tables 2.1 and 2.2,
respectively. Rate of progress between cycles at Palmira and Medellin
is presented in Figure 2.

From table 2.2 it appears that no significant differences were
obtained between the two cycles for selections of small leaflet sixe
(SB) in either one of the two locations. However, 1h relative
units of progress for SB at the end of the 2nd cycle were obtained
in Palmira; on the contrary in Medellin, even though 1h units of
change were observed, this change was opposite to the direction of

selection. These results are presented graphically in Figure 2.

15

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Table 2.1 t-tests and mean values of families elected for high
size of leaflets per plant (SA), in two cycles of
recurrent selection at Palmira and Medellin. Data
are expressed as percentage of the modal class.

_yalues of_h selected families

 

 

 

 

 

Locations lst cycle 2nd cycle t-values
Palmira 153.35 252.13
' 150.39 250.35
lh6.1l 218.39
___ 138g92 229.0h

Averggg» lh7.l9 237.h8 10.23**
Medellin 187.50 211.h3
183.25 23h.51
169.02 2h0.70
l56.h8 222.86

__¥Average_ 17h.06 227.38 5.56*§__,
**P < .01

Table 2.2 t-tests and mean values of families selected for low
size of leaflets per plant (SB) in two cycles of
recurrent selection at Palmira and Medellin. Data
are expressed as percentage of the modal class.

 

Xalues of h selected families

 

 

 

 

Locations lst cycle 2nd cycle t-values

Palmira 59-66 39.77
59.31 h8.65
67.98 60.72
fi_ 69.63 h9.71

Average 6h.lh h9.7l 2.84
Medellin h1.6h 60.70
58.1h 73.80
59-90 79.05
65.3h 67.62

___Averaggy 56.25 70.29 2.17

 

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18

c. Number of Pods Per Plant (x)

Tables 3.1 and 3.2 contain mean values of selected families
in the two cycles of recurrent selection for high (XA) and low
(XB) number (of pods per plant at three locations: Palmira, Medellin
and East Lansing. Progress in selection between the two cycles
is shown graphically in Figure 3, at three different locations,
and two levels of expression, XA and 1:13.

A highly significant difference between cycles for XA was
obtained at East Lansing, a significant difference at the 5 per-
cent level, and no significant difference were obtained at
Palmiraand Medellin, respectively, as may be seen in Table 3.1.

In selecting for high number of pods per plant (XA) the
greatest 3.1a ... obtained at East Lansing with 70 relative units
of progress between the first and the second cycle; sixty and 30
relative units were obtained at Palmira and Medellin, respectively.

Selections for XB proved to be significantly lower at the end
of the 2nd cycle as compared with the 1st cycle, at the l percerit
level of significance in mdellin and East Lansing, and at the 5
percent level of significance at Palmira, as shown in Table 3.2.

Figure 3 shows graphically the progress made in selecting for
XB from the 1st to the 2nd cycle. Forty-four relative units of gain

were obtained at thellin, 17 in Palmira and 1% in East lensing.

19

Table 3.1 t-tests and mean values of families selected for
high number of pods per plant (XA), in two cycles of
recurrent selection at Palmira, Medellin and East
Lansing. Data are expressed as percentage of the
modal class.

 

Values of h selected familie§_

 

 

 

 

 

 

 

 

 

**‘P‘<.Ol

Location lst cycle 2nd cycle t-values
15h.82 260.1h
Palmira 1h2.19 213.8h
1h8.83 182.82
__, V__ 155.58 182.82
fiveraggfi w ___. 150.33 209.91 ,3:22*
172.12 166.67
Medellin 1h3.03 236.08
lh3.03 lh2.83
fi__ __ 138.18 17l.h2
Average e_.. 1H9.09 179.25, ”l.hl
East Lansing lh3.10 220.50
1h3.60 211.50
lhh.00 213.90
fi_ 1hh.50 209.00
QIEEEEC lh3.80 213.70 28.99**
* P (.05

20

Table 3.2 t-tests and mean values of families selected for low
number of pods per plant (X3), in two cycles of
recurrent selection at Palmira, Medellin and East
Lansing. Data are expressed as percentage of the
modal class.

 

_!§lues of_h_se1ected_£amilies

 

 

 

 

 

 

 

 

H P (.01

_Locationa_ __W__ let cycle __ 2ndggycle t-values-
Palmira 58.h7 h2.72
65.78 35.80
59.80 h0.57
h8.50__ hh.15
532535: '58.1h no.8}: u.2o*
Medellin 56.97 8-33'
59-39 25.00
61.82 1h.16
__ _ emu _ 16.67
Aggra§g_ ‘__ 60.60 16.0h ~rxy7n**
East Lansing 51.10 36.80 ‘-
uh.5o 31.10
50.20 35.20
fg53.70 38.50
.Average 59.90 p35.h0 <_5.79**
*‘P‘<.05

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22

D. Number of Seeds Per Pod (Y)

Mean values of the selected families and t-tests between the
two cycles of recurrent selection, for high (IA) and low (YB)
number of seeds per pod at Palmira, Medellin and East Lansing are
presented in Tables h.l and h.2. Rates of progress between cycles
in the three different locations are shown in Figure h.

From the t-tests presented in Table h.l it may be seen that
the differences between the two cycles for IA ranged from
highly significant in East Lansing to no significance in Medellin.
Palmira shows a difference between cycles significant at the
5 percent leVel.

Even though Medellin does not show a significant difference
between cycles, a progress of 25 relative units for IA was
obtained, as shown in Figure h. In Palmira and East Lansing, 69
and 58"relative units of progress were observed.

Table h.2 shows that a highly significant difference between
cycles for the low level of expression of number of seeds per
pod was obtained in Medellin. A significant difference at the 5
percent level was observed in Palmira and no significance was
found at East Lansing.

Thirty five relative units of progress were obtained at
Medellin, followed by Palmira with 21 and East Lansing with h, as

shown in Figure h.

23

Table h.1 t-tests and mean values of families selected for high
number of seeds per pod (IA), in two cycles of re-
current selection at Palmira, Medellin and East Lansing.
Data are expressed as percentage of the modal class.

 

values of h selected families

 

 

 

 

Locations lst cycle 2nd cycle t-values
Palmira 130.68 265.13

127.8h 181.3h

127.8% 177.06
_‘ 139.20 176.75
Average 131.39 200.07 3.19*
Medellin 131.91 172.h1

126.78 13h.h9

125.6h 13h.h9

125.07 170.69_

 

 

 

 

Average __127535 153.02 2.37
East Lansing 137.30 203.20
‘ ' 138.90 190.30
1&8.10 209.70
fi_ 152.30 206.h0
Average lhh.10 202.h0 10.h0**
*P (.05

**P < .0].

211

Table h.2 tetests and mean values of families selected for low
number of seeds per pod (YB), in two cycles of re-
current selection at Palmira, Medellin and East Lansing.
Data are expressed as percentage of the modal class.

 

Values of 1+ selected families#

 

 

 

 

 

 

 

 

 

 

Locations lst cycle 2nd cycle t-values
Palmira 71.02 110.36

73.86 £16.78

73.86 55.96
_ fl 68.18 59.63
Average___' 71.73 50.68 h.60*
Medellin 62.68 29.31

70.66 36.21

70.66 31.03

72-93 31293
average"- 69.23 3: . 11.6277“
East Lansing h8.1 51+.83

53-95 51.61
Average 453.h9 h9.18 1.19
*P <.05

25

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26

Tables 5.1 and 5.2 contain mean values of selected families
and t-tests between 2 cycles of recurrent selection for high (ZA)
and low (ZB) levels of expression of seed weight, at Palmira,
Medellin and East Lansing. Figure 5 shows the progress made in
the 2 cycles at the three different locations, for ZA and ZB.

From the t-values shown in Table 5.1 it may be seen that a
highly significant difference between the lst and the 2nd cycle
of recurrent selection for ZA was obtained in East Lansing. No
statistically significant difference was found either at Palmira
or at Medellin. However, a progress of 58 relative units for ZA
was achieved between the two cycles at Medellin; forty-eight
relative units were obtained at East Lansing and four in Palmira.

In Table 5.2 it may be seen that significant differences at
the 5 percent level between the two cycles for ZB were obtained
~at Medellin and East Lansing but differences were not significant
at Palmira.

Figure 5 shows essentially parallel lines for selection gain
at the three locations when selections were made for ZB. In each
one of the locations eleven relative units of progress in the

selected directions were obtained.

27

Table 5.1 t-tests and mean values of families selected for high
seed weight (ZA), in two cycles of recurrent selection
at Palmira, Medellin and East Lansing. Data are
expressed as percentage of the modal class.

 

value of h selected families

 

 

 

 

 

 

Locations lst cycle 2nd cycle t-values
Palmira lhh.68 166.03

1h0.h2 135.8h

136.17 135.8h

136-17 135.8h
Average 139.36 1h3.39 0.516
Medellin 165.99 326.67

1h9.79 180.00

lhl.70 160.00

1h1.70 166.67, __
Average 149373, 208.39 1.27
East Lansing 126.h0 181.30

130.00 181.30

132.90 18h.h0

1u2.60 178.10
Average 132.90 181.30 13.Q5**

 

**P (.01

28

Table 5.2 t-tests, and mean values of families selected for low
seed weight (ZB) in two cycles of recurrent selection,
at Palmira, Medellin and East Lansing. -Data are
expressed as percentage of the modal class.

 

Values of h selected families

 

 

 

 

 

 

Locations 1st cycle 2nd cycle t-values
Palmira 63.82 h5.28
72. 3h 60.37
68.08 60.37
72.3h 6h.15
Average 69.1h 57.5h 2.20
Medellin 56.68 53-33
6h.78 53-33
68.82 53-33
W 68.82 53.33
Average" 6h.77 53.33 h.00*
East lensing 58.23 116.87
60.29 53.12
63 .82 50.00
_. 65.00 350.00
Averag; 61 . 83 1+9 .99 5 . 13*

 

*P <.05

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30
F. Seed Yield (w)

Mean values of the selected families and t-tests between the
two cycles of recurrent selection, for high (WA) and low (VB)
levels of expression of seed yield are presented in Table 6.
Figure 6 shows the response of selection for RA and NB at East
Lansing between the two cycles and also the rate of progress of
the individual yield components at high (A) and low (B) levels
of expression.

From table 6 it appears that significant differences at
the 5 percent level existed between the two cycles of recurrent
selection for WA. In the case of ND no significant difference
was found.

In Figure 6 it appears that even though 1% relative units
of progress were obtained for WA and three for NE, these units
were in the direction opposite to that for which they had been

selected.

G. Discussion

A ceiling upon possible progress in straight pedigree
selection is established by the genotype of the foundation
plants.“ Recurrent selection breaks this ceiling inasmuch as cyclic
selection and recombination increases the frequency of desirable

genes and gene combinations in the population.

31

 

 

 

 

 

 

 

Table 6 t-tests and mean values of families selected for high
(WA) and low (WB) seed yield, in two cycles of re-
current selection at East Lansing. Data are expressed
as percentage of the modal class.

East Lansing:
values of h selected families
__Leve1 lst cycle 2nd cycle t-values
WA 150.h5 1&5.h9
155.5h 142.09
156.58 1h2.99
l6h.0h 1h0.66
Avergggr 156.65 1h2.81 h.6h*
we 78.70 60.83
hh.20 h2.03
h6.h0 hl.85
59-72 87.ho
Average 5h.75 58.03 0.28%

*P<.05

32

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33

From the results shown in the preceding sections, it is clear
that progress due to selection was made for each one of the com-
ponents of both yield and leaf area. The rate of progress for each
particular component, at either the high or low level of expression,
was not the same at each location. ‘Genes are expressed differently
as the environment varies. Full expression of these genes could
be obtained under certain environmental conditions, whereas under
other conditions intermediate expression or almost complete
suppression of their effects could be inferred.

Considering total leaf area components, namely, number of
leaflets per plant (N) and leaflet size (S), it was seen in Figures
1 and 2 that more progress for EA was achieved in Medellin than in
Palmira.

The opposite situation was true when selection was carried
out for large leaflet size (SA); the gain in the latter was
markedly higher in Palmira than in Medellin. This situation may
be interpreted on the principle that through recurrent selection
and recombination, genes favoring certain traits can be recovered
in greater frequency at one location than at another for they are
expressed more in one environment than in another.

There is also the possibility that the superior adaptiveness
associated with the.Algarrobo genotype at Medellin tends to be
reflected in the kinds of plant characteristics that are selected
under that environment. This might explain why selection for smaller

leaflet size at Medellin was ineffective, the Algarrobo type, with

3h

relatively large leaflets, being favored by natural selection forces
over the Michelite type with relatively small leaflets.

The range of variability between low and high levels of N and
S appears to be different at each one of the locations when
selections were performed at the completion of the second cycle.
While for N at Medellin the range goes from h6.06 to 2h5.65
(percent based on the modal class 3 100%), the range for the
same character at Palmira was from hh.52 to 180.h3 (Figure 1).

These differences in realized gain from selection for two
characteristics in two different environments can probably be
accounted for by differential heritabilities of the traits selected
for at Medellin and Palmira. Putting it another way, the first
cycle selections for RA at Medellin produced upon intercrossing
an array of genotypes some of which showed very high expression
under the Medellin environment of the second cycle. Similar first
cycle selections at Palmira either did not have the recombination
potential or the new genotypes produced by intercrossing were
less strongly expressed in the Palmira environment.

A similar situation to that discussed for leaf area prevails
for yield components. From the results it is clear that
greater progress for the high expression of number of pods per
plant (XA) and number of seeds per pod (YA) was obtained at
East Lansing and Palmira than at Medellin. However, for high
level of seed weight (ZA) greater gain was achieved at Medellin
than at either East Lansing or Palmira (Figures 3, h, 5 - Tables

3.1, n.1, 5.1).

35

Selection for the low expression of yield components re-
sulted in more progress for KB and YB at Medellin than at
East Lansing or Palmira (Figures 3, h, 5 - Tables 3.2, n.2,
5.2). For lower expression of seed weight (ZB) no differences
among locations were detected. “ -

Here again, genotypic-environmental interactions, and the
association of the parental type at certain locations seems to
be true. The Michelite type has been recovered more often
than expected at East Lansing, as suggested by response in higher
number of pods per plant and seeds per pod. 0n the contrary,
at Medellin the Algarrobo type seems to be predominant as
suggested by the heavier seeds recovered in that location.
Palmira behaves as intermediate between the other two locations,
even though more progress was observed for higher expressions
of number of pods per plant and number of seeds per pod, than
for seed weight.

These findings demonstrate that selection directed toward
increasing the level of certain components at each location is
worthwhile. Much more progress could be made in yield if, for
instance, at East Lansing and Palmira, selection were directed
more toward increasing X and Y than Z, the Opposite being true
at Medellin. Similar reasoning could be applied to leaf area
components at the two locations in Colombia.

Thus far, selection for yield components has been discussed

and shown to be effective. ‘But what happens when selecting for

36

yield itself? From Table 6 and Figure 6, it may be seen that
even though progress was made for yield it was in the ”negative"
direction; that is, when selections were made for high seed yield
level (WA), instead of increasing, yield actually decreased; the
opposite situation arose when selecting for low yield (WB), -

an increase was noticed. Although the comparison between the ’
two cycles was significant at the 5 percent level for WA, only

1h relative units of "negative" progress were obtained and for
WB only 3 relative units.

Figure 6 shows graphically the response of selection for '
yield components, namely X, Y and Z, as compared to selection
for yield itself (East Lansing). Great progress was obtained
for each one of the components in both directions - high and
low levels of expression. However, as was discussed, "negative"
progress was observed for yield. This is not to say that select-
ing for high yield will always render lower yields. It was true
for this particular cross at this particular location, it is
also necessary to recall that in Figure 6 the values are expressed
as percentage of the modal class in both cycles, and also that the
modal class changed slightly from the let to the 2nd cycle.

Table 7 shows average values of yield in grams per plant when
selections were made for X, Y, Z and W at high (A) and low (E)
levels. It is interesting to note from this table that actual
seed yield was higher when selections were made for XA and IA than

when selection was for WA, being in the case of ZA more or less

37

the same as WA. The same situation prevails when selections
were performed for low levels of yield components and seed yield
itself; lower yield values were obtained for XB and YB than WB,
being in the case of ZB a little higher than WB. Hewever, these
differences were not of sufficient magnitude to be regarded as
important. Practically speaking all values are the same.

This means that progress for yield was not really made. Progress
in the values of individual components were obtained, but the
progress in one component was at the expense of another or other
components, giving through their multiplicative interaction more
or less the same result as far as seed yield was concerned. This
implies negative correlations among yield components, a discussion
of which will be postponed for a later section of this thesis.

Yield is greatly modified by environmental factors; however,
it shows a kind of homeostatic stability to offset the force of
selection, in any direction, high or low, without appreciable
changes in magnitude. This homeostatic stability of seed yield
seems also to be true, when selection of individual components
was performed.

In some cases, and especially at Medellin, nonpsignificant
differences between means were obtained when comparing the two
cycles of recurrent selection, even though the progress
measured in relative units showed patently that progress was made;
the explanation lies in the fact that large variances were ob-

tained, resulting in a non-significant t-test. The amount of the

38

variance could be very large in magnitude even if only a single
family out of four exhibits a different value. This is the case,
for example, shown in Table 5.1 at Medellin. The t-test shows
a nonesignificant value; however, it may be seen that the first
family in each one of the cycles shows a much higher value than
the remaining three. If a t-test is performed Just among the
three families a highly significant difference is obtained.
Table 7. Average seed yield in grams per plant, for X, Y, Z

. and W. Selected families at the end of the 2nd

cycle of recurrent selection,in two Levels, high
and low, at East Lansing.

High Level Low Level

Seed Yield (W) 23.92 9.72
Number of pods per plant (X) 26.00 5.56
Number of seeds per pod (Y) 26.66 6.

Seed weight (z) 18.3l 10,69

II. Compensation Among Yield Components

In the preceding section of this thesis the response to
selection for individual yield components and yield itself
was discussed. This section will be concerned with the
effects that selection for a given component has upon the
‘Inoneselected components, for example, the effect that
selection for number of pods per plant (X) has upon the number
of seeds per pod (Y) and the seed weight (Z) in the same
families.

This situation is graphically presented for the first
and second cycles of recurrent selection at three locations,
Palmira, Medellin and East Lansing, in percentages based on
the appropriate modal class as 100 percent (Figures 7, 8,

9, 10, 11, 12).

A. First Cycle

Palmira

Figure 7 shows the effect of selection for each one of the
yield components upon the non-selected ones, at Palmira in the
first cycle of recurrent selection. Families selected for XA
reached an average of 150 percent, that is 50 relative units
above the modal class, while Y for the same set of families is
near the 100% point, and Z 15 units lower than the modal class.
Selections for XB with an average of 58 percent (#2 relative
unité below the modal class) exhibit a Y value of 85% and a“*z

value of 108%. It should be noted that the slopes of the lines
39

hO

representing the relative effects on sequential components Y and
Z, by selection for X, are generally downward for the XA selec-
tions and upward for the XB selections.

Selection for YA and YB present a pattern similar to that of
selection for X. The slope of lines converging at X, though near
the average, shows a negative relationship with Y; this effect
is more pronounced for unselected Z.

Selection for ZA depressed the values of X and Y, bringing
them down 10 and 18 relative units respectively below the modal
class; on the contrary, selection for ZB resulted in increased
values of Y and X, 8 and 9 relative units over the 100 percent.

It is interesting to notice that the two X lines for selected
levels of expression (XA and X8) cross at certain points; the same
thing is true for YA and YB, as well as for ZA and Z3 selections,
suggesting particularly that Z is often involved in these component
adjustments. .

Relationships in the first cycle of recurrent selection
among selected yield components and nonpselected ones at Medellin
and East Lansing are presented in Figures 8 and 9 respectively.

Patterns of variation similar to those obtained at Palmira
were found at Medellin and East Lansing. The relationship between
the selected and unselected components was essentially the same,
showing negative associations; however, if one of the unselected
characters goes too far in a direction Opposite to the selected

one, the third component varies directly as the selected one,

ul

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stabilizing in this manner the final product yield.
This pattern of relational symmetry and reversion toward
the modal values for the non-selected components is typical of

all locations.

B - Second Cycle

Figures 10, 11 and 12 show graphically the effect of
selection upon selected and nonpselected yield components, at
Palmira, Medellin and East Lansing, respectively.

The second cycle results in patterns of variation similar
to the first one. The compensation among the yield components
is particularly clear in the second cycle. Because of the
great progress made by selection for individual components, the
negative relationships with the unselected ones were exaggerated,
as indicated by the slope of the lines, which are much steeper
than in the first cycle.

The reversion of the non-selected components toward the
modal class is very clear, showing a pattern of relational symmetry

which is practically the same at all locations.

143

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C. Correlation Coefficients

In the preceding sections the relationship among selected
and unselected yield components was presented and discussed.
Correlation coefficients were not calculated inasmuch as only
four families were selected for each character at each level,
therefore, the number of pairs being too few, the expected
error would have been of high magnitude.

Phenotypic correlation coefficients for 36 families
selected for yield components at each location, Palmira,
Medellin and East Lansing, are presented in Tables 8 and 9
for the first and the second cycle of recurrent selection,
respectively.

Considering the first cycle, it may be seen in Table 8
that X and Y are positively correlated at all locations, though
none reached the significance level. The association.XZ was
negative and significantly different from zero at the .05 level
in Palmira and Medellin and near significance at East Lansing.
There was significant negative correlation between Y and Z at
the three locations.

X, Y and Z are positively correlated with yield at all
locations except for East Lansing where ZN is negative although
of very low magnitude. X is the component which shows most
association with W. It is interesting to notice that in Medellin

the magnitude of association of XW, even though is highly

#8

49

significantly different from zero, is lower than in Palmira or

East Lansing. 0n the contrary the correlation coefficient

between Z and‘w at Medellin is positive and significant, being

not different from zero at the other two locations.

Table 8. Simple correlation coefficients of families selected
for yield and its components, in the first cycle of
recurrent selection at Palmira,.Medellin.and East

Lansing.

Comparison
XY
XZ
XW

YZ
YW
ZW

Palmira

.265
”31.7.
.832“
'- 0 SW
.h67er
.016

Locations

Medellin East Lansing

.189
'- 0366*
.6u8**
-.53h**
..198
-393*

.021
-0305

~737**
-.h01*

.h28**
-.003

Table 9. Simple correlation coefficients of families selected
for yield and its components, in the second cycle‘of
recurrent selection, at Palmira, Medellin and East

Lansing.

cpmparison

assess

 

.. Locations
P‘a’ Elmira Medellin East Lansing
-.207 -.2h6 -.137
.287 .lhO é.33h*
.8h8** .596** .803**
"' 0&63“ " 0016 - 01‘61“
.162 .250 :h95**
o 22]. o " 0018

D. Discussion

 

From the results presented in the preceding sections there
is apparent a similar pattern of variation with respect to the
behavior of unselected yield components at the three locations
under study during the first cycle of selection. Progress for
selected components was somewhat different especially between
the Colombian locations and East Lansing. While in the latter
location greater gain was obtained for X and Y than for Z, in
Palmira and Medellin more progress was achieved for Z and X,
especially for Z at Medellin. The unselected components
exhibit negative relationships with the selected ones, the
magnitude of the association depending upon the response to
selection.

The second cycle of recurrent selection presents some
aspects similar to the first cycle as far as negative associa-
tion ameng selected and non-selected yield components is con-
cerned. However, as may be seen from Figures 10, 11 and 12, the
slope of the lines is steeper than in the first cycle. This
results from the fact that progress in selection for yield com-
ponents was greater in the second cycle, and in the same manner
the degree of compensatory relationship between selected and non-
selected components increased in magnitude. For both cycles if

one of the unselected components reverts too far in a direction

50-

Sl

opposite to the selected one, the third component varies in the
same direction as the selected one, stabilizing in this manner the
final product, yield. In general, this pattern of compensation
among components holds true at all locations. To illustrate

this situation, let us take as an example the case of selection
for XA at Medellin and East Lansing during the second cycle
(Figures 11, 12). It can be seen that in the former case a high
negative relationship exists between selected XA and unselected

Y, whereupon Z shows positive association with XA, going up from
the mean value of Y; at the latter location XA.exhibits a negative
relationship with Y but not as strong as in Medellin, therefore,
the line continues downward to a lower value of Z, giving negative
associations with both unselected components Y and Z. Another
example of this harmonic balance among yield components is
furnished by ZA selections at Palmira (Figure 10), where the value
of Y was the lowest one, (with the exception of YB selections),
suggesting strong negative association with ZA; however, the un-
selected X shows much higher value with respect to Y, having a
positive association with ZA. A similar situation prevails for
ZB selections although it is not as striking as in the case of ZA.
These examples and the fact that in most cases the trend lines
connecting values of non-selected characters at the high and low
levels of expression, cross over once or even twice at different

points, tends definitely to support the hypothesis that yield

52

exhibits homeostatic stability, implying that no greater changes
could be obtained either selecting for yield itself or independently
for its cemponents because of compensatory mechanisms existing in
the plant.

The idea of negative associations among components of yield
is supported by the phenotypic correlations presented in Tables
8 and 9. These correlations were expected to be in that direction,
but the point of interest lies in the nature and course of this
association.

Assuming that the correlation coefficients shown in this
study are of genetic origin, and having in mind that X, Y and Z
6Videnced positive relationship with‘w, does it really mean that
yield and its components are controlled by the same genetic system?
This is not necessarily true. Genetic correlations may be origi-
nated between different characteristics due to genetic linkage,
or pleiotropic effects; correlation will also result when
characters share a common pool of metabolic resources for their
development, generated by a given set of genes.

This seems to be the case with respect to yield and its com-
ponents in the present study in beans. For if it were otherwise
then changes of environment, or changes in mean values of com-
ponents due to selection, would not be reflected in the direction
of the association, shifting it from positive to zero or to

negative or vice versa. Opposite findings should demonstrate

53

that more or less independent genetic system condition each of
the components.

The correlation coefficients observed in the first cycle
(Table 8) are different from those of the second cycle (Table 9).
Although the degree of association between.X and Y is not
significantly different than zero in both cycles, is interesting
to note that the correlation coefficients were positve in the
first cycle and became negative after the second cycle of '
selection at all locations. A.similar situation prevails
between.x and Z; whereas in the first cycle the correlations
are‘fl negative at the three locations, being significantly
different from zero at Palmira and.lbdellin, in the second cycle
they became positive at the Colombian locatiom. However, in
East Lansing, the association is still negative and significant.
At Medellin the correlation between I and Z is highly signifi-
cantly different from zero in the first cycle, but becomes zero

after the second cycle of selection. These findings demonstrate

, “...—“m “fits-M

‘0.-
“-....‘h
h‘--

that the effect of selection and/or environment can change the

me‘"“-w*‘¥

degree of associatigngamongmcompgnents.
zrflfifflmwi_iw-s .. ,
The correlations coefficients presented agreed completely with-‘
the results shown in Figures 7 to 12, already discussed. The
compensatory mechanisms among the yield components are able to
change the direction of the association between them when selection
pressure is applied to an individual component, giving rise to

changes in signs of the correlation coefficients.

5h

Not only selection can change the direction and magnitude
of the association between yield components in beans; under
greenhouse conditions Montoya and Adams (8) were able to in-
crease the number of seeds per pod and seed size by removing half
of the pods in navy beans. Archibong (1) showed that in beans
the correlation between components could be strong and negative
when they are planted at high densities but they can become
zero or even positive when the plants are spaced greatly.

Rendel (10) studied the number of scutellar and abdominal
bristles in Drosophilg_melanogaster. He found positive corre-
lations between the two characters in unselected stocks. The
correlation was negative in selected genotypes but it became
positive with further selection. He explains these facts by
showing that total resources for making bristles can be varied,
and the proportion allocated to the two kinds of bristles can
also be varied. The former variation results in positive, the
latter in negative correlations.

Changes in the direction of the correlations similar to
those found by Rendel (22, 233,) occurred in some cases between
unselected and selected families in the present investigation.
As an example from the location at Medellin, a comparison of
correlations between the 768 F3 unselected families and the 36
selected ones in the second cycle of recurrent selection is pre-

sented in Table 10. From this table it may be seen that the

55

degree of association between number of pods per plant (X) and
number of seeds per pod (Y), which exhibits a positive and signi-
ficant correlation coefficient in the unselected stock, became
negative and non-significant in the selected one. The magnitude
of the degree of association also changed; as in the case of Y and
Z, the correlation coefficient is negative and highly significantly
different from zero among the non-selected progenies but is not
significant among the selected families. Also the magnitude of
influence of Z upon W becomes higher after selection, increasing
the correlation coefficient from .36 to .66, although both are
significant at the 1 percent level.

The results of the present investigations, coupled with the
findings of other authors, strongly suggest that the correlations
among yield components are not truly genetic in the sense of linkage“
or pleiotropism inasmuch as they could be changed by selection
pressure and environmental conditions. It also furnishes evidence
indicating that mainly independent genetic systems are controlling
each one of the yield components in beans. The idea of very
close linkage among the genetic systems of the components is also
precluded, because the changes in the direction of the correlation
coefficients are found in much higher proportion than eXpected from

crossing over alone.

56

Table 10. Simple correlation coefficients for yield and its
components, for 768 unselected and 36 selected
families during the second cycle of recurrent
selection, at Medellin.

 

 

unselected Selected

Comparison Families Families
H h e109* - .2166
X2 “ e005.- .lh-O

XV .731fi* .596**

YZ " e 1781“! - 0016 - .
w and?! .250

zw .362”: .662”

 

Calculated ”genetic" correlations could arise in different
ways as was stated before. One way to Obtain them could be when
characters controlled by essentially different genetic systems
share a common pool of metabolic resources for their development,
the genetic regulation of the amount of these resources to be
apportioned to the component characters may itself be the most
acceptable hypothesis to account for the component relationships
under consideration in the case of beans.

In the discussion of this hypothesis to follow, reference
will be made to the folloiing symbols: A, those genes condition.
ing high values of any of the yield components; B, those genes for
low values of yield components; R, genes or sets of genes con-

trolling metabolic resources; and U, the amount of metabolic

57

resources available during the time of yield component deve10p-
ment. It is also implied that the components are sufficiently
flexible in their development to be responsive to the amount of
resources available, except when limited by genotype.

This hypothesis is stated briefly as follows: There is a
common pool of metabolic resources U whose amount is controlled
by genes R; this pool should be shared by X, Y and Z. The dis-
tribution of U among yield components depends on an interaction
between the genotype of each one of the components and one or
more of the R genes. This interaction which takes the form of
an induction or "turning on" process occurs at certain stages
prior to floral development. At that time the genes controlling
X, Y and Z are activated by interaction with R genes; the share
that each component receives depends on this interaction. If
by selection pressure A genes for high level of expression have
been accumulated for a given character, for example, this
character would receive proportionally greater amounts of U than
X and Y. The opposite result with the same mechanism operating
would be true if selection were for B genes conditioning a low
expression of Z, thereby generating negative correlations,
correlations that are at the deve10pmental or morphological level
rather than at the genetic level.

An alternative hypothesis would also postulate a common p001

of metabolic resources, these resources to be shared by X, Y and Z.

58

Yield components follow a sequential pattern of development,

and each one has its own genetic basis. When selection is for

a high level of expression of X, A genes are accumulated and

the character, number of pods, would receive a greater share

from the common pool. However, if a proportionately greater

share of the resources were used in producing high X, a proportion-
ately lesser amount would be available for producing high Y-values,
or possible Z values, which follow X in the developmental sequence.
On this account, negative correlations might be expected

between X and Y, possibly between.X and Z.

If selection is for low values of X, then there are more
resources available for Y and Z, so once again negative relation-
ships might be induced. For this pattern of cauee-effect
relationship to prevail, however, it is necessary to assume a
flexibility of development of Y and Z particularly, such that
they are affected in their development not only by the underlying
genotypes but by the amount of growth resources available.

When selection is for high values of a component such as Z,
which follows X and Y in the sequence, how might it be effective,
under this alternative hypothesis? One explanation could be
that A-genes for Z could only be expressed when resources U are
plentiful, which implies that ZA genes would be selected for most
readily in a background of XB genes and YB genes, backgrounds which
utilized a relatively minor share of resources, ahead of utilization

by Z. This is a case of adaptive compensation, referred to by

59

Stebbins (ll), and which in this instance, results once more
in negative correlations.

Highly significant correlations were observed between each
one of the yield components and the total seed yield per plant
(W), as was expected since seed yield per plant is a product of
the three components, namely: number of pods per plant (X); num-
ber of seeds per pod (Y); and average weight of the seed (Z).

Selection for high levels of any one of the components
should increase yield. From results presented here, even though
selection progress was obtained separately for each one of the
components, the unselected components exhibited almost counter-
balancingilower values, leaving the final product yield.practically
unchanged. This is not to say that yield through the enhancement
of components can not be increased. By artificial means, appli-
cation of fertilizers, proper space-planting, cultural practices,
etc., the pool of metabolic resources could be augmented. By
these means, along with selection of A genes for each one of the
components, the possibility of maximizing yield may be realized.

At the present it seems to be worthwhile to select for two com-
ponents at the same time instead of one. moreover, the selection
pressure ought not to be very strong, in order to avoid within-
plant competition for resources and hence negative associations.
In Palmira and East Lansing, simultaneous selection for X and Y
seems to be valuable. In Medellin, selection for X and Z would be

much better.

Hewever, by increasing two of the components even at the
expense of stronger negative correlations with the third-one,
yield was also increased. .A good example is furnished by the
results at Palmira during the 2 cycles of recurrent selection.
One family of the modal class selection during the first cycle
has the following average values per plant: X equals 13.1, Y
equals 3.0, Z equals 0.33 and W equals 13.0. In the second
cycle one of the families selected for high X shows X equals
38.3, Y equals 3.9, Z equals 0.2h, and U equals 35.9. Yield
was increased almost 3 times by selecting X and involuntarily also
Y. However, the value of Z went down, hence increasing the
magnitude of the negative correlation.

As a practical application of the results obtained in this
thesis it appears that in order to increase yield at Palmira
and East Lansing selections for X and Y should be made at the
same tiie.' In Medellin Joint selections for X and Z would be
advisable. Thisjrecommendation seems to be true at least for
this particular cross. The greater progress in Z at Medellin
‘might be related to the natural superiority of the Algarrobo type,
the same thing being true for the Michelite type at East Lansing.

neither type seems to be preferentially selected at Palmira.

III. Path Coefficients Analyses

Seed yield in beans is a product of number of pods per
plant (X), number of seeds per pod (Y), and average seed
weight (Z); thus the variation in yield depends on the
variation of the components; besides that, the variation of
the components depends on several other factors among which
are number of leaves per plant (N), and size of the leaves
(3).

Correlation coefficients show the degree of association
between two variables but they provide no information concern-
ing the dependence of one upon the other. When the direction
of this dependence is known, as in the case of yield components,
the correlation coefficients can be used in path coefficient
analyses to obtain information on the magnitude of direct and
indirect effects of the components upon more complex traits.

Two path analyses were made in this study. The first one
was to get information of the effects of number of pods per plant,
number of seeds per pod, and seed weight upon yield. The second
one was conducted in order to obtain some knowledge about the
effect of number and size of leaves upon the yield components
and through them to the seed yield.

Figure 13 shows the path diagram for factors influencing yield.

Direct effects are represented by single-arrowed lines and the

61

62

correlation between two variables by double-errowed lines.f
The correlation cOefficients are broken down into direct and
indirect effects and this relationship may be expressed as

follows:

:‘1

i‘ P P
(EXW.+-§XY. YW 4-;XZ ZN

gXW +-PYW +-rYZgZW

PYW+a

rxr

B

P

§

rXZ 2XW‘45rYZ

where r is the correlation coefficient between two variables, P
is the path coefficient or direct effect, and roP is the measure

of the indirect effects.

The path coefficients were obtained by solving the correla-
tion matrix by the use of determinants. To illustrate this
with an example, the path coefficient between number of pods
per plant (X), and seed yield (W), was obtained in the following

"y' W): rxr 1L'xz
. rwr rn rarz
,wa = I'wz rzr 1L'z.z
'rxx "'" Fir rxz "'"""""
”x In 1‘12
I“xz Pzr rzz

 

In a similar manner the path coefficients between Y and W,

PZW are obtained; replacing Y for W in’

PYW, ind between Z and W,

the second column of the numerator of the c-matrix and Z for W in

the third column PYW and PZW respectively are obtained. The

 

rxz

 

.4
.
a“

I

- Total seed yield

= Wunher 0‘ pods Der plant
= ”usher OF seeds per nod
— €eed weight

: Path coefficient

= Porrelation coefFicient

'3 dNe<><
I

Fipure 13. Direct effects and associations 0‘ nownonents
deterwininy yield.

R3

 

LZ*J><><E

-’)

'1 'J

 

Total seed Vield

Number 0‘ node oer olant
Wumher o‘ seeds oer nod

Seeo weirht

Wumber o“ leaflets oer nlant
Rize 0‘ one Jea’let

Dath coef’icinnt

Porrelation coeF‘icient

Fiyure I”. “irect eF‘ectfi and associations 0‘ oovoonents

of vield and 4rectors intlnencinr thD coooonents.

65

denominator was the same in all cases.

The diagram presented in Figure 1% shows the path coeffi-

cients and correlations between yield and its components, X,

Y and Z and also the direct effects of number of leaflets N

and size of the leaflets S upon the yield components.

The relationship between correlations and path coefficients

for N and S upon yield components are expressed in the following

equatibns: .

Table 11.

 

r P P

NX = nx+ rNS sx
rsx = Psx + rNS Pm:
rNY = PNY + I‘Ns PSI
1‘31 s PSI + rNS PNY
rNZ = PNZ + rNS Psz
rsz = 1’82 + 1‘N5 PNZ

Simple correlation coefficients for yield and its
components, in families selected for X, I, and Z
at high (A), intermediate (M) and low (B) level of
expression, at Palmira, Medellin and East Lansing
during the first cycle of recurrent selection.

 

 

 

 

gomparison Selected-X Selected-I Selected-Z
KY '0218 -0168 -0298
X2 .102 .277 -.l3h
YW .888** .852** .793**
YZ -.219 -.h57** -.h20*
xv -.098 A96“ .389*
ZW .h76** .309 .377*
* P< .05

** P<.01

Table 12. Simple correlation coefficients for yield and its
components, in families selected for X, Y, and Z
at high (A), intermediate (u) and low (B) level
of eXpression at Palmira, Medellin and East
Lansing, during the second cycle of selection.

 

 

 

 

 

Comparison, Selected-X Selected-Y Selected:§_
XY " e263 " e322 - 0177
X2 -.1’+2 -0196 -0185
XW ' .925** .898** .863**
YZ -.379* -.h12* -.388*
Yw .h01* .h68** .358*
zw .075 -193 ~355*
* P<<.05

** P < .01

Table l3.- Simple correlation coefficients for N and S,

Cogparison__

yield and its components, in families selected
for N and s at high (A), intermediate (n) and
low (B) level of expression, at Palmira and
Medellin during the first cycle of recurrent
selection.

 

 

 

 

Selected-N Selected-S
NS -.lh8 -.19h
NX .606** .7h3**
NY .123- .100,
NZ --190 -.280
NW ~525** .721**
SX -.23h -.o77
SY .lhh .072
32 -519** .521e*
SW -.030 .108
KY .366 -.010
XZ -~5l7** -.3h2
XV 'o913** .931se
YZ -.hhh* -.297 ,
YW .53h** .136
ZW _#4 -.283 -,099
* P <.05

** P (.01

67

The relationships between correlations and path coefficients
for X, Y, and Z upon W are the same as those described for the
previous case.

Table 11 shows correlation coefficients for yield and its
components in sets of 36 selected families for each one of the
components X, Y, and Z, at the high, intermediate, and low levels
of expression at Palmira, Medellin, and East Lansing for the first
cycle of selection. Similar sets of correlations for the second
cycle are presented in Table 12. The correlations presented
in Tables 11 and 12 show a pattern similar to those in the pre-
ceding sections of this thesis. 0

Estimates of the correlations between number (N) and size of
leaflets (S), and yield and its components are presented in
Table 13. These correlations were calculated from 2h families
selected for N, and 2h for S, at the high, intermediate and low
levels of expression, during the first cycle of selection at
Palmira and Medellin.

Similar patterns of correlation are exhibited by families
selected for N as well as those selected for S. Estimates
involving number of leaflets and size of leaflets are negative
although of low magnitude. This type of association between the
components of total leaf area seems to be at the developmental or
morphological level rather than at the genetic level, as was

clearly demonstrated by Duarte and Adams (3).

68"

The highly significant correlation between number of leaf-
lets (N) and number of pods (X), and between N and seed yield W,
suggests that yield is greatly influenced by number of leaflets
through number of pods which also show a high correlation with
yield. Seed size (Z) seemsrtO'be greatly influenced by size of
the leaflets (S). ‘However, the correlation of the latter with
yield is not significantly different than zero, the same being
true for Z which shows a non-significant negative association
with yield.

Associations of low magnitude are observed between number
of leaflets (N) and number of seeds per pod (I), and N and Z.
The same pattern prevails for correlations between S and.X and

S and Y.

69

Table 1h. Path coefficient analysis of the influence of X, I
and Z upon yield (W), in families selected for X at
all levels, A, M, and B, at Palmira, Medellin and
East Lansing in the first cycle of selection.

 

Type of effect Coefficient
Effect of number of pods per plant (X);

Direct effect (Pm W) P .885
Indirect effect via number of seeds per pod (rXY YW) -.Ohl
Indirect effect via seed weight (rXZ ZW) .Ohh
Total (rxw) .888
Effect of number of seeds per pod (Y)

Direct effect (Pm) P .188
Indirect effect via number of pods pe;Zw plant (fXY’IXW) -.l93

 

Indirect effect via seed weight (rXZ -.093
Total (rYW) -.098
Effect of seed weight (Z)

Direct effect ( Pzw) .1127

Indirect effect via number of seeds per pod (rYZ PYW) -.0hl
Indirect effect via number of pods per plant(rXZ BXW) .090
Total (rzw) .h76

 

70

Table 15. Path coefficient analysis of the influence of X, I
and Z upon yield (W), in families selected for I at
all levels, A, M, and B, at Palmira,.Medellin and
East Lansing infthe first cycle of selection.'

 

$311” 01’ effect Went—

Effect of number of pods per plant (X)

Direct effect (PXW) P .868
Indirect effect via number of seeds r pod (rXY YW) -.1h3
Indirect effect via seed weight (rXZ ZW) .127
Total (rxw) .852

Effect of number of seeds pergpod (I)
_“.

Direct effect (PYW) .851
Indirect effect via number of pods peg plant (rXY EXW) -.1h6
Indirect effect via seed weight (rrz zw) -.209
Total (rYW) .h96

Effect of seed weight (Z)_

Direct effect (PZW) .h57
Indirect effect via number of seeds per pod (rYZ PYW) -.388
Indirect effect via number of pods per plant (rXZ EXW) .2h0
Total (rzw) .309

 

71

Table 16. Path coefficient analysis of the influence of x,
Y and Z upon yield (W) in families selected for
Z at all levels, A, M, and B, at Palmira, Medellin
and East Lansing in the first cycle of selection.

 

Type of effect Coefficient

Effect of number of pods per plant (X);

Direct effect (Pkw) 1.300
Indirect effect via number of seeds per pod (rXY PYW) -.36h
Indirect effect via seed weight (rxz Pzw) -.1h3
Total (rxw) .793

Effect of number of seeds per pod (I)

Direct effect (PYW) 1,221
Indirect effect via number of pods peg plant (rXY PXV) -.388
Indirect effect via seed weight (rYZ zw) ' -.hh7
Total (rfw) .389

Effect of seed weight (Z)

Direct effect (PZW) 1.065
Indirect effect via number of seeds per pod (rYZ P5W) -.Slh
Indirect effect via number of pods per plant (rXZ XW) -.17h
Total (rzw) .377

 

72

Table 17. Path coefficient analysis of the influence of X, Y,
and Z upon yield (W) in families selected for X at
all levels, A, M, and B, at Palmira, Medellin and
East Lansing in the second cycle of selection.

 

Type of effect Coefficient

Effect of number of pods per plant (X)

Direct effect (PXW) P 1,269
Indirect effect via number of seeds per pod (rXY IV) -.256
Indirect effect via seed weight (rxz Pzw) -.088
Total (rXW) .925

Effect of number of seeds per pod (Y)

Direct effect (PYW) .971
Indirect effect via number of pods per plant (PX! BXW) -.33h
Indirect effect via seed weight (rYZ PZW) -.236
Total (rYW) .h01

Effect of seed weight (Z)

Direct effect ( Pzw) 521
Indirect effect via number of seeds per pod (r YZ P¥W) -.368
Indirect effect via number of pods per plant (rXZ -.178
Total (rZW) .075

 

73

Table 18. Path coefficient analysis of the influence of X, Y and
Z upon yield (W) in the families selected for I at all
levels, A, M, and B, at Palmira, Nedellin and East
Lansing in the second cycle of selection.

 

Type of effect Coefficient

Effect of number of pods per plant (X)

 

Direct effect (Pkw) P 1.568
Indirect effect via number of seeds pfir pod (:XY YW) -.LSS
Indirect effect via seed weight (rxz zw) -.21h
Total (rxw) .899
Effect of number of seeds per_pod (I)

Direct effect (PYW) 1,h1h

Indirect effect via number of pods peg plant (rXY 3xw) -.505

 

Indirect effect via seed weight (rIX ZW) -.uh7
Total (rrw) .h62
Effect of seed weight (Z)

Direct effect (PZW) P 1.085
Indirect effect via number of seeds per pod (rYZ YW) -.58h

Indirect effect via number of pods per plant (rXZ P)(W) -.308
Total (rzw) ~193

 

7h

Table 19. Path coefficient analysis of the influence of X, X
and Z upon yield (W) in families selected for Z at
all levels, A, M, and B, at Palmira, Medellin and
East Lansing in the second cycle of selection.

 

Type of effect Coefficient
Effect of number of_pods per plant (X)

Direct effect (Pkw) P 1.203
Indirect effect via number of seeds pfir pod (rXY YW) -.l66
Indirect effect via seed weight (rxz zw) -.l7h
Total (rXW) .863

Effect of number of seeds per pod (I)

Direct effect (PYW) P .936
Indirect effect via number of pods peg plant (tXY XW) -.213
Indirect effect via seed weight (rYZ ZW) -.365
Total (rYW) _ .358

Effect of seed weight (Z)

Direct effect (Pzw) .9hl
Indirect effect via number of seeds per pod (rYZ P¥W) -.363
Indirect effect via number of pods per plant (rXZ XW) -.223
Total (rZW) .355

 

75

Tables 1h, 15 and 16 show the direct and indirect effects of
components upon yield, in families selected for number of pods
per plant, number of seeds per pod and seed weight'respectively
at the three locations under study, during the first cycle of
selection. ‘Results for the second cycle of selection are pre-
sented in Tables 17, 18 and 19.

A general pattern of effects is detected during the two
cycles of selection. The influence of number of pods upon yield
is the“most important among the yield components, followed by
number of seeds per pod and seed weight.

To illustrate this situation,let us take the case of families
selected for number of seeds per pod (I) during the first cycle
of selection presented in Table 15. The correlation between
number of pods and yield is made up mostly of direct effects
indicating, therefore, the importance of this character in deter;
mining seed yield; the first effect of number of seeds per pod
upon yield is also of great magnitude, although some negative
influence was registered indirectly especially via seed weight.
An examination of the correlation of seed weight with yield reveals
that its direct effect has importance in influencing seed yield,
although it is of smaller magnitude than the effect of X or Y
upon W. As was expected, a negative indirect effect through

number of seeds per pod is observed.

76'

It may be seen in Table 18, with respect to families
selected for number of seeds per pod in the second cycle, that
in general a pattern similar to that in the first cycle is
observed, as far as the order of importance of direct influ-
ences upon yield is concerned. The magnitude of the direct
'effect of number of seeds per pod upon yield increased a
great deal as compared with the first cycle, indicating the
influence of selection in raising the magnitude of direct
effects of selected components upon yield.

Negative indirect effects were also greater as might have
been expected; the negative influence via number of pods per
plant was larger than the one via seed weight due to the
negative association between.XY and the great magnitude of
the direct effect of number of pods upon yield.

Although the correlation coefficient between number of
pods per plant and seed yield 1% more or less the same as in
the first cycle in families selected for I, its direct effect
upon yield is of higher magnitude; however, an indirect nega-
tive influence upon yield is detected through number of seeds
per pod, because of the negative correlation between X and I
and the importance in magnitude of the path coefficient between
Y and W.

The low value of the correlation coefficient between Z
and W is made up mostly of negative indirect effects, especially

via seeds per pod although the effect via number of pods also has

77

appreciable value. The direct effect of seed weight upon yield
is nevertheless of great importance in determining yield.

As a general pattern it could be said that the direct effect
of a component upon yield increased in magnitude when selection
pressure was applied for that component.

Table 20 shows a path coefficient analysis of the influence
of components of yield upon yield and the influence of number
of leaflets and size of the leaflets upon yield components at
Palmira and Medellin in the first cycle of selection in families
selected for number of leaflets per plant (N). Similar sets of
path coefficients and indirect effects are presented in Table

21 for families selected for leaflet size (S).

78

Table 20. Path coefficient analysis of the influence of X, Y,
and Z upon yield (W) and the influence of N and S
upon yield components, in families selected for N
at all levels, A, M, and B at Palmira and Medellin
in the first cycle of selection.

 

 

 

 

 

 

 

 

$199 of effect Coefficient
Effect of number of leaflets (n)_upgn x
Direct effect (PNX) P .58h
Indirect effect via leaflet size (rNS sx) .022
Total (rnx) .606
Effect of leaflet size (3) upon x
Direct effect (2X8) P -.1h7
Indirect effect via number of leaflets (rNS RX) -.087
Total (rSX) -.23h
Effect of number of leaflets (N) up22;1_
Direct effect (PNY) P .lh8
Indirect effect via leaflet size (rNS SY) -.025
Total (TM) .123
Effect of leaflet size (5) upon r
Direct effect (PSY) .166
Indirec; effect via number of leaflets (rNS PNY) -.022
Total ( SY) .lhh
Effect of number of leaflets (N) upon Z
Direct effect (PNZ) P -.116
Indirect effect via leaflet size (rNS SZ) -.07h
Total (rNZ) -.190
Effect of leaflet size(S) upon Z

P
Direct effect ( sz). r .502
Indirect effect via leaflet size ( NS PN7.) .017

Total (rsz)

~519

79

Table 20 (Continued)

 

 

 

 

 

Type of effect Coefficient
Effect of number of_pods (X) upon W

Direct effect (PXW) .982
Indirect effect via number of seeds (rXY PYW) .125
Indirect effect via seed weight (rXZ PZW) -.19h
Total (rxw) .913
Effect of number of seeds (Y) upgn W

Direct effect (PYW) P .3hl
Indirect effect via number of pods (rxr xv) .359
Indirect effect via seed weight (rYZ PZW) -.166
Total (rYW) «53%
Effect of seed weight (Z) upon W

Direct effect (Pzw) .376
Indirect effect via number of pods (rxz ka) -.508
Indirect effect via number of seeds (rYZ PYW) -.151
Total (rzw) -.283

 

80

Table 21. Path coefficient analysis of the influence of X, Y,
and Z upon yield (W), and the influence of N and S
upon yield components, in families selected for S
at all levels, A, M, and B at Palmira and Medellin

in the first cycle of selection.

 

Type of effect
Effect of number of leaflets (N) upon X

- P
Direct effect ( NX) P
Indirect effect via leaflet size (rNS sx)
Total (rNX)
Effect of leaflet size (3) upon x

Direct effect (3x3) P
Indirect effect via number of leaflets (rNS NX)
Total (rsx)

Effect of number of leaflets (N) upon Y
Direct effect (PNY)

Indirect effect via leaflet size (rNS Psr)
Total (rNY)

Effect of leaflet size (S) upgn Y

Direct effect (PSY)

Indirect effect via number of leaflets (rNS
Total (ray)

PNY)

Effect of number of leaflets(N) upon Z

Direct effect (PNZ) P
Indirect effect via leaflet size (rNS SZ)
Total (er)

Effect of leaflet size (S) upgn Z
P
Direct effect ( sz)

Indirect effect via leaflet size (INS PNZ)
Total (rsz)

Coefficient

.757
- eOlh

.7h3

.070
-.m
-.077

.119
-.019
.100

.095
- 0023
.072

-0186

"' 009!"
-.280

.uss
.036
.521

81

Table 21 (Continued)

 

Type of effect Coefficient

Effect of number of_pods (X) upon W

Direct effect (EXW) 1.0h7
Indirect effect via number of seeds (EXY PYW) -.002
Indirect effect via seed weight (rxz zw) -.113
Total (1304) .931

Effect of number of seeds (Y)_upon W

Direct effect (PYW) .2hh
Indirect effect via number of pods (r Y BXW) -.011
Indirect effect via seed weight.(rYZ zw) -.098
Total (rYW) .135

Effect of seed weight(Z) upon W

Direct effect (PZW) .331
Indirect effect via number of pods (rxz P’xw) -.358
Indirect effect via number of seeds (rYZ PYW) -.072
Total (rzw) -.099

 

It is interesting to notice the very strong association be-
tween characters specified by numbers, as number of leaflets and
number of pods per plant, and also between characters whose measure
is size, size of the leaflets and seed size.

The high correlation between number of leaflets and number of
pods is made up mostly of direct effects, indicating the importance
of N in determining number of pods, with the latter exerting a
strong direct influence upon number of pods in families selected
for N and positive in families selected for S. However, in both
cases these effects are of small magnitude and may be regarded as

unimportant.

82

The direct and indirect effects of number of leaflets per
plant and size of the leaflets upon number of seeds are quite low.
The low and negative correlation between number of leaflets
and seed weight is made up of small direct and negative effects

that may be considered negligible. On the contrary, the high
correlation between leaflet size and seed size acts almost
completely through direct effects of the former upon the latter.
Even though seed size shows a small negative correlation with
yield, its direct influence upon yield is positive, as it should
be. However, the negative correlation is composed mainly of
negative indirect effects through number of pods, due to the
fact that seed size was negatively correlated with number of
pods which in turn has a strong direct effect upon seed yield.

It is necessary to point out that the negative correlations
‘between number of pods and seed size were of higher magnitude
than the correlations between number of seeds per pod and seed
size when selection pressure was applied to number of leaflets
and size of leaflets. This situation could result from the strong
positive associations between N and X and S and Z. In turn, N
and S exhibit negative relationships, the same being true as far

as the associations between N and Z and S and X are concerned.

DISCUSSION

A path coefficient is a standarized partial regression coefficient,
and in that way measures the direct effect of one variable upon
another and permits the separation of the correlation into direct
and indirect effects. To apply this method the cause and effect
relationship must be known. Yield of beans 18 a product of its
components, therefore, the requirement of cause and effect is ful-
filled.‘

The results of the path.analysis for yield and its components
indicate that number of pods per plant exerts the greatest influp
ence in determining seed yield. This signifies that selecting for
a higher number of pods should increase yield. However, some
negative influence upon yield is registered via number of seeds
per pod which deserves some attention when selection pressure
is exerted upon number of pods.

The direct effect of number of seeds per pod is of appreciable
magnitude especially in families selected for this character,
indicating its strong influence upon yield, when the other two
components are held constant. However, some negative indirect
effects mask the direct effect of seeds per pod upon yield, the
chief ones of which function through seed weight, as was expected.

The correlation coefficient between seed weight and yield is in
general of low magnitude except when,selection was applied to seed
weight, the degree of association being then of much greater

magnitude. However, the path analysis reveals that the direct

83

effect of seed weight is of considerable importance in deter-
mining yield. The low value of the correlation is made up
mainly of indirect effects especially through number of seeds,
although in cases in which selection was made for numbers of
pods the negative influence of the latter is mostly of negligible
magnitude. This means that selection for seed size alone does
not have a very strong influence upon yield; selection should be
conducted either for seed weight and number of pods or seed
weight and number of seeds per pod depending on the environment
in which the selections are going to be made.

The correlation between number of leaflets and number of
pods shows that it is made up mainly of direct effects, indi-
cating that the number of leaflets has great importance in deter-
mining number of pods which in turn has primary importance in
determining seed yield.

Leaflet size has strong influence in determining seed size as
shown by a path coefficient of high magnitude. The indirect
effect are small and non-important.

The influence of number of leaflets and leaflet size in
determining number of seeds per pod is of low magnitude at least
in the present study. This may be due to the fact that the path
analyses were made with data coming from families selected for
Inumber and size of leaflets; these two characters influence, as

teas said before, number of pods and seed size respectively, the

85

seed number thus being dependent on the magnitude of the other
two yield components.

The findings of the direct and indirect effects of the yield
components upon yield and in turn the effect of number of
leaflets and size of leaflets upon yield components agreed with
those discussed in the second part of this thesis about compen-
sation among yield components. It was said that the magnitude
of each component depends on the total amount of resources.
available in a common pool and its distribution among the comp
ponents, this distribution depending on the genetic make-up of
each one of the components and on their developmental sequence.

It was also proposed that the distribution of resources could

be determined even before the floral stage of development starts,
the greater share being appropriated by the component with more
genes for high expression, the remaining resources being distri-
buted between the other two components according to their genetic
constitution.

The fact that number of leaflets determines to a large extent
the number of pods suggests that the share in the distribution among
yield components was already fixed at the late vegetative stage
prior to floral initiation. The same pattern is apparent in the
case of seed size; size of the leaflets has a strong direct influ-
ence upon seed size suggesting that according to the genetic make
up of Z, the genes that condition the expression of this character

are "turned on" at an earlier stage of growth of the plant.

86

Number of seeds per pod may be influenced through the relaion-
ship between number of leaflets and size of the leaflets, which

in turn is reflected in number of pods and size of the seed.

SUMMARY AND CONCLUSIONS

The results of two cycles of recurrent selection in a bean
hybrid population are described. This population originated
from intra-specific crosses of Phaseolus vulgaris variety Algarrobo
by variety Michelite; Algarrobo is from Colombia, South America,
and Michelite from Michigan, U.S.A. These two varieties are
contrasting in several vegetative and reproductive characteris-
tics.

The aim of this investigation was to obtain fuller knowledge
of the response to selection components of complex traits, and
also to evaluate the relationships among selected and non-selected
components, these relationships being of definite importance in
the phenotypic expression of the complex trait.

This study was carried out at three different locations; two
of them in Colombia, S.A. and the third in.East Lansing, Michigan.
These locations differ in climatic conditions, such as temper-
ature, rainfall, day-length, and length of growing season.

Selection in Colombia was practiced independently for leaf
area components, namely number of leaflets per plant (N), and
leaflet size (S), and for yield (W) components namely number of
pods per plant (X), number of seeds per pod (Y), and seed weight
(Z). In East Lansing selections were made for yield components

and also for yield itself. Selections were made at three levels

87

88

of expression for all locations, high (A), intermediate (N),

and low (B).

The results obtained in this study can be summarized as

follows:

1.

Progress was made from one cycle to another for each one

of the components of the complex traits, both toward high
and low levels of expression.

The rate of progress for each particular component at

each level of expression was not the same at all locations.
The involvement of genes that are expressed differently at
different locations is inferred; also the better adaptedness
of the parental types at certain locations seems to have
played a role in character-location association.

Progress for yield itself was not really made. Progress

in the values of individual components was obtained,

but the gain in one component was at the expense of another
or other components, giving through their multiplicative
interaction quite similar results in seed yield.

The unselected components showed negative relationships with
the selected ones, the magnitude of the association depending
upon the response to selection; however, if one of the un-
selected components responded too far in the direction
opposite to the selected one, the third component reverted
and varied in the same direction as the selected one, can.
ferring in this way a moderate level of buffering upon yield

itself.

89

The correlation coefficients obtained supported the find-
ings Just described. Assuming that the correlations were
genetic they could be originated by several factors such

as, linkage, or pleiotropic effects; but negative correlations
can also result when characteristics share a common pool of
metabolic resources for their development, generated

by a given set of genes.

The results showed that correlation coefficients among the
yield components changed in sign from one cycle to another

in several instances. Also the correlations in the total
number of families present differences in sign as compared
with the selected ones. These findings are in good agreement
with results obtained by other authors, and strongly suggest
that the correlations among yield components are not truly
genetic in the sense of linkage or pleiotrOpism inasmuch as
they could be changed by selection pressure and/or environ-
mental conditions. The data also furnish evidence indicating
that mainly independent genetic systemsare controlling each
one of the yield components in beans.

Two hypothesis are presented to account for the negative
correlations. The first one states that the different
genetic systems of X, Y and Z share a common pool of metabolic
resources, the amount of these resources being controlled by

genes, and their distribution depending on the interaction

90

between the genotype of each component and the genes that control
the resources. This interaction, which takes the form of a "turning
on" process, occurs prior to floral development and the share that
each component receives is fixed at that time. The second
hypothesis would also postudate a common pool of developmental
resources to be shared by X, Y and Z. The relationships among
yield components depend on the views that (1) components follow

a sequential pattern of development, (2) each one has its own
genetic system and (3) they are sufficiently flexible in develop-
ment to be responsive to the amounts of resources available for
their growth. If a proportionately greater share of the resources
were used in producing high.X, a pr0portionately lesser amount
would be available for producing high I values, or possibly Z
values.. In selecting for a component such as Z, its high ex-
pression would depend on plentiful resources, which in turn implies
genotypes of low level of expression for Y and X.

Neither one of the hypotheses presented precludes the possibility'
that by artificial means the pool of resources can be increased
and that by selecting for genes that give high level of expression
to each one of the components when resources are unltmited, the
possibility of maximizing yield could be realized.

Direct and indirect effects of the components upon the complex

traits were analyzed by means of path coefficients. The results

.show that N has a direct positive effect upon X, and the main

effect of S is upon Z. In turn, X exerts the greatest influence

upon seed yield, followed by Y, then by Z. Indirect negative

91

effects were detected and discussed.
10. Selection for two components at the same time are suggested for

each location.

10.

ll.

LITERATURE C ITED

Archibong, D. On the correlation among yield components in
the naVy bean, as influenced by spacing and interstrain
competition. M.S. Thesis, Michigan State University
(Library). 1963.

Camacho, L. H., Cardona C. and Orozco, S. H. Genotypic
and phenotypic correlation of components of yield
in kidney beans. Bean Improvement Cooperative
Annual Report. 196%.

Duarte, R. A. and Adams, M. W. Component interaction in
relation to expression of a complex trait in a
field bean cross. Crop Sci. 3:185-186. 1963.

Grafius, J. E. Components of yield in oats: A geometrical
interpretation. Agron. Jour. h8:hl9-h23. 1956.

Hoen, K. and Andrew, R. H. Performance of corn hybrids
with various ratios of flint-dent germ plasm.
Agron. Jouro SlflJ-Sl-hSh. 19590

Hutchinson, J. B. The application of genetics to plant
breeding. I. The genetic interpretation of plant
breeding problems. Jour. of Genetics. h0:27l-282. l9h0.

Manning, H. L. Response to selection for yield in cotton.
Cold Spring Harbor Symposia on Quantitative Biology.

Montoya, J. L. and Adams, M. W. Personal communication.

1965.

Olsson, G. Some relations between number of seeds per pod,
seed size and oil content and effect of selection of
these characters in Brassica and Sinapis.

Hereditas h6:29-70. 1955.

Rendel, J. M. Correlation between the number of scutellar
and abdominal bristles in Drosophila'melanogaster.

 

Stebbins, G. L. variation and Evolution in Plants.
Columbia University Press. New York 6&3 pp. 1957.

92

93

12. Whitehouse, R. N. B., Thompson, J. B., and Dovalle
Ribeiro, M. A. M. Studies on the breeding of
self-pollinating cereals. 2. The use of a
diallel cross analysis in yield prediction.
Euphytica 7:1h7-l69. 1958.