Biological Sciences: Robert Dorit (Smith College)
Statistics: Nicholas Horton (Smith College)
Biological objects, from ecosystems to molecules, exist in three-dimensional space. Over the past century, considerable progress has been made not only in the measurement and description of these objects, but in the elucidation of the underlying rules that generate their form. The mathematical description of biological shape, whether in the form of coupled equations describing gastropod coiling or of folding algorithms for RNA secondary structure, make it possible to describe a “shape space” for the relevant objects. That description of shape space, in turn, makes it possible to examine the occupancy of that space. The data suggest that existing objects are not isotropically distributed in shape space, but are instead clumped and that large amounts of shape space are unoccupied. We are exploring the underlying reasons for that non-isotropic distribution, which may be functional, historical, stochastic or developmental. mathematical statistics and geometry are integral parts of this project.