A new study published in the journal Royal Society Open Science confirms that a diverse range of shark species adheres to a fundamental biological principle known as the “two-thirds scaling law.” Researchers from James Cook University and the University of Massachusetts found that this rule, which governs how an animal’s physical properties change with its size, holds across a massive scale. The discovery provides crucial, real-world validation for a theory that helps explain how animals exchange heat, energy, and waste with their environment. This is significant because the relationship between an organism’s surface area and its internal volume dictates many life-sustaining processes, from breathing to regulating body temperature.

The two-thirds scaling law is a mathematical concept stating that as an organism increases in size, its volume increases faster than its surface area. Specifically, it predicts that surface area will scale with volume raised to the power of 0.67. While this phenomenon has been observed in individual cells and tissues, it has been rarely tested at the whole-organism level in a large group of related species. To tackle this, the research team created highly detailed 3D digital models of 54 different shark species, which varied in body mass by a factor of nearly 19,000. These precise models enabled them to measure the surface area accurately and the volume of each shark, providing a robust dataset to test the century-old theory.

Using a statistical method that accounts for the evolutionary relationships between species, the team found that the surface area of sharks scales with volume raised to the power of 0.64. This figure is remarkably close to the theoretical prediction, differing by only 3%. “This ratio is fundamental,” said Dr. Jodie Rummer, a co-author and marine biology professor at James Cook University, in a university press release. “It underpins how animals breathe, regulate temperature, and process waste. Moreover, now, for the first time, [we have] shown it holds […] in animals as complex and diverse as sharks.” The researchers found no evidence that the sharks’ environment or lifestyle influenced this relationship, suggesting a more deep-seated cause.

The study proposes that this near-perfect adherence to the scaling law is likely due to developmental constraints. Altering the distribution of tissue throughout the body may require significant and energetically costly changes during early embryonic development. This could effectively “lock” sharks into this specific surface-area-to-volume ratio, regardless of whether they evolve to live in the deep sea or a shallow reef. The findings have important practical applications, as these ratios are essential for models that predict how animals will respond to climate change. “Now, we can use those equations with much greater confidence in sharks and other large animals,” said lead author and Ph.D. candidate Joel Gayford.

References

• Gayford, J. H., Irschick, D. J., Martin, J., Chin, A., & Rummer, J. L. (2025). The geometry of life: Testing the scaling of whole-organism surface area and volume using sharks. Royal Society Open Science, 12(6), 242205. https://doi.org/10.1098/rsos.242205

• James Cook University. (2025, June 18). Size matters: Sharks follow two-thirds scaling law, proving theory. Phys.Org; James Cook University. https://phys.org/news/2025-06-size-sharks-thirds-scaling-law.html