Floral formula

✶K5[C(5)A5]G(5)

Floral formula ofAnagallis arvensis.Polysymmetric flower. The perianth consists of5 free sepalsand5 joined petals,which are fused with androecium. Flower is bisexual,it contains 5 stamens,pistil is fused of five carpels, ovary is inferior.

Afloral formulais anotationfor representing the structure of particular types offlowers.Such notations use numbers, letters and various symbols to convey significant information in a compact form. They may represent the floral form of a particular species, or may be generalized to characterize highertaxa,usually giving ranges of numbers of organs. Floral formulae are one of the two ways of describing flower structure developed during the 19th century, the other beingfloral diagrams.The format of floral formulae differs according to the tastes of particular authors and periods, yet they tend to convey the same information.

A floral formula is often used along with afloral diagram.

History

Floral formulae were developed at the beginning of the 19th century.The first authors using them were Cassel(1820) who first devised lists of integers to denote numbers of parts in named whorls; and Martius(1828). Grisebach(1854) used 4-integer series to represent the 4 whorls of floral parts in his textbook to describe characteristics of floral families, stating numbers of different organs separated by commas and highlighting fusion. Sachs(1873) used them together with floral diagrams, he noted their advantage of being composed of "ordinarytypeface".

Cassel formula

AlthoughEichlerwidely used floral diagrams in hisBlüthendiagramme,he used floral formulae sparingly, mainly for families with simple flowers.Sattler'sOrganogenesis of Flowers(1973) takes advantage of floral formulae and diagrams to describe theontogenyof 50 plant species. Newer books containing formulae includePlant Systematicsby Juddet al.(2002) and Simpson(2010). Prenneret al.devised an extension of the existing model to broaden the descriptive capability of the formula and argued that formulae should be included in formaltaxonomicdescriptions.Ronse De Craene (2010)partially utilized their way of writing the formulae in his bookFloral Diagrams.

Contained information

Organ numbers and fusion

The formula expresses counts of different floral organs;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 to the inside:

Bracts	Bracteoles	Tepals (perigonorperianth), orsepals(calyx) andpetals(corolla)		Stamens(androecium)	Carpels(gynoecium)	Ovules
B	Bt	Por CaCo		A	G	Vor O
		Kor Ca	Cor Co

The labels with darker backgrounds are less common. "V" used by Prenneret al.for the number of ovules per gynoecium is followed by lowercase letter describing the type ofplacentation.Forepicalyx/calyculus,the letter "k" is used.

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" or it is omitted, 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 petals

Groups of organs can be described by writing the number of instances in the group as superscript.

A5² – 5 groups of 2 stamens

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 byties,as e.g. in Juddet al.Prenneret al.state that this method is difficult to achieve via standard typesetting.Joining of organs can be more readily written usingparentheses"(…)" if instances of the same organ are fused. Fusion between different organs can be achieved bysquare"[…]", eventuallycurly brackets"{…}".

• A(5) – five fused stamens
• [C(5) A5] – corolla fused from 5 petals, fused to stamens

Prenneret al.propose superscript zero for a lost organ, and superscript "r" for a reduced one. Ronse De Craene uses adegree symbolto mark astaminode(infertile stamen) orpistillode(infertile carpel).

• A3:2^r+5⁰– (Prenneret 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 stamens in Ovary position

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
Prenneret al.,Ronse De Craene	G	Ĝ, Ğ	-G-
Sattler		G	G
Simpson	G…, superior	G…, inferior	G…, half-inferior

Symmetry

Symmetryor arrangement 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. It is described by following symbols:

	polysymmetry (actinomorphic)	disymmetry	monosymmetry (zygomorphic)	asymmetry	spiral arrangement
Prenneret al.	*	┼	↓, → or Ø, depending on the symmetry plane orientation	∂	not mentioned
Ronse De Craene	✶	↔	↓, arrow orientation depending on symmetry plane orientation	↯	↺
Sattler	✳	+	∙|∙		not mentioned
Juddet al.	*	not mentioned	X	$
Subrahmanyam	⊕		% in median plane, ÷ in lateral plane	not mentioned
Rosypal	✳	⤧	↓	↯

Sexuality

Sexuality of the flower can be highlighted by ☿ or ⚥ for hermaphrodite (bisexual), ♂ 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. Prenneret al.recommend to use the corresponding symbols (♀ and ♂) only for flowers of separate sexuality. Ronse De Craene utilizes the words "pistillate" or "staminate" instead of the symbols.

Floral formula can also incorporate the fruit type, Juddet al.place it at the very end.

Examples

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

B Bt^CK3:(2)^C↓ C3:2^r↓ A(3):2^r↓+4^r:1⁰G1↓ Vm8–10– the formula ofTamarindus 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.

Using boxes

Narcissus Floral formula

Br ✶ ☿P3+3+CorollaA3+3G(3) Bracteate, Actinomorphic, Bisexual Perianth: 6 tepals in 2 whorls of 3 Stamens: 2 whorls of 3 Ovary: Superior - 3 fused carpels

✶P3+3A3+3G(3)

LiliaceaeFloral formula
Flowers actinomorphicand hermaphrodite with 6undifferentiated tepalsintwo whorls of three,the samenumber and arrangementofstamens,and asuperior ovarywith3 fused carpels.Individual species and genera may have more or less derived formulas.

Haloragaceae Floral formula

✶$\mathrm {K} ^{3-4}$$\mathrm {C} ^{3-4}$or$\mathrm {C} ^{0}$$\mathrm {A} ^{2-8}$$\mathrm {G} ^{\overline {(2-4)}}$ 3-4 free sepals, 3-4 free petals (or absent), 2-8 stamens, inferior ovary with 2-4 fused carpels

See also

• Floral diagram

Bibliography

• N S Subrahmanyam, Modern Plant Taxonomy, Vikas Publishing House Pvt Ltd, 2009.ISBN0706993462

External links

• Kvetné vzorce– a website dedicated to floral formulae (in Slovakian)
• Table 2.1. Floral formulae; symbols used in this book. In Ronse De Craene, p. 39
• Symbols employed in floral formula. In Subrahmanyam, p. 42
• Floral Diagram Generator– a website to generatefloral diagramsfrom floral formulae.