Dimensionamento e transformações acentuadas capturam a variação de formato de bicos nos tentilhões de Darwin

sexta-feira, fevereiro 19, 2010

Scaling and shear transformations capture beak shape variation in Darwin’s finches

O. Campàs a,b, R. Mallarino b, A. Herrel b, A. Abzhanov b,1,2, and M. P. Brenner a,1,2

-Author Affiliations

aSchool of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138; and

bDepartment of Organismic and Evolutionary Biology, Harvard University, 16 Divinity Avenue, Cambridge, MA 02138

↵1A.A. and M.P.B. contributed equally to this work.

Edited* by Marc W. Kirschner, Harvard Medical School, Boston, MA, and approved January 5, 2010 (received for review October 7, 2009)


Evolution by natural selection has resulted in a remarkable diversity of organism morphologies that has long fascinated scientists and served to establish the first relations among species. Despite the essential role of morphology as a phenotype of species, there is not yet a formal, mathematical scheme to quantify morphological phenotype and relate it to both the genotype and the underlying developmental genetics. Herein we demonstrate that the morphological diversity in the beaks of Darwin’s Finches is quantitatively accounted for by the mathematical group of affine transformations. Specifically, we show that all beak shapes of Ground Finches (genus Geospiza) are related by scaling transformations (a subgroup of the affine group), and the same relationship holds true for all the beak shapes of Tree, Cocos, and Warbler Finches (three distinct genera). This analysis shows that the beak shapes within each of these groups differ only by their scales, such as length and depth, which are genetically controlled by Bmp4and Calmodulin. By measuring Bmp4 expression in the beak primordia of the species in the genus Geospiza, we provide a quantitative map between beak morphology and the expression levels of Bmp4. The complete morphological variation within the beaks of Darwin’s finches can be explained by extending the scaling transformations to the entire affine group, by including shear transformations. Altogether our results suggest that the mathematical theory of groups can help decode morphological variation, and points to a potentially hierarchical structure of morphological diversity and the underlying developmental processes.

Bmp4   craniofacial evolution and development    Geospiza    morphogenesis   morphological hierarchy


2To whom correspondence may be addressed. E-mail:brenner@seas.harvard.edu or abzhanov@fas.harvard.edu.

Author contributions: O.C., R.M., A.A., and M.P.B. designed research; O.C., R.M., A.A., and M.P.B. performed research; O.C. and A.H. contributed new reagents/analytic tools; O.C. analyzed data; O.C., R.M., A.A., and M.P.B. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0911575107/DCSupplemental.

†We analyzed all species of Darwin’s Finches available in the Harvard Museum of Comparative Zoology.


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