Spatial and functional modeling of carnivore and insectivore molariform teeth.

The interaction between the two main competing geometric determinants of teeth (the geometry of function and the geometry of occlusion) were investigated through the construction of three-dimensional spatial models of several mammalian tooth forms (carnassial, insectivore premolar, zalambdodont, dilambdodont, and tribosphenic). These models aim to emulate the shape and function of mammalian teeth. The geometric principles of occlusion relating to single- and double-crested teeth are reviewed. Function was considered using engineering principles that relate tooth shape to function. Substantial similarity between the models and mammalian teeth were achieved. Differences between the two indicate the influence of tooth strength, geometric relations between upper and lower teeth (including the presence of the protocone), and wear on tooth morphology. The concept of "autocclusion" is expanded to include any morphological features that ensure proper alignment of cusps on the same tooth and other teeth in the tooth row. It is concluded that the tooth forms examined are auto-aligning, and do not require additional morphological guides for correct alignment. The model of therian molars constructed by Crompton and Sita-Lumsden ([1970] Nature 227:197-199) is reconstructed in 3D space to show that their hypothesis of crest geometry is erroneous, and that their model is a special case of a more general class of models.