Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


Simple math explains dramatic beak shape variation in Darwin's finches

Scaling and shear link morphology, genotype and developmental genetics

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 Campàs 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 Campàs, 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 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."

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.

Brenner, Glover Professor of Applied Mathematics at SEAS, says he is "astonished" that so few variables can help explain such great diversity. The mechanism that allows organisms to adapt so readily to new environments may be a relatively "easy" process.

"This is really significant because it means that adaptive changes in phenotype can be explained by modifications in a few simple parameters," adds Mallarino. "These results have encouraged us to try to find the remaining molecules responsible for causing these changes."

In fact, the mathematical findings also have a parallel genetic basis. Abzhanov, an assistant professor in OEB, and his collaborators explored the role of the two genes responsible for controlling beak shape variation. Bmp4 expression affects width and depth and Calmodulin expression relates to length. It turns out that the expression levels of the two genes, in particular Bmp4, are fundamentally related to the scaling transformations.

"We wanted to know how beaks changed on a fundamental level during evolution of Darwin's finches and how many unique beak shapes we need yet to explain using our developmental genetics approach," says Abzhanov. "Our joint study demonstrates that we understand the species-level variation really well where scaling transformations match up perfectly with expression and function of developmental genes which regulate precisely such type of change. Now we want to understand how novel beak shapes resulting from higher order transformations evolved in Darwin's finches and beyond."

Campàs reflects that the finding helps to address an idea that Darwin raised nearly 175 years ago in the Voyage of the Beagle: "The most curious fact is the perfect gradation in the size of the beaks in the different species of Geospiza, from one as large as that of a hawfinch to that of a chaffinch, and even to that of a warbler … Seeing this gradation and diversity of structure in one small, intimately related group of birds, one might really fancy that from an original paucity of birds in this archipelago [Galapagos], one species had been taken and modified for different ends."

The researchers acknowledge the support of the National Science Foundation through the Division of Mathematical Sciences, and the Materials Research Science and Engineering Center, both at Harvard; the Kavli Institute for Bionano Science and Technology at Harvard University; and the National Institutes of Health.

Michael Patrick Rutter | EurekAlert!
Further information:

More articles from Studies and Analyses:

nachricht Rutgers-led innovation could spur faster, cheaper, nano-based manufacturing
14.02.2018 | Rutgers University

nachricht New study from the University of Halle: How climate change alters plant growth
12.01.2018 | Martin-Luther-Universität Halle-Wittenberg

All articles from Studies and Analyses >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Space observation with radar to secure Germany's space infrastructure

Satellites in near-Earth orbit are at risk due to the steady increase in space debris. But their mission in the areas of telecommunications, navigation or weather forecasts is essential for society. Fraunhofer FHR therefore develops radar-based systems which allow the detection, tracking and cataloging of even the smallest particles of debris. Satellite operators who have access to our data are in a better position to plan evasive maneuvers and prevent destructive collisions. From April, 25-29 2018, Fraunhofer FHR and its partners will exhibit the complementary radar systems TIRA and GESTRA as well as the latest radar techniques for space observation across three stands at the ILA Berlin.

The "traffic situation" in space is very tense: the Earth is currently being orbited not only by countless satellites but also by a large volume of space...

Im Focus: Researchers Discover New Anti-Cancer Protein

An international team of researchers has discovered a new anti-cancer protein. The protein, called LHPP, prevents the uncontrolled proliferation of cancer cells in the liver. The researchers led by Prof. Michael N. Hall from the Biozentrum, University of Basel, report in “Nature” that LHPP can also serve as a biomarker for the diagnosis and prognosis of liver cancer.

The incidence of liver cancer, also known as hepatocellular carcinoma, is steadily increasing. In the last twenty years, the number of cases has almost doubled...

Im Focus: Researchers at Fraunhofer monitor re-entry of Chinese space station Tiangong-1

In just a few weeks from now, the Chinese space station Tiangong-1 will re-enter the Earth's atmosphere where it will to a large extent burn up. It is possible that some debris will reach the Earth's surface. Tiangong-1 is orbiting the Earth uncontrolled at a speed of approx. 29,000 km/h.Currently the prognosis relating to the time of impact currently lies within a window of several days. The scientists at Fraunhofer FHR have already been monitoring Tiangong-1 for a number of weeks with their TIRA system, one of the most powerful space observation radars in the world, with a view to supporting the German Space Situational Awareness Center and the ESA with their re-entry forecasts.

Following the loss of radio contact with Tiangong-1 in 2016 and due to the low orbital height, it is now inevitable that the Chinese space station will...

Im Focus: Alliance „OLED Licht Forum“ – Key partner for OLED lighting solutions

Fraunhofer Institute for Organic Electronics, Electron Beam and Plasma Technology FEP, provider of research and development services for OLED lighting solutions, announces the founding of the “OLED Licht Forum” and presents latest OLED design and lighting solutions during light+building, from March 18th – 23rd, 2018 in Frankfurt a.M./Germany, at booth no. F91 in Hall 4.0.

They are united in their passion for OLED (organic light emitting diodes) lighting with all of its unique facets and application possibilities. Thus experts in...

Im Focus: Mars' oceans formed early, possibly aided by massive volcanic eruptions

Oceans formed before Tharsis and evolved together, shaping climate history of Mars

A new scenario seeking to explain how Mars' putative oceans came and went over the last 4 billion years implies that the oceans formed several hundred million...

All Focus news of the innovation-report >>>



Industry & Economy
Event News

New solar solutions for sustainable buildings and cities

23.03.2018 | Event News

Virtual reality conference comes to Reutlingen

19.03.2018 | Event News

Ultrafast Wireless and Chip Design at the DATE Conference in Dresden

16.03.2018 | Event News

Latest News

For graphite pellets, just add elbow grease

23.03.2018 | Materials Sciences

Unique communication strategy discovered in stem cell pathway controlling plant growth

23.03.2018 | Agricultural and Forestry Science

Sharpening the X-ray view of the nanocosm

23.03.2018 | Physics and Astronomy

Science & Research
Overview of more VideoLinks >>>