What links a T. rex to a hummingbird: the surprising mathematical formula that explains it all
The way we think about dinosaurs and their evolutionary tree has changed plenty over the years.
Jurassic Park’s Dr. Alan Grant knew it back in 1993, but even so the science is always evolving. When looking at the 75 million-year-old Velociraptor buried in the soil, he said:
“Look at the half-moon shaped bone in the wrist. No wonder these guys learned to fly... Well maybe dinosaurs have more in common with present-day birds than reptiles. Look at the public bone - - it’s turned backwards, just like a bird. The vertebrae - - full of hollows and air sacs, just like a bird. Even the word raptor means ‘bird of prey’.”
And he was exactly right: modern day birds are, effectively, dinosaurs, and our understanding of everything from Triceratops to Pachycephalosaurus is is constant motion, with new discoveries changing the way we think about these huge creatures that roamed the Earth all those years ago.
The foot of the Cassowary, a large, Australian bird that can reach speeds of 31mph, looks suspiciously like a dino. The evidence is there, and it’s growing.
Recently, a study published in iScience reveals that the way the faces of therapods (the two-legged, T-Rex type dinos) were shaped might well follow what’s known as The Power Cascade Model, a universal power law for modelling the growth and form of teeth, claws, horns, thorns, beaks, and shells of modern fauna.
Common developmental origins of beak shapes and evolution in theropods (abstract):
Vertebrate beaks show a remarkable diversity of forms, epitomized by birds and non-avian theropods. Few studies have investigated how underlying developmental processes influence beak shape. The power cascade is a model of growth describing the log-log linear relationship of the beak radius with distance from the tip. We measured beak and toothed snout shapes in 127 species across 120 families of extant birds and extinct non-avian theropods and found that 95% followed the power cascade model. Ancestral state estimation suggests that the power cascade constitutes a fundamental growth pattern of the theropod rostrum, and perhaps all vertebrate rostra. The morphospace defined by the power cascade shows how bird beak shape explores the geometries associated with ecological specializations while adhering to the growth model. We show that the power cascade influences the macroevolutionary exploration of rostrum morphospace, enabling extant birds to inhabit all components of Earth’s biosphere.
The study, led by Kathleen Garland and Alistair Evans, sampled species from 106 out of 253 extant bird families and 42 out of 44 orders.
They say that beaks follow the logarithmic spiral, which “has long been recognised as a universal model of biological growth... [and] is formed when one side of a structure grows faster than the other at a constant rate and angle relative to the origin of the spiral.”
This is how beaks have their distinct shape. Now they’re saying dinosaurs followed the same mathematics. After laying out the evidence for the undisputed case that modern day beaks are evolved forms of dinosaur ‘snouts’, the scientists then draw back the maths and write that they expect to see “convergently evolved theropod beaks follow[ing] this growth model if the power cascade is a shared developmental pattern.”
A Southern Cassowary claw. Just in case you didn't think that birds are dinosaurs pic.twitter.com/1q9V1rIQxv
— Nature is Amazing ☘️ (@AMAZlNGNATURE) May 25, 2024
Their conclusions are striking. After presenting the evidence, they write the following: “the power cascade model describes a large majority of theropod beak shapes and rostrum shapes, in general... The power cascade, while not unbreakable, is strongly adhered to, pointing to underlying biophysical or developmental mechanisms forming the face of theropods."
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