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Size matters: Sharks follow two-thirds scaling law, proving theory

A new study has used cutting-edge 3D modeling to confirm that sharks follow the "two-thirds scaling law" almost perfectly, with the discovery set to help reshape how we understand biology across the animal kingdom.

The study has confirmed that when it comes to body size, sharks play by the rules—and it could reshape how we understand biology across the animal kingdom.

For more than a century, scientists have relied on a theory that predicts how an animal's surface area and volume scale with size.

Now, researchers from James Cook University (JCU) and the University of Massachusetts have used cutting-edge 3D modeling to confirm this theory in sharks—one of the ocean's most iconic predators. The paper is in the journal Royal Society Open Science.

"We found that sharks follow what's known as the 'two-thirds scaling law' almost perfectly," said Joel Gayford, JCU Ph.D. candidate and lead author on the study.

"This law helps explain how animals exchange heat, energy, and oxygen with their environment—so confirming it in full-sized animals, not just cells, is a big deal."

The team digitally modeled the body shapes of 54 shark species using high-resolution 3D scans created in collaboration with computer graphics artist Johnson Martin.

These scans allowed the researchers to precisely measure surface area and volume, offering rare insights into how body shape influences physiology.

"This ratio is fundamental," said JCU marine biology professor, Dr. Jodie Rummer, a co-author on the study.

"It underpins how animals breathe, regulate temperature, and process waste. And now, for the first time, we've shown it holds true in animals as complex and diverse as sharks."

To rigorously test the rule, the team used phylogenetic regression—a statistical method that considers evolutionary relationships—and found that shark surface area is proportional to volume raised to the power of 0.64. That's just 3% off the theoretical prediction of 0.67.

"It's remarkable," said Prof Rummer. "This suggests sharks have evolved to stick to this ratio, possibly because deviating from it is too costly or constrained by early development."

Indeed, the team believes evolutionary and developmental constraints could explain why sharks from vastly different habitats and lifestyles still obey the same scaling rule.

"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.

Importantly, these findings have real-world applications.

"Surface area-to-volume ratios are key inputs in equations used to model how animals respond to climate change, like how fast they regulate their body temperatures or how efficiently they use oxygen," Gayford said.

"Now, we can use those equations with much greater confidence in sharks and other large animals."

The research highlights how modern imaging technology—and some very patient digital modeling—can answer age-old biological questions.