Scientists have long wondered if there are physical constraints that limit the possibility of how large an organism can become through evolution. A new study involving 54 species of sharks indicates that they—and other life forms—may follow a centuries-old geometric rule known as the two-thirds scaling law.
Introduced for generic 3D objects, the rule relates surface area to volume. As an object increases in length, its surface area will increase with the square of length, while volume will increase with the cube. This becomes biologically important because of the many essential life processes that occur at the surface. One prominent example is the intake and outtake of gas in the lungs or gills, such as carbon dioxide or oxygen. This process is dependent on surface area; however, the amount of oxygen or carbon dioxide required to function is dependent on volume. The two-thirds scaling law says that total surface area is a function of volume to the two-thirds power. Following this law would make it difficult for organisms to exist if they continually increase in size, as surface area would increase too slowly to maintain the necessary ratio with volume.
Prior to sharks, the largest organisms that underwent thorough testing of this rule were insects. A major reason for this was the technical limitations researchers were working with. When it came to measuring surface area, the options were limited to running a measuring wheel across an animal’s hide and marking units in chalk or skinning the creature and measuring it by hand. Finding volume required dropping an animal into a water-filled tub and checking how much water was displaced.
Those methods may seem primitive compared to what Joel Gayford, shark biologist at James Cook University in Australia, who led the study, had access to when working with his team. They used CT scans of top-notch museum exhibits to create high-resolution 3D models. When the sharks were too big to fit in a CT scanner, the use of photogrammetry was employed. This technique allows for approximating a 3D structure using only photographs of that structure’s surface. Using a software originally designed for rendering video games, Blender, they refined the models and were able to garner surface area and volume data on all 54 species of sharks.
Sharks may not seem like the most obvious choice, especially when technology is no longer a limiting factor. However, Gayford claims that they are ideal for studying the scaling rule. They can range in size as far as the six-inch-long dwarf lantern shark to the 40+ foot whale shark. Many sharks with unique shapes (hammerheads) and lifestyles (Greenland sharks) further qualify them due to the challenges posed for physiology and movement. The ecological importance and endangered nature of many sharks also give further motivation to study their biology in hopes of altering fate.
With the surface area and volume data they gathered, Gayford and his team applied phylogenetic regression—a statistical method that accounts for shared evolutionary history—to determine how closely sharks follow the two-thirds scaling law. This led them to the conclusion that sharks have surface area as a function of volume raised to the power of 0.64, which is almost exactly the theoretical 0.67. One possible explanation for why heavily varying species of sharks all follow the same rule is developmental constraints imposed early in life. Working around these may require rewiring how tissues are allocated during the development of the embryo, which is almost impossible through natural evolution.
More research is needed in other animal groups to determine whether this rule is truly universal. Gayford’s team is acting to further this goal on their end, and he hopes that other scientists will test biological scaling in their own animal studies.
The details of this study were published in Royal Society Open Science on June 18, 2025.
