
Birds of the birds exist in almost all shapes and sizes-from the straw-shaped beak of a hummingbird to the sharp and knife-shaped nozzle of an eagle.
However, this incredible diversity is supported by a hidden mathematical rule that governs the growth and shape of the nozzles of almost every living birds.
In addition, this rule even describes the shape of the oldest ancestors’ beak – the dinosaurs – according to new discoveries, now published in the magazine.
By studying the nozzles in the light of this mathematical rule, we can understand how the faces of birds and other dinosaurs have evolved over 200 million years. It is also possible to find out why, in rare cases, these rules can be broken.
When nature follows the rules
Finding universal rules in biology is rare and difficult – there seems to be few cases where physical laws are so widespread to all organisms.
But when we find a rule, it is a powerful way to explain the standards we see in nature. The team previously discovered a new rule of biology that explains the form and growth of many pointed structuresincluding teeth, horns, hooves, shells and, of course, nozzles.
This simple mathematical rule captures the way the width of a sharp structure, like a beak, expands from the end to the base. This rule is called “cascade of power”.

After this discovery, we became very interested in knowing how the power cascade could explain the shape of bird nozzles and other dinosaurs.
Dinosaurs have their nozzles more than once
Most dinosaurs, such as the Tyrannosaurus rexhas a robust muzzle with pointed teeth. But some dinosaurs (like Ema Ornithomimus edmontonicus) had no teeth and had nozzles.
In the theopods, the group of dinosaurs to which it belonged o T. rexthe nozzles evolved at least six times. At a time, the teeth have been lost and the muzzle stretched to a beak shape over millions of years.
But only one of these impeccable groups of dinosaurs survived mass extinction occurred 66 million years ago. These survivors eventually became the current birds.
The Madrugador Bird Caught the Rule
To investigate the power cascade growth rule, the authors investigated 127 species of theopod And they found that 95% of the spot and muzzle of the theopods follow this rule.
Using state -of -the -art evolutionary analyzes through computational modeling, the study that the ancestral theopod cute that followed the power cascade rule.
This suggests that the power cascade describes the growth not only of the nozzles and muzzles of the theopods, but perhaps muzzles of all vertebrates: mammals, reptiles and fish.
Followers and rules offenders
After surviving mass extinction, birds went through an incredible period of changes. Today, birds live around the world and their nozzles are adapted to each place in very special ways.
We see chickman shapes to eat fruit, catch insects, pierce and tear meat and even drink nectar. Most follow the power cascade growth rule.
Although rare, some birds violate the rules. One of them is the EURÁSIA HARIERwhose highly specialized chickman helps him to sift the mud to capture aquatic life. Perhaps your unique eating style has led you to break this common rule.
Rule offenders further enhance how informative the power cascade is. Most bird nozzles grow according to the rule, and these nozzles can satisfy the Most feed styles.
But occasionally the strangest birds, such as the spoonfuls, break the growth rule in power cascade to Picking up your special worms.
Now that we know that most birds and dinosaurs are following the cascade of power, the next big step in the investigation is to study how bird nozzles grow from the dick to the adult.
If the power waterfall is really a fundamental growth rule in bird nozzles, we can expect to find it hidden in many other forms In the tree of life.
