The primary objective of this research is to develop mathematical models that describe growth patterns and to develop alternate methods for the comparison of growth patterns between different species of animals. It has long been thought that the process of growth plays an important role in producing the changes in appearance of animals through evolution. One major theory is that changes in either the timing or rate of growth can produce profound changes in the appearance of an animal. The investigators propose to mathematically model changes in the timing of growth. This will be done using three-dimensional data from modern animals, providing a realistic representation of how structure changes through time. Using the mathematical models that they develop and three-dimensional data on the structure of living forms, the researchers will predict what that form would look like if it's growth pattern was changed in a prescribed way. These methods can be used to test ideas about how the structure of modern animals emerged from more primitive forms.