In constructional morphology - an explanatorily higher level of functional morphology - three types of relations are studied: function x function, function x form and form x form (fig. 2). In this paper methodology and techniques for the relation form x form are discussed, and illustrated by the topographic relations between two joining forms, viz. the eye and the suspensorium of African lacustrine Cichlidae. Planar geometric models explain to a major extent the anatomically observed complex relation between the considered form-features of the two forms, viz. the shape, size and position of the eye (fig. 6) and the shape and structure of the suspensorium (figs. 4, 5). Although eye and suspensorium are not in close contact, it is demonstrated that the shape, size and position of the eye are geometrically closely related to the form of the suspensorium-orbit (i.e. the indentation of the suspensorium accommodating a ventral section of the eye, fig. 4). In turn, the form (viz. size and shape) of the suspensorium-orbit is geometrically related to the suspensorium-form, but this relation is more complex than that between eye and orbit. Of all structural elements of the suspensorium (SESUSP'S), only the form (viz. size and shape; position was not investigated) of metapterygoid, entopterygoid and of the hyomandibula are clearly correlated with orbit-form; there is no, or only a far less evident, correlation between orbit-form and the form of the more distal SESUSP'S. This anatomically based correlation is mathematically explained by a direct as well as indirect geometric relation between orbit-form and the form of the three SESUSP'S; the indirect one is through the geometric relation between orbit-form and the suspensorium-shape. The observed geometric relations are general properties of the cichlid Bauplan: they are the same for cichlids from different lakes, are independent of size and hold interspecifically as well as intraspecifically. The observations and the facts refute the hypothesis that adaptive morphological differentiation of cichlids is mainly an allometric effect of overall size (contra STRAUSS, 1984). In the analysis of the relation between geometric constellations and function, the term constructional demand is introduced. It refers to geometric differences directly linked with differences in function. Not all geometric differences result from different functions, nor do different functions necessarily have a geometric effect. The necessity in constructional morphology to distinguish between constructional and functional context is accentuated. With the Opthalmotilapia-Assemblage (LIEM, 1980; GREENWOOD, 1983) as an example it is demonstrated that a particular character-state observed in different species could be the indirect geometric effect of different functions not involving that character state, e.g. a shallow metapterygoid resulting in species A from a streamlined head-profile pressing a normally sized eye into the suspensorium and resulting in species B from a large eye intruding the suspensorium (fig. 19). Distinguishing such geometrically convergent character-states is a critical tool for refuting the synapomorphic status of characters. The extreme character states observed among cichlids from Lake Tanganyika are often terminal sections only arbitrarily separable from graded morphoclines holding for lacustrine cichlids in general. It is argued that such a character-state is per se not a sufficient criterion for its synapomorphic status (contra LIEM, 1981). As the complete geometric and other argumentations are by necessity somewhat cumbrous, the reader not interested in the details of this argument is advised to omit this section and to start with the extensive summary (p. 473). This should provide sufficient basic information for the general discussion and implications which are the subsequent sections.
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Cornelis D. N. Barel (1983) studied this question.
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