Biology 137 2008 Spring Semester
Meta-report 3: Assessing Petal Number in Floral Forms of Dahlia

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Please count the floral parts of some of your dahlias
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Let's work together to see if dahlias follow the Fibonacci Sequence.


Dahlia Seedling 0503MX3, a stellar type flower selected by Corralitos Gardens
to propagate and trial. This cultivar consistently forms irregular flowers.

Introduction

       The genetics of floral development were initially explored in the small crucifer Arabidopsis thaliana and the common snapdragon Antirrhinum majus, both of which produce four distinct types of floral organs arranged in concentric whorls. The outermost whorl contains sepals, while successive whorls contain petals, stamens, and carpels, with each of these organs being produced in a characteristic, highly reliable number (Coen and Meyerowitz 1991).

           Based on floral homeotic (conversion of an organ into another organ such as a petal into a stamen) mutations observed in these two species, the “ABC” model of floral development was proposed, in which combinatorial interactions between three classes of genes acted to specify floral organ identity. In this model, A class genes are active in the perianth whorls, B class genes are active in the middle two whorls, and C class genes are confined to the two innermost whorls, and the combination of gene activities in a given whorl determines the identity of the organs it produces. Thus, A alone confers sepal identity; A+B produces petals; B+C specifies stamens; and C alone yields carpels (Coen and Meyerowitz 1991).

          While the ABC model, notably the “BC” component, has proven reasonably descriptive of floral development programs in diverse species, it cannot provide a complete description of the remarkable variety of floral forms observed in nature (reviewed in Krizek and Fletcher 2005). Composite flowers evident in the Compositae, including dahlias, do not follow the typical pattern of perianth and reproductive organs being arranged in one set per flower. Compositae flowers are groups of small flowers, called ‘florets’ grouped together in a head. It is important to note that when looking at a dahlia, the ‘petal’ is actually an individual flower, and all the ‘petals’ combined represent a composite head of flowers termed a capitulum. The existence of more complex mechanisms for patterning the flower is particularly evident in species that have been selected to display aesthetic floral forms, such as the dahlia.

Figure 1a. The Fibonacci sequence begins at 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself.
F0
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
F11
F12
F13
F14
F15
F16
F17
F18
F19
F20
0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765

Figure 1b. A Fibonacci spiral created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34; image from Wikipedia.

          The Fibonacci numbers are named after Leonardo of Pisa (aka Fibonacci) who described his sequence in a book in 1202. The first two numbers are 0 and 1, and each subsequent term is the sum of the two terms before it (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…). The Fibonacci sequence appears in nature surprisingly frequently, including in branching patterns and the arrangements of floral parts, in the helices of pinecones and pineapples, and in many other forms (Klar 2002). Fibonacci numbers are disproportionately represented in the petal counts of flowers. While 1- and 2-petaled flowers are rather rare, 3-, 5-, and 8-petaled flowers are relatively common. The higher terms (34, 55, 89) are occasionally seen in the Compositae, although with great variability i.e. there is variation with species and among the flowers on one plant and even within a single capitulum as some floral parts are found in a Fibonacci number and others are not. Because dahlias belong to the Composite family and because some dahlia floral forms, such as orchids, mignon singles, singles, and collarettes create capitulums with eight ray florets, or eight ‘petals’, it was hypothesized that other dahlia varieties might also have floret counts following the Fibonacci sequence. In the present investigation, we present a preliminary analysis of petal number and form in several different dahlia cultivars. This report synthesizes the analysis of petal number and form in several different dahlia cultivars conducted by students in the Spring 2008 quarter of Biological Sciences 137; Dahlias in Plant Genetics: E. Abrash, A. Christian, R. Kamber, J. McCallen, A. Schultink, W. White, and C. Young.

Objectives

          There was one major objective of this study:

  1. Determine the pattern of florets in dahlia flowers, particularly ray florets and their petalloid structures; does this pattern follow the Fibonacci sequence?

Materials and Methods

          Six dahlia cultivars were selected based on morphological differences in gross floral anatomy: Dixie’s Winedot (an informal decorative form), Lakeview Premier (a formal decorative form), Clear Choice and Pinot Noir (both cactus forms), Alpen Diamond (a collarette form), and River Dance (an anemone form). Ray florets were removed and counted. Data were recorded either as a single counts representing the total number of petalloid organs, or as a series of counts representing petalloid organs of different whorls. Most cultivars examined displayed some variability in floret number, and each floral form typically differed from other floral forms in terms of numbers of petalloid organs. It is worth noting that petalloid organs (a class likely encompassing petal-stamen chimeras, accessory petals fused to larger petals in individual ray florets, and modified bracts) were reported for all cultivars.

Summary Table of Results

Image

Name

Ray Floret Count

Fibonacci Estimate

Alpen Diamond

8

 

Alpen Diamond

8

 

average

8

8

Clear Choice

54

 

Clear Choice

64

 

Clear Choice

69

 

Clear Choice

70

 

Clear Choice

71

 

Clear Choice

97

 

average

70.83

55

Dixie's Winedot

56

 

Dixie's Winedot

57

 

Dixie's Winedot

69

 

average

60.67

55

Lakeview Premier

99

 

Lakeview Premier

115

 

Lakeview Premier

138

 

average

117.33

144

Pinot Noir

85

 

Pinot Noir

100

 

average

92.5

89

River Dance

39

 

River Dance

41

 

 

average

40

34

Individual Organ Counts

 

   

 

Floret Counts in Dahlia Clear Choice

Floral Bracts

82

89

Ray Florets

71

51

Disc Florets

17

13

Floret Counts in Dahlia Lakeview Premier

Ray Florets

138

144

Petalloid Stamens

29

34

Disc Florets

51

51

Floral Bracts

200

233

Floret Counts in Dahlia Alpen Diamond

Disc Florets

8

8

Petalloid Stamens

16

13

 

Results and Discussion

          Based on these counts, some interesting information emerges. First, dahlia cultivars and forms can differ appreciably in the number of florets they produce. Formal decorative cultivars (Lakeview Premier) produced the largest number of florets, followed by cactus (Clear Choice, Pinot Noir) and informal decorative (Dixie Winedot), with collarette cultivars (Alpen Diamond) producing the fewest florets. Second, most dahlia cultivars produce a variable number of florets per flower, although Alpen Diamond, and in fact most singles and collarettes should in exceptional cultivars consistently produce eight ray florets. One important observation to note is that this inconsistency is tied to the overall developmental stage of the plant. For instance, flowers produced earlier in the plant’s lifetime tend to have fewer florets and higher irregularity, and consistent with that observation is that some cultivars produce few or no ray florets in their very first flowers in a season. Third, a substantial fraction of dahlia cultivars appear to produce floral organs that do not fall neatly into the ABC model organ categories, as reflected by reports of “petalloid” organs in all varieties examined. It would be interesting to use in situ hybridization or immunolocalization techniques to see whether expression of ABC gene orthologues was detectable in these plants, and if so, how their expression might correlate with the observed production of petalloid organs. These observations of dahlia floral forms confirm that a simple ABC model specifying stereotyped production of four organ classes cannot fully account for the diversity of floral forms observed in nature, as indicated by previous studies in the grasses and other systems beyond Arabidopsis and Antirrhinum (reviewed in Krizek and Fletcher 2005). Of course, dahlias and all composites do not follow a typical floral form, and have multiple petalloid organs on individual flowers within the capitulum. Perhaps the ABC model is therefore not the best model for dahlias.

Figure 2. Petalloid stamens form the "collars" of the collarette Dahlia Alpen Diamond.

          Apparently forcing floret numbers into Fibonacci sequence-like predictions is likewise untenable, although more data are required to rule out that “typical” flowers produce organs close to Fibonacci predictions. For example, if 30 flowers were counted from formal decorative types would the “average” be similar to an expected number? Given the variability of dahlia flowers early in the season, perhaps the first few flowers should be ignored in the counting, or perhaps greenhouse conditions result in subpar or irregular flowers. Similarly, how close to a Fibonacci number does a form have to be to qualify? In other words, if 144 is the expectation are 140 – 148 florets acceptable?

Figure 1. Multiple types of floral defects in flowers on F1 plant, SDP ID# 1.

          To explore the genetic control of dahlia floral form we have started a crossing program between cultivars. In particular, we will be interested in answering how many petals will be found in a cross between a single flower (8 petals) and a variety with many petals (formal decorative)? In observing the progeny (F1 progeny of the cross) we found many irregular flowers with mis-shapen petals, missing petals in flowers with 8 petals and more:

Figure 2. Multiple types of floral defects in flowers on F1 plant, SDP ID# 2.

Figure 3. Multiple types of floral defects in flowers on F1 plant, SDP ID# 10.

Figure 4. Multiple types of floral defects in flowers on F1 plant, SDP ID# 33.

Figure 5. Multiple types of floral defects in flowers on F1 plant, SDP ID# 37.

Figure 6. Multiple types of floral defects in flowers on F1 plant, SDP ID# 39.

 References

Coen, E.S., and E.M. Meyerowitz. 1991. The war of the whorls: genetic interactions controlling flower development. Nature. 353:31-7.

Klar, A. 2002. Plant mathematics: Fibonacci's flowers. Nature. 417: 595.

Krizek, B.A., and J.C. Fletcher. 2005. Molecular mechanisms of flower development: an armchair guide. Nature Reviews Genetics. 6:688-98.


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