The mathematical treatment of leaf venation: the variation in secondary vein length along the midrib.

Abstract:

BACKGROUND AND AIMS:In some dicotyledonous leaves and leaflets, the secondary veins run more-or-less straight to the margins and have well-defined lengths. For a given half-lamina of length L, an equation, previously proposed, relates the lengths of these veins, p, to the distances, l, between the leaf tip and their insertions on the midrib: p = B2(x+y)l(x)(L - l)(y)/L(x+y-1), where B, x and y are fitted parameters. Aspects of the formula are re-examined, including its general applicability, significance and usefulness. METHODS:Length measurements were made on leaves of various dicotyledons, notably Ulmus glabra, U. procera, Alnus viridis, A. glutinosa, Corylus avellana and Crataegus monogyna. Equations were fitted by non-linear regression. KEY RESULTS:The equation has now been applied descriptively to 23 species of eight families, but it is sometimes preferable or necessary to replace the measured length, L, with a fourth parameter that may differ significantly from it. Within a given species, values of the indices x and y are positively correlated. Leaves of some U. glabra depart qualitatively from the general pattern. As an example of hypothesis testing, the equation was used to show that the retuse or emarginate leaf tips of A. glutinosa are not due to stunting. CONCLUSIONS; That the equation applies to many species suggests that the underlying processes of leaf growth are quantitatively similar. Although relevant knowledge of these is scant, consideration of mathematical relationships may help their elucidation.

journal_name

Ann Bot

journal_title

Annals of botany

authors

Burton RF

doi

10.1093/aob/mch024

keywords:

subject

Has Abstract

pub_date

2004-02-01 00:00:00

pages

149-56

issue

2

eissn

0305-7364

issn

1095-8290

pii

mch024

journal_volume

93

pub_type

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