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Two quite different conceptual areas are understood today under the umbrella term of theoretical morphology: (1) the mathematical simulation of form, and (2) the analysis of the possible spectra of form via hypothetical morphospace construction. The second concept follows from the first, but has quite different goals.

Using a geometric model of shell morphology, it is demonstrated that biconvex brachiopods occupy only a small region of the potential geometric space available to organisms with planispiral exoskeletons composed of two articulated valves. Measurements taken for a sample of 324 genera of the articulate orders Pentamerida, Rhynchonellida, Spiriferida, and Terebratulida were analyzed using a simple geometric model of shell form and ontogeny. The frequency distribution of brachiopod shell morphologies exhibited by the four orders represents the biological optimization of the spatial relationships between area and volume. Biconvex brachiopods develop shells which are designed to minimize shell surface area while maximizing internal shell volume. The means by which optimization is achieved is related directly to the effects of increase in absolute size during ontogeny. The boundaries upon shell geometries utilizable by biconvex brachiopods are determined by (1) limitations of articulation, and (2) limitations of surface and volume.