Cambridge, Mass., February 22, 2010 -- From how massive humpbacks glide through the sea with ease to the efficient way fungal spores fly, applied mathematicians at Harvard have excavated the equations behind a variety of complex phenomena.
The latest numerical feat by Otger Camps and Michael Brenner, working closely with a team of Harvard evolutionary biologists led by Arhat Abzhanov, zeroes in on perhaps the most famous icon of evolution: the beaks of Darwin's finches.
In a study appearing in the February 16 Early Edition of the Proceedings of the National Academy of Sciences (PNAS), the researchers 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.
The investigation began at Harvard's Museum of Comparative Zoology, where Camps, a postdoctoral fellow at the Harvard School of Engineering and Applied Sciences (SEAS), and Ricardo Mallarino, a graduate student in the Department of Organismic and Evolutionary Biology (OEB) at Harvard, obtained photographs of beak profiles from specimens of Darwin's finches.
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 Camps. "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
|Contact: Michael Patrick Rutter|