Mathematical rule found to have shaped bird beaks for 200 million years 

Discover the hidden mathematical rule governing the growth and shape of bird and dinosaur beaks in nature.

Bird beaks come in almost every shape and size – from the straw-like beak of a hummingbird to the slicing, knife-like beak of an eagle.

We have found, however, that this incredible diversity is underpinned by a hidden mathematical rule that governs the growth and shape of beaks in nearly all living birds.

What’s more, this rule even describes beak shape in the long-gone ancestors of birds – the dinosaurs. We are excited to share our findings, now published in the journal iScience.

By studying beaks in light of this mathematical rule, we can understand how the faces of birds and other dinosaurs evolved over 200 million years. We can also find out why, in rare instances, these rules can be broken.

Finding universal rules in biology is rare and difficult – there seem to be few instances where physical laws are so pervasive across all organisms.

But when we do find a rule, it’s a powerful way to explain the patterns we see in nature. Our team previously discovered a new rule of biology that explains the shape and growth of many pointed structures, including teeth, horns, hooves, shells and, of course, beaks.

This simple mathematical rule captures how the width of a pointed structure, like a beak, expands from the tip to the base. We call this rule the “power cascade”.