Beak shape variation in Darwin's finches 


Illustrations by John Gould showing 4 species of Darwin's finches. Adapted from C. Darwin (1845) Voyage of the Beagle, 2nd edition. 

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. The possible morphologies of organisms seem unlimited but, are they? How can we make sense of morphological diversity and relate morphology (phenotype) to the underlying developmental genetics (genotype)? We use the classic case of morphological diversity in the beaks of Darwin’s finches to address these questions, not only because it is a textbook example for many of the central questions in ecology and evolutionary biology, but also because the developmental genetics underlying beak shape variation is fairly well known, allowing for a quantitative comparison of genotype and phenotype.
The question of how to describe morphological diversity has been extensively studied from many different perspectives. D’Arcy Thompson was the first to propose that the morphologies of different organisms could be mathematically related to each other (On Growth and Form, 1917). In spite of the major influence of his work on the early ideas of evolutionary theory, its impact was considerably dampened due to the absence of a direct link between the mathematical morphological relations proposed and the underlying developmental processes and evolutionary relations. More recent studies of morphological diversity focus on the molecular level. Indeed, many of the studies of morphological diversity concentrate on conserved modules of gene regulatory networks that explain similar body plans or morphological structures. While it is essential to understand the genotypic structure behind morphological diversity, it is also necessary to quantitatively understand the phenotypic structure, as otherwise they cannot be connected to each other in a quantitative manner. Our approach is complementary to genotypic studies, focusing on the quantification of morphological phenotype as an essential step to relate phenotypic structure to genotypic structure.
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. 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 Bmp4 and 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.
Scaling and shear transformations capture beak shape variation in Darwin’s finches. O. Campàs, R. Mallarino, A. Herrel, A. Abzhanov and M.P. Brenner. Proc. Nat. Acad. Sci. USA 107, 335660 (2010).
Closely related bird species demonstrate flexibility between beak morphology and underlying developmental programs. R. Mallarino, O. Campàs, J.A. Fritz, K.J. Burns, O.G. Weeks, M.P. Brenner and A. Abzhanov. Proc. Nat. Acad. Sci. USA 109, 162227 (2012). 