7 November 2008
Otger Campàs
Mahadevan Applied Math Lab
Harvard University
Darwin's finches are a group of 14 closely related species that live in the Galapagos and Cocos islands. The most striking difference between them resides in the remarkable variation of their beak shapes, spanning morphologies that range from the pointed and slender beaks of warbler finches to the very deep and broad beaks of ground finches. Recently, the genes controlling the main morphological differences in the beaks of Darwin's finches have been identified; namely, Bmp4 and Calmodulin modulate the major differences in the shape of the beaks. In an attempt to quantify this variability, we analyzed the geometry of the beaks and show that the beak shape of the different species of ground finches are related through a simple scaling transformation. Further study shows that Darwin's finches beaks can be classified, using only scaling transformations, in 3 groups. The same scheme, with the beak shape of different species related by a scaling transformation, is also found in the Caribbean bullfinches. However, Darwin's finches and Bullfinches beaks are not related through a scaling transformation. The goal of our work is to relate, at a quantitative level, the geometric transformations that map the beak of one species onto that of another to the underlying developmental processes and, in particular, to the genetics of beak morphogenesis. Our results suggest that there may be a simple enough framework behind morphological diversity.