Title: Inheritance of photoperiod-induced flowering and a glabrous-stem maker gene in Aeschynomene americana /
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Title: Inheritance of photoperiod-induced flowering and a glabrous-stem maker gene in Aeschynomene americana /
Physical Description: v, 103 leaves : ill. ; 28 cm.
Language: English
Creator: Deren, Christopher W., 1949-
Publication Date: 1986
Copyright Date: 1986
 Subjects
Subject: Aeschynomene americana   ( lcsh )
Agronomy thesis Ph. D
Dissertations, Academic -- Agronomy -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1986.
Bibliography: Bibliography: leaves 100-102.
Statement of Responsibility: by Christopher W. Deren.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00099328
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000897040
notis - AEK5687
oclc - 015523240

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INHERITANCE OF PHOTOPERIOD-INDUCED FLOWERING AND A
GLABROUS-STEM MARKER GENE IN Aeschynomene americana

















BY

CHRISTOPHER W. DEREN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY




UNIVERSITY OF FLORIDA


















ACKNOWLEDGMENTS


Several people have helped me carry out this project. I thank my

advisor, Dr. Quesenberry, for providing assistance so that I could

study here at Florida. He has given very generous support and been an

active participant throughout the program. My committee members, Drs.

Horner, Popenoe, Moore, and Lyrene, have each contributed from their

own areas of expertise, providing valuable opinions from different

perspectives. Finally, I thank Dr. Kretchner, Tom Wilson, and Maude

Macquarrie for all their help at Ft. Pierce.


















TABLE OF CONTENTS


PAGE

ACKNOWLEDGMENTS...... ......................................... ii

ABSTRACT..... ................ .................................... iv

CHAPTERS

I INTRODUCTION..... ........................... ............ 1

II GLABROUS/PUBESCENT STEM: A SEEDLING MARKER GENE......... 4

Introduction............................................... 4
Materials and Methods ..................................... 4
Results and Discussion ................................. 6
Conclusion................................................ 9

III INHERITANCE OF PHOTOPERIOD INDUCED FLOWERING............ 12

Introduction............................... .............. 12
Literature Review of Photoperiod Induced Flowering ....... 12
Materials and Methods.......... ........................ 16
Results and Discussion. ........................... ....... 22
Photoinsensitive Allele ........... ...................... 22
Analysis of Crosses 55 x 206 and 232 x 206............. 37

IV CONCLUSION.................................... ............ 79

APPENDICES

A FREQUENCY DISTRIBUTIONS OF 55 x 206 AND 232 x 206........ 82

B CHI-SQUARE CONTINGENCY TABLES OF 55 x 232 AND 232 x 206
F2 ............................. .......................... 88

C CHI-SQUARE CONTINGENCY TABLES OF BACKCROSSES............. 94

LITERATURE CITED......................... ..... ................. 100

BIOGRAPHICAL SKETCH...................... ....................... 103


















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

INHERITANCE OF PHOTOPERIOD-INDUCED FLOWERING AND A
GLABROUS-STEM MARKER GENE IN Aeschynomene americana

By

CHRISTOPHER W. DEREN

December 1986

Chairman: K. H. Quesenberry
Major Department: Agronomy

A study of the inheritance of photoperiod-induced flowering and a

glabrous/pubescent stem character was conducted on the tropical forage

legume Aeschynomene americana L. A pubescent, photoperiod-insensitive

line and a glabrous, late-flowering, photoperiod-sensitive line were

crossed with two pubescent lines, each of which was photoperiod

sensitive and flowered at about mid-range. Parents, Fl, F2, and

reciprocal backcrosses of each cross were grown at two Florida

locations, Gainesville and Ft. Pierce. Approximately 2000 plants were

planted at each location in a randomized complete block design with

five replications. Individual plants were classified as pubescent or

glabrous, and date of first flowering was recorded. Analysis of the

pubescent x glabrous crosses revealed that this trait is controlled at

one locus with a glabrous allele completely dominant over a pubescent

allele. In crosses of the photoperiod-insensitive parent x the two

mid-range, photoperiod-sensitive parents, sensitivity to photoperiod

was completely dominant to insensitivity in a one locus, two allele













system. Mather and Jinks's scaling test and method of partitioning

components of variation were employed in initial analysis of the

crosses between the two mid-range parents and the late flowering line.

The data fit an additive-dominance model with most genetic variance

being additive. After further analysis with Powers's partitioning

method, it was concluded that a completely additive genetic system

involving two loci, each with two alleles, was primarily responsible

for induction of flowering by photoperiod. Expression appeared to be

modified by minor genes and environment.


















CHAPTER I
GENERAL INTRODUCTION


Much of the world's crop production is concentrated on a

relatively small number of plant species such as wheat, rice, maize,

and beans. But as demand for agricultural products increases, the

potential contributions of many of the countless other crop plants

that are cultivated, including those in the tropics, are being more

intensively investigated. Associated with increased interest in

evaluation and conservation of cultivated germplasn is the parallel

enterprise of collecting and evaluating wild species for potential use

as domesticated plants. Most agricultural research has been conducted

on temperate climate crops; research on management and improvement of

many tropical species is, by comparison, an untouched area of study.

Due to its unique geography and climate, Florida is well

suited both for the study of tropical/subtropical plants and for their

inclusion in local agricultural production. A good example of this is

the forage research presently being carried out in the state. As a

ma3or beef producer, Florida grows a substantial amount of forage,

making it one of the state's major agronomic crops. Yet the poor

nutritive quality of native range and pastures has prompted interest

in the possibility of using various exotic tropical plants as forage

resources. One such plant is Aeschynomene americana L., also commonly

known by its genus name aeschynomene or as American jointvetch.













Aeschynomene is a woody tropical/subtropical legume

distributed throughout much of Central and South America as well as

the eastern gulf coastal states of the U.S. (24). Although it is

considered undomesticated, in Florida the plant is grown as a

reseeding annual forage to supplement grass pastures which are of low

quality during late summer and fall (9). Aeschynomene's main

attributes for Florida are its relatively high nutrient quality, and

the fact that it is particularly well adapted to the periodically

flooded flatwoods soils that are common in the cattle producing areas

of the state (1,9,15). Recognizing the potential of aeschynomene,

forage workers have recently begun collecting and evaluating plant

introductions from diverse origins, with the objective of developing

an improved cultivar.

Development of a cultivar from a wild plant is both exciting

for its potential and risky due to the unknown genetic nature of the

material. Aeschynomene has many characteristics that show promise for

its use as a forage, yet genetic studies are entirely lacking.

Although a breeding program does not by any means require genetic

definition of every plant character being manipulated, understanding

the genetics of some major traits can facilitate development of

prudent and efficient breeding plans and thereby help avoid wasted

effort. In addition, a knowledge of the genetics of certain

characters can aid in defining the genetics of other traits.

Initial characterization of aeschynomene accessions showed a

great deal of variation in several traits, including growth habit,

plant size, pubescence, flower color, nematode tolerance, and













flowering response to photoperiod (23). The latter is of particular

concern in Florida and other subtropical areas where annual

fluctuation of daylength can be great. As mentioned, aeschynomene is

grown as a reseeding annual; thus ample seed must be produced to

establish the subsequent year's crop. However, flowering drastically

reduces foliage production, so ideally it must take place as late as

possible in the growing season to assure maximum forage yield yet soon

enough before the first killing frost to provide the seed necessary

for the following year's stand. An understanding of the inheritance of

photoperiod induced flowering can aid the breeder in determining if

and how he can manipulate this character to maximize forage

production.

Another character of interest was the glabrous/pubescent stem.

Most aeschynomene lines are pubescent, yet one was distinctly

glabrous. While no agronomic benefit can be attributed to either

condition, the interest in this character is in its potential value as

a marker gene.

After traits of practical importance were identified, the

following specific objectives of this research were formulated:

1) Attempt to define the genetics of inheritance of the

glabrous/pubescent stem character.

2) Investigate the inheritance of photoperiod-induced

flowering in aeschynomene.


















CHAPTER II
GLABROUS/PUBESCENT STEM: A SEEDLING MARKER GENE


Introduction


Simply inherited, easily discerned marker genes can be valuable

in a variety of genetic studies, ranging from biochemical genetics to

practical plant breeding. For the breeder, a seedling marker can be

especially useful in that it facilitates early classification of

phenotypes, thus eliminating the necessity of growing plants to

maturity before evaluation. One objective of our preliminary work on

Aeschynomene americana genetics conducted in Florida, was to identify

the inheritance of a glabrous/pubescent stem character that appeared

to be simply inherited and potentially useful as a seedling marker

gene.


Materials and Methods


In 1985 two pubescent accessions identified as 55 and 232 were

grown in the greenhouse and crossed with the glabrous accession 206

(Table 2-1). Single Fl plants, one from each of the two crosses, were

grown in the greenhouse, allowed to self-pollinate to set F2 seed, and

were also backcrossed to both of their respective parents. In the

summer of 1985 seed from the P1, P2' Fl' F2' BCpl' and BCp2

generations of each cross were planted in pet pellets. Three week old

seedlings, 15 to 20 cm high, were evaluated for the presence or









5


Table 2-1. Accessions of Aeschynomene americana used as parents.


Accession no. Phenotype Origin


55 pubescent Florida

206 glabrous Panama

232 pubescent Brazil













absence of stem pubescence. Next, samples of plants were randomly

selected from each generation and planted into the field where they were

again observed for pubescence as mature plants of about 150 days age.



Results and Discussion


Seedlings


The definite classification of a seedling as either pubescent or

glabrous is difficult until it is about 15 to 20 cm high or at the

fifth to seventh node stage of growth. The results of classification

at this growth stage are given in Table 2-2.

All offspring arising from self-pollination of the pubescent

parent accessions 55 and 232 were pubescent, and all progeny from the

selfed glabrous 206 plant were glabrous. The Fls were all glabrous in

both the 55 x 206 and 232 x 206 crosses, evidence that glabrousness is

completely dominant. However, in a few plants which were almost

completely glabrous, a very few hairs could be seen on the distal ends

of some branches, frequently in a row running along the axis of the

stem. These plants were noted for the possibility of their

constituting an intermediate class.

The F2 generations of both crosses were observed to segregate

rather distinctly into a larger glabrous class and a smaller pubescent

class. Again, in evaluation of the F2, there was some incidence of

what appeared to be glabrous plants with a very low level of

pubescence. The degree of this was noted as above for the possibility

of intermediate classes. When these plants were totaled as an

intermediate class, however, the results were inconclusive. When they












Table 2-2. Seedling data and chi-squares of glabrous/pubescent stem
character in Aeschynomene americana.


No. No.
glabrous pubescent Observed Expected
Generation Pedigree plants plants ratio ratio X p


Parent 55 0 278 no segregation -*

Parent 206 153 0 no segregation

Parent 232 0 192 no segregation

F1 55x206 43 0 no segregation

F2 55x206 201 67 201:67 201:67

BCPI (55x206)x55 47 49 47:49 48:48 0.042 0.9-0.8

BCp2 (55x206)x206 96 0 no segregation

F1 232x206 191 0 no segregation

F2 232x206 170 65 170:65 176:59 0.815 0.4-0.3

BCpI (232x206)x206 75 64 75:64 69.5:69.5 0.870 0.4-0.3

BCp2 (232x206)x232 100 0 no segregation



*For generations that did not segregate or segregated exactly as expected
no chi-square was calculated.













were pooled with the totally glabrous group, there was a 3:1

segregation of glabrous to pubescent. This was true for both the 232

x 206 F2 and the 55 x 206 F2; data of the latter cross fit the

expected ratio exactly. The data for 232 x 206 also showed a good

fit, with a chi-square probability of 0.30 to 0.40.

Backcrosses behaved as expected based on the performance of

the F1 and F2 generations. In backcrosses to the glabrous parent (55

x 206) x 206 and (232 x 206) x 206, all progeny were glabrous, but in

these populations too there were some plants with very low levels of

pubescence near the branch tips. The backcrosses to the pubescent

parents, (55 x 206) x 55 and ( 232 x 206) x 232, segregated in a 1:1

ratio, again with some glabrous plants showing some tip pubescence.

The (55 x 206) x 55 backcross fit a 1:1 ratio almost exactly. The

chi-square for (232 x 206) x 232 also showed good fit, with a

probability of 0.30 to 0.40.


Mature Plants


Smaller numbers of mature plants were classified in the field

after 150 days to determine if the seedling classification would be

similar to that of mature plants. This was found to be so. In the

mature plants, those glabrous types with some pubescence by the branch

tips were observed more closely than in the seedlings. These plants

were then classified as follows: G was completely glabrous; G1 had

very few hairs (less than 10) near the tip; and G2 had up to 100 hairs

scattered on the branch but still far fewer than a true pubescent type

of plant would have. When classified thus, no general trend or













modality was obvious. However, when these subcategories of

glabrousness were ignored and all these plants were classified simply

as glabrous, very distinct ratios were obvious, just as in the

seedling data. The Fls were all glabrous, and the F2s segregated at

3:1 glabrous to pubescent. The backcrosses to the glabrous parent

were all glabrous and the backcrosses to the pubescent parent

segregated at 1:1. Chi-square values and probabilities are listed in

Table 2-3.



Conclusion


From the data on both seedlings and mature plants, it appears

that there is a simple one gene-two allele system controlling the

glabrous/pubescent character, where the glabrous allele, Gl, is

completely dominant over the recessive pubescent allele, gl. There

does appear to be, however, variable expressivity of this character

which results in some plants of the glabrous phenotype having a very

slight pubescence, but this is so minimal that it does not interfere

with plants being classified simply and quickly as pubescent or

glabrous. Therefore, from a practical standpoint, this expressivity

should not be a problem in using the glabrous/pubescent character as a

marker gene in either seedlings or mature plants.

From a theoretical standpoint, this characteristic is

something to ponder. Although there are some other glabrous

aeschynomene accessions, they are uncommon (24). Since they are of

such low frequency in the specie, they could be termed mutant. Now it

is sometimes said that all or most mutations are recessive, yet













Table 2-3. Mature plant data and chi-squares of glabrous/pubescent stem
character in Aeschynomene americana.


No. No.
glabrous pubescent Observed Expected
Generation Pedigree plants plants ratio ratio 2 P


F1 55x206 19 0 no segregation

F2 55x206 113 35 113:35 111:37 0.144 0.7

BCp1 (55x206)x55 26 28 26:28 27:27 0.074 0.8-0.7

BCP2 (55x206)x206 74 0 no segregation

F1 232x206 50 0 no segregation

F2 232x206 108 38 108:38 109.5:36.5 0.082 0.8-0.7

BCpl (232x206)x206 70 0 no segregation

BCp2 (232x206)x232 32 43 32:43 37.5:37.5 1.613 0.3-0.2



*For generations that did not segregate or segregated exactly as expected,
no chi-square was calculated.









11


here is an example of a dominant mutant, and it is of low frequency.

From our observations, the glabrous plant does not seem to be

particularly favored by cattle or insects; herbivory seems identical

to that on the pubescent plants. Perhaps geographic isolation has

kept the glabrous types from becoming more prevalent, but we have no

information on this. One could speculate any number of reasons for

glabrousness being uncommon, but nevertheless, its peculiarity lies in

its being a dominant mutant allele.



















CHAPTER III
INHERITANCE OF PHOTOPERIOD-INDUCED FLOWERING


Introduction


As already outlined in the general introduction, several

aeschynomene accessions appeared to be induced to flower by

photoperiod. In aeschynomene, as in so many other crops, the timing

of flowering can be crucial to yield. To maximize forage production,

flowering must be delayed as long as possible, yet still occur at

least five weeks before frost to allow ample seed set. To investigate

the genetics of flowering, a study employing four parent lines was

conducted from 1983 through 1985, culminating in a field experiment at

two locations involving approximately 4000 plants.


Literature Review of Photoperiod-Induced Flowering


Since there are virtually no genetic studies published on

Aeschynomene, there is little work to refer to for this investigation.

On the other hand, studies of the flowering response to photoperiod in

other papilionaceous legumes are extensive and can indicate the

various modes of inheritance of this character, as well as possible

methodologies for experimental design and analysis. Examples of

photoperiod induced flowering in Pisum, Phaseolus and Vigna are

reviewed below.













Flowering in Pisum


Control of flowering response in Pisum appears to vary from

readily identifiable ma]or genes to polygenic systems, depending on

the cultivar and environment. Watts et al. employed Jinks's

regression of the parent-offspring covariance (Wr) on the variance

(Vr) to test the stability of flowering response of Pisum sativum

under what he hypothesized as polygenic control (32). He concluded

that the genetic system was primarily additive in effect, with

dominance insignificant. No major genes were identified.

A similar investigation by Snoad and Arthur (26) utilized seven

pea cultivars, which were crossed in a diallel and analyzed by various

methods as described by Mather and Jinks (14). Conclusions from these

analyses were in agreement that dominance was unimportant in the

genetic system controlling flowering. For the cultivars studied, this

character appeared to be controlled entirely by a simple additive

system.

Snoad and Arthur performed another experiment of similar design

but included primitive and wild Pisum accessions in the diallel (27).

Since many cultivars may have been developed from a relatively narrow

genetic base, this study's inclusion of wild Pisum afforded an

opportunity to investigate flowering response in a wider segment of

the genome. And, as might be expected, different genetic mechanisms

were observed in this set of data. Early flowering resulted from an

accumulation of dominant alleles, in contrast to the conclusion

reached in the study of seven cultivars mentioned above. Thus, there













was strong evidence of more than one genetic system controlling early

flowering in peas.

A more complex genetic system was elucidated by I.C. Murfret

(16,17,18). His work identified loci, alleles and their interactions.

Relationships involving major genes, dominance, additivity, epistasis,

and even pleiotrophy were described. Dominance was definitely

important in some systems. Significantly, it was emphasized that what

had at first appeared to be quantitatively inherited was actually

under qualitative genetic control. Choice of appropriate

environmental conditions, large enough populations and following a

cross for a number of generations made it possible to recognize and

identify major gene systems.

One may conclude from the extent and number of studies of

flowering in Pisum that there are a series of genetic systems

influencing expression of this character, ranging from quantitative

inheritance to identifiable major genes. Therefore, it would be

difficult to describe a general genetic model for flowering in the

genus, since the hypothesized models frequently vary according to the

lineage of the crosses. These genetic systems may indeed be related,

but information at this time does not allow for development of a

single model that encompasses all described inheritance.


Flowering in Phaseolus


Inheritance of flowering response to photoperiod in beans is

similar to that of Pisum in that there seems to be a number of systems

ranging from simple inheritance to polygenic (31). And, like peas,













expression of flowering in Phaseolus is sometimes modified by

environment.

By using growth chambers, the effect of temperature on flowering

response in Phaseolus vulgaris was investigated by Coyne in Nebraska

(4). High nighttime temperatures interacted with long photoperiod to

greatly delay flowering. Early flowering was found to be determined

by a dominant allele in a monogenic system.

In a different set of crosses involving another set of parents,

Coyne found expression of flowering response was again affected by

temperature. What appeared to be quantitatively controlled at one

location showed more obvious modality in a different environment. In

the latter, late flowering was found to be controlled by two

complementary dominant genes. Such results further illustrate that

identification of genetic systems for flowering may be very dependent

upon the environmental background of the experiment and that

conclusions may hold for only the parents involved in the study, not

the whole genome.


Flowering in Vigna


Interaction of temperature and flowering was evident in mungbean,

Vigna radiata, which is classified as a short-day plant (30). In a

study at Missouri using growth chambers, this interaction was

controlled so that the genetics of flowering could be identified in

crosses between various plant introductions. A dominant or partially

dominant gene for photosensitivity was observed in growth chambers













with photoperiods of 14 hours or greater. It was not expressed in the

field at Missouri or at 12 hour photoperiods in the growth chamber.


Summary


A thorough review of the genetics of flowering was presented by

Murfret (19), so it is unnecessary to attempt to duplicate that work

here. What is of primary interest for our study of aeschynomene is

not the specific genetics controlling flowering in other legumes but

rather what the trends are. From this brief review of Pisum,

Phaseolus, and Viyna we may conclude that with each species there

appears to be a number of different genetic systems governing

flowering. Generalizations are difficult, and conclusions reached for

one set of crosses may not hold true for another, let alone for all

members of the species.

Although polygenic or quantitative inheritance was invoked as an

explanation of some flowering genetics, there were also a number of

major gene systems identified. Since environmental variables,

particularly temperature, greatly influence expression of the

flowering character, a major gene system could be masked as a

quantitative character until adequate environmental background or more

sensitive methods of analysis are employed.


Materials and Methods


Four plant introductions of A. americana were selected for use as

parents in a series of crosses. These parents were chosen for their

collective range of flowering dates at Gainesville, Florida based upon













previous years' observations (Table 3-1). Parent 197 was a very early

(long day) flowering plant with an upright, open growth habit and

distinctively small, purplish-blue flowers. Two mid-range parents, 55

and 232, were not only similar in flowering date but also in flower

color and general growth habit. The fourth parent, P.I. 206 flowered

very late at Gainesville and had a procumbent growth habit, glabrous

stems and large, yellow-orange flowers.

In December 1983, seeds were scarified with sandpaper and

germinated in petri dishes containing moistened filter paper.

Seedlings were then transplanted into 15 cm diameter, black plastic

pots, each filled with a mixture of 50% potting soil and 50% fumigated

field soil. Plants were grown in greenhouses, where they were

fertilized and watered as needed. Observations were made for

uniformity of phenotype within each P.I., based upon various

characteristics such as flower color, plant architecture, pubescence

and general appearance. A single plant from each accession was then

chosen for use as a parent in crossing. All four parent plants were

crossed in a half-diallel, creating six crosses (Table 3-2).

Artificial pollinations were made by emasculating the female plant in

the late afternoon or evening and pollinating these flowers with donor

pollen the next morning. As seeds matured at five to six weeks, they

were harvested, bagged and labelled.

In the winter of 1984-85, seed for the backcross and F2

generations were grown. Seeds of the F1 were germinated and planted

in the manner described above. At least six or more F1 plants from

each cross were observed for various morphological characteristics to













Table 3-1. Aeschynomene accessions used as parents in study of inheritance
of photoperiod-induced flowering.


Flowering date at
Gainesville based on Distinguishing
PI no. Origin initial observations characteristics


55 Florida Late September Prolific foliage; upright;
pubescent stem; pale yellow
flower; yellow pollen

197 Argentina? Before September Very open; upright; sparse
foliage; pale green; pubescent;
very small purple flower; white
pollen

206 Panama November Procumbent; glabrous stem; large
(after frost) yellow-orange flower; yellow
pollen

232 Brazil Early October Similar to 55


Argentina was our source of germplasm but location of original collection
is unknown.









19


Table 3-2. Half diallel crossing scheme of aeschynomene parents.



55 197 206 232


55 55x197 55x206 232x55

197 -197x206+ 232x197

206 232x206

232


+
F of 197x206 and the reciprocal 206x197 died as seedlings and so
were eliminated from the experiment.













ascertain that they were indeed Fls and not the result of accidental

self-pollination. Then a single Fl plant was selected from each cross

to be backcrossed to its original parents, which had been maintained

through the summer. Cuttings of the parents and F1s were grown to

provide additional material for crossing. In addition, the F1 were

allowed to self-pollinate, creating seed for the F2 generation. Self-

pollinated seed was also harvested from each original parent plant for

later use in the field. F1 seedlings from the cross between parents

with the most extreme flowering dates, 197x206, died for unknown

reasons on three separate plantings. Thus this cross was eliminated

from the experiment, leaving five crosses for analysis.

On May 10, 1985, seeds from the P P2' FI F2, BCp1' and BCp2

generations of each cross were scarified and germinated. Seedlings

were transplanted three to four days later into commercial peat

pellets. When plants were about six weeks old and roots had protruded

well through the peat pellets, they were transplanted into the field

at two locations, Gainesville and Ft. Pierce, Florida. Gainesville is

at approximately 290N. latitude and Ft. Pierce is at about 27N.

latitude. The soil at the Gainesville site was a well drained

Kendrick fine sand (loamy, siliceous, hyperthermic Arenic Paleudult),

-1
which was fertilized preplant with 30 kg ha of P05 and 60 kg ha

K20. Plants were set out in an randomized complete block design with

five replications. Each replicate was divided into five equal-sized

units, one for each of the five crosses. Within each unit P, p2' F ,

F2, BCp., and BCp2 generations were planted in 16 five-plant rows;

that is, each unit contained a family. Each family unit contained one













row of P1, one row of P2, two rows of Fl, six rows of F2, and three

rows of each backcross generation. Plants were spaced 1.5 m apart

within and between the rows and there were 2 m alleys between units.

Irrigation was applied as needed and weeds were controlled by hand. An

outbreak of Rhizoctonia was noticed in approximately 15% of the field

on about August 12. Benlate was applied twice with a backpack sprayer

and once as a drench at the rate of 1 kg ha-1

The Ft. Pierce location was approximately 320 km south of

Gainesville on Florida's Atlantic coast. The soil there was an

Oldsmar fine sand (sandy, siliceous, hyperthermic family of Alfic

Arenic Haplaquods) and very prone to prolonged flood. Two separate

but adjacent fields were planted. Two replications of the experiment

were established in a field that had been fertilized and used for

growing tomatoes three months earlier. The other three replications

were planted in a field that had been in bahia (Paspalum notatum)

grass for several years and had not been fertilized. Because of

residual fertilizer in the old tomato field, no fertilizer was applied

at the Ft. Pierce location. Layout of plants was a duplicate of that

at Gainesville. Every plant was observed for the day of the year on

which it first flowered; this date was then converted into hours of

daylight for that particular day (7). Separate conversions were done

for each location to account for the difference in duration of

daylight between the two latitudes.

Data that appeared to segregate in distinct classes were analyzed

with chi-square goodness-of-fit. Where inheritance appeared

quantitative, generation means were analyzed with Mather's scaling













test (13,14). Estimates of broad sense heritability, number of

effective factors and components of variance were calculated by Mather

and Jinks's partitioning components of variation method (13,14).

Powers's partitioning method was employed to further analyze these

data (20,21,22). Details of the methods are in the following

discussion.



Results and Discussion


Photoinsensitive Allele


After observing the flowering behavior of these parent accessions

for two seasons both in the field and in the greenhouse, it became

apparent that P.I. 197, initially identified as early flowering, may

be uninfluenced by photoperiod, at least under daylength of 14 hours

or less. As a six to eight week old plant, this accession was

observed to flower in very early July, ]ust after the summer solstice.

Plants of the same age grown in the greenhouse flowered in late

December, just after the winter solstice. Since these two dates are

the maximum and minimum of natural photoperiods, it appears that 197

can flower under any photoperiod after it has reached a certain

physiological maturity at about eight weeks of age. Therefore, for

the daylength conditions in Florida, this parent may be considered

photoperiod insensitive.


Analysis of data


The various generations of crosses between 197 and the two mid-

range parents, 55 and 232, were plotted in frequency distributions













with ten-day intervals constituting a class (Tables 3-3 through 3-8).

Days of the year rather than hours of daylight were the data analyzed

because of our observation that 197 was not induced to flower by

daylength, but rather by age of the plant. It was therefore

unnecessary to convert the days of the year to hours of daylight.

With the data displayed in such a fashion there appeared to be a

definite pattern; this was particularly obvious in the 55 x 197 cross

at Gainesville (Table 3-3). The F flowered at the same time as did

parent 55, an indication of dominance. In the F2 there was a flush of

flowering at about the same time as the flowering of the 197 parent,

then a break, and then a second, larger flush, the majority of which

coincided with the flowering of 55. The backcrosses had the same

trend, with the backcross to 197 having two definite modes and the

backcross to 55 showing no obvious segregation. Similar, but less

distinct, patterns were evident in the other frequency distributions.

Based upon these observations, it appeared that a simple major

gene system may have influenced flowering in crosses 55 x 197 and 232

x 197. A single gene model having a completely dominant allele, Pr,

for photoperiod responsive, and a recessive allele, pr, for

photoperiod insensitivity was tested with a Chi-square goodness-of-fit

statistic. Classes in the segregating populations were not always

perfectly distinct, so they were separated at day 230. All plants

flowering before that date were classified as photoperiod insensitive,

prpr, and those after that date as photoperiod responsive, PrPr, or

Prpr. That particular day was chosen for separating the classes for









24


Table 3-3. Frequency distributions of generations from 55x197 at Gainesville.
Data are numbers of individual plants observed to flower in a
given 10-day period.



Days of year
181 191 201 211 221 231 241 251 261 271 281 291 301
Gen. 190 200 210 220 230 240 250 260 270 280 290 300 310 n x a2



P1 (55) 32 42 74 260.54 8.17

P2 (197) 39 11 50 200.42 4.41

F1 15 23 38 261.63 10.67

F2 1 13 12 1 8 7 28 51 13 4 1 139 260.17 687.23

BCpl 5 10 17 32 5 69 258.80 103.13

BC2 3 29 7 8 13 3 1 64 229.03 850.98
-2












two reasons: it was the latest date at which 197 flowered, and it was

frequently where an obvious modal break occurred.

The model was tested for each cross at each location and also for

each cross with data from both locations pooled. The pooled tests

were run with the idea that larger populations may provide a better

sample, and that a primarily Mendelian character should manifest

itself the same in two environments that are not greatly dissimilar.

Noting that the generation means of the crosses were very similar at

both locations, pooling seemed reasonable. When generation means were

plotted at each location there was some evidence of genotype by

environment interaction (G x E), particularly in the crosses involving

197 (Figures 3-1 through 3-3 and Table 3-9) (12). Even though some

means indicated the presence of G x E, conclusions drawn from the

pooled data were in agreement with those drawn from individual

location data. Thus the G x E was not so great in these two

environments that it prevented consistent conclusions from the pooled

data.

Most chi-square probabilities for the expected 3:1 PR :pr pr

of the F2 generation ranged from .20 to .50 (Table 3-10) (6). The

single exception was the 55 x 197 F2 which had a probability of .05 to

.02 when data from both locations were pooled. This is not

particularly disconcerting since all of the other 15 segregating

generations tested fit the model well. A possible reason for lack of

fit may be the arbitrary division of these distributions into ten day

classes. It is conceivable that a few or pr plants could have been

classified as Pr if they were recorded as flowering on day 231

























232x197 4
A


A 55x197


232x206




55x206


A
206


IV i I I I


Figure 3-1.


197


^A


55 A


232


14.0_




13.5_




13.0_


12.0_




11.5




11.0_




10.5




inn


I
Gainesville Ft. Pierce Gainesville Ft. Pierce


Parent and FI means at Gainesville and Ft. Pierce.















13.5




13.0




12.5




12.0




11.5




11.0




10.5




10.0


Gainesville Ft. Pierce
Gainesville Ft. Pierce


Figure 3-2. F2 means at Gainesville and Ft. Pierce.


232x197
A



55x197





232x206




55x206











I i


,











13.5


(232x197)x197
13.0

(55x 97)x197
A
12.5 (55x197)x55 A
A -- (232x197)x232


S 12.0 A (55x206)x55


(232x206)x232

o 11.5


(232x206)x206 _

11.0 -
11.0 (55x206)x206




10.5




10.0

Gainesville Ft. Pierce


Figure 3-3. Backcross means at Gainesville and Ft. Pierce.








29


Table 3-4. Frequency distributions of generations from 55x197 at Ft. Pierce.
Data are numbers of plants observed to flower in a given 10-day
period.


Days of year
181 191 201 211 221 231 241 251 261 271 281 291 301
Gen. 190 200 210 220 230 240 250 260 270 280 290 300 310 n X


P1 (55) 7 43 16 5 1 2 1 75 250.61 131.54

P2 (197) 14 33 3 50 213.22 19.48

F1 7 16 22 2 47 261.04 57.22

F2 6 9 8 7 12 12 22 39 27 6 148 252.43 597.76

BCp 1 4 24 8 4 17 14 3 75 253.17 377.42

BCP2 10 17 1 6 7 11 10 5 67 244.16 858.23












Table 3-5. Frequency distribution of generations from 232 x 197 at
Gainesville. Data are numbers of plants observed to flower in
a given 10-day period.


Days of year
181 191 201 211 221 231 241 251 261 271 281 291 301
Gen. 190 200 210 220 230 240 250 260 270 280 290 300 310 n X 2




P1 (197) 39 11 50 200.42 4.41

P2 (232) 2 6 39 26 1 74 257.62 36.07

F1 23 24 47 260.19 14.64

F2 21 12 1 1 15 3 34 40 5 3 1 136 244.19 755.58

BCpl 12 22 3 1 15 14 67 229.55 841.86

BCp2 6 11 16 30 11 1 75 260.00 128.11









31


Table 3-6. Frequency distribution of generations from 232 x 197 at Ft. Pierce.
Data are numbers of plants observed to flower in a given 10-day
period.


Days of year
181 191 201 211 221 231 241 251 261 271 281 291 301
Gen. 190 200 210 220 230 240 250 260 270 280 290 300 310 n X

P1 (197) 14 33 3 50 213.22 19.48

P2 (232) 11 21 14 12 10 3 4 75 257.35 276.12

F1 2 8 17 17 6 50 260.02 91.00

F2 1 11 11 8 11 12 20 41 25 8 2 150 252.97 572.49

BCpl 15 23 4 4 5 5 12 4 2 74 233.66 963.21

BCp2 4 20 3 11 20 16 1 75 255.61 272.89
P2












Table 3-7. Frequency distributions of generations
locations combined.


from 55 x 197, data from


Days of year
181 191 201 211 221 231 241 251 261 271 281 291 301
Gen. 190 200 210 220 230 240 250 260 270 280 290 300 310 n i o2

P1 (55) 7 43 48 47 1 2 1 149 255.54 94.60

P2 (197) 39 25 33 3 100 206.82 53.20

F1 7 31 45 2 85 261.31 36.12

F2 1 20 20 8 8 20 19 50 90 40 6 5 287 251.34 640.12

BCpl 1 4 29 18 21 49 19 3 144 255.87 252.30

BCp2 3 39 24 1 6 15 24 13 2 4 139 236.77 905.78









33


Table 3-8. Frequency distribution of generations from 232 x 197 with location
data combined.


Days of year
181 191 201 211 221 231 241 251 261 271 281 291 301
Gen. 190 200 210 220 230 240 250 260 270 280 290 300 310 n X 02

P1 (197) 39 25 33 3 100 206.82 53.20

P2 (232) 13 27 53 38 11 3 4 149 257.48 155.87

F1 2 8 40 41 6 97 260.10 53.47

F2 22 23 12 9 26 15 54 81 30 11 3 286 248.79 676.48

BC 12 37 26 4 4 6 20 26 4 2 141 231.71 762.58

BC2 4 26 14 27 50 27 1 1 150 257.81 204.00













Table 3-9. Generation means in hours of daylight at Gainesville and Ft.
Pierce, and test for genotype by environment interaction
(G x E).


Gainesville Ft. Pierce
Generation Mean Std. error Mean Std. error G x E

hours of daylight


Parent


12.316
13.872
10.551
12.402


0.010
0.005
0.015
0.021


12.534
13.391
10.866
12.360


0.034
0.012
0.023
0.049


55x197
55x206

232x197
232x206

55x197
55x206


232x197
232x206

Backcross (55x197)x55
(55x197)x197
(55x206)x55
(55x206)x206
(232x197)x197
(232x197)x232
(232x206)x206
(232x206)x232


12.281 0.016
11.399 0.058

12.326 0.017
11.468 0.016

12.576 0.059
11.417 0.036

12.471 1 0.062
11.547 0.039


12.366
13.150
11.947
10.920
13.133
12.327
11.069
11.927


0.037
0.098
0.046
0.032
0.094
0.039
0.036
0.044


12.267 0.028
11.389 0.019

12.293 0.035
11.402 0.013

12.460 0.048
11.472 0.030

12.452 0.047
11.577 0.036


12.462
12.654
11.853
11.224
12.908
12.401
11.211
11.852


0.057
0.086
0.064
0.028
0.072
0.048
0.010
0.047


between means were greater than the sum of their standard


*Differences
errors.













Table 3-10. Summary of chi-squares of segregating generations from crosses
55x197 and 232x197.



Observed Expected
Generation Cross Location ratio ratio X P


55x197
55x197
55x197

232x197
232x197
232x197


Backcross:


(55x197)x55
(55x197)x55
(55x197)x55

(55x197)x197
(55x197)x197
(55x197)x197

(232x197)x197
(232x197)x197
(232x197)x197

(232x197)x232
(232x197)x232
(232x197)x232


Gainesville
Ft. Pierce
Loc. combined

Gainesville
Ft. Pierce
Loc. combined




Gainesville
Ft. Pierce
Loc. combined

Gainesville
Ft. Pierce
Loc. combined

Gainesville
Ft. Pierce
Loc. combined

Gainesville
Ft. Pierce
Loc. combined


27:112
30:118
57:230

35:101
31:119
66:220


34.75:104.25
37:111
71.71:215.25

34:102
37.5:112.5
71.5:214.5


no segregation
no segregation
no segregation


39:25
28:39
67:64

37:30
42:32
79:62


32:32
33:33
65.5:65.5

33.5:33.5
37:37
70.5:70.5


no segregation
no segregation
no segregation


2.304
1.760
4.042

0.039
1.50
0.564


0.2-0.1
0.2
0.05-0.02

0.5
0.2
0.5


3.062
2.180
0.069

0.731
1.351
1.050


0.1-0.05
0.2-0.1
0.5-0.2

0.5-0.2
0.5-0.2
0.2-0.1













rather than on 230. Four plants were, in fact, recorded on day 231,

and if they had been recorded on day 230, the data would have fit the

expected 3:1 at P>.05.

Backcrosses also fit the model well, with no segregation in the

backcrosses to the dominant 55 or 232 parents and a 1:1 segregation in

backcrosses to the recessive 197 parent. Means of the non-segregating

backcrosses were similar to those of the dominant parent and Fl.

Probabilities of Chi-squares ranged from about .10 to .50, indicating

a good fit between the data and the genetic model.

Although there is substantial evidence to support the contention

that a major gene system is involved in controlling flowering in these

crosses, it is apparent that other genetic or environmental factors

may also influence this behavior. The fact that there was a

relatively large range of flowering dates in the parental and F1

generations indicated that environment could be involved. There is

ample evidence that environment, particularly temperature, affects

flowering in several legumes (4,10,19), although one would not expect

great variation in temperature over a one hectare field. Environmental

variability due to flooding, disease, rabbit herbivory, and fertility

was observed. Part of the spread in 197 may also be due to disuniform

germination, resulting in staggered maturation.


Conclusion


A single locus with a completely dominant and a completely

recessive allele appeared to be controlling photoperiod response in

these three aeschynomene lines, but there are probably other












environmental and genetic factors influencing this character as well.

Different genetic and environmental backgrounds may alter the

expression of this gene, as indicated by the G x E observed.


Analysis of Crosses 55 x 206 and 232 x 206


Preliminary analyses

Parents of cross 232 x 55 were too similar in their flowering

behavior to provide the variability necessary for genetic evaluation.

Therefore this cross was not analyzed and will not be discussed further.

When data from the crosses 55 x 206 and 232 x 206 were displayed

in frequency distributions, no obvious modality was observed in the

segregating populations, indicating the possibility of quantitative

inheritance. Refer to table 3-11 for an example; all other frequency

distributions are in Appendix A. The generation means showed a trend

for additive gene effects. That is, if genes for a character are

primarily additive in effect, the mean of the F1 should be

approximately equal to the average of the means of the two parents.

The F2 mean should be equal to the Fl mean and the backcross means

should be equal to the average of the mean of the respective parent

and F1 (22). When these theoretical means were calculated, they were

indeed very similar to the means observed (Tables 3-12, 3-13). From

this it could be concluded that one of two possible modes of

inheritance was affecting flowering date. The genetics of this

character could be quantitative, with a series of minor genes which

together have additive effects. This hypothesis of quantitative

inheritance would be supported by the lack of obvious modality in the















Table 3-11. Frequency distributions of 55 x 206 generations at Gainesville. Numbers are individual
plants per class (cell).



Upper class limits in hrs of daylight 2
Gen. 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 n X a


P1(55) 9 57 8 74 12.316 0.008

P2(206 3 32 11 1 47 10.551 0.010

F1 1 1 2 16 20 11.399 0.067

F2 1 4 11 11 18 17 47 14 8 12 5 1 149 11.417 0.190

BCpI 16 7 2 12 13 3 53 11.947 0.112

BCp2 6 28 15 10 10 5 74 10.920 0.077









39


Table 3-12. Comparison of F and F2 means with calculated average
of parent means.


Cross Location F1 F2 Avg. of parent means

------------- hrs of daylight --------------

55 x 206 Gainesville 11.40 11.42 11.43
55 x 206 Ft. Pierce 11.39 11.47 11.70
55 x 206 Loc. combined 11.39 11.44 11.57

232 x 206 Gainesville 11.47 11.55 11.48
232 x 206 Ft. Pierce 11.40 11.58 11.61
232 x 206 Loc. combined 11.44 11.56 11.55









40


Table 3-13. Backcross means compared to average of F1 mean plus parent
mean.


Location
Gainesville Ft. Pierce Loc. combined
Cross BC (F +P) BC (FI+P) BC (F +P)
2 2 2

------------------ hrs of daylight -- --------------

(55x206)x55 11.95 11.86 11.85 11.96 11.90 11.91

(55x206)x206 10.92 10.98 11.22 11.13 11.07 11.05

(232x206)x206 11.07 11.01 11.22 11.13 11.13 11.02

(232x206)x232) 11.93 11.94 11.85 11.88 11.89 11.91












segregating populations. The alternative hypothesis is one of simpler

inheritance, where major gene action is additive and gene numbers are

very few.

Scaling Test. To further test these ideas, the data were

subjected to Mather's scaling test (13,14,28,29). The basis of this

test is similar to the ideas just discussed, that the mean of the

backcross is equal to the average of the parent and Fl means, or BC =

1/2(P+F ). Likewise, the same basis allows for a similar calculation

for the F2 mean. Formulas are given in Table 3-14. If the means

perform as predicted in the equation, then their effect is additive on

the average, i.e., the additive-dominance model is adequate. It

should be emphasized that this does not necessarily mean solely

additive gene action; in fact, there will be additive average effects

if there is dominance or linkage. Failure of this test implies either

that epistasis is a factor and an alternative model is required, or

that an alternative scale must be sought to fit the data to the

additive-dominance model.

Results of the scaling test were not consistent. At Gainesville,

both 55 x 206 and 232 x 206 gave insignificant values for A, B, and C,

indicating that the additive-dominance model was appropriate (Tables

3-15, 3-16). However, the Ft. Pierce data yielded three significant t

tests, an indication of epistasis or that the scale was not adequate

for the model. When the data from both locations were combined, again

two tests showed a significant deviation from zero, both in the 232 x

206 cross. But these did so only by a very slight margin and, in

fact, are not significant at the .01 probability level. If this were











Table 3-14. Formulas for Mather's scaling test (26, 21).



BC is the symbol for backcross generations.

Subscripts on on BC1 and BC2 refer to the parent backcrossed to.

P stands for parent.

BC = 1/2 P + 1/2 F

F2 = 1/4 (PI+P2+2Fl) = 1/2 BC1 + 1/2 BC2

A = 2 BC1 P1 F

B = 2 BC2 P2 Fl

C = 2 F2 2F1 2 -

VA = 4 v- +V- + V-

VB = 4 V-2 + V-2 + V1

V = 16 V72 + 4 V-1 + Vl + VP2


It should be noted that in the reference this formula contains the
typographical error "4 V2-."












Table 3-15. Mather's scaling test applied to data of cross 55 x 206
to test adequacy of additive-dominance model.


Gainesville Ft. Pierce loc. combined


A = 0.179

B = -0.110

C = 0.003


A = -0.217

B = 0.193

C = -0.290


= 0.0114

= 0.0372

= 0.0343




= 1.68

= -0.57

= 0.02


A = -0.020

B = 0.040

C = -0.160


0.0183

0.0041

0.0032




-1.60

3.01**

-5.12**


VA


V =

VC






tB =


tC =


0.0025

0.0048

0.0127




-0.40

0.58

-1.42


**t = 1.96 and t = 2.58 at infinite
.05 .01


degrees of freedom.













Table 3-16. Mather's scaling test applied to data of 232 x 206 cross
to test adequacy of additive-dominance model.


Gainesville Ft. Pierce loc. combined


A = -0.093

B = -0.016

C = 0.299


A = 0.154

B = -0.058

C = 0.278




VA = 0.0022

V = 0.0113

V = 0.0209




t = 3.28**

t = 0.55

t- = 1.92


= 0.0057

= 0.0087

= 0.0274




= -1.23

= -0.17

= 1.81


A = 0.110

B = -0.040

C = 0.270


= 0.0025

= 0.0048

= 0.0127




= 2.2*

= -0.58

= 2.39*


**05 = 1.96 and t = 2.58 at infinite
05 .01


degrees of freedom.












acceptable, the scaling tests would prove the model adequate for both

crosses at Gainesville and for both crosses when the data from both

locations were combined. The Ft. Pierce data do show significant

deviations from zero for B and C of 55 x 206. Since there was good

indication that the gene effects are additive in the other data sets,

it is likely that the significance of these tests is due to scaling

rather than some interallelic interaction.

Partitioning of Components of Variation. Further testing of the

data was done using Mather's and Jinks's methods of partitioning

components of variation (3,14,28,29). By manipulation of the means

and variances of the various generations, it was possible to estimate

the genetic and environmental components that make up those variances.

Formulas are given in Table 3-17. As the results in Table 3-18

demonstrate, the environmental variance for both crosses was

relatively low, meaning that the majority of the total variation was

genetic. The dominance component of the genetic variation was

negligible, being zero in four of the calculations. Thus most of the

genetic variance was additive. Again, additive variance does not

necessarily imply additive gene action. But since the genotypic

variance was nearly all additive, that is, there was little or no

dominance, then we may conclude that genes showed neither dominance

nor epistasis (5). Therefore, if there was no or very little

dominance or epistasis, then we may also conclude that the gene action

was additive.












Table 3-17. Formulae for Mather's
of variation (21).


and Jinks's partitioning components


Environmental variance




Dominance variance

Additive variance

Genetic variability
(broad sense heritability)


Number effective factors (loci)


(V21 + VP2 + VF1
3

H = 4(VC1 + VBC2 E)

D = 2(VF2 1/4 H E)

(D + H)
V = ----
VG
(D + H + E)


(P P2)2
14
4D












Table 3-18. Values for components of variance of crosses 55 x 206
and 232 x 206 using Mather's and Jinks's partitioning
method.



No. effective
Cross Location E H D V factors
G


55x206 Gainesville 0.028 0 0.324 0.92 2.40

55x206 Ft. Pierce 0.039 0.039 0.078 0.79 8.92

55x206 Loc. combined 0.044 0.030 0.111 0.76 6.66

232x206 Gainesville 0.018 0 0.416 0.96 2.06

232x206 Ft. Pierce 0.071 0 0.186 0.72 3.00

232x206 Loc. combined 0.053 0 0.280 0.84 2.49


Refer to Table 3-17 for definitions of E, H, and D.












Estimates of the number of effective factors, which may be

interpreted as the number of loci, were also calculated (Table 3-18).

Although there were two high estimates for 55 x 206, most numbers

ranged between two and three. If these estimates were at all

accurate, then it appears that flowering in aeschynomene may be

controlled by a few ma3or genes.

Summary of preliminary tests on data. The results of the tests

just discussed showed a definite trend. The means showed additivity

both in simple observation and in Mather's scaling test. This

additivity was further defined as additive gene action by partitioning

the components of variance. And finally, an estimate of the number of

effective factors indicated the possibility of a few major genes being

responsible for most of the control of this character. All of this

evidence leads to a reasonable argument that a major gene model with

additive gene action should be tested on the data.


Powers's partitioning method of analysis applied to data


With reasonably strong evidence suggesting that inheritance of

flowering response was controlled by a few genes, the data were tested

for fit to a two gene model, each locus with two alleles which act

additively and with equal effect. Since no obvious modality was

observed in the segregating generations' frequency distributions,

Powers's partitioning technique was employed to analyze the data.

This method of analysis is based on the premise that if the

homogeneous populations (parents, Fl) are normally distributed, the

effect of environment is normally distributed, since there is no












genetic variability. Lack of normality in the distributions of

segregating populations, then, is due to the genetic makeup of the

population. Powers envisions populations so distributed as being

composed of various genotypes, each of which has its own normal

distribution around its own mean. In other words, a few major genes

are primarily responsible for control of the character. In contrast,

quantitative inheritance would have many genes, each with minor

effects, and the resulting distributions would be expected to be

normal (11,20,22).

Tests for Normality. The first step in Powers' analysis then is

to test for normality in all generations. This is done by creating a

theoretical normal distribution from the normal probability table

based upon the frequency distributions of the observed data (6). The

two distributions are then tested with a chi-square goodness-of-fit

statistic. Again, parental and F1 generations are expected to be

normally distributed if they are homogeneous. If major genes are

controlling the character under study, the F2 and backcross

generations should not be normally distributed.

F, and parent generations. Results of the tests for normality

are in Table 3-20. An example of a distribution tested is in Table 3-

19; others can be found in Appendix B. In general, the parental and

F1 generations were distributed as expected. Most flowered fairly

uniformly, that is, within the range of only a few classes. Following

the example of Powers and others, classes with a few outlying plants

were combined to get at least ten plants per class (11,20,22,25).

Because of the uniformity of flowering and the low number of classes,














Table 3-19. Frequency distributions for 55 x 206 at Gainesville tested for normality. Data are numbers
of individual plants observed to flower in a given period of daylight.



Hrs of daylight 2
10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 X 0 n


P (55)

P2(206) 3 32 11

F. 1 -


9 57 8


- 2 16


F2 obs. 1 4 11 11 18 17 47 14 8 12 5 1

exp. 3 6 11 19 25 27 24 17 10 4 2

BCp obs. 16 7 2 12 13 3


exp.


BCp2 obs.

BCP2 exp.


8 10 13 11

6 28 15 10 10 5

9 15 21 17 9 3


7 3


12.32 0.008 74

10.55 0.01 47

11.40 0.067 20

11.48 0.19 149



11.95 0.112 53




10.92 0.077 74












Table 3-20. Chi-squares of goodness-of-fit test for normality of parent,
F F, and backcross generations of crosses 55 x 206 and
232 x 206.


Location
Gainesville Ft. Pierce Loc. combined

Entry X2 P X2 2 P


55 -* 98.16 <0.001

206 -

232 7.38 0.05-0.02

F155x206

F 232x206

F 55x206 32.05 <0.001 62.71 <0.001 38.75 <0.001

F2232x206 27.44 <0.001 67.18 <0.001 80.84 <0.001

BCpl(55x206)x55 13.06 <0.001 4.95 0.10-0.05 15.81 <0.001

BCp2(55x206)x206 9.51 0.001 -10.09 0.001

BCp (232x206)x206 4.57 0.10 -- 2.98 0.3-0.2

BCp2(232x206)x232 16.94 <0.001 12.80 0.01-0.001 37.10 <0.001


*Entries with no values did
chi-squares.


not have enough degrees of freedom to calculate












degrees of freedom were frequently too few to test the distributions

with a chi-square. Thus it may be assumed that since there was a

narrow range, the plants in those generations were homogeneous and

that any variation was due to environment. In the three parental

populations that could be statistically evaluated, one population of

55 had a probability of less than 0.001, indicating a distribution

that was not normal. Parent 232 also had one population that had a

probability of 0.05 to 0.02, indicating another poor fit. However,

the uniformity evidenced in the other parental populations leads me to

believe that these deviations from expected behavior were probably due

to environmental effects not being normally distributed rather than

heterozygosity of the parent genotypes. These two exceptions

notwithstanding, evidence clearly demonstrated that the environment

was normally distributed.

Segregating generations. For the most part the segregating

generations were not normally distributed. All of the F2 tests had

high chi-square values, with probabilities of less than 0.001, but

backcrosses were not as consistent in their distribution (Table 3-20).

Although most did have high Chi-square values which indicated a lack

of normality, there were three backcrosses that had normal

distributions. Since the majority were not normal, these may be

ignored and further testing of the hypothesis continued.

It may be appropriate at this point to at least question and

discuss the assumptions of normality as they apply to this method.

Just because a segregating population does or does not fit the normal

distribution as it is expected to, must further testing be abandoned?












I think not, partly because of some examples which come to mind.

First of all, if a character were controlled by an additive gene

system at any number of loci, it seems that the distribution could be

normal, rather than abnormal, if alleles had equal absolute effects

and broad sense heritability were low (Figure 3-4)(2). For example, a

1:2:1 or 1:4:6:4:1 F2 segregation could be normally distributed, even

when that distribution itself is composed of other normal

distributions. Therefore it seems that, in some situations where

major genes were suspected, one could accept a normal curve in the F2

distribution and still be justified to test it. However, since the

aeschynomene data sets show little environmental variance and high

broad sense heritability, a multi-modal distribution could be

expected.

To restate the argument, the point of this example is that

distributions of a data set should be interpreted only as an indicator

of the type of inheritance. I believe that Powers is often read as

stating that homogeneous populations must always be normally

distributed and segregating populations must be not normal. But broad

sense heritability (i.e., amount of environmental variance) and type

of gene action greatly influence the distributions of segregating

populations, as illustrated in Figure 3-4. So those distributions

which do not conform to these generalities about normality should not

necessarily be considered inappropriate for partitioning. Indeed, if

major genes are suspected, partitioning may be recommended even if

some tests for normality in segregating populations do not perform as

predicted. With the aeschnomene flowering data, we hypothesized an













No Dominance HERITABILITY Dominance
75

50 -
A
100%
25-

30 40 50 60 70 80 30 40 50 60 70 80
40


30 -


20 B \
20 87.5%

10


30 40 50 60 70 80 30 40 50 60 70 80
Z 30

20






10 -


30 40 50 60 70 80 30 40 50 60 70 80
10 50%

0
30 40 50 60 70 80 30 40 50 60 70 80


25%
30 40 50 60 70 80 30 40 50 60 70 80
Units of size





Figure 3-4. Theoretical distributions in F2. The model
postulates monogenic inheritance, and that the
effect of environment varies from nil (100 per
cent heritability) to the point where environ-
mental effects account for three fourths of the
total variability (25 per cent heritability).
The left column depicts no dominance; the
right column, full dominance.
Source: Allard, R.W. 1960. Principles of
plant breeding. John Wiley and Sons, Inc.,
New York.












additive major gene system with relatively high heritability, so the

segregating populations should be abnormally distributed for the most

part. However, occasional departures from what is expected may occur

due to experimental error. In data sets which demonstrate a clear lack

of normality in the homogeneous populations, other iterative methods

can be employed (21).

Partitioning of the F2

Method. With the hypothesized two locus, additive model, the F2

should segregate into ratios of 1:4:6:4:1. Following Powers's

detailed procedure and Sage and Isturiz's example of its application

to an additive system, the F2's of 55 x 206 and 232 x 206 were

partitioned into component genotypes (11,21,25). Details of the

method can be found in the references, but a general outline of

procedure will be presented here. Refer to Tables 3-21 through 3-24

of the 55 x 206 cross at Gainesville as the method is described.

Frequency distributions were created for P1, P2' Fl, and F2

generations (Table 3-11) and then converted to percent (Table 3-21).

For example, the ratio 1:4:6:4:1 converted to percent as

6.25:25:37.5:25:6.25. The parental phenotypes therefore should each

have made up 6.25 percent of the F2 population. In this model parent

206 was designated as genotype AABB and parents 55 and 232 as

A'A'B'B'. The Fl, then, was of the A'AB'B (two prime) genotype.

Since alleles are assumed to have equal effect, all other two prime

genotypes (A'A'BB, AAB'B') also had the F1 phenotype. Therefore the

F1 phenotype made up 37.5 percent of the F2. When this 37.5 percent

and the two parental 6.25 percent were subtracted from the F2, a 50













Table 3-21. Partitioned F2 distribution of 55 x 206 at Gainesville expressed as percent.



Upper class limits in hrs of daylight Theoretical
Population Genotype 10.4 10.6 10.8 11.0 11.2 11.40 11.6 11.8 12.0 12.2 12.4 12.6 %


F2 AABB... 0.70 2.70 7.30 7.40 12.10 11.40 31.60 9.40 5.30 8.10 3.10 0.70 100.00
AA'AB'B'

P2 (206) AABB 0.40 4.19 1.46 0.13 6.26


F A'A'BB, AA'BB' 1.88 1'.88 3.75 30.0 37.50
AAB'B'

P1 (55) A'A'B'B' 0.76 4.81 0.68 6.25


Residual A'A'B'B, 0.30 5.84 5.39 12.1 7.65 1.60 9.40 4.56 3.29 2.42 0.70 50.00
AA'B'B'
A'ABB, AAB'B














Table 3-22. Theoretical distribution of residual genotypes from partitioned 55 x 206 F expressed as percent.



Class centers in hrs of daylight Total
Genotype 10.3 10.5 10.7 10.9 11.1 11.3 11.5 11.7 11.9 12.1 12.3 12.5 % SX X o 0


A'ABB, 0.30 -3.37 5.84 5.39 12.10 3.83 0.80 24.89 275.73 11.08 0.0450 0.2121
AAB'B

A'A'B'B, 3.83 0.80 9.40 4.54 3.29 2.42 0.7 24.98 294.81 11.80 0.0408 0.2020


AA'B'B'


Single prime allele

(A'ABB, AAB'B)





Three prime alleles

(A'A'B'B, AA'B'B')


2 2
F 206 0.067-0.010
m= = 0.067
X -X 11.40-10.55
F 206


2
a -o
F 55
F1 0 0.067-0.008
m=- -0.064
X X55 11.40-12.32
1


2
b= 06 (m*206

=0.010-(0.067*10.55)

=-0.6974


2
b=( 55 (m*X5)

=0.008-(-0.064*12.32)

=0.796


y = mx + b

= 0.067 (11.08)+(-0.6974)

= 0.045


y = mx + b

= (-0.064*11.80)+0.796

= 0.0408














Table 3-23. Theoretical F2 distribution of 55 x 206 at Gainesville built from theoretical frequency
distributions of component genotypes.


Upper class limits in hrs daylight Theor.
Population Genotype 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 %


206 AABB 6.38 68.09 23.40 2.13 6.25

One prime A'ABB, AAB'B 0.07 1.12 8.15 29.63 32.59 21.88 5.84 0.68 25.00
allele

F A'A'BB, A'AB'B, 5.0 0 5.0 0 10.0 80.0 37.50
AAB'B'

Three prime
alleges A'A'B'B, AA'B'B0.15 2.24 13.72 33.89 33.89 13.72 2.24 0.15 25.00
alleles A'A'B'B, AA'B'B'U,

55 A'A'B'B' 12.16 77.02 10.81 6.25

F2 AABB...A'A'B'B' 0.42 6.41 3.50 9.42 8.19 9.78 34.89 8.64 8.47 4.19 5.37 0.71 100













Table 3-24. Chi-square contingency table of 55 x 206 at Gainesville.


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


10.3

10.5

10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5


0.82

6.78

8.11

12.52

15.1

15.79

49.49

13.43

10.31

9.12

6.5

1.03


0.63

9.55

5.22

14.04

12.20

14.57

51.98

12.87

12.62

6.24

8.00

1.06


0.0057




0.1845

0.5569

0.0927

0.1253

0.0242

0.5175




0.1095




1.6163


1/2 X2 = 1.6163 X2 = 3.2326


df = 5 P = 0.70 to 0.50












percent residual made up of the A'ABB, AAB'B (single prime) and

A'A'B'B, AA'B'B' (triple prime) genotypes remained. Single prime and

triple prime genotypes each made up 25 percent of the F2.

To obtain actual values for the residual distribution, parent, F

and F2 distributions were converted to percent within each class or

cell of the distribution. For example, the distribution of the 206

parent was converted to percent so that the sum of all cells of the

distribution equaled 6.25. The same was done for the other

generations. Then the Fl and parent distributions were subtracted

from the F2, leaving a residual distribution that had percent in each

cell, which in total equaled 50.

The residual distribution was then partitioned into its two

component distributions, one for single prime genotypes A'ABB, AAB'B

and one for triple prime genotypes A'A'B'B, AA'B'B' (Table 3-22). The

assumption was that those entries falling on one side of the F mean

were of the single prime genotypes and those on the other side had

triple prime genotypes. Since the classes were arbitrary, tails of

the two distributions could fall into the same cells. Hence the

values in the two cells on either side of the F1 mean were divided

equally between the two distributions.

Next means and variances were calculated for these theoretical

distributions using the formula y = mx + b. The resulting parameters

were necessary to construct theoretical normal curves for both the

single prime and triple prime genotypes. To do so, means were

subtracted from the higher value of each cell and divided by the

standard deviation, i.e., the usual procedures for building normal












curves from means and variances. These values were then looked up in

a normal probability table and the percentages entered into a

theoretical distribution containing all possible genotypes (6) (Table

3-23). Note that in this table frequencies for each cell of the

parent and Fl distributions were converted to percentages.

Finally a theoretical F2 was created by multiplying the

individual cell frequencies of each genotype by the genotype's

theoretical percentage. For example, if cell 10.8 had a frequency of

23.40 percent for the parent 206 genotype, AABB, then 23.40 was

multiplied times 6.25 percent, the theoretical percent of the F2 made

up of the 206 genotype. The same procedure was repeated for each

distribution with an entry in the 10.8 cell. These values were then

summed and entered as the percent of the theoretical F2 that fell into

that particular cell.

Theoretical F2 distributions so constructed were then tested for

homogeneity against the observed F2 using a Chi-square statistic. A

contingency table was built by dividing the total number of F

observations by 100 and multiplying this number by the percent in each

class of the theoretical F2 (Table 3-24). These calculations gave a

theoretical number of plants for each class. A subtotal of the

observed plus theoretical values for each class was calculated and

divided by two, producing the expected value for each class to be

tested against the observed. As in the test for normality, outlying

individuals in the tails were pooled until the last cell contained at

least ten plants.












Degrees of freedom in contingency tables are calculated as (rows-

1) (columns-1). But since means were calculated for the two

theoretical distributions of A'ABB, AABB' and A'A'B'B, AA'B'B', two

more degrees of freedom were lost. So the final degrees of freedom

was equivalent to n-3 where n equaled the number of classes.

Both the observed and the theoretical values had to be tested

against the expected. Since the expected values were half way between

the observed and theoretical, testing the observed against the

expected and multiplying the resulting chi-square by two gave the same

result as separately testing both the observed and theoretical

separately.

It is not clear to me why Powers chose to test the data with a

Chi-square test for homogeneity rather than a goodness-of-fit test.

In building and testing the contingency table, the expected is half-

way between the observed and theoretical values, which, of course,

favors a good fit. While the procedure is correct, the appropriateness

of its application to this type of data has not been justified in the

references that I have followed or criticized in discussion of the

method (8). So, even though I do question the method, I have employed

it exactly as described by the authors.

Results of F2 Chi-square probabilities listed in Table 3-25

demonstrated that the genetic model fits the data fairly well.

Contingency tables and calculations are in Appendix C. All

probabilities were 0.05 or greater except for 232 x 206 at

Gainesville. When the tails of the distribution were combined to give

ten or more plants per cell, the calculated Chi-square of this cross












had a probability of <0.01. The lack of fit cannot be attributed to

inadequate scale because the data for 232 x 206 at Gainesville tested

satisfactorily in Mather's scaling test (Table 3-16). Epistasis can

also be ruled out if we accept the scaling test conclusion that the

additive-dominance model was adequate. The data also were distributed

as expected in tests for normality. We might then conclude that the

flowering dates for this cross at Gainesville were slightly more

affected by errors in taking data or environment, and thus did not

have the background to fully reveal the genetically controlled

behavior.

The relatively high probabilities of the other five data sets

were strong evidence that flowering response to photoperiod in crosses

55 x 206 and 232 x 206 was primarily under the genetic control of two

loci, each with two alleles with additive gene action. It should be

emphasized that these two major loci appear to be a predominant

genetic feature but by no means the sole factor affecting induction of

flowering. To further test the model analysis was done on backcross

data.

Partitioning the Backcrosses

Method. The general procedure for the backcross analysis was the

same as that of the F2. Again the hypothesized genetic model was that

206 was of genotype AABB, 55 and 232 were A'A'B'B', and that each of

the four alleles had equal absolute effect with additive gene action.

Using Tables 3-26 and 3-27 of the (232 x 2C6) x 206 backcross at

Gainesville as an example, one can see that plants were expected to

segregate phenotypically in a 1:2:1 or 25:50:25 percent ratio. In












other words 25 percent should be of the 206 parental genotype AABB; 25

percent should be of the F1 AA'BB' genotype; and 50 percent should

have single prime genotypes A'ABB or AAB'B (Table 3-26). In the

backcross to the 232 parent, ratios were identical but the genotypes

were 25 percent A'A'B'B'; 25 percent A'AB'B; and 50 percent triple

prime A'A'B'B or AA'B'B'. Since the 50 percent group was

theoretically unlike either the parent or F1 in genotype, it made up

the residual frequency distribution, which was then used in creating

the theoretical backcross distribution.

Testing of the observed backcross frequencies against the

theoretical was done the same as in testing the F2. The one

difference was that since only one set of parameters was calculated

for each backcross, degrees of freedom were equivalent to n-2. Again

tails were combined until they had data from at least ten plants

(Table 3-28).

Results of backcrosses. At first glance the backcross data did

not support the proposed hypothesis quite as definitively as did the

F2. As can be seen in the summary of backcross Chi-squares in Table

3-29, there were six tests that fit the genetic model. These results

lend strong support to the conclusion reached after analysis of the F2

that the gene model was adequate. However, there were also six

backcrosses with P = <0.01, indicating lack of homogeneity.

Two main reasons may be suggested as causes of poor fit between

the observed and theoretical data in those six backcrosses. One is

cell size which is compounded by environmental effects. Although

there appears to be a major gene system at work, there are also other









65


Table 3-25. Chi-squares of test for homogeneity between F2 data and
theoretical distributions.


Cross Location Chi-square Probability


Gainesville

Ft. Pierce

Loc. combined

Gainesville

Ft. Pierce

Loc. combined


3.23

7.22

12.02

16.30

6.13

12.03


0.70 to 0.50

0.10 to 0.05

0.10 to 0.050

<0.01

0.20 to 0.10

0.20 to 0.10


55x206

55x206

55x206

232x206

232x206

232x206















Table 3-26. Partitioned frequency distribution of (232 x 206) x 206 at Gainesville expressed as percent.


Upper class limits in hrs of daylight Theoretical
Population Genotype 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 %


BC AABB...
AAB'B'

P (206) AABB

F AAB'B', A'AB'B
A'A'BB

Residual A'ABB,


5.63 18.31 21.31 18.31 16.90 19.72


1.60 17.02 5.85 0.53


7.0 15.00 3.00


-1.60 -11.39 12.46 20.60 18.31 9.90 4.72 -3.00


100.00


25.00

25.00


50.00
















Table 3-27. Theoretical
theoretical


frequency distribution of (232 x 206) x 206 at Gainesville built from
frequency distributions of component genotypes.


Upper class limits in hrs of daylight Theoretical
Population Genotype 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 %


P1 (206) AABB 6.38 68.09 23.40 2.13 25.00

F Any two prime
1 alleges 28.00 60.00 12.00 25.00
alleles

Residual Any one prime
Resu a e 0.17 13.39 63.16 22.76 0.51 50.00
allele

BC AABB...
PI AABB. 1.60 17.02 5.94 7.23 31.58 18.38 15.26 3.00 100.00
AAB'B'












Table 3-28. Chi-square contingency table for (232 x 206) x 206 at
Gainesville.


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


10.3 0 0.57 1.14

10.5 4 8.04 12.08 0.0028

10.7 .13 8.61 4.22

10.9 15 10.07 5.13 2.4136

11.1 13 17.71 22.42 1.2525

11.3 12 12.53 13.05 0.0224

11.5 14 12.42 10.83

11.7 0 1.06 2.131 0.0201




3.7115


1/2 X2 = 3.7115


X2 = 7.423 df = 3 P = 0.10 to 0.05












factors, probably both genetic and environmental, which blur the

effects of the ma3or genes. That environment can affect expression of

major genes controlling photoperiod induced flowering is well

established (3,10,17,19). It is conceivable then that plants with

similar but different genotypes such as A'AB'B and A'ABB may

occasionally be classed as the same phenotype (that is, they may fall

into the same cell) if some other factor has blurred the distinction

between the two. Distributions could have been influenced by

environmental conditions such as Rhizoctonia, herbivory by rabbits,

flooding, and soil fertility, which were observed in localized areas

of the experiment. Larger populations or more and smaller cells in

the frequency distribution may facilitate partitioning and minimize

the effect of these factors.

A second suggestion as to the cause of poor fit in these six

backcrosses is that the total range of the parents is too narrow.

Backcrosses by definition are narrower in range than the F2 and

contain fewer genotypes. All genotypes lie between the Fl and the

parent. For example, possible genotypes in (55x206)x206 are AABB,

A'AB'B, and A'ABB or AAB'B. The latter genotypes, A'ABB and AAB'B,

differ from the parent and F1 by only one allele. If the effect of

each allele is slight, the effects of environment or minor genes may

blur the distinction between phenotypes. If two parents represented

the two extremes of the character under study, the effects of these

alleles would be greater and classifications would be easier. But

these aeschynomene accessions used as parents represented perhaps less












Table 3-29. Chi-squares from test of homogeneity between backcross data
and theoretical distributions.


Cross Location Chi-square Probability


(55x206)x55

(55x206)x55

(55x206)x55

(55x206)x206

(55x206)x206

(55x206)x206

(232x206)x206

(232x206)x206

(232x206)x206)

(232x206)x232

(232x206)x232

(232x206)x232


Gainesville

Ft. Pierce

Loc. combined

Gainesville

Ft. Pierce

Loc. combined

Gainesville

Ft. Pierce

Loc. combined

Gainesville

Ft. Pierce

Loc. combined


14.14

3.12

24.89

0.93

0.57

2.79

7.42

11.05

3.39

16.29

18.81

16.41


(1.20)




(7.73)
















(2.58)

(12.46)

(4.41)


<0.01 (0.70 to 0.50)

0.70 to 0.50

<0.01 (0.10)

0.50 to 0.30

0.50 to 0.30

0.30 to 0.20

0.10 to 0.05

<0.01

0.50 to 0.30

<0.01 (0.20 to 0.10)

<0.01 (0.05 to 0.01)

<0.01 (0.20 to 0.10)


Note: Chi-squares and probabilities in parentheses are calculated by
combining two adjacent cells to account for environmental error. See text
for discussion.












than half the observed range of initiation of flowering. Greater

variation would facilitate a more conclusive backcross analysis.

Some examples taken from Tables 3-30 through 3-33 can be used to

illustrate how environmental factors may have resulted in some

backcrosses failing the homogeneity test. It is interesting to note

that in four of the six backcross distributions that did not fit the

model, very low observed values were in cells with class center 11.9,

and higher than expected values were observed for cells with class

center 11.7. The low values in 11.9 resulted in high Chi-squares for

those cells and the subsequent failure of the observed distribution to

fit the theoretical. But if values in cells 11.9 and 11.7 were

combined, Chi-squares were greatly reduced and, in fact, three of

those four distributions would statistically fit the theoretical (see

values in parentheses Table 3-29). Only (232 x 206)x232 at Ft. Pierce

did not and then ]ust barely with a P = 0.05 to 0.01. It is

conceivable that some environmental factor occurring at the daylength

period around 11.9 hours delayed flowering in several plants so that

they fell into the 11.7 cell. These daylengths occurred during the

first fifteen days of October, a time of year known to have erratic

and variable weather. Of course, weather conditions would be equal

over the general area of a one hectare field, and not so localized as

to affect one area differently than another. But weather conditions

interacting with minor genes of some segregants or compounding other

environmental factors such as flooding could quite possibly affect the

physiology of flowering, causing a delay. Therefore the combining of












Table 3-30. Chi-square contingency table for (232 x 206) x 232, data
from locations combined.


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


0.01

0.16

21.23

24.60

22.86

26.46

19.31

15.12

10.04

6.56

2.76

0


1.3228




0.9074

1.2735

4.9444(0.2163)+

0.0012

0.6376






0.0248




8.2043


Combined classes:
1/2 X = 8.2043 X = 16.4085 df = 5

Combined classes 11.7 and 11.9:
1/2 X = 2.2027 X = 9.4054 df = 3


P = <0.01


P = 0.20 to 0.10


10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5

12.7

12.9

13.1


0.005

0.08

16.62

29.80

28.93

17.23

19.15

18.56

11.02

5.78

1.38

0.5












Table 3-31. Chi-square contingency table for (232 x 206) x 232 at
Gainesville.


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


5.19

11.87

10.63

18.88

10.15

8.77

6.51

1.25

0.75

0


0.1166


0.9457

6.8231(0.9151)+

0.0764






0.1808







8.1426


classes:
8.1426 X = 16.2852 df = 3

classes 11.7 9nd 11.9:
1.2889 X = 2.5778 df = 2


P = 0.001



P = 0.20 to 0.10


11.3

11.5

11.7

11.9

12.1

12.3


18

18

12

12

15

6

0

0

1


3.60

14.94

14.32

10.44

11.08

11.89

6.25

0.63

0.38

0.50


Combined
1/2 X =

+
Combined
1/2 X =












Table 3-32. Chi-square contingency table
Ft. Pierce.


for (232 x 206) x 232 at


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


0.4437

2.7022

0.0747

4.8257(1.7250)+

0.2683

1.0658




0.0238




9.4042


Combined classes:
1/2 X2 = 9.4042


X2 = 18.8084 df


Combined classes 11.7 an9 11.9:
1/2 X = 26.2288 X = 12.4576 df = 4


P = 0.05 to 0.01


11.3

11.5

11.7

11.9

12.1

12.3

12.5

12.7

12.9


12.34

11.44

15.91

14.31

5.76

4.75

4.38

5.13

1.00


14.67

5.87

14.82

22.62

4.51

2.50

2.75

5.25

2.00


P = <0.01













Table 3-33. Chi-square contingency table
Gainesville.


for (55 x 206) x 55 at


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


0.1283









3.0479

3.4157(0.2143)+

0.2203



0.2589




7.0711


Combined classes: 2
1/2 X 7.0711 X = 14.1422
+
Combined classes 11.7 9nd 11.9:
1/2 x =0.6015 X = 1.203


df = 3 P = 0.01 to 0.001


df = 2 P = 0.70 to 0.50


10.5

10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5


0.33

0

0.33

0

0.67

13.3 1

3.66

6.83

13.74

11.88

2.22


0.66

0

0.66

0

1.33

10.6 J

0.32

11.66

15.48

10.75

1.43













two adjacent cells may be justified in order to overcome this

environmentally caused error.

If this proposition is acceptable it could also be applied to (55

x 206)x55 data in Table 3-34 for cells 11.3 and 11.5. Pooling these

two classes results in a Chi-square probability of 0.10. Since cells

11.3 and 11.5 occurred about October 16 through October 25, it is

quite possible this backcross was affected by environment in a manner

similar to that described above. Accounting for this source of error

then would result in eleven of the twelve backcross populations

supporting the model.

Attempts to explain the poor fit of some of the backcrosses

should not be construed as an attempt to make the data conform to a

preconceived idea. There is considerable evidence from the F2 and

other backcrosses that the model is plausible. It is imperative,

then, to look for possible reasons why certain segregating populations

behaved differently than expected. Acknowledging some of the possible

sources of error described above, it can be concluded that, as a

whole, the backcross data support the hypothesized genetic model.

Summary. Initial observations of the generation means of crosses

55 x 206 and 232 x 206 indicated that genes controlling photoperiod

induced flowering were additive in effect. Testing the data with

Mather's scaling test supported this contention; most tests showed the

additive-dominance model was adequate. Further testing revealed

little or no dominance variance and suggested that the number of

effective factors was two or three. Hence it seemed reasonable to

propose that inheritance of flowering in these crosses might be













Table 3-34. Chi-square contingency table
from locations combined.


for (55 x 206) x 55 data


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


10.3

10.5

10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5

12.7

12.9


Combined classes:
1/2 X = 12.4436

With 11.5 combined:
1/2 X = 3.8653


2
X = 24.8872


df = 5 P = <0.01


2 = 7.7306 df = 4 P = 0.
X 7.7308 df = 4 P = 0.10


C.28

0

0.28

0.28

5.30

11.41

12.74

14.84

11.91

15.49

14.64

7.38

3.07

0.41


0.55

0

0.55

0.55

10.61

12.82

4.47

12.67

17.82

12.97

13.28

6.75

4.141

0.82


3.2480









5.3534 (0.0166)

0.3144

2.9327

0.4067

0.1263




0.6810




12.4436













controlled at two loci, each with two alleles and all alleles acting

additively with equal absolute effect. The late flowering parent 206

was designated AABB. Parents 55 and 232, which both flowered in late

mid-season, were designated A'A'B'B'.

Since segregating generations showed no obvious modality,

Powers's partitioning method was used to test the genetic model. F2

data sets fit the model well in five of the six analyses performed.

Chi-square probabilities were generally in the 0.20 to 0.30 range.

Backcrosses also supported the model in half of the data sets

analyzed. Since most evidence fit the model, it was suspected that

the six backcrosses that did not fit were affected by minor genetic or

environmental effects, small populations, flowering dates of the

parents being too similar, and the arbitrary nature of the frequency

distribution cells. Minor manipulation of the data resulted in eleven

of twelve backcrosses tested fitting the model. Despite the fact that

some analyses did not support the hypothesis, the majority of the

evidence demonstrates that flowering in these two crosses is

controlled primarily by an additive genetic system with two loci, each

with two alleles of equal effect.

















CHAPTER IV
CONCLUSION


In this study the genetics controlling stem pubescence and

photoperiod-induced flowering were examined. The interest in stem

pubescence lies in its potential use as a marker gene which is

detectable in seedlings. Evidence from crosses between one glabrous

and two pubescent parents showed that this trait is governed by two

alleles at one locus. Glabrousness, Gl is dominant over

pubescence, gl gl. With such simple inheritance and easily classified

phenotypes, the glabrous trait can be readily incorporated into other

genetic backgrounds and employed in further genetic studies.

The genetics of the effect of photoperiod on flowering induction

appeared to involve two separate genetic systems. At one level was

the responsiveness (or lack of it) to photoperiod. The F2 generations

from crosses between two photoperiod responsive genotypes and a

photoperiod insensitive genotype segregated in a 3:1 ratio of

photoperiod responsive to insensitive, indicating complete dominance

at one locus. The backcross data confirmed this. Thus,

responsiveness to photoperiod appeared to be controlled by a dominant

allele Pr and the lack of photoperiod response was conditioned by the

homozygous recessive pr pr genotype. Although there was clearly a

major gene system involved in expression of this trait, the breadth of

each class in the segregating generation indicated that other minor

genetic factors or environment may also affect flowering.













At the second level was the genetics controlling those genotypes

that were photoperiod responsive. Means and variances of segregating

generations from crosses between mid-range and late flowering parents

indicated additive gene action. Further analysis demonstrated that

two loci, each with two alleles, controlled the initiation of

flowering as induced by duration of daylight. Although there was no

clear division of classes, due in part to the limited range of the

parents involved, partitioning analysis indicated that the data fit an

additive gene model and that all four alleles had equal effect. Even

though there appeared to be a major.genetic system, minor genes and

environment surely modify its expression.

It should be emphasized that the conclusions reached in this

study are only for the accessions involved. While the identified

genetics apply to other aeschynomene lines, by no means is it implied

that inheritance of photoperiod response is limited to these genetic

systems. As is so frequently demonstrated in other studies of this

trait, several additional genetic mechanisms may be identified from

other sources of germplasm.

Because environment, particularly temperature, frequently

modifies genetic expression of flowering, a study using growth

chambers could help define this interaction. Although the data

generated in this experiment yielded fairly well defined conclusions,

the presence of an environmental effect was evident. Controlled

temperature and exposure to light could help clarify the relationship

between environment and genetics and how they affect flowering in

aeschynomene.









































APPENDIX A
FREQUENCY DISTRIBUTIONS OF 55 x 206 AND 232 x 206















Table A-i. Frequency distributions of 55 x 206 generations at Ft. Pierce.


Upper class limits in hrs of daylight 2
Gen. 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 13.2 n X o


3 1


6 31 25 5


6 36


1

5 30



2 12 16


17 6

62 18 10


7 6 6 5


10 5 10 4 6 3

37 2 1


5


75 12.534 0.086

45 10.866 0.023

24 11.389 0.009

149 11.472 0.139

45 11.853 0.187

70 11.224 0.055


P (55)

P2(206)

F1
F2

F2

BCp1
BCp2
BCP2















Table A-2. Frequency distributions of 232 x 206 generations at Gainesville.


Upper class limits in hrs of daylight 2
Gen. 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 n X 0


P (206) 3 32 11

P2(232)


3 6 10 10


14 30

31 33


11


4 13 15 13 12 14

2 18 18


47 10.551 0.010

1 7 32 26 5 3 74 12.402 0.032

50 11.468 0.013

7 15 16 3 145 11.547 0.226

71 11.069 0.094

2 12 15 6 74 11.927 0.145


F2

BCpI

BCp2














Table A-3. Frequency distributions of 232 x 206 generations at Ft. Pierce.


Upper class limits in hrs of daylight 2
Gen. 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 n X o


6 36 3

4 1 3 7

35 13

1 3 13 57 23 17 7

7 31 23 3

10 17 17 6


45 10.866 0.023

10 10 11 21 8 15 12.360 0.180

48 11.402 0.009

7 9 7 1 145 11.57" 0.164

64 11.211 0.023

7 7 6 5 75 11.852 0.167


P (206)

P2(232)


2

BCPl

BCp2

















Table A-4. Frequency distributions of 55 x 206 generations, location data combined.


Upper class limits in hrs of daylight 2
Gen. 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 n X o


P (55)

P2 (206) 3 32 17 37

F1 1 1


- 3

1 19


1 4 11 16 48 79

10

6 30 27 26 47


3 1 13 63 39 25 5 149 12.425 0.058

92 10.705 0.041

22 44 11.393 0.034

65 24 15 18 11 6 298 11.444 0.162

21 17 6 18 16 8 2 98 11.903 0.147

5 2 1 144 11.067 0.089


BCp2















Table A-5. Frequency distributions of 232 x 206 generations, location data combined.


Upper class limits in hrs of daylight
Gen. 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 n X o2


P (206) 3 32 17 37

P2(232)

F1
1


F2

BCpI

BCp2


3 7

4 13


- 3


4 1 3 8 17 42

49 43 6

88 56 28 14 22 25

35 17

12 35 35 8 19 22


92 10.705 0.041

37 26 11 149 12.380 0.106

98 11.435 0.012

10 1 290 11.562 0.193

135 11.136 0.065

12 5 1 149 11.889 0.156






































APPENDIX B
CHI-SQUARE CONTINGENCY TABLES OF 55 x 232 AND 232 x 206 F2s













Table B-1. Chi-square contingency table for 55 x 206 at Ft. Pierce.


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5

12.7

12.9


0.625

6.94

24.52

60.59

22.23

13.35

7.13

3.67

3.38

4.42

1.55

0.32


1.25

8.87

19.04

59.18

26.46

16.69

7.26

1.34

0.75

3.84

3.10

0.63


0.2657




0.0328

0.8048

0.8406

0.0024

1.4792






0.1858




3.6113


1/2 X2 = 3.6113 X2 7.2226


df = 4 P = 0.10 to 0.05













Table B-2. Chi-square contingency table for
locations combined.


55 x 206 data from both


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


10.3

10.5

10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5

12.7

12.9


0.82

6.56

8.54

20.27

39.93

76.78

71.75

26.23

17.35

12.64

9.76

5.45

1.55

0.32


0.63

9.12

6.08

24.53

31.86

74.56

78.49

28.46

19.69

7.27

8.52

4.89

3.10

0.63


0.0004




0.8995

1.6309

0.0642

0.1896

0.3183

2.2729

0.1575






0.0004




6.0110


2
1/2 X = 6.011


2
X = 12.02 df = 6 P = 0.10 to 0.05













Table B-3. Contingency table
Gainesville.


for Chi-squares of 232 x 206 at


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


10.3

10.5

10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5

12.7

12.9


0.29

4.59

4.10

7.53

16.45

27.33

33.10

12.27

12.56

12.72

10.50

3.10

0.31

0.18


0.58

6.18

2.19

5.05

22.90

23.46

33.19

13.53

18.11

10.44

4.99

3.19

0.61

0.36


0.3788




2.5290

0.5219

0.0003

0.1315

2.4613

0.4086






1.7200




8.1514


1/2 X2


X = 16.3028 df = 5 P = <0.01


8.1514













Table B-4. Chi-square contingency table for 232 x 206 at Ft. Pierce.


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


11.9

12.1

12.3

12.5

12.7

12.9


1.11

5.16

9.77

61.40

25.34

13.37

8.59

7.15

6.32

4.47

1.77

0.49


X2 = 6.1346


1.22

7.32

6.54

65.79

27.67

9.74

10.18

7.29

3.64

1.94

2.54

0.97


0.0575




0.3153

0.2160

0.9855

0.2943

0.0031






1.1956




3.0673


df = 4 P = 0.20 to 0.10


1/2 X2 = 3.0673













Table B-5. Chi-square contingency table of
locations combined.


232 x 206 data from


Class center (0-E)2
in hrs daylight Observed Expected Theoretical E


10.3

10.5

10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3

12.5

12.7

12.9


0.61

6.29

3.60

13.37

30.33

87.23

62.06

25.56

24.77

16.70

9.60

5.22

3.16

1.33


0.30

4.65

5.30

13.19

26.67

87.66

59.03

27.28

19.39

19.35

17.3

7.61

2.08

0.67


0.0061




26.37

53.33

175.32

118.06

54.56

38.77

38.70

34.60




0.0395




6.0174


X2 = 12.0348 df = 7


1/2 X2 = 6.0174


P = 0.20 to 0.10








































APPENDIX C
CHI-SQUARE CONTINGENCY TABLES OF BACKCROSSES












Table C-l. Chi-square contingency table of
Pierce.


(55 x 206) x 55 at Ft.


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


11.1 0 0.25 0.50

11.3 10 9.31 8.61 0.0203

11.5 5 6.27 7.55 0.2572

11.7 10 9.60 9.20 0.0167

11.9 4 5.40 6.80 0.3630

12.1 6 4.08 2.16 0.9035

12.3 3 2.01 1.02

12.5 5 4.83 4.65

12.7 2 2.88 3.75 0.0008

12.9 0 0.38 0.75

1.5615


df = 4 P = 0.70 to 0.50


X = 3.123


1/2 X 2=1.5615













Table C-2. Chi-square contingency table of
from locations combined.


(55 x 206) x 206, data


Class center (O-E)2
in hrs daylight Observed Expected Theoretical E


10.3

10.5

10.7

10.9

11.1

11.3

11.5

11.7

11.9

12.1

12.3


0.61

9.89

21.51

31.91

27.16

38.54

12.69

1.08

0

0

0.5


1.21

13.78

13.02

36.82

28.31

30.08

20.38

0.16

0

0

0


0.0500




0.7555

0.0495








0.0908







1.3958


1/2 X2 = 1.3958 X2 = 2.7916 df = 2


P = 0.30 to 0.20




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