Floral formula

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* P3+3 A3+3 G(3)
General floral formula of the Liliacaeae: Flowers actinomorphic and hermaphrodite with 6 undifferentiated tepals in two whorls of three, the same number and arrangement of stamens, and a superior ovary with 3 fused carpels. Individual species and genera may have more or less derived formulas.

Floral formula is a means to represent the structure of a flower using numbers, letters and various symbols, presenting substantial information about the flower in a compact form. It can represent a taxon, usually giving ranges of the numbers of different organs, or particular species. It is one of the two ways of describing flower structure developed during the 19th century, the other being floral diagrams.[1] The format of floral formulae differs between authors, yet they tend to convey the same information.[2]

History[edit]

Floral formulae were developed at the beginning of 19th century and their use has declined since.[1] The first authors using them were Cassel[3] (1820) and Martius[4] (1828). Grisebach[5] (1854) used them in his textbook to describe characteristics of floral families, stating numbers of different organs separated by commas and highlighting fusion. Sachs[6] (1873) used them together with floral diagrams, he noted their advantage of being composed of "ordinary typeface". Although Eichler widely used floral diagrams in his Blüthendiagramme,[7][8] he used floral formualae sparingly, mainly for families with simple flowers. Sattler's[9] Organogenesis of Flowers (1973) takes advantage of floral formulae and diagrams to describe the ontogeny of 50 plant species. Newer books containing formulae include Plant Systematics by Judd et al.[10] (2002) and Simpson[11] (2010). Prenner et al. devised an extension of the existing model to broaden the descriptive capability of the formula and argued that formulae should be included in formal taxonomic descriptions.[1] Ronse De Craene (2010)[2] partially utilized their way of writing the formulae in his book Floral Diagrams. He stated that the format of floral formulae differs between American and European tradition, yet the information contained is generally analogical.[2]:38

Contained information[edit]

The formula expresses counts of different floral organs,[note 1] these are usually preceded by letters or abbreviations according to the organ type. They are ordered corresponding to the arrangement of the parts of the flower from the outside in:

Bracts Bracteoles Tepals (perigon or perianth), or sepals (calyx) and petals (corolla) Stamens (androecium) Carpels (gynaeceum) Ovules
B[1] Bt[1] P[1] or CaCo[12] A G V[1] or O[9]
K[1] or Ca[12] C[1] or Co[12]

The labels with darker backgrounds are less common. "V" used by Prenner et al. for the number of ovules per gynoecium is followed by lowercase letter describing the type of placentation.

The numbers are inserted after the labels, they may be formatted as sub- or superscript. If an organ is absent, its number is written as "0", if there are "many" (usually more than 10–12) instances, it can be written as "∞". Whorls of the same organ are separated by "+". Organ counts within a whorl can be separated by ":", for example when part of the whorl is morphologically different. A range can be given if the number is variable, e.g. when the formula summarizes a taxon.

K3+3 – a calyx with six free sepals, arranged as two separate whorls
A∞ – many stamens
P3–12 – perianth from three to twelve tepals

The formula can also express organ fusion. Fusion of one organ type can be shown by enclosing the number in a circle, fusion of different organs can be represented by ties, as e.g. in Judd et al.. Prenner et al. state that this method is difficult to achieve via standard typesetting.[1]:242 Joining of organs can be more readily written using parentheses "(…)" if instances of the same organ are fused. Fusion between different organs can be achieved by square "[…]", eventually curly brackets "{…}". Prenner et al. propose superscript zero for a lost organ, and superscript "r" for a reduced one. Ronse De Craene uses a degree symbol to mark a staminode (infertile stamen) or pistillode (infertile carpel).

A(5) – five fused stamens
[C(5) A5] – corolla fused from 5 petals, fused to stamens
A3:2r+50 – (Prenner et al.) androecium in two whorls, first contains 3 stamens and 2 staminodes, second whorl lost
A1+2° – (Ronse De Craene) androecium in two whorls, first whorl containing a stamen, second whorl containing two staminodes

Ovary position is shown by alternating the "G" label. Simpson circumvents the intricate formatting by expressing the ovary position by words.

superior ovary inferior ovary half-inferior ovary
Prenner et al.[1]:243, Ronse De Craene[2]:39 G Ĝ -G-
Sattler[9]:xviii G G
Simpson[11] G (…), superior G (…), inferior G (…), half-inferior

Symmetry may be described for the whole flower, in such case the corresponding symbol is usually placed at the beginning of the formula. It may be also outlined separately for different organs, placing it after their labels or numbers, or it may not be included in the formula at all. The symbols describing symmetry are as follows:

polysymmetry disymmetry monosymmetry asymmetry spiral arrangement
Prenner et al.[1]:242 * ↓, → or Ø, depending on the symmetry plane orientation not mentioned
Ronse De Craene[2]:39 ↓, arrow orientation depending on symmetry plane orientation
Sattler[1]:xviii + ∙|∙ not mentioned
Judd et al.[10]:66 * not mentioned X $

Sexuality of the flower can be highlighted by ☿ or Male and female sign.svg for hermaphrodite, ♂ for male (staminate) and ♀ for female (pistillate) flower. The symbols are usually placed at the beginning of the formula, after or before the symmetry symbol, if there is any. Prenner et al. recommend to use two formulas preceded by ♀ and ♂, respectively, for flowers of separate sexuality.

Floral formula can also incorporate the fruit type, Judd et al.[10] place it at the very end.

Examples[edit]

↯ K3 [C3 A1°–3°+½:2°] Ĝ(3)[2]:39 – the formula of Canna edulis; asymmetric flower; calyx of three free sepals; corolla of three free petals joined with androeceum; androeceum in two whorls, the outer whorl contains 1–3 staminodes, the inner contains ½ of a stamen and 2 staminodes; gynaeceum fused of 3 carpels, inferior ovary

B BtC K3:(2)C↓ C3:2r↓ A(3):2r↓+4r:10 G1↓ Vm8–10[1]:246 – the formula of Tamarindus indica; bract and petaloid bracteoles; monosymmetric calyx of three and two petaloid sepals; monosymmetric corolla of three and two reduced petals; two whorls of stamens, the outer monosymmetric from three fused and two reduced stamens, the inner of 4 reduced and 1 lost stamen; monosymmetric gynoecium of 1 carpel with superior ovary; marginal placentation with 8–10 ovules per gynoecium

Notes[edit]

  1. ^ Bracts and bracteoles are not considered parts of the flower itself, yet they may be included in the floral formula

References[edit]

  1. ^ a b c d e f g h i j k l m n Prenner, Gerhard; Richard M. Bateman; Paula J. Rudall (2010-02). "Floral formulae updated for routine inclusion in formal taxonomic descriptions". Taxon 59 (1): 241–250. ISSN 0040-0262. 
  2. ^ a b c d e f Ronse De Craene, Louis P. (2010-02-04). Floral Diagrams: An Aid to Understanding Flower Morphology and Evolution. Cambridge: Cambridge University Press. ISBN 978-0-521-49346-8. 
  3. ^ Cassel, F. P. (1820). Morphonomia botanica: sive observationes circa proportionem et evolutionem partium plantarum. Colonia Agrippina [Cologne]: M. DuMont-Schauberg. 
  4. ^ Martius, C. F. (1828). "Über die Architectonik der Blüthen". Isis (Oken) (21): 522–529. 
  5. ^ Grisebach, A. (1854). Grundriss der systematischen Botanik. Göttingen: Verlag der Dieterichschen Buchhandlung. 
  6. ^ Sachs, J. (1873). Lehrbuch der Botanik nach dem gegenwaertigen Stand der Wissenschaft. Leipzig: Engelmann. 
  7. ^ Eichler, August Wilhelm (1875). Blüthendiagramme, erster Theil: Enthaltend Einleitung, Gymnospermen, Monocotylen und sympetale Dicotylen. Leipzig: Wilhelm Engelmann. 
  8. ^ Eichler, August Wilhelm (1878). Blüthendiagramme, zweiter Theil: Enthaltend die apetalen und choripetalen Dicotylen. Leipzig: Wilhelm Engelmann. 
  9. ^ a b c Sattler, Rolf (1973). Organogenesis of flowers; a photographic text-atlas. Toronto, Buffalo: University of Toronto Press. ISBN 0-8020-1864-5. 
  10. ^ a b c Judd, Walter S.; Christopher S. Campbell; Elizabeth A. Kellogg; Peter F. Stevens; Michael J. Donoghue (2002). Plant Systematics: A Phylogenetic Approach (2nd ed.). Sunderland, Mass., U.S.A.: Sinauer Associates. ISBN 0878934030. 
  11. ^ a b Simpson, Michael George (2010). Plant Systematics. Oxford (Great Britain): Academic Press. ISBN 978-0-12-374380-0. 
  12. ^ a b c http://www.cactus-art.biz/note-book/Dictionary/Dictionary_F/dictionary_floral_formula.htm

External links[edit]

  • Kvetné vzorce – a website dedicated to floral formulae (in Slovakian)