Iterating the expression x2-1 yields a regular repeating pattern. Iterating the only slightly different 2x2-1 (0 < x < 1) produces chaotic variation. From simple beginnings and subtle differences endless forms, beautiful and wonderful, result. Luckily for us, biological form often owes less to chaos than it does to the interaction of geometry and biology. Requirements of particular modes of life, richness of resources, mechanical demands of form: every component of an organism's life opens particular doors in the warehouse of possible morphology and closes others. Modeling is a way of investigating this warehouse's blueprint, i.e., the rules governing the production of form. Theoretical models of form can help us understand the contributions that genetics and development, the constraints of physical law, and the demands of function make to the generation of morphology. These same theoretical models can also serve as a foundation for studies of the patterns of the evolution of form.

Here I model crinoid calyxes using two simple plate parameters. With few exceptions, the resulting theoretical geometries replicate the range of crinoid calyx morphology observed in the natural world. I then use the parameters of this model to create a theoretical morphospace encompassing both the realized and unrealized possibilities of crinoid calyx construction. The model and the associated morphospace demonstrate that the occupation of crinoid cup space is nonuniform in time and space. Much of the space available for colonization has been occupied. However, fringe areas are more sparsely populated than central areas; many of these fringe forms are functionally as well as morphologically specialized. Unlike coiling shell morphospace, higher taxa do not generally preoccupy particular areas of morphospace, reinforcing the general understanding that convergence is rife within the group. Where departures from the standard cup morphologies do exist, the organisms are typically divergent from standard crinoid functional and/or ecological habits.

75/125 YEARS