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On Relative Proportions in Serially Repeated Structures (Seriometry. —I. Limbs and Body‐Segments of Lithobius forficatus (L.).
Author(s) -
NEEDHAM A. E.
Publication year - 1946
Publication title -
proceedings of the zoological society of london
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.915
H-Index - 96
eISSN - 1469-7998
pISSN - 0370-2774
DOI - 10.1111/j.1096-3642.1946.tb00098.x
Subject(s) - allometry , mathematics , series (stratigraphy) , smoothness , dimension (graph theory) , inflection point , maxima , polynomial , mathematical analysis , combinatorics , geometry , biology , art , ecology , paleontology , performance art , art history
Summary.1 . There is a graded change in each dimension along a series of repeated structures. It is not usual to find any two consecutive members of the series absolutely identical in size and proportions. 2 . The “seriogressive” change is typically smoothly graded. There are rarely sharp “breaks” or sudden turning‐points in the series‐profiles of the various dimensions. 3 . The form of a profile for a particular dimension is usually quite characteristic and may show no very close correlation with that of the profiles for other dimensions, even of the same structure. Maxima, points of inflection, etc., of such profiles may be situated at different points in the series. 4 . The series‐profiles show a number of age‐differences. Sex differences are not marked in Lithobius. 5 . The differential variation between two dimensions in seriogression does not follow the simple allometry relation, as it often does between two dimensions of a structure in ontogeny. Along the limb, however, there is a gradient in the magnitude of the seriogressive increment which compares with the growth‐gradient along the limb. 6 . The smoothness of a series‐profile does not indicate that a simple mathematical formula will express its seriogressive change. Many factors may be involved. Polynomial expressions are usually required. The profiles for different dimensions, and even the different parts of one profile, may require polynomials of different power. The addition of one more determining factor has little effect on the form of a profile. 7 . Seriometric proportions may be determined by functional requirements and a smooth series‐profile may be a reflection of the way in which functional factors change along such a series. It is less probable that profiles are the incidental result of growth‐patterns involving smooth gradients in growth‐rates. 8 . A study of the seriometric features of repeated structures may help to understand their functions. Both seriometric and ontogenetic growth‐changes may help towards a functional solution of such problems as the homology between the various limb‐segments in different‐groups of arthropods.