In a study appearing in the February 16 Early Edition of the Proceedings of the National Academy of Sciences(PNAS), the researchers — Otger Campàs and Michael Brenner, working closely with a team of Harvard evolutionary biologists led by Arhat Abzhanov — demonstrate that simple changes in beak length and depth can explain the important morphological diversity of all beak shapes within the famous genus Geospiza. Broadly, the work suggests that a few, simple mathematical rules may be responsible for complicated biological adaptations.
Using digitization techniques, the researchers found that 14 distinct beak shapes, that at first glance look unrelated, could be categorized into three broader, group shapes. Despite the striking variety of sizes and shapes, mathematically, the beaks within a particular group only differ by their scales.
“It is not possible, however, to explain the full diversity of beak shapes of all Darwin's finches with only changes in beak length and depth,” explains Campàs. “By combining shear transformations (basically, what happens when you transform a square into a rhombus by shoving the sides toward one another), with changes in length and depth, we can then collapse all beak shapes onto a common shape.”
CT scans used
Using Micro-Computed Tomography (CT) scans on the heads for the different species in the genus Geospiza, Anthony Herrel, an Associate of the Museum of Comparative Zoology, helped the team go one step further, verifying that the bone structure of the birds exhibits a similar scaling pattern as the beaks.
Thus, beak shape variation seems to be constrained by only three parameters: the depth of the length for the scaling transformation and the degree of shear.