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GROWTH CORRELATIONS AND COMPETITIVE
RELATIONSHIPS BETWEEN YIELD COMPONENTS
OF SELECTED VARIETIES OF THE DRY BEAN

Dissertation for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
HASSAN HOJATI
1977

  
  

LIBRARY

Michigan Stan
Univer‘ity

This is to certify that the

thesis entitled

GROWTH CORRELATIONS AND COMPETITIVE
RELATIONSHIPS BETWEEN YIELD COMPONENTS
OF SELECTED VARIETIES OF THE DRY BEAN

presented by

Hassan Hojat

has been accepted towards fulfillment
of the requirements for

Ph.D. Crop Science

degree in

 

 

Major professor

 

Date [éZ/KW/MZ 9: /9”/7

0-7639

ABSTRACT
GROWTH CORRELATIONS AND COMPETITIVE RELATIONSHIPS

BETWEEN YIELD COMPONENTS OF SELECTED VARIETIES
OF THE DRY BEAN

By

Hassan Hojat

Growth processes of plants and their specialized organs
have been under study for a long time, each researcher
approaching the subject with the prevalent methodology in his
area of specialization at the time of investigation. The
approach taken up in the present study is by means of fitting
the incremental data of leaflet and pod growth in two groups
of field bean varieties,differing in leaf sizes,to the
Gompertz growth equation. No attempt has been made to attri-
bute a specific physiological function to any of the three
parameters of the asymptotic curve. However, it has been
assumed that the metric values of 2 parameters of leaflet
and pod growth curves of varieties grown under constant envi-
ronmental conditions belong to normally distributed popula-
tions. Parameter b is a measure of scale or spread of the
curve along the time axis and denotes the rate of change in
relative growth rate or the rate of approach to asymptotic
value. Treating the b parameters of leaflet and pod growth
curves as metric traits with normal distribution lends them
to statistical analysis. Significant differences were found
between 2 parameters of leaflet and pod growth curves of the

eight varieties. This parameter could be used not only to

Hassan Hojat

differentiate the growth patterns of the organs of distinct
groups of varieties but it could also distinguish any of the
varieties demonstrating a distinct growth pattern of its
organs. Generally the small leaf varieties showed a remark-
able similarity in the form of growth and rate curves of
their leaflets and pods and proximity of the average maximum
growth rates of these organs while the large leaf varieties
were more divergent with different forms of rate curves for
leaflets and pods and a higher maximum growth rate for leaf-I
lets as compared to pods. Highly negative correlation between
the 2 parameters of leaflets and pods in the large leaf group
signified different orders of priority for utilization of
growth resources in leaflet and pod growth of the constituent
varieties of this group.

The assumption of organ homology between leaflets, pods,
and seeds is based on the premise that all these organs,
regardless of their particular functions as photosynthetic,
reproductive, and storage entities, are essentially similar
in structure. Pods and seeds are modified leaves in the sense
that the elongated ovary is anatomically similar to a leaf
and contains the seeds which are in turn mainly composed of
cotyledons. These are storage organs functionally and modi-
fied leaves structurally. So, in addition to being regulated
by organ-specific genes, they are influenced by a common gene
set. Positive and reasonably high correlations between average
maximum growth rate of leaflets and pods on one hand and seed

size on the other hand substantiate this hypothesis.

Hassan Hojat

Furthermore, highly significant positive correlations between
leaflet growth rate and leaflet sizes provide additional
evidence, though a highly positive correlation between pod
growth rate and pod length is only present in the large leaf
group.

The correlations between mature leaflet, pod, and seed
sizes in the small, medium, and large leaf groups were pre-
dominantly positive, reasonably substantial and occasionally
significant regardless of location or the level of competition
between plants. In other words, the influence of the common
set of genes regulating the size of these homologous organs
did not have a decisive role as compared to the organ-specific
genes and non-genetic factors.

The correlations between the three components of yield
in field beans in the three groups of varieties generally
follow the pattern described by Adams (1967) though no clear
trend was visible as to the influence of location or inter-
plant competition levels on these correlations for any of the

three groups of varieties.

GROWTH CORRELATIONS AND COMPETITIVE
RELATIONSHIPS BETWEEN YIELD COMPONENTS
OF SELECTED VARIETIES OF THE DRY BEAN

BY

Hassan Hojat

A DISSERTATION

Submitted to

Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of CrOp and Soil Sciences

1977

To the memory of

my father

ii

ACKNOWLEDGEMENTS

I am greatly indebted to my major professor,

Dr. M. W. Adams for his support, advice, and guidance.

I am especially indebted to Dr. C. M. Harrison for
his genuine interest and concern during the course of my
studies.

I wish to express my thanks to the other members of
my guidance committee, Drs. N. R. Thompson and A. W.
Saettler for their encouragement and constructive criticism
of this manuscript during its preparation.

I am grateful to Professor R. J. Kleis for his sincere
concern about my well-being in the final stage of the
preparation of this thesis.

I am greatly indebted to my friends, Ardeshir Ghaderi,
Mehdi Ghods, and Gholamhossein G. Hamedani for their self-
less moral support and encouragement in a critical stage of
my studies.

I wish to thank Ms. Lieselotte Heil for her assistance

in the preparation of this manuscript.

iii

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . v
LIST OF FIGURES . . . . . . . . . . . . . . . . . . vii
INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1
REVIEW OF LITERATURE . . . . . . . . . . . . . . . . 4
MATERIALS AND METHODS . . . . . . . . . . . . . . . 12
RESULTS AND DISCUSSION . . . . . . . . . . . . . . . 15

The growth rates . . . . . . . . . . . . . . . 42

Correlations between yield, its components,
and final leaflet and pod sizes . . . . . . . . 51

SUMMARY AND CONCLUSIONS . . . . . . . . . . . . ,’. 62
LITERATURE CITED . . . . . . . . . . . . . . . . . . 69
APPENDIX A . . . . . . . . . . . . . . . . . . . . . 72
APPENDIX B . . . . . . . . . . . . . . . , . . . . . 85

LIST OF TABLES

Table Page

1. Estimated parameters of the Gompertz curve
fitted to the data for leaflet growth . . . . . 16

2. Estimated parameters of the Gompertz curve
fitted to the data for pod growth . . . . . . . l8

3. Analysis of variance for b_parameters of
leaflet growth curves . . . . . . . . . . . . . 35

4. Analysis of variance for 2 parameters of
pod growth curves . . . . . . . . . . . . . . . 35

5. Differences between the means of 2 parameters
for leaflet growth . . . . . . . . . . . . . . 37

6. Differences between the means of b parameters
for pod growth . . . . . . . . . . . . . . . . 38

7. Average maximum growth rates of leaflets
(cm./day) . . . . . . . . . . . . . . . . . . . 43

8. Average maximum growth rates of pods
(cm./day) . . . . . . . . . . . . . . . . . . . 43

9. Correlation between average maximum leaflet
and pod growth rates and yield, its components,
leaflet size and pod size . . . . . . . . . . . 44

10. Correlations involving leaflet size, pod size,
seed size, and seeds per pod compared for the
effect of environmental change . . . . . . . . 52

ll. Correlations involving leaflet size, pod size,
seed size, and seeds per pod compared for the
effect of different competition regimes . . . . S3

12. -Correlations between yield and its components
compared for the effect of environmental
change . . . . . . . . . . . . . . . . . . . . S4

13. Correlation between yield and its components
compared for the effect of different
competition regimes . . . . . . . . . . . . . . SS

A-Z.
A-3.
A-4.
A-S.
A-6.
A-7.
A-8.
A-9.
A-10.-
A-ll.
A-lZ.
B-l.
B-Z.
B-3.
B-4.

Appendix Tables

Charlevoix leaflets

Manitou leaflets

Cranberry 8247 leaflets
Swedish Brown leaflets
Navy-01 leaflets

Navy-02 leaflets

Navy-03 leaflets

Navy-O4 leaflets

Charlevoix and Manitou pods
Cranberry 8247 and Swedish Brown pods
Navy-01 and Navy-02 pods
Navy-03 and Navy-04 pods
Test 23, East Lansing

Test 24, Gratiot County
Test 25A, Gratiot County .

Test 25B, Gratiot County

vi

Page

73
74
75
76
77
78
79
80
81
82
83
84
86
88
91
94

LIST OF FIGURES

Figure Page

1. Observed and estimated growth curves (A)
and observed rate curve (B) of a Charlevoix
leaf . . . . . . . . . . . . . . . . . . . . . 22

2. Observed and estimated growth curves (A)
and observed rate curve (B) of a Charlevoix
pod . . . . . . . . . . . . . . . . . . . . . . 23

3. Observed and estimated growth curves (A)
and observed rate curve (B) of a Cranberry
8247 leaf . . . . . . . . . . . . . . . .'. . 24

4. Observed and estimated growth curves (A)
and observed rate curve (B) of a Cranberry
8247 pod . . . . . . . . . . . . . . . . . . . 25

5. Observed and estimated growth curves (A)
and observed rate curve (B) of a Swedish
Brown leaf . . . . . . . . . . . . .'. . . . . 26

6. Observed and estimated growth curves (A)
and observed rate curve (B) of a Swedish
Brown pod . . . . . . . . . . . . . . . . . . . 27

7. Observed and estimated growth curves (A)
and observed rate curve (B) of a Navy-04
leaf . . . . . . . . . . . . . . . . . . . . . 28

8. Observed and estimated growth curves (A)
and observed rate curve (B) of a Navy-04
pod . . . . . . . . . . . . . . . . . . . . . . 29

9. Observed growth (A) and rate (B) curves of
Charlevoix leaf and pod . . . . . . . . . . . . 3O

10. Observed growth (A) and rate (B) curves of
Cranberry 8247 leaf and pod . . . . . . . . . . 31

11. Observed growth (A) and rate (B) curves of
Swedish Brown leaf and pod . . .7. . . . . . . 32

12. Observed growth (A) and rate (B) curves of
Navy- 04 leaf and pod . . . . . . . . . . 33

vii

INTRODUCTION

The analysis of growth in higher plants is a complex
subject. It deals with a constellation of characters and
their interrelationships, making the analysis more problematic
since any particular approach deals with one or a few facets
of a subject eventually related to the whole developmental
history of the plant. From the earliest periods when Sachs
described the ”Grand Period of Growth” to the present,
different disciplines of biology have used the techniques and
methods available to them in order to shed some light on
different aspects of a complex problem. The study of plant
growth processes has been taken up by plant morphologists,
plant anatomists, plant physiologists, plant geneticists, and
plant breeders in different times with certains theories and
concepts having gained currency and predominance in each
period.

From the first decades of the 20th century different
growth equations have been developed, and relevant metrical
data dealing with the increase in height, weight, length,
volume, and surface of a plant or its organs in time have
been fitted to them in order to gain, hopefully, a better
understanding of the processes which giVe rise to the parti-
cular shape of growth curves. These quantitative methods

deal with the parameters Of growth curves and their ability

to distinguish between different patterns of growth and by
this to distinguish different genetic constitutions, even
though environmental influences in the broad sense make the
detection of genetic differences very difficult. The most
commonly used growth curves in the case of higher plants are
different forms of autocatalytic (logistic) expressions and
the Gompertz Growth Equation. In the present study, the
Gompertz curve with three parameters was fitted to the leaf-
let and pod growth data taken from two sets of varieties
grouped according to the size of their leaves. The parameter
b, which denotes the rate of change in the relative growth
rate or the rate of approach to the asymptotic value, was
treated as a metric value and the mean values of this parameter
for different varieties were compared. Since the absolute
rate of growth during the growth period first rises, reaches
a maximum and then declines until it approaches zero, it was
considered important to calculate correlations between the
rates of leaflet and pod growth on one hand, and yield, its
components, and mature leaflet and pod sizes on the other hand.
This was done on the assumption that the time period in which
the rate was at or near its maximum represents the maximum
utilization of resources (metabolites) either in increasing
the size of the principal organ of photosynthesis and conse-
quently increasing the source capacity or extending the sink
capacity in order to utilize the resources directed from
source to sink. The general intent has been the analysis of

possible interactions between pod and leaf growth rates and

pursuit of relevant explanations for this relationship, and
the impact it has on yield and its components under different

environmental conditions.

REVIEW OF LITERATURE

Growth has been defined as a process of increasing size,
complexity and substance in an organism or any of its organs
through time (28, 30). Change in size is the most conspicuous
characteristic which occurs in terms of length, area or volume
(6). Changes in dry weight and leaf area have been widely
used in studies of plant growth, although change in length is
also taken as an index of growth of plant parts and organs
such as internodes, roots and fruits.

Growth of an organ or organism in time often follows the
form of an s-shaped or Sigmoid curve. The initially slow
increase in size at the beginning of the elongation or expan-
sion process enters the phase of exponential growth, with a
constant relative rate which follows the "compound interest
law" of Blackman (7). The next phase consists of linear growth
with a constant absolute rate. Eventually, in the third phase,
the growth rate declines gradually until growth ceases.
Sigmoid curves have a point of inflection which varies in
position depending on the specific equation used. This is the
point of maximum growth rate at which the increase in growth
rate ceases and the decrease begins. Weight or height of
plants, leaf area, and length of root and shoot follow this
pattern of growth (7, 28, 36).

Internal and external factors determine the longitudinal

5

growth rate of a plant or any of its parts, although there
is a genetically determined limit for growth rate regardless
of how favorable environmental conditions become (33).

The growth of leaves commences with a phase in which
cell division in leaf primordia has precedence over cell
elongation. Cell division under constant Conditions continues
at an approximately constant relative rate until the leaf
emerges from the bud. The average rate of cell division con-
tinues to decline after unfolding until the leaf reaches .25
to .75 its final size. After unfolding, the rate of cell
expansion increases and this, combined with cell division,
rapidly increases the leaf size until the final size is
attained. Both Monocotyledonous and Dicotyledonous leaves
demonstrate this pattern of growth with reasonable consistency
in constant environments (21).

The processes of cell division and cell expansion cannot
be clearly separated in time. They occur simultaneously for
a considerable portion of the leaf expansion period. Dale
and Sunderland (9, 32) investigated the growth of leaves of

lupin (Lupinus albus), sunflower (Heliantus annus) and the

 

 

dry bean (Phaseolus vulgaris). Their observations confirmed

 

this point although the latter part of leaf development in
beans appeared to be dominated by cell expansion.

Watada and Morris (35) studied the growth pattern of
snap bean fruits and found it to be sigmoid. Four days
following anthesis the pod weight and length started to

increase until the maximum length was reached about the

thirteenth day. This growth occurred mainly due to the
enlargement of fleshy endocarp.

There have been many growth equations developed over
the past 50 years. Those used widely at the present time are
the Von Bertalanffy equation, the logistic equation, and
different forms of the Gompertz equation (10).

All these curves are asymptotic at their two ends to the
base lines W = O and W = K, respectively.

The Von Bertalanffy equation was developed upon the
physiological premise that growth rate is the end result of
a balance between the rates of catabolism and anabolism (12).
This curve was generally used in animal growth studies in
which catabolism and anabolism could be more accurately
defined. Richards developed a more generalized form of the
equation in which by changing the value of a constant, both
logistic and Gompertz equations could be arrived at (27, 34).
The autocatalytic or logistic function is a 3-parameter sym-
metrical sigmoid curve with the inflection point located
midway between the upper and lower asymptotes. Pearl and
Reed (23) arrived independently at this function for explain-
ing human population increases. It has been widely used in
both studies of human population growth and growth studies in
higher plants and their parts and organs.

The Gompertz function, which was used by actuaries for
a long time in order to describe population increases, is a
3-parameter asymmetrical sigmoid curve with a point of inflec-

tion before the midpoint at K/e or 0.3679 the upper asymptote.

Wright (38) revived this equation and suggested its use in
the study of biological growth. Weymouth, McMillin and Rich
(36) used this curve in the study of shell growth of razor
clam and obtained an excellent fit to experimental data.
They attached no biological meaning to the inflection point
of the curve. Winsor (37) discussed the possibilities and
limitations of this curve for the purpose of growth studies.

The Gompertz function, though commonly used in animal
growth and population studies, has not been widely applied
to the growth of higher plants.

Laird, Taylor and Barton (19) derived a form of the
Gompertz equation based on previous experimental observations
made on animals, indicating an almost exponential decay of
the specific growth rate over time. They advanced the follow-

ing hypothesis:

"the major part of the growth of the normal organism
from conception to early maturity is the resultant
of two genetically determined processes whose magni-
tudes are defined by exponential coefficients;

these processes operate on an initial mass to
determine 1) the magnitude of the initial exponen-
tial proliferation of the system and 2) the magni-
tude of the exponential decay of this primary
exponential growth rate."

Laird and Howard (20) demonstrated that the Gompertz equation
was proper and suitable to fit the weight growth data of an
average mouse from two to ten weeks of age. They further
demonstrated that the differences between growth curve para-

meters in mice were related to sex, level of heterozygosity,

and maternal influence. They stated that a sigmoid curve is

indispensible for description of the growth of animals and
their parts and organs. Furthermore, they argued that the
growth curves of distantly related animals such as cows, mice,
and chickens are different only in scale and can be super-
.imposed due to the similarity in pattern. Therefore the
growth parameters responsible for the differences of scale
must be acted upon by genetic factors.

They suggested that three growth parameters may be geneti-
cally determined and species-specific. These are the initial
specific growth rate, its rate of exponential decay, and the
initial weight.

In a later study, Kidwell, Howard and Laird (18) suggested
the possibility of treating "the estimated parameters of a
mathematical expression of the weight-time relation, i.e. a
'growth model', as metric traits, amenable to the usual ana-
lytic methods of quantitative genetics." They recognized
that the model would not be of any value in genetic studies
if only an insignificant portion of the variance of the growth
parameters were found to have a genetic origin. The results
of a diallel analysis of all posSible crosses between four
inbred lines of mice, in which weight data from two to ten
weeks of age were fitted to the Gompertz equation and the
growth parameters were treated as metric traits, proved to
be ambiguous and failed to provide clear—cut proof for the
hypothesis put forward.

Amer and Williams (3) used a Gompertz equation for the

study of growth in area of Pelargonium leaves. These leaves

 

reached the maximum growth rate in one week but continued to
grow for eight weeks. The asymmetry of the curve, thus, was
pronounced and a logistic equation seemed to be inappropriate.
Although the Gompertz equation, permitting only a slight
asymmetry, did not seem to match the strong asymmetry of the
data, Amer and Williams used the equation (Y = Kab ) quite
satisfactorily. There were three different watering regimes

for plants of Pelargonium zonale in this experiment. These

 

regimes had a pronounced effect on parameter E and to a

lesser degree on parameter 3) but parameter b remained reason-
ably constant under widely divergent watering regimes and

this led them to conclude that parameter b might be species-

specific for Pelargonium zonale.

 

Plant breeders are turning increasingly away from single-
objective selection, and more toward selecting for multiple
goals. This is particularly the case where the breeder has
adopted the plant design approach to achieve optimum perfor-
mance, the most widely known of such approaches being that
described by Donald (10). Plant designs, or ideotypes,
largely involve selecting for a combination or package of
both morphological and physiological traits that, in the
judgement of the breeder, will lead under specified environ—
mental-management conditions to superior performance. But
herein lies a problem -- that of association between favorable
and unfavorable characteristics. With several objectives in
mind, each influenced by at least one to possibly several

genes, some association is expected. Johnson, Robinson, and

10

Comstock (l6) pointed out the importance of correlations,
favorable and unfavorable, in soybean improvement. Yap and
Harvey (39) discussed a similar situation in barley. Recently,
Peet, Bravo, Wallace and Ozbun (24) noted the association in
dry beans involving several morpho-physiological characteris-
tics. Stebbins (29) based his fundamental cause of "develop-
mental correlations" among traits in plants upon pleiotropy --
a gene or a set of genes regulating certain basic metabolic
and/or developmental process(es) that lead to several traits
being affected. It is expected that traits associated due to
pleiotropy would be developmentally related. A simple example
is the length and width of a leaf. Adams (1) postulated
developmental associations between components of the yield
system. The basis of this ”component compensation" was the
sequential demand for metabolites needed for growth and
development by successive components of the yield system,
where the demand was directed at common metabolites of a
limited source. Component compensation was shown (4, S, 8,
14, 15, 17, 25) to be widespread among grain crops.

Duarte and Adams (11) pointed out a common kind of
developmental association in grain legumes, namely, the
correlation between number of pods per plant and number of
leaves. Since both these metrical characters are functions
of number of nodes, or axillary positions, this correlation
is explicable. Stebbins (29) and Grant (13) might see this
as a case of pleiotropy -- the genes affecting node number

thus being also responsible for leaf number and pod number

potential.

In beans, Duarte and Adams (11) also observed a signifi-
cant positive relationship between leaflet size and seed size.
They could not postulate a direct morphological-developmental
basis for this relationship, but did suggest the possibility
that the relationship depended upon homology of organ systems.
It is possible that leaves and seeds are, therefore, depen-
dent upon a common gene system regulating the size of homo-
logous organs. It was stated that the amount of photosyn-
thate produced by a leaf, the amount per unit of time being
proportional to its size, could be a regulating factor on the
size of seed produced in the raceme borne in the axil of that
leaf. Grant (13) postulated the concept of multifactorial
linkage where with numerous genes involved in the expression
of each of several traits, and a limited number of chromosomes
or linkage groups, there will be a strong tendency for some of
the traits to associate in inheritance -- to vary together
from one generation to the next. With time and opportunity
for breaking up of linkage groups new associations will form,
but the multifactorial nature of the genetic base of each
trait will tend to resist abrupt and drastic change in the
association. This system provides a kind of cohesiveness to
certain character associations that may be of positive fitness

value to some wild populations.

Materials and Methods

Fourteen varieties of the field bean, divided into three
groups on the basis of leaf size (five with large leaves,
four with medium leaves, and five with small leaves), were
planted in two replications in East Lansing during the summer
of 1970. Plant spacing within rows was 10 centimeters and
rows were 70 centimeters apart. Measurements of leaflet and
pod growth were made on randomly selected plants of 4 varie-
ties with large and 4 varieties with small leaves in order to
study the comparative rates of continuous growth. This non-
destructive method, in spite of the apparent difficulties
and the care which should be taken to avoid damaging young
growing plant parts, is preferable to the destructive sampling
method which involves selection and tagging of very young
leaves and pods, taking into consideration the approximate
equivalence of length, and harvesting them in different time
intervals for measurements, and averaging of the samples.

The length of the middle leaflet of the first and second
leaves appearing on the main axis of each of five plants and
also the length of three to five normally developing pods
(with more than two seeds) per each selected plant were
measured, beginning at the time of appearance and continuing
in two-day intervals until growth had ceased. The precision

was to the nearest millimeter. Final yield (W) and its three

13

components, namely, average number of pods per plant (X),
average number of seeds per pod (Y), and average seed weight
(2) were also measured on one meter harvested sections of
each plot. The same varieties were planted in Gratiot County,
Michigan, under three levels of competition. Four replica-
tions of closely spaced plants in the row (10 centimeters)
and four replications of wide spacing (30 centimeters) were
grown. In two of the replications of closely-spaced plants
half of the length of plots was shaded with semi-translucent
plastic screens to reduce the light intensity. Size of five
fully eXpanded leaves and ten mature pods per plot was
measured. Yield and its components were also measured.

Leaf and pod growth data were fitted to a Gompertz growth
curve which is generally given as

Y = fight
and is fitted in its logarithmic form

Log Y = Log 5 + Log 3.21:,
where Y is the measured length at time t, E is the upper
asymptote or the value of Y at t = tw, a_is the difference
between the Y value and the upper asymptote when t = 0, and
b‘is a measure of change or the rate constant which represents
the ratio between successive increments of growth and is a
declining ratio of increase.

Parameter'b_is the most important of the three parameters
and signifies that each difference between successive loga—
rithmic values of the dependent variable is a constant per-

centage of the preceding difference.

14

For calculation of the three parameters the data were
divided into three groups each consisting of n observations.
Then the Log E, Log 3, and p values were calculated from the

following expressions:

1 (éilggY)(Xalong-(leongz

 

Log K = n (leogY + 23logY - ZzzlogY)
b-l
Log 3 - (leosY ' illogY) (Eh-152

1

Z3logY - illogY n
ZzlogY_- leogY

 

For all experiments, the correlations r r

ZL’ rLP’ rPZ’ PY’ rXY’
rXZ’ rYZ’ rXW’ rYW’ and rZW were calculated where X, Y, and Z
are components of yield, W; L is the length of a fully
expanded leaflet and P is the length of a mature pod.

The correlations between average maximum leaflet and
pod growth rates and yield, its components, and mature leaf-

let and pod lengths for both variety groups were also calcu-

lated.

RESULTS AND DISCUSSION

A summary of leaflet and pod growth data of the eight
varieties and the data related to yield, its components, and
mature leaflet and pod measurements is given in the appendices.

The estimated values of the three parameters of the
Gompertz curve are summarized in Table l for leaves and in
Table 2 for pods. Although at first a method Of averaging
the growth curves was tried for both leaflet and pod growth,
the following disadvantages were inherent in the application
of this method.

The average of several Gompertz curves only approximates
a Gompertz curve and does not precisely represent a real
curve. By averaging several curves the existing variation in
the experimental material would be reduced drastically and
consequently the decrease in the available degrees of freedom
makes significance tests very insensitive to small differ-
ences. The measurements on leaflets and pods of different
plants could not begin at exactly the same stage of growth
due to time limitations. Because of this displacement in
time, the average curve (averaged over several leaflets or
several pods) would not represent the actual process of
growth in length because each data point on the curve repre-
sents the mean of several measurements whose magnitudes differ

by as much as three centimeters.

*4
U1

l6

aaoa. m¢am.oa omoo. maaa. mmmo.¢a oqmm.

 

 

coco. manm.na nnmo. mama. ounm.ma mnam.
mmma. nnoo.m mmmn. moma. ommm.oa «nae.
aano. ammo.ma swam. . waoo. mmom.ua name.
mama. comm.ua omen. aa «cea. mmwm.oa once. aa
nnno. ommn.oa cone. oaaa. amqm.~a Noam.
oqmo. mono.ma omwe. moea. ouqo.ma mamm.
n~oo. oeaq.0a. «mac. . nqaa. aaoc.aa waaq.
ommo. ommu.oa sham. :3oum anaa. ammm.aa eewe.
ammo. «amm.~a mace. a smavoam . amoa. ammm.aa «ace. a souaaaz
menu. omoo.w maom.
mace. mamm.oa aqu. Nama. oam~.w mmom.
.eamc. aaao.ma aoem. omea. Nm~0.¢ Mann.
ammo. coo~.aa «mac. ammo. .qann.wa come.
ammo. mmua.~a moqq. aa qqaa. nuqo.m mmoc. aa
ammo. camm.~a momq. aaaa. moam.ma omwe.
Nave. maa¢.0a unme. «mma. quo.oa mmoc.
ammo. muom.oa acme. mmna. cash.oa unme.
ammo. mucm.aa «mnq. zuuopawuu. coma. ~¢o~.aa wmae.
noaa. emno.oa «woe. a sewn amma. ooom.na vase. a xao>maucnu
a a a acaumu auoauu> a x n :oauuu huoauo>
uaaoou >,III r Laaquu
.su30pm

uoammOa pom mpmw on» on wepuaw o>p3u NapomEou 0:“ mo mpouoEmhmm woumEaumm .a mam<e

17

 

 

mmqa. nem~.m «eon. ammo. mmmo.m whee.

memo. eqem.m mace. memo. om~u.m name.

coca. memo.oa mmee. Neaa. qem~.m meme.

emma. aam~.m naee. mmmo. Nmoo.oa mace.

mnea. hmum.a «man. .aa oomo. mome.m mmme. aa

emmo. aoea.m mean. nema. ~nmm.m mane.

mumo. mamm.m omNm. mmmo. o~¢~.m emme.

muma. umee.m meme. aqua. enmepm amue.

mama. moa~.m «nee. anew. ea¢N.m meme.

aaea. moan.» . mane. H so-a>az emna. waoom.m. Name. a No-s>az
eemo. emo~.m muee.

emma. en~¢.m ennm.. amma. ammo.m mmae.

mmma. mmma.m mmme. emaa. mama.m eaae.

omea. nmam.n nmme. mwoa. emem.m meme.

omna. n¢eo.m mmue. aa «mmo.. qun.m mmeq. aa

mmma. en¢m.m eaae. mmua. suma.m meme.

emqa. mnmm.m eomm. mmeN. Ne~0.m eeoq.

moua. mmm¢.m mnae. mama. smam.m maem.

mmmo. ~mm~.m eaee. omma. ne-.m mmmm.

omea. nmem.m name. a menmemz ouma. mmeo.m Name. a acum>uz

o x n coaumo muuaum> a a n coauwo huoaua>
uaanou uaaaou

 

a.e.ueoue a mqm<e

18

 

 

mama. emmm.m mmme.
mmmm. oeem.m maee.
«emu. emee.m Heme.. emmm. meem.ma meme.
emem. mame.m meme. Ha eemm. emme.mm omme. Ha
«mam. eoem.m meee. mama. mamm.~a emme.
emmm. moee.m same. mmaa. maeo.em Name.
eeom. memm.oa «mee. amem. oemm.mm mmme.
meom. mam~.m «mmm. . czoum meem. momm.~m mmme.
«mmm. .emmm.m «see. a emaemsm mmam. memo.mm mmme. a acumen:
amom. emmm.mm amen.
emom. moem.ma meme.
mama. mmee.m meme. memo. memm.em mane.
mmea. aeee.om emoe. Ha memo. eamm.ea meme. Ha
meea. mmem.oa meme. mmmm. Neme.em meme.
ammo. ~ee~.Na mame. eomo. mmem.mm eeme.
eoem. mmom.oa eeee. mama. mmea.ma mmme.
meoa. ceme.oa Nmme. muumeemuu meme. momm.~a meme.
amma. memm.m meme. H meme eeeo. oomm.ea name. H xmoseaumeu
a x n coauuo .muuauu> u. x a coauau huuauu>
uaaamu uaaaou
.AuSoum

eon pom mume may ou emppam m>pzu uphoasdo

may we mpouoEmumm eoumEaumm

.N mam<b

19

 

 

«cam. amae.m mmmm.
nqew. mamm.m mmmm.
mmmm. mam~.m eome.
ommu. mm¢m.m meme.
mmom. «mum.m aqae. aa
eeeu. mmme.m mowq.
Nnaa. oemm.m meme. Noom. eemm.m meme.
mmea. o~ma.m eaoe. eemm. aemh.m aume.
emma. emqm.m same. «mew. ~mmm.m. Nmee.
amqa. .nqem.m «nae. a ecum>ez nmmm. ~me0.m umee. a No-h>mz
«mum. meao.m mumm.
nmmm. omem.m mmme. .
camu. amom.m mmqm. mmme. emao.m mmme.
maum. maue.m meme. eoee._ omaa.m eame.
eemm. mmum.n emae. aa emnm. eoam.n mmmm. aa
emem. mmue.m mmaq. enme. mmNo.m some.
«men. unaa.m ammm. mmwm. aemm.n seem.
omem. emmo.m «Nee. eeoe. mmmn.m mmee.
aeam. nmo~.m «mom. mace. mace.m smme. .
mmnm. emmmmm eene. a maum>nz eemm. eene.n mmne. a acam>uz
a x p coaumo muoaua> a x A coauao muoaum>
. uaamou . uaaaou

 

a.e.meoum m mmm<m

20

For the above reasons, curves were individually fitted
to the data from each leaflet and pod. The estimated para-.
meters of these Gompertz curves were then treated as metric
traits for statistical analysis. The assumption was made
that estimated 2 parameters of the curves of individual leaf-
lets or pods were normally distributed, The same assumption
could be made about parameters E and a: Among the three para~
meters of the Gompertz curve, E is the parameter of final size
and its value fluctuated around the final value obtained by
actual observations. Parameter g was the parameter of time
origin or a measure of location, related to the point at which
the first measurement was made. If a < l/e, the measurements
started before the time the maximum absolute growth rate was
reached and, as such, the rate curve would rise, reach the
maximum point and then fall. Iflg > 1/e, the measurements
started after the point of maximum absolute rate had passed
and the growth rate curve would fall from the beginning.
Parameters E and a_were more or less self—evident and their
comparison did not furnish much more information about the
varieties concerned. The parameter b was the important one.

If we write the equation in the following form:
d -
a%--(lnb)Y(_lni<-lnY)

the relationship of the absolute rate of growth (dy/dt) to b
and to the asymptotic value (E) becomes apparent. Parameter
2 gives an indication of the extent to which growth rate at

any moment is dependent upon the size at that moment and the

21

difference between this size and the final size, given that
conditions remain constant.

Figures 1 through 8 represent the observed and fitted
curves of leaflet and pod growth of three varieties with
large leaves, namely Charlevoix (dark red kidney), Cranberry
8247, and Swedish Brown, and also a variety with small leaves
(Navy-04) and the corresponding observed rate curves of these
varieties. For each variety the measured leaflet and pod
were located on the same plant. For the purpose of comparison,
the observed growth and rate curves of a leaflet and a pod-
from each of these varieties are shown together in Figures 9
through 12. There was a reasonably close approximation
between observed and estimated curves of leaflet and pod
growth of these varieties. In the Figures comparing observed
growth curves of leaflets and pods, the leaflets of Charlevoix
and Cranberry varieties are slightly longer than pods. In the
navy bean variety the mature lengths of leaflet and pod were
very close. The pattern of leaflet and pod growth in these
varieties was also very similar. In Swedish Brown the pod
was shorter than the leaflet and their growth patterns were
somewhat different, the leaflet reaching a higher maximum
growth rate than the pod and declining in rate less abruptly
than the pod. As the comparison of the rate curves demon-
strated, the maximum growth rate of leaflets in all varieties
reaches a higher level than the maximum growth rate of pOds,
though this difference was more pronounced in the large leaf

varieties than in the navy bean variety. This trend held

Length (Cm)

dy/dt (Cm/day)

Fig.

I.5

I.O

0.5

1.

22

   

 

 

 

 

 

,.
- A
" -—-- observed
- -- estimated
L.
l l l l l l l l l
O 2 4 6 8 l0 l2 l4 l6
Time (days)
I J l l l L l
I 3 5 7 9 ll l3 i5
Time (days)

Observed and estimated growth curves (A) and observed
rate curve (B) of a Charlevoix leaf.

23

I2-

   

IO -
—- observed
—- estimated

 

Length (Cm)
on
I

 

() I I L I I l I I I
O 2 4 6 8 IO I2 I4 I6

 

 

Time (days)
I.5 r-
; B
U
'U
\. I.O r-
E
. 8
=6 0.5 -
\
>5
‘0
c) I J I I I I
I 3 5 7 9 II I3 l5
Time (days)

Fig. 2. Observed and estimated growth curves (A) and observed
rate curve (B) of a Charlevoix pod.

24

   
 

 

 

 

 

i4 -
12 - A
A IO :-
E _.
8 e —
:E
2’ * 6E -— observed
3 _ —— estimated
4 ._
2 _..
_. /
O L I I I I I l I l
O 2 4 6 8 ' IO l2 l4 I6
TimeIdays)
I.5 - B
3‘.
S
\ I.O *-
E
8
35 0.5 -
\
>5.
‘0
C) I I I I I
l 3 5 7 9 ll l3 15
Time (days)

Fig. 3. Observed and estimated growth curves (A) and observed
rate curve (B) of a Cranberry 8247 leaf.

:4

I2
,1. i0
E
L)

V 8
f3
0'3
5 6
.J

4.

2

O

I.5
'9.

8

‘\
ELO

8
30.5
>
U

0
Fig. 4.

25

   
 

-— observed

 

 

 

 

: -—— estimated
I L I I I I I l l I
o 2 4 '6 8 IO l2 l4 l6
Time (days)
*- B
l l l I I i l a
I 3 5 7 9 ll l3 :5
Time (days)

Observed and estimated growth curves (A) and observed
rate curve (B) of a Cranberry 8247 pod.

26

    
 

 

 

 

 

I4—
l2 - A
,1 IOI-
E _.
8 s—
f ..
0’ Observed
‘3 6- .
3 __ -— estimated
4—
2...
— /
0 l I l I I I I I #1
O 2 4 6 8' IO I2 l4 I6
Time (days)
I 5- B
3‘.
O
3 I.
E- I.O
8
E 0.5 -
>5
'0
O l I I I J
I 3 5 7 9 II I3 I5
Time (days)

Fig. 5. Observed and estimated growth curves (A) and observed
rate curve (B) of a Swedish Brown leaf.

l4
l2
6 IO
E
o
v 8
:5
0‘!
.53 e
4
2
O
I.5
>
U
E
E- LO
0
30.5
>5
‘0
0
Fig. 6.

27

 

  
 

 

 

 

 

 

.. A
: —- observed
--- estimated
__ /
l I l I I I I I I
O 2 4 6 8 IO I2 l4‘ l6
Time (days)
"' B
L l I l I I
I 3 5 ' 7 . 9 ll l3 I5
Time (days)

Observed and estimated growth curves (A) and observed
rate curve (B) of a Swedish Brown pod.

IO

A 8
E'
8 6
.f
8‘ 4
Q)
.J
2
0
I.5
32
U
3
E-I.O
C)
30.5
>
‘O
0
Fig. 7.

28

    
 

-— observed
-- estimated

 

L I III I I
6 8 IO

Time (days)

 

I l l l I l
5 7 9 I I

Time (days)

l3 I5

Observed and estimated growth curves (A) and observed
rate curve (B) of a Navy—04 leaf.

29

     
 

 

 

 

 

'OI— .
" A

8 .—
E. _
e 6 -
.5 -- / -— observed
8’ 4— --— estimated
0.)
._I *- -

2—

-— /
0 l I l I I I l J l
O 2 4 6 8 IO I2 I4 I6
Time (days)
I.5 -

’>‘. B
O
3
E‘ l.O -
8
i; 0.5 —
>
.0

0 L I l I I

3 5 7 9 II l3 I5
Time (days)

Fig. 8. Observed and estimated growth curves (A) and Observed
rate curve (B) of a Navy-04 pod.

30

 

 

 

 

 

 

 

'4‘. .--"_'—"'
I2—
ff IC>"
E ...
L)
v 8.—
£ ._
8’
a) 6"
—J _.
4....
2....
0 I I I I I I I I I
O
A I.5—
>5
0
13 .
\.
E I.O—
8
30.5—
>5
'0
O
I 3 5, 7 9 II I3 I5
Time(days)

Fig. 9. Observed growth (A) and rate (B) curves of Charlevoix
leaf and pod.

31

I4-

 

Length (Cm) .

 

 

 

 

 

 

A I .5 '-
>5
0
‘U
\.
E I .O I-
8
'3 0.5 -
>5
D
O l 3 5 7 9 II I3 l5
Time (days)

Fig. 10. Observed growth (A) and rate (B) curves of Cranberry
8247 leaf and pod.

I4

l2

Length (Cm)

O

I .5
3
O
'3

EEI'C)
8

E 0.5
>~
'D

0

Fig. 11.

 

 

32

 

 

l I I l I I l I I
O 2 4 6 8 IO I2 I4 I6

Time (days)

 

 

 

\I\ I I
I 3 5 7 9 II I3 I5
Time (days) I

Observed growth (A) and rate (B) curves of Swedish
Brown leaf and pod.

33

 

 

 

 

 

 

 

IO—
"? 8—
E ..
o
v 6,...
f _.
I?
a) 4"
—l —
2....
O I I I I I I I I J
O 2 4 6 8 IO I2 I4 I6
Time (days)
3" 5— B —- Leaf
U
3
Emo-
8
30.5-
>5
'0
O .
I 3 5‘ 7 9 II I3 I5
Time (days)

Fig. 12. Observed growth (A) and rate (B) curves of Navy-O4
leaf and pod.

34

true for the four large leaf and the four small leaf varie-
ties with only a few exceptions.

The analysis of variance for the b parameters of leaflet
growth curves (Table 3) and pod growth curves (Table 4) of
the eight varieties demonstrated significant differences (at
the .01 level) among varieties for this parameter in both
leaflet and pod growth. Block effect was only significant in
the case of pod growth (at the .05 level). This may be due
to a more sensitive response of pod develOpment to small
environmental differences since the experimental plots were
located in a homogeneous field as far as the cultural prac-
tices were concerned and all indications are that block
differences in soil condition were not substantial.

The high level of significance observed for the variety
effect in the analysis of variance made a multiple-range test
of differences between variety means of b_parameters feasible.
The means of 2 parameters of leaflet and pod growth curves

of the two groups of varieties are as follows:

 

Leaflets Pods
Charlevoix .4493 .5726
Manitou .4165 .5967
Cranberry 8247 .4734 .5845
Swedish Brown .5500 .4608
Navy-01 .4173 .4391
Navy-02 .4410 .4503
Navy-O3 .4247 .4255
Navy-04 .4903 .4157

For the comparison of mean 2 parameters, Tukey's multiple-

range test, which is a conservative one, was employed. Table

35

 

 

 

 

 

 

TABLE 3. Analysis of variance for 2 parameters of leaflet
growth curves.
, _ level of
SOurce df 53 MS F-ratio Slgnlflcance
.05 .01
Blocks 1 .0033 .0033 2.20 4.00 7.08
Varieties 7 .1445 .0206 l3.73** 2.17 2.29
Block x varieties 7 .0038 .0005
Sampling error 62 .0913 .0015
Total 77 .2429
**P: .01
TABLE 4. Analysis of variance for 2 parameters of pod =
growth curves.
level of5
Source df SS MS F-ratio significance
.05 .01

Blocks 1 .0100 .0100 7.14* 4.08 7.31
Varieties 7 .3110 .0444 31.71** 2.18 2.99
Block x varieties 7 .0008 .0001
Sampling error 48 .0676 .0014
Total 63 .3894
**P< .01

* P< .05

36

5 shows the differences between the means of B parameters
of leaflet growth curves of four large leaf and four small
leaf varieties. The differences are generally small and
only three of them show significance at the .05 level.
These include the one between Swedish Brown and Manitou
within the large leaf group and between Swedish Brown and
Navy-01 and Navy-03, which belong to the second group.
Swedish Brown is an early bush type variety. Manitou is also
a determinate variety while the two Navy Bean varieties are
late vines. Examination of the means for b shows that
Swedish Brown possesses the highest value for the above
parameter. Since 2 is a measure of the magnitude of decline
in the rate, Swedish Brown approaches the mature size at a
higher rate than all other varieteis. Differences between
Swedish Brown and three of the small leaf and two of the
large leaf varieties are considerably high (Table 5). This
might be an indication of the higher rate of photosynthetic
efficiency in this variety. In other words, Swedish Brown
leaves grow at a higher rate than do those of the other
varieties. There are no sizable or significant differences
between varieties making up the small leaf group.

The difference between the means of B parameters of pod
growth curves of the same varieties are presented in Table 6.
Here the size of differences is much larger and the number
of significant differences considerably higher, with the
distinction that the direction of differences among the large

leaf varieties has been reversed. While in the case of

37

 

 

emee. em-m>mz
mmeo. memo. mm-m>mz
mmam. same. ammo. mm-m>mz
mmmo. «mmma. omoa. «mmma. czopm :maeozm
meao. mmeo. ammo. aemo. eemo. memm mppeecmpu
mmmo. Nmoo. memo. memo. «mmma. memo. . :oaacmz
oaeo. eemo. mmoo.. ammo. mooa. aemo. mNmo. xao>oaamcu
eo-x>mz mo->>mz Nc-m>mz ao->>mz czoam. . memm souacmz
:maeozm mnaonampo

.cuzopm poawmoa pom mpoueEmpmm m mo memos esp coozuoe moucomoweaa .m mam<h

38

me. v& .m

 

 

am. mee
mmoo. moI>>mz
eemm. memo. mm-m>mz
memo. eeam. Name. am-m>mz
ammo. mmmo. moao. mamo. azopm :maemzm
..mmem. «momma. .meea. «memem. gamma. memm mepeeemeu
«aoama. «emama. «eeeea. «eemma. emmma. NNao. souacmz
memema. «mamea. «mmma. «mmma. maaa. maao. ammo. xao>eapmnu
eouN>mz mo-x>mz No-x>mz ao-x>mz czoam memm nowaamz
smaeozm mhuoncmau

.guzohm eon mom maeuoEmumm m mo memos ecu :oozuoe meoceaemmam .e mam<e

39

leaflets Swedish Brown has the highest b_value, in the case
of pods it shOws the lowest. Within the large leaf group
large differences were observed between Swedish Brown on one
hand, and Charlevoix, Manitou, and Cranberry 8247 on the
other, the last two values showing significance at the .05
level. The differences between Charlevoix, Manitou, and
Cranberry 8247 and all four varieties of the small leaf group
are significant or highly significant. The differences
between Swedish Brown and the Navy bean varieties, unlike
the case of leaflets, are neither sizable nor significant.
There were no substantial or significant differences among
varieties of the small leaf group.

Comparison of Table 5 and Table 6 demonstrates that the
differences between the p parameters of varieties with small
leaf for both leaflet growth and pod growth are very small
and always non-significant. This is an indication of the
similarity of growth process of the small leaf varieties.
These varieties are similar in their mature leaflet and pod
sizes, the pattern of growth, and finally the rate of decline
of growth rate as the mature size is approached. In spite of
the divergent leaf sizes of the two groups of varieties, when
comparing them, the only sizable difference is that between
Swedish Brown and three of the small leaf varieties. However,
for pods the difference between Swedish Brown and the small
leaf varieties is negligible. In other words the high rate
of approach to mature size demonstrated by the leaves of

Swedish Brown is not repeated in the process of pod developv

40

ment in this variety. Consequently Swedish Brown pods reach
the mature size at almost the same rate that is characteris-
tic of the pods of the small leaf varieties. The same
reasoning holds true for the large leaf group. Within the
large leaf group the mean b parameter of Swedish Brown leaf-
lets is conSiderably larger than that of Charlevoix and
Manitou and somewhat larger than Cranberry 8247. But this
pattern is reversed for the case of pods and the latter
varieties show considerably larger E values than that of
Swedish Brown. It can be stated that the comparatively high
rate of approach to mature leaf size observed in Swedish
Brown does not imply that the same process would be true for
pod growth in that variety. Therefore, Swedish Brown pods
reach their mature size more slowly than do the pods of the
other three large leaf varieties. This may be associated
with the lesser re-mobilization and utilization of stored
starch in this variety as compared to Charlevoix (2).

Another interesting point is the difference between the
leaflet B parameters of Charlevoix, Manitou, and Cranberry
8247 on one hand and the leaflet B parameters of the four
Small leaf varieties on the other hand as contrasted to the
corresponding difference between pod 9 parameters of the two
groups. While in the first instance the differences are
negligible, in the second instance all the differences are
significant or highly significant.

It could be argued that while the rates of approach of

leaflets to the mature size in Charlevoix, Manitou, and

41

Cranberry 8247 are very similar to the corresponding rates

in the small leaf varieties, when comparing pod growth
between these two groups, the pods of the three large leaf
varieties reach the mature size considerably faster than do
the pods of the small leaf varieties. In the case of Swedish
Brown the reverse of this holds true. While its leaflets
reach maturity with a rate higher than most small leaf and
large leaf varieties, its pods approach the mature size with
almost the same rate as the pods of the small leaf varieties.
Large and mostly significant differences between pod b para-
meters of Charlevoix, Manitou, and Cranberry 8247 and Swedish
Brown clearly demonstrate this point since the pod B parameter
of Swedish Brown has almost the same size of the 2 parameters
as the small leaf varieties.

I The correlation between 2 parameters of leaflets and
pods within each of the two groups of varieties was calculated
in order to understand the pattern of correlated growths of
these organs. For the large leaf group it was r = -.6084 and
highly significant (at the .01 level). For the small leaf
group it was —.1202 and nonsignificant. Thus the rate of
approach to the mature size in leaflets and pods of the large
leaf varieties is not the same. Generally, lower rates of
decline in the growth rate of leaflets in approaching the
mature size was associated with an opposite trend in pods.

In other words, for Charlevoix, Manitou, and Cranberry 8247
varieties the lower rate of approach to the asymptote by the

leaves was associated with a substantially higher rate of

42

approach to maturity by the pods. This process was reversed
for Swedish Brown, in the sense that the high rate of approach
to maturity in leaves was associated with a low rate of pod

elongation to maturity.

The growth rates

The maximum absolute growth rates of leaflets and pods
were considered in order to investigate the nature and the
degree of their association. When all the eight varieties
were pooled together, the overall correlation between maximum
growth rates of leaflets and pods was r = .3822 and highly
significant (at the .01 level). However, when the two groups.
of varieties were taken separately this significant correla-
tion disappeared. For the large leaf group the correlation
was r = .0171 and for the small leaf group it was r = .0668,
both nonsignificant. This discrepancy could be explained as
follows: combination of two distant clusters of points, each
with a small value of correlation coefficient, could result
in some sizable value for this coefficient in the combined
data. Examination of the plotted data for the maximum growth
rates of leaves and pods in two groups of large and small
leaf varieties revealed such a relationship.

Since the two groups of varieties differ in terms of
growth rates, the correlations between average maximum growth
rates of leaflets (Table 7) and pods (Table 8) and yield and
its components and mature leaflet and pod lengths were

calculated for both groups and are summarized in Table 9.

43

 

 

 

 

 

mm. om. om. am. mm. me.a oe.a aa
mom

oa.a em. mm. mm. eo.a 4o.a mm.a mm.a a
eo-%>mz moim>mz NoIm>mz aosmwmz . czoum memm :ouaamz xao>eapmno xuoapm>

:maeozm xhaenamao
.amme\.Eug meom mo momma auzoam EDEame ommae>< .m mam<b

eN.a ma.a om.a mN.a mm.a Ne.a mm.a am.a aa
gem

ma.a em.a mN.a oa.a me.a mm.a mm.a me.a a
eoux>mz merx>mz Nowm>mz HonMmz CSopm memm :ouacmz xpoaam>

nmaeozm mhpoecmhu

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44

 

 

 

TABLE 9. Correlation between average maximum leaflet and
pod growth rates and yield, its components,
leaflet size, and pod size.

4 large leaf 4 small leaf
varieties varieties

Y vs leaflet rate .2678 .2162

pod rate -.6766* -.3789
Y vs leaflet rate -.4641 .7665*
pod rate .2008 .2885
Z vs leaflet rate .3159 .6882*
pod rate .7715** .3139

W vs leaflet rate .5285 .6982*

pod rate -.3220 -.l497

L vs leaflet rate .9102** .8047**

pod rate — - -

P vs leaflet rate .1952 .7140*

pod rate .9369** -.0108

**P: .01

* P< .05

45

Correlation between growth rates and pod number

For both groups the leaflet rate showed positive corre-
lation values in the lower middle range, although they were
nonsignificant. The pod growth rate showed sizable negative
correlations with X (pod number) for both groups and in the
case of the large leaf group was significant at the .05 level.
The negative correlation between pod growth rates and the X
component, especially in the large leaf group with higher
maximum growth rate, underlines the importance of competition
for environmental resources and the negative impact of the
rate of growth of pods on the formation and development of

other pods, the latter being at an earlier stage of growth.

Correlation between the growth rates and seeds per_pod

 

In the large leaf group the leaflet growth rate shows a
sizable negative correlation with the Y component, but for
the small leaf group this correlation was positive and sig-
nificant, demonstrating an opposite direction of association
as compared to the first group. On the other hand, the pod
growth rates produced positive and similar correlations in

the lower medium range with the Y component for both groups.

 

Correlation between the rates and seed size

This relationship was a positive one for both groups and
both rates though its degree varied. It was significant
between leaflet rate and seed size of the small leaf group
and highly significant between pod growth rate and the Z com-

ponent of the large leaf varieties.

46

Correlation between growth rates and yield

 

For leaflet rates this was positive and high for both
groups and significant for the small leaf group. The opposite
was found for pod growth rate which showed negative and low

correlations for both groups.

Correlation between leaflet growth rate and fully expanded

 

leaf size

 

This was a positive and highly significant correlation
for both groups. If the final size of leaflets under constant
environmental conditions is a genetically determined character,
being developmentally linked with the rate and duration of
growth though not necessarily determined by them, this large
and highly significant correlation between the growth rate
and final size may be an indication of the primacy of favor-

able environment at the stage of maximum rate of leaf growth.

Correlation between the rates and mature pod size

 

The pattern of this association was very similar to the
one observed for seed size. Its degree varied from highly
positive to zero. For leaflet rates it was low with the large
leaf group, but high and significant for the small leaf group.
Pod rates showed a highly significant correlation with pod
size within the large leaf group while no correlation was
present within the small leaf group.

Comparing the two groups for the correlation between
maximum leaflet growth rate and yield and its components, the

general trend was a positive one except for the case of seeds

47

per pod in the large leaf group. In the large leaf group

the positive association of maximum rate with pod number and
seed size was countervailed by a negative correlation with
seeds per pod. This results in a reasonably high correlation
with yield. In other words, the high rate of leaf growth
exerted its positive influence on yield through an increase
in pod number and seed size but not in number of seeds per
pod. In the small leaf varieties the association between
maximum leaflet growth rate and the three yield components
was always positive and in the case of seeds per pod and seed
size was significant. The correlation with yield was also
significant. Here the maximum rate of leaf growth positively
influenced yield mainly through an increase in the number of
seeds per pod and seed sizes while its influence on pod num-
ber was moderately positive. Thus, the high rate of leaf
growth in the small leaf varieties plays a much more impor-
tant role in determining the final yield than in the large
leaf varieties. The association between maximum leaflet rate
and mature leaflet sizes in both groups was positive and
highly significant. Since the maximum size of leaf for each
variety is genetically determined, and a function of rate and
duration of growth, this high correlation might be an indica-
tion that optimal environmental conditions and availability
of nutrients would strongly influence yield through acceler-
ation of rate of leaf growth which makes it possible for
leaves to reach their mature size in a shorter period of time

and become fully active sources of metabolites.

48

The association between leaflet growth rate and pod
length was positive for both groups and significant for the
small leaf varieties. The pattern was similar to the corre-
lation between leaflet rate and leaflet length but much
stronger in the small leaf group. One possible reason for
this discrepancy is that the varieties comprising the small
leaf group were much more uniform in growth habits and leaf
and pod sizes than varieties of the large leaf group. So the
positive association between rate and the sizes of leaflets
and pods was more consistent.

Considering the associations between maximum pod growth
rate and the yield system, the correlation with pod number
was negative and considerably large for both groups, the one
for the large leaf group, which had a higher maximum growth
rate, being significant. This underlines the importance of
competition for the sources of nutrients. Since within the
nutritional unit defined by Adams (1) young pods have the
lowest priority in competition for nutrients, the high growth
rate of those pods which have passed the first stages of
growth exerts a negative impact on formation and development
of the pods at a very early stage of development. This impact
occurs through appropriation of the major portion of resources
available, cutting the flow of metabolites to the young pods
and causing them to abort. This matter was substantiated in
a study by Subhadrabandhu (31) of Black Turtle Soup, Michelite,
and Seafarer cultivars of dry bean. The chance of develop—

ment to full maturity for the pods of all three cultivars was

49

greater when they developed from earlier borne flowers. The
high growth rate of these pods was the cause of cessation in
further growth of pods initiated later.

The correlation between maximum pod growth rate and
number of seeds per pod in both groups was positive but not
large or significant. The speed of pod elongation did not
have a strong bearing on the number of fertilized ovules
retained within pods because of the lower order of priority
they have in appropriating available nutrients for full
development.

The association between maximum pod growth rate and seed
size was positive in both groups and highly significant for
the large leaf group. This might be a corollary of the pre-
vious correlation, the one between the rate and number of
seeds per pod. Since the average maximum pod growth rate of
the large leaf group was higher than that of the small leaf
group, the pods of the former group reached their full length
sooner and a greater portion of metabolites became available
for seed development while the pods of the latter group
reached their full length later and a lesser part of nutrients
could be appropriated for seed enlargement. This argument
holds true only if a genetic basis is assumed for the magni-
tude of the maximum rate. The correlation between average
maximum pod growth rate and seed yield in both groups was
negative though nonsignificant. This could be explained on
the basis of generally high negative correlations between

the maximum pod growth rate and the number of pods per plant,

50

which, due to the primacy of pod number in yield determina-
tion, negates the small positive impact of maximum pod growth
on the number of seeds per pod and its more substantial
positive effect on seed size.

The correlation between maximum pod growth rate and pod
length was positive and highly significant for the large leaf
group and near zero for the small leaf group. Here the
contrast between leaflet and pod growth rate correlations
with mature pod size is worth noticing. It was the small
leaf group which had positive and significant correlation of
the leaflet rate with pod size, while the large leaf group
showed a small positive correlation with this rate. In the
large leaf group the average maximum grwoth rate of pods had
an association of the same degree and direction with the
mature pod size as the average maximum leaflet rate of the
small leaf group. Since the same pattern was present in the
case of rate correlations with seed size, in the large leaf
group of varieties the average maximum pod growth rate was
strongly associated with pod size and seed size while in the
small leaf group it was the average maximum leaflet rate

which was highly correlated with pod size and seed size.

51

Correlations between yield, its components, and final leaflet
and pod sizes

 

Phenotypic correlations calculated were as follows:

rLB: Between fully expanded leaflet length and its
breadth.

rLP: Between leaflet length and mature pod length.

rLZ: Between leaflet length and seed size.

rPZ: Between pod length and seed size.

rPY: Between pod length and seeds per pod.

rXY: Between pod number and seeds per pod.

rXZ: Between pod number and seed size.

Between seeds per pod and seed size.

rXW: Between pod number and yield of seed.

rYW: Between seeds per pod and yield of seed.

rzw: Between seed size and yield of seed.

These were calculated for the three leaf size groups
and are presented in four tables (Tables 10-13). Table 10
and Table 11 show correlations between leaflet and pod sizes
and seed size and seed number and also correlation between
leaflet length and breadth, the latter only for the Gratiot
County experiments. Table 12 and 13 show correlations between
yield and its components. Test 23 and Test 25A had the same
planting regime (row and plant spacing), but the former was
planted in East Lansing while the latter was planted in
Gratiot County. Since the level of inter-plant competition

for both of these experiments was the same, they are compared

52

TABLE 10. Correlations involving leaflet size, pod size,
seed size, and seeds per pod compared for the
effect of environmental change.

 

Large-leaf Medium-leaf Small-leaf
Correlation Experiment varieties varieties varieties

 

 

r 23A .0683 .0933 .2573
LP 25A .4875* .1935 .4150
23 .1175 .4616 .3914
1‘L2
25A .1099 .4696* .3252
r 23 .7112** .6178 .3427
P2 25A .3407 .1071 .1752
23 .1598 .8245** .2790
rPY
25A .6983** -.0522 .1090
**P< .01

* P: .05

53

TABLE 11. Correlations involving leaflet size, pod size,
seed size, and seeds per pod compared for the
effect of different competition regimes.

 

Large-leaf Medium-leaf Small-leaf

 

 

Correlation Experiment varieties varieties varieties
24 .8673** .8151** .8454**
rLB 25A .8450** .5833** .8707**
25B .7706** .6183** .7698**
r 24 .3164 .2218 -.0619
LP 25A .4875* .1935 .4150
25B .7626* .4053 .5694
24 .4526* .4186 .6460**
rLz 25A .1099 .4696* .3252
25B .4889 .2439 .2537
r 24 .3525 '-.2381 -.2336
P2 25A .3407 .1071 .1752
25B .8154** .1481 -.0444
24 .4839* .3885 .2727
rPY 25A .6983** -.0522 .1090
25B -.3877 .2827 .3763
** P< .01

* P: .05

54

TABLE 12. Correlations between yield and its components
compared for the effect of environmental change

 

Large-leaf Medium-leaf Small-leaf

 

 

Correlation Experiment varieties varieties varieties
r 23 .1063 .7080* -.0629
KY 25A .5998** .1518 -.4721*
rxz 23 .S790* .6433* -.3466
25A .2429 .2672 -.0063
rYZ 23 .3963 .4878 .1692
25A .3902 .2581 —,3939
rXW 23 .9051** .7316* .7318**
‘ 25A .4483 .8069** .4957*
rYW 23 .1354 .6753* .2819
25A .2255 .1630 —.3128
rZW 23 .2228 .0078 .3265
25A .5470* .0766 .7720**
**P< .01

55

TABLE 13. Correlation between yield and its components
compared for the effect of different competition

 

 

 

regimes.
Large-leaf Medium-leaf Small-leaf
Correlation Experiment varieties varieties varieties
24 -.5519* -.0208 -.6286**
rXY 25A -.5998** -.1518 -.4721*
25B .6012 —.l762 .0896
24 -.3266 -.6385** .6445**
rXZ 25A -.2429 -.2672 -.0063
25B -.8157** 5.3852 -.S787
24 -.2051 -.3111 -.6818**
rYZ 25A -.3902 «.2581 «.3939
25B -.4706 -.5417 -.Sl72
24 .8339** ..7072** .9225**
IYW 25A .4483 .8069** .4957*
‘ 25B .4130 .6976* .6912*
24 ~.4l43 .3249 -.5224*
rvw 25A -.2255 .1630 -.3128
ZSB .5420 -.2847 -.0045
24 .0947 -.0895 .8391**
r2w 25A .5470* .0766 .7720**
25B .0642 .2144 .2424
**P: .01

* P< .05

56

for the study of environmental differences. Test 24, test
25A, and test 25B on the other hand were all planted in
Gratiot County and shared the same environment; each repre-
sents one distinct level of competition (wide plant spacing,
close plant spacing, close spacing with shade, respectively)
and therefore are compared for the effect of stress levels

upon correlations.

Correlation between leaf length and breadth

 

Calculated for only one location, this correlation was
always positive and highly significant. The factors deter-
mining the length and width of leaflets in varieties of all

groups were strongly associated.

Correlation between leaf length and_pod length

 

This correlation was generally positive and higher in
degree in Gratiot County as compared to East Lansing. In
Gratiot there was also a general trend of increase in the
magnitude of correlation accompanied with the increase in
severity of stress, the highest values observed for all
groups in the artificial shading experiment. Thus, the
correlation showed the tendency to vary rather widely in
degree from one location to another with the same density of
planting having always considerably higher values in Gratiot
County. This correlation varied in magnitude from group to
group, location to location, and across different stress
regimes ranging from zero to .76. The expression of this

positive association was environmentally determined. It

57

could be argued that in Gratiot County the environment was
much more favorable for its expression. This is demonstrated
by the coefficients of the large leaf group, with a value
close to zero in East Lansing, but in Gratiot County gener-

ally substantial and in two cases significant.

Correlation between leaflet length and seed size

This correlation was always positive. The degree of
correlation remained unchanged for each of the three groups
while in Gratiot County it varied within each group by the
change in the competition level. The plants in the wide
spacing experiment had large coefficients for all three
groups varying from significant to highly significant, indi-
cating that this positive association was best manifested at
lower intensities of competition. The plants in the small

leaf group had the highest correlation coefficient.

Correlation between pod length and seed size

 

Unlike the previous correlation,the correlation between
pod length and seed size varied in sign and magnitude from
location to location and also across competition levels. The
large leaf group always showed positive and in two cases high
and highly significant correlations. These two occurred in
closely planted experiments, one in East Lansing, another one
in Gratiot County with artificial shading. For the large
leaf group this correlation appeared to be positive and

environmentally influenced.

58

Correlation between pod length and seeds per pod

From location to location the correlations between pod
length and seeds per pod were mostly positive, but they
varied widely in degree from group to group, ranging from
zero to .82 and highly significant. Across the stress
regimes the correlations were generally positive, but fluctu-
ated in magnitude, except for the large leaf group under
shade which showed a negative correlation. The large leaf
group showed wide fluctuation in magnitude and sign ranging
from .70 to -.39 across locations and stress regimes. It
had significant correlations for widely spaced and closely
spaced experiments in Gratiot County. The medium leaf group
had coefficient values varying from zero to .82 with no clear
trend. The small leaf group had always positive, but mostly

low correlation coefficients.

Correlation between pod number and seeds per pod

 

This correlation was predominantly negative. The large
leaf group across locations varied from slightly negative to
highly negative and significant. Across stress regimes the
coefficients varied from highly negative and significant to
highly positive, the last one being in the shading experiment.
The medium leaf correlations fluctuated across locations from
highly positive and significant to slightly negative while in
different competition regimes they varied from zero to the
low negative range. The small leaf group across locations

varied from zero to negative and highly significant. Across

59

competition levels the coefficients varied from zero to nega-
tive and highly significant, the size of the negative corre-
lation decreasing with the increase in the severity of

competition.

Correlation between ppd number and seed size

Excepting one occasion, this correlation was negative
but highly varied in degree for all groups according to locav
tion or competition levels. It was significant in East
Lansing and highly significant in Gratiot County under
shading. For the medium leaf group the East Lansing value
was significant while in Gratiot the wide spacing experiment
showed a highly significant value. The small leaf group
showed a positive and highly significant value in the wide
‘spacing experiment which was in contrast to the rest of the
correlations. Overall, the plants in the East Lansing
experiment showed higher values for all groups. In Gratiot
County experiments the large leaf and the small leaf groups
showed a substantial increase in the degree of negative

correlation in shade.

Correlation between seeds‘per pod and seed size

 

This correlation was generally negative except for the
small leaf group in East Lansing which was slightly positive.
Fluctuations across locations and competition levels were not
great. Across competition levels the large and medium leaf
groups showed a trend of increasing degree with intensifica-

tion of stress and the small leaf group showed higher values

60

than the other three groups at different competition levels,
one being significant. The shading experiment had a value

in the medium range for all groups.

Correlation between pod number and yield

This correlation was always positive and mostly signif-
icant. This correlation was very consistent in its sign
across location and competition levels. The East Lansing
experiment had a higher degree of correlations than the same
experiment in Gratiot County. The wide spacing experiment
showed the highest magnitude for all groups and was always
highly significant. The large leaf group demonstrated a
distinct response to intensification of competition by a

gradually decreasing coefficient trend.

Correlation between seeds‘per pod andAyield

 

This correlation showed no clear trend in sign or degree
across locations or competition levels. The medium leaf
group values varied from low positive towards low negative
with increase in stress level. Large and small leaf groups

showed an opposite trend.

Correlation between seed size and yield

 

This correlation was mostly positive with the highest
values belonging to the small leaf group. Only the large
leaf group in East Lansing showed a small negative correla-
tion. The number of correlations close to zero was substan-

tial. Overall, the large leaf group had contradictory signs

61

across locations and no clear trend across stress regimes.
The medium leaf group showed generally no correlation across.
locations or competition levels except for the shading
experiment having a small positive one. The small leaf
group coefficients, though varying considerably in magnitude
by change in environment, had large and highly significant
values for both wide and close spacing experiments but a

small and nonsignificant one for the shading experiment.

SUMMARY AND CONCLUSIONS

There have been numerous attempts to define specific
physiological meaning for the parameters of growth curves.
Specifically, those parameters which are measures of scale
or spread of the growth curve along the time axis (parameter
p in the Gompertz curve) and which determine the general
pattern of growth or the shape of the curve have been exten-
sively studied. These attempts have not been successful.

It has not been possible to associate any of the parameters
of growth curves with any particular physiological function.
Nevertheless, growth curves provide an economical summary of
growth data. In fitting the data to any particular growth
function, some of the variation in the actual measurements
is lost, however, the estimated parameters of growth of any
genotype or its organs can be treated as metric traits.

This assumption has been made in the present study. Further-
more, it has been assumed that any significant differences
between the parametric values of growth of the same organs
on different genotypes can be attributed to genetic effects.

In comparing two groups of field bean varieties, one
group c0nsisting of large leaf and another of small leaf
varieties, grown under similar environmental conditions,
significant differences were found between ijarameters of

leaf growth curves. This was in contrast to the findings of

62

63

Amer and Williams (3) who found reasonably constant p para-

meters for leaves of Pelargonium zonale plants grown under

 

different watering regimes. Amer and Williams imply that
this parameter is species~specific. From the present study
it appears that this parameter is not species-specific in
field beans. Furthermore, it could be used in differenti—
ating among groups of varieties of varying leaf sizes. This
differentiation was even more pronounced when the significant
differences between the b parameters of pod growth curves of
the two groups of field bean varieties were taken into con—
sideration.

One of the objectives of the present study was to
elaborate on the basis of expected relationships between the
sizes of organs, such as leaflet, pod, and seed. Duarte and
Adams (11) reported a significant path correlation between
leaflet size and seed size in lines derived from a cross
between the variety Michelite with small leaves and small
seeds and the variety Algarrobo which is a mottled kidney
bean with large leaves and large seeds. The explanation they
offered was based on the assumption of organ homology, that
in the plant's ontogeny pods are modified leaves, and that
seeds which are composed mainly of cotyledons may also be
Considered modified leaves. Each of these organs is homo-
logous to the other and they should all be regulated to some
extent by a common set of genes. Clearly, having different
functions as photosynthetic, reproductive, and storage organs,

these organs are also subject to genetic and non-genetic

64

influences different from those exerted by the common set of
genes. On the basis of this reasoning, the growth curve
parameters of leaflets and pods are expected to show some
degree of correlation but not necessarily complete correla-
tion. The magnitude of this correlation would depend upon
the relative contribution of the common set of genes versus
the specific set of genes regulating the particular function
of each of the two organs. There was a highly negative
association between b_parameters of leaflet and pod growth
curves of large leaf varieties. Closer inspection showed
that lower b_parameters of leaflet growth curves of Charlef
voix, Manitou, and Cranberry 8247 were associated with higher
E values of pod growth in these varieties, while for Swedish
Brown the reverse was true. Since B is a measure of decline
in the rate of growth of leaflet or pod, it could be inferred
that in kidney and cranberry beans the partition of growth
resources - water, carbohydrates, growth hormones, proteins -
is regulated to favor pod and seed development at the expense
of leaf development. In Swedish Brown leaf development is
favored over pod develOpment. Swedish Brown pods are unusu-
ally short, with fewer seeds per pod, for a variety of its
seed size class. The contrast between red kidney Charlevoix
and Swedish Brown in leaflet and pod growth pattern may be
associated with the recent finding (2) that starch remobili-
zation from root and lower stem is more restricted in Swedish
Brown than in Charlevoix. Clearly, in Swedish Brown the

restricted pod development was not a result of deficiency in

65

carbohydrates. The competition between leaf and pod must
have been for some other resources. An alternative expla~
nation is regulation of growth at genetic and hormonal levels.
No clear-cut evidence for either system of regulation is
presently available.

In the small leaf group the p parameters of leaflet and
pod growth curves differed very little (Figure 12). Here,
it could be implied that both organs were competing for
growth materials on an equal basis. Consequently the rate
of approach to the asymptote for both organs is very similar,
Although the general form of the leaflet and pod growth curves
was similar in both large leaf and small leaf varieties
(Figures 9, 10, ll, 12), the growth rates of leaflets consis-
tently exceeded the grthh rate of pods in the large leaf
varieties. These varieties differ in the time point at
which the leaflet and pod growth rates are the greatest. In
the small leaf varieties the growth and rate curves of leaf-
lets and pods were very similar.

A highly significant correlation was found between the
average maximum growth rates of leaflets and pods when both
groups of varieties were taken together. However, within
each group this correlation became zero. (This means that the
significant correlation was due to group differences; large
leaf varieties having longer peds and the small leaf varie-
ties having shorter pods. If the objective of a breeding
program is to develop a variety with small leaves and long

pods the data analyzed in the present study would not be

66

sufficient and measurements on a genetically-segregating
population would be required.

Leaflet growth rates were positively correlated with
pod number in both large leaf and small leaf groups. Pod
growth rates were negatively correlated with pod number.

The higher the growth rate of pods, the smaller the number

of pods. The simplest explanation is based on competition
for Carbohydrates and proteins between pods which are at
different stages of growth.and the priority of rapidly
developing pods in appropriating the available nutrients.

The correlations between leaflet and pod growth rates and
seed sizes were positive for both groups. This could be
explained on the ground that seed size, the seed being com-
posed mainly of storage leaves or cotyledons, is a reflection
of leaf growth rates. That is, leaves whether photosynthetic,
reproductive (as pods), or storage (as seeds) are regulated
in their growth by a common set of genes due to their homo-
logous nature. In spite of the specific functions of these
organs, the basis of the positive association is strong
enough to be expressed by the positive correlations. This
interpretation requires that the growth rate of a leaflet be
correlated with its mature size. This correlation was in
fact positive and highly significant for both groups of
varieties. Pod growth rates also had a highly significant
correlation with mature pod length in the large leaf group,
but not in the small leaf group. This Correlation was absent

in the small leaf group, probably because all varieties

67

belonging to this group were so similar that there was little
or no variation in pod growth rates and their mature lengths.

In general, leaflet growth rates were positively corre-
lated with yield. This may be interpreted as either the
effect of a favorable environment influencing both yield and
growth rates, or as an indication that high leaflet growth
rates are a sign of plant vigor which in turn results in high
yield.

As far as the interaction between mature leaflet, pod,
and seed sizes is concerned, the correlation coefficients
listed in Table 10 should be taken into consideration. Among
eighteen correlations involving leaflet size, pod size, and
seed size, only three were statistically significant and only
one was high enough (rPZ = .71) to account for 50% of the
variation in seed size. However, all but one of the corre-
lations were positive. The same correlations from other
experiments are presented in Table 11. Again the correla-
tions among the three organs even under different competition
levels were nearly always positive and though relatively high
in magnitude only occasionally significantly higher than zero.
It could be concluded that the effect of common genes regu-
lating growth of these homologous organs, though substantial,
plays a relatively minor role as compared to the effect of
genes regulating specific functions of these organs and the
influence of non-genetic factors. Therefore, the breeder has
a relative freedom that would allow him to select for a

desired combination of leaflet, pod, and seed sizes. This

68

might not be true across the extreme types of these traits,
but certainly the expectation should hold within the limits
of more narrow size combinations. Here, there is enough
flexibility in the develOpmental systems to allow for some
recombination between genes controlling organ sizes. Gener-
ally, the basic correlations attributed to organ homology of
leaflet, pod, and seed by Duarte and Adams (11) were confirmed
in the present study. Correlation patterns previously
described among yield components themselves (1) were also
confirmed in this study. As has been found in many grain
legumes, the correlation of pod number with yield was always
positive and almost always significant, pod number being the

single most important component of yield.

10.

11.

12.

LITERATURE CITED

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7:505-510.

 

Adams, M. W., J. V. Wiersma, and Julio Salazar. 1977.
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cultivars (submitted to Crop Science).

Amer, F. A. and W. T. Williams. 1957. Leaf-area growth
in Pelargonium zonale. Ann. Bot. 21:339-342.

 

Bal, B. S., C. A. Suneson, and R. T. Ramage. 1959.
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Berlamaqui, P. F. 1975" Variation in soybean yield
components in relation to genotype and productivity
level. Ph.D. Thesis, Iowa State University, Ames,
Iowa.

Black, M. and J. Edelman. 1970. Plant Growth. Harvard
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Blackman, V. H. 1919. The compound interest law and
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Brinkman, M. A. 1977. Yield-component analysis of oat
isolines that produce different grain yields. Crop
Science 17:165-168.

Dale, J. E. 1964. Leaf growth in Phaseolus vulgaris.
1. Growth of the first pair of leaves under constant
conditions. Ann. Bot. 28:579-589.

 

Donald, C. M. 1968. The breeding of cr0p ideotypes.
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Duarte, R. A. and M. W. Adams. 1972. A path-coefficient
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APPENDICES

Appendix A

Measurements of leaflet and pod lengths in centimeters

taken in 48-hour intervals

R1: First replication

R2: Second replication

72

73

 

 

 

 

- ~.HH - ~.mm - ~.Hm - m.mm - m.ea - m.m. - m.a - «.4 - ~.~ m m
m.m H.mm m.m m.mH m.m H.mH m.m A.NH e.m e.~H A.a H.em e.e m.a «m4 m.4 m.~ m.m a m
- e.mH - e.eH - e.em - m.ee - H.mH - m.m - m.a - e.m - m.~ m 4
m.m e.ma H.m e.mm m.m e.ma m.m N.HH 4.A m.oa 4.e m.m e.4 A.m e.m m.~ o.m e.m a 4
m.m - m.m - m.m - e.m - e.m - m.m - m.e - a.m - m.H - N m
m.ea m.mm m.m~ m.mm m.em a.em e.mm m.em m.om m.om m.m o.m e.e m.e m.4 e.4 ~.~ m.~ a m
- ~.Hm - ~.me - ~.mm - H.mm - e.mm - e.m - 4.5 - m.4 - e.~ m m
M.NH I n.~a I ”.ma I a.~a I a.aa I 0.0 I m.m I m.N I 5.H I a N
m.m e.ee m.m e.eH e.m m.mm m.m e.eH ~.m m.m 4.m a.m m.e A.“ m.m 4.m m.a A.H m H
- ~.mm - N.mH - ~.mm - m.~m - m.~m - e.mm - a.m - 4.4 - ~.m a H
mm mm mm mm mm mm mm Am mm Hm mm Hm mm mm mm Hm Nm Am m.“m
em 4m 2. S m e e oN w
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e.45 e.55 e.45 e.55 e.45 e.55 5.45 5.55 5.45 m.55 e.55 m.e5 e.m 5.5 5.5 5.4 5.5 m.5 5 m
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- e.55 - e.55 - e.55 - 5.55 - e.55 - 5.m - m.5 . 5.4 - 5.5 5 5

55 5.5 5m 5m 5m 5m 55 55.5 5m 5m 5m 5m 5m 5m 5m 5m 5m 55 mm
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5.0 5.0 5.0 5.0 0.0 5.5 5.0 e.0 0.5 5 m

0.0 0.0 0.0 5.0 0.0 5.5 5.0 0.0 5.5 5

0.0 0.0 0.0 e.0 0.0 e..0 0.5 0.0 0.5 4.0 0.5 0.0 0.0 0.0 0.0 0.0 4.0 0.0 0
5.0 0.0 5.0 0.0 5.0 0.0 0.0 0.0 4.0 0.5 0.5 5.5 5.0 0.0 e.4 0.4 0.0 5.0 40
0.0 0.0 0.0 0.0 0.0 0.0 5.0 0.5 5.0 0.5 0.0 0.5 5.e 0.e 0.4 5.4 5.0 0.0 0.
m

4.0 5.0 4.0 5.0 4.0 5.0 0.0 0.0 5.0 0.0 0.5 5.5 5.e 5.e 0.0 5.4 0.0 5.0 5

0.5 0.5 0.5 0.5 0.5 0.5 5.5 0.5 e.5 5.5 5.5 5.5 0.0 0.0 5.4 0.4 5.0 5.0 5
5m 50 50 50 50 .50 50 50 50 50 .50 50 50 50 50 50 50 50 4A
- u m
2 45 55 05 0 e 4 5 0 w m.
N.m

55000 0055 e

 

.0000 40-5002 0:0 00-m>0z .55-< 05005

-Appendix B

Values, by replication, of yield and yield-related character-

istics.

Large leaf group: Charlevoix, Manitou, Michigan Improved

Cranberry, Cranberry 8247, Swedish Brown

Medium leaf group: Yellow Eye, Great Northern, Merithew,

Perry Marrow, Red Mexican

Small leaf

X = Number
Y = Number
2 = Single
w 0

L 0

B

P

group: Navy-01, Navy-02, Navy-03, Navy-04, Navy-05

of pods per one meter of plot.
of seeds per pod.

seed weight in grams.

Seed yield in grams per one meter of plot.
Leaflet length in centimeters.
= Leaflet width in centimeters.

= Pod length in centimeters.

85

86

Table B-1. Test 23, East Lansing.

 

Variety Rep. X Y Z W L P

 

Charlevoix 1 ‘85 3.55 .4441 134 11.73 13.5
66 4.00 .4735 125 9.83 13.5
Manitou 100 3.25 .4862 158 12.24 12.3
93 3.40 .5471 173 11.92 12.8
Michigan 104 3.25 .4320 146 10.01 10.6
Improved -
Cranberry 151 3.00 .4636 210 11.00 10.8
Cranberry 116 3.50 .3842 156 11.05 10.4
8247 105 3.40 .4118 147 11.53 10.1
Swedish 167 4.00 .3234 216 11.64 410.1
Brown 116 3.50 .3744 ' 152 10.98 8.6
Yellow 109 4.05 .3760 166 12.51 10.3
Eye 122 4.00 .3873 189 12.01 10.0
Great 179 4.50 .2843 229 9.41 10.5
Northern 167 4.65 .2820 219 10.02 10.8
Merithew 140 4.00 .2750 154 11.09 10.6
142 4.55 .2430 157 11.49 10.6
Perry 137 3.80 .3150 164 8.97 10.1
Marrow 126 3.75 .2942 139 9.03 10.0

 

Table B-1 (Cont'd.)

87

 

 

Variety Rep. X Y Z W
Navy - 01 285 .50 .1146 147 8.09
373 4.95 .1159 214 8.93
Navy - 02 1 245 5.05 .1568 194 8.74
2 254 5.15 .1384 181 9.41
Navy - 03 319 5.00 .1404 224 8.60
246 5.10 .1227 154 8.67
Navy - 04 214 4.95 .1293 137 8.77
240 4.80 .1441 166 8.97
Navy - 05 248 5.20 .1279 165 8.93
244 4.60 .1488 167 8.84

 

88

 

 

Table B-2. Test 24, Gratiot County.
Variety Rep. X Y Z W B
1 75 4.30 .3411 110 11.90 9.54 11.1
Charlevoix 2 93 4.90 .3292 150 11.50 8.82 12.0
3 111 4.95 .2512 138 11.80 10.08 11.3
4 100 4.30 .3628 156 12.96 9.58 11.2
1 76 4.05 .4191 129 12.72 9.92 11.3
Manitou 2 92 4.20 .4063 157 13.00 9.34 11.2
3 89 4.30 .4547 174 13.12 10.00 10.9
4 74 4.55 .3475 117 11.32 9.04 11.4
Michigan 1 98 3.70 .3447 125 9.22 7.32 8.3
Improved 2 135 4.20 .3316 188 10.34 7.76 8.6
Cranberry 3 180 3.75 .3467 234 11.50 8.32 7.8
4 139 4.15 .3328 192 9.24 7.38 8.8
1 133 4.10 .2861 156 12.46 9.60 8.8
Cranberry 2 103 3.35 .2753 95 11.16 9.40 8.1
8247 3 184 3.20 .3601 212 12.20 10.56 9.3
4 159 4.00 .2596 163 10.56 8.12 9.8
l 111 4.25 .3052 144 12.70 8.88 8.7
Swedish 2 102 3.70 .3233 122 11.68 9.22 8.7
Brown 3 113 4.70 .2957 157 11.72 9.38 9.0
4 128 4.60 .3108 183 12.68 10.52 9.1

 

Table B-2 (Cont'd.)

89

 

 

Variety Rep. X Y Z W B
l 101 4.95 .2760 138 11.18 9.04 9.5
Yellow 2 90 5.20 .2692 126 11.50 8.06 9.3
Eye 3 95 4.55 .3008 130 12.24 9.04 8.8
4 103 4.60 .3039 144 11.10 8.46 9.2
l 136 6.50 .1912 169 9.72 7.68 10.7
Great 2 153 5.60 .1926 165 9.52 8.12 9.4
Northern 3 114 5.70 .2355 153 9.22 7.78 .8
4 168 5.60 .2338 220 9.98 8.28 .7
l 175 4.90 .1644 141 10.44 8.16 9.4
Merithew 2 169 5.15 .1792 156 11.16 9.10 10.0
3 154 4.25 .2108 138 10.56 8.76 9.0
4 192 4.00 .2135 164 11.02 8.90 9.5
1 106 4.60 .2584 126 9.34 8.08 9.7
Perry 2 130 4.35 .2140 121 9.18 8.20 9.5
Marrow 3 209 4.60 .2268 218 10.64 9.40 9.5
4 98 4.25 .2617 109 9.50 8.70 9.4
1 135 5.00 .1556 105 8.58 7.20 8.8
Red 2 138 5.05 .2353 164 8.44 7.06 8.3
Mexican 3 184 5.10 .2312 217 10.04 8.54 8.5
4 127 5.10 .2023 131 7.74 6.44 8.5

 

Table B-2 (Cont'd.)

90

 

 

Variety Rep. X Y Z W L B
l 238 5.15 .0922 113 8.34 6.54 7.2
Navy 01 2 187 5.45 .0834 85 8.40 6.88 7.2
3 166 5.40 .0814 73 7.96 6.82 7.0
4 372 4.25 .1271 201 10.02 8.10 6.8
1 247 5.20 .1098 141. 8.95 7.15 8.3
Navy 02 2 259 5.30 .1020 140 9.40 8.00 8.1
3 341 5.10 .1219 212 9.34 7.34 8.4
1 189 5.80 .0930 102 8.06 6.48 7.5
Navy 03 2 184 5.35 .0853 84 8.86 6.86 7.7
3 197 5.45 .0913 98 9.14 7.46 7.7
4 230 5.10 .1014 119 9.14 7.66 8.2
1 274 5.15 .1176 166 9.78 7.50 7.7
Navy 04 2 206 5.60 .1075 124 9.94 7.64 7.7
3 226 5.35 .0926 112 8.84 6.98 8.4
4 232 6.20 .0820 118 8.60 7.04 7.6
l 208 5.00 .1221 127 9.20 7.70 6.
Navy 05 2 253 5.60 .1172 166 9.02 7.52 7.
3 260 5.35 .0906 126 9.00 7.20 7

 

91

 

 

Table B-3. Test 25A, Gratiot County.
Variety Rep. X Y Z W L B P
1 78 5.35 .2924 122 10.52 8.36 12.6
Charlevoix 2 74 4.35 .2982 96 10.32 8.48 11.4
3 77 4.65 .3966 142 11.48 8.94 12.3
4 90 4.20 .3624 137 10.66 8.28 11.5
1 67 4.90 .3168 104 10.92 8.94 11.4
Manitou 2 121 4.25 .3734 192 10.56 7.60 11.8
3 102 4.15 .4063 172 12.04 9.70 11.7
4 86 4.50 .4186 162 11.80 8.88 11.9
Michigan 1 108 3.40 .3649 134 9.04 6.82 7.9
Improved 2 102 4.05 .2953 122 8.12 6.54 8.5
Cranberry 3 123 4.20 .3136 162 9.82 7.18 8.8
4 139 2.95 .4268 175 8.46 7.24 8.5
1 148 4.00 .1926 114 10.76 9.54 9.0
Cranberry 2 132 4.45 .2554 150 11.38 10.20 9.8
8247 3 118 4.45 .2780‘ 146 9.90 8.82 9.6
4 108 4.10 .3794 168 11.64 9.30 9.7
1 11.18 8.46
Swedish 2 119 4.10 .3054 149 10.90 8.44 8.3
Brown 3 110 4.05 .3075 137 10.70 9.34 8.2
4 110 3.75 .3103 128 11.38 8.74 7.8

 

Table B-3 (Cont'd.)

92

 

 

Variety Rep. X Y Z W B
1 96 4.35 .2514 105 9.38 7.32 8.3
Yellow 2 98 4.95 .2371 115 10.74 8.28 9.0
Eye 3 106 4.90 .2638 137 11.20 8.84 8.8
4 131 4.20 .2781 153 10.94 8.00 8.1
l 121 5.40 .1714 112 8.34 7.12 9.1
Great 2 112 5.85 .1480 97 8.12 7.28 9.4
Northern 3 142 5.70 .2335 189 9.38 7.96 8.6
4 157 5.60 .2104 185 10.00 8.90 8.6
l 136 4.15 .1984 112 9.40 8.68 8.8
Merithew 2 227 4.00 .1971 179 10.76 9.10 9.3
3 154 5.15 .2307 183 10.86 9.12 9.3
4 160 4.25 .2176 148 9.88 8.76 8.6
1 108 4.75 .2203 113 8.72 7.54 9.6
Perry 2 118 4.40 .2619 136 8.82 7.76 9.2
Marrow 3 178 4.55 .2482 201 8.60 8.78 ,9.4
4 120 4.20 .2401 121 9.88 8.88 9.1
l 125 4.55 .2286 130 7.92 6.72 8.2
Red 2 131 5.30 .1700 118 8.02 7.08 8.4
Mexican 3 227 4.60 .2078 217 8.20 7.64 8.1
' 4 149 5.25 .1969 154 8.04 7.32 8.4

 

Table B-3 (Cont'd.)

93

 

 

Variety Rep. X Y Z W B
1 185 4.95 .0841 77 7.56 6.38
Navy 01 2 220 5.60 .0820 101 7.50 6.20
3 323 4.60 .1137 169 8.80 7.36
4 281 5.05 .0712 101 8.32 7.50
1 156 5.50 .1084 93 8.12 6.72
Navy .02 2 236 5.45 .1026 132 9.06 7.76
3 242 4.90 .1214 144 9.30 7.86
4 243 5.00 .1374 167 9.96 7.94
1 128 6.00 .0794 61 7.88 6.32
Navy 03 2 236 5.40 .0949 121 8.70 6.88
3 230 5.10 .1228 144 8.76 6.86
4 231 5.35 .1044 129 9.96 8.04
1 206 5.30 .0934 102 9.28 7.88
Navy 04 2 165 6.00 .0889 88 8.36 6.64
3 276 5.30 .1039 152 9.84 7.64
4 215 5.40 .1068 124 9.44 7.66
1 248 6.25 .0903 140 8.08 6.66
Navy 05 2 211 5.30 .1082 121 8.24 7.10
3 241 5.40 .1322 172 7.88 7.02
4 204 5.55 .1025 116 8.40 6.62

 

94

 

 

Table B-4. Test 25B, Gratiot County.
Variety Rep. X Y Z W L B P
3A 84 3.90 .4121 135 11.48 8.94 10.3
Charlevoix 3B 76 "4.65 .3594 127 11.48 8.94 12.4
4A 81 4.15 .2737 92 10.66 8.28 11.7
4B 64 5.45 .2985 104 10.66 8.28 12.5
3A 71 4.10 .4328 126 12.04 9.70 11.4
Manitou 3B 66 3.95 .4526 118 12.04 9.70 11.7
4A. 65 4.00 .4385 114 11.80 8.88 11.3
4B 48 4.25 .4412 90 11.80 8.88 11.7
Michigan 3A 82 3.80 .3113 97 9.82 7.18 8.
Improved 3B 106 3.80 .3401 137 9.82 7.18 8.
Cranberry 4A - - - - 8.46 7.24 -
4B 89 4.55 .2914 118 8.46 7.24 10.0
3A 101 4.00 .3267 132 9.90 8.82 9.3
Cranberry 3B 110 4.35 .2564 127 9.90 8.82 9.7
8247 4A 107 4.35 .2621 122 11.64 9.30 9.8
4B 92 4.75 .2838 124 11.64 9.30 10.3
3A 105 4.80 .2837 143 10.70 9.34
Swedish 3B 110 4.25 .3016 141 10.70 9.34
Brown 4A 94 4.30 .2845 115 11.38 8.74
4B 99 3.60 .2862 102 11.38 8.74

 

Table B-4 (Cont'd.)

95

 

 

Variety Rep. X Y Z W L B
3A 101 4.80 .2702 131 11.20 8.84 9.0
Yellow 3B 108 4.90 .2759 146 11.20 8.84 8.9
Eye 4A 79 4.60 .2889 105 10.94 8.00 9.3
4B 102 4.30 .2668 117 10.94 8.00 8.2
3A 130 6.10 .1740 138 9.38 7.96 9.8
Great 3B 130 6.06 .1373 108 9.38 7.96 10.1
Northern 4A 94 5.65 .2146 114' 10.00 8.90 9.5
4B 102 5.35 .1942 106 10.00 48.90 10.2
3A 152 4.70 .2044 146 10.86 9.12 9.6
Merithew 3B 157 4.30 .2089 141 10.86 9.12 9.5
4A 115 4.80 .1884 104 9.88 8.76 9.5
4B 118 4.80 .2048 116 9.88 8.76 9.5
3A 138 4.10 .3005 170 8.60 8.78 9.6
Perry SB 110 4.50 .2869 142 8.60 8.78 9.4
Marrow 4A 63 3.60 .2778 63 9.88 8.88 8.2
4B 68 3.90 .2715 72 9.88 8.88 8.5
3A 151 4.65 .1894 133 8.20 7.64 7.5
Red 3B 146 5.05 .1926 142 8.20 7.64 8.6
Mexican 4A 79 5.10 .1812 73 8.04 7.32 8.3
4B 84 4.10 .2236 77 8.04 7.32 8.0

 

Table B-4 (Cont'd.)

96

 

 

Variety Rep. X Y Z W B
3A 188 5.50 .0890 92 8.80 7.36 7.0
Navy 01 3B 153 5.25 .0921 7 8.80 7.36 7.1
4A 189 6.30 .0705 84 8.32 7.50 7.7
4B 159 5.30 .0783 66 8.32 7.50 7.1
3A 195 6.15 .0859 103 9.30 7.86 8.5
Navy 02 3B 209 5.30 .1065 118 9.30 7.86 8.8
4A 143 6.00 .1096 94 9.96 7.94 7.9
4B 116 5.50 .1082 69 9.96 7.94 6.7
3A 188 5.50 .1006 104 8.76 6.86 8.0
Navy 03 3B 154 5.45 .1048 88 8.76 6.86 7.7
4A 144 5.60 .0980 79 9.96 8.04 8.2
4B 134 5.25 .0981 69 9.96 8.04 8.1
3A 181 5.35 .0898 87 9.84 7.64 7.6
Navy 04 3B 188 5.90 .0875 97 9.84 7.64 8.2
4A 127 5.60 .1069 76 9.44 7.66 8.0
4B 110 4.90 .0946 51 9.44 7.66 7.6
3A 201 5.60 .1066 120 7.88 7.02 7.0
Navy 05 3B 239 5.55 .0973 129 7.88 7.02 7.2
4A 150 5.30 .0956 76 8.40 6.62 7.6
4B 143 4.80 .0962 66 8.40 6.62 7.5