How the shark's body grows with geometric precision

For centuries, scientists have tried to understand how sharks and other animals grow and function as they increase in size.

At the heart of this inquiry lies a simple geometric principle: surface area grows more slowly than volume. The “two-thirds scaling law” captures this relationship, suggesting that surface area scales with volume to the power of 2/3.

While the idea is elegant, proving it in large, complex animals like sharks has been a challenge.

Now, a new study led by researchers from James Cook University (JCU) and the University of Massachusetts offers compelling proof that this rule holds true for one of the most diverse and ancient animal groups on the planet – sharks.

Sharks grow by the rules

Using digital models of 54 shark species, the team uncovered remarkable consistency in how these animals scale in size. Their work not only strengthens a foundational principle in biology but also reveals hidden constraints that may shape evolution itself.

“We found that sharks follow what’s known as the ‘two-thirds scaling law’ almost perfectly,” said Joel Gayford, lead author and PhD candidate at JCU.

This means that as the body of a shark gets larger, the surface area increases in a predictable way based on their volume.

3D models map the shark’s body

The team created high-resolution 3D meshes from CT scans and photogrammetry of museum specimens. The models were cleaned and processed in Blender software to remove distortions caused by preservation. Surface area and volume were measured digitally for accuracy.

The sample ranged from the tiny Euprotomicrus bispinatus to the massive Rhincodon typus, the whale shark. Across these, the team observed nearly perfect adherence to the expected geometric rule.

They scaled every species to the same body length (500 cm) and still found minimal differences in surface area and volume. This step removed body length as a confounding factor.

Shark scaling stays consistent

The study grouped sharks by habitat – pelagic, reef-associated, demersal, and others. Most showed near-identical surface area-to-volume relationships.

Only reef-associated sharks showed minor deviation, with a scaling exponent of 0.60. Pelagic sharks matched the theoretical 0.66 almost exactly.

The team also accounted for evolutionary history using phylogenetic generalized least squares (PGLS) analysis. This ensured close relatives did not skew the results. Even after this, the average scaling value was just 0.64, only 3% off from 0.66.

Biology restricts growth

“This ratio is fundamental,” said Professor Jodie Rummer. “It underpins how animals breathe, regulate temperature, and process waste.” The near-perfect fit hints at deep-rooted evolutionary and developmental constraints.

Developmental limitations may prevent major changes in tissue distribution. Altering body geometry early in development is likely energy-intensive.

“Changing the way tissue is distributed throughout the body might require major changes during early embryonic development, and that’s expensive, energetically speaking,” said Gayford.

Why shape stills matters

The two-thirds law is not just theoretical. It supports models predicting how animals regulate heat, absorb oxygen, or respond to climate change.

“Surface area-to-volume ratios are key inputs in equations used to model how animals respond to climate change,” said Gayford. These equations can now be applied with greater confidence to sharks and other large animals.

The authors also observed that surface area in sharks did not follow phylogenetic patterns as strongly as volume did. This suggests that surface area may be more flexible but still constrained by developmental factors.

Shark body follows deep biology

Despite massive variation in shark ecology and movement, some are sluggish bottom-dwellers and others fast-swimming predators, their surface-to-volume relationships stay constant.

Even differences in shape and lifestyle do not seem to change the rule. That consistency points to deeper biological limits rather than ecological demands.

This study adds weight to the idea that body design follows strict physical and developmental rules. It also shows how new tools like 3D imaging can answer long-standing questions in biology.

Although researchers still need to explore the energy costs of body shape changes, this study lays a strong foundation.

Sharks obey the geometry of life, their body surfaces grow in lockstep with volume in a way that supports a basic biological law. The rule holds true across shape, size, and ecological function.

That’s a rare kind of simplicity in biology and one that might apply far beyond sharks.

The study is published in the journal Royal Society Open Science.

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