Researchers Use 3D Models to Determine the Presence of 'Two-Third Scaling Law' in Shark Specimens

Scientists have detected an intriguing mathematical law in sharks. The principle was confirmed through analysis of 3D models of these beasts, as stated by Phys.org. Insights from the examination have been published in the journal Royal Society Open Science. Moreover, researchers associated with the study determined the "two-thirds scaling law" in sharks. This principle indicates that there is a certain rule by which an animal's surface area and volume scale with size. Researchers are ecstatic to confirm the law in sharks as it gives them a clear picture of how these "sea dogs" and other beings exchange oxygen, heat, and energy with the environment. 

Taking an example of a cube, the "two-thirds scaling law" implies that when a person increases the length of one side of the cube by "y" times, then the cube's surface will increase by "y2" times and the cube's volume by "y3" times, according to IFL Science. This relationship between these three elements is called the two-thirds law. In the past, the law has either only been noted in single cells, a small selection of whole organisms, or through theoretical measurements. Therefore, the theory's confirmation on full-sized animals in this study was a big feat. 

For this study, experts analyzed 54 species of sharks. The subjects were diverse in several aspects, such as body size, lifestyle, morphology, and physiology. The largest shark was 16 times longer than the smallest, while the heaviest shark weighed 19,000 times more than the lightest one. The variation allowed for an expansive dataset to confirm the "two-thirds scaling law." Experts took CT scans and high-resolution 3D images of shark specimens in the museum. Based on the garnered data, they formulated models of these beasts.

Researchers applied phylogenetic regression to figure out the relationship between the creatures' surface area and volume. This method essentially applies many regression techniques to cross-species data. The process supposedly works even if the species under consideration are similar in many aspects. This method benefited researchers for this study, as it allowed them to regard the models they were examining as truly separate species, reducing the effect of their shared ancestry. It gave them a more tangible outcome of the entire process. 

The examination determined that the relationship between a shark's surface area and volume possibly follows the "two-thirds scaling law." Results indicated that the beasts' surface area is directly proportional to their volume raised to the power of 0.64. As per the law, the value in place of 0.64 should have been 0.67. Since there is only a 3% deviation, researchers believe that the outcome implies the theory has indeed been followed by sharks as a whole throughout their evolution. 

A marine biology professor and a co-author in the study, Dr. Jodie Rummer from James Cook University (JCU) in Australia, believes the sharks followed the law across millennia since it would have either been too "costly" energy-wise to deviate from the principle or because it is a consequence of early development in these sharks, making the law very difficult to alter in the later stages of life. "Changing the way tissue is distributed throughout the body might require major changes during early embryonic development—and that's expensive, energetically speaking," explained Joel Gayford, JCU Ph.D. candidate and lead author in the study.

Knowledge about how fast these creatures can regulate their body temperature in the face of certain changes, along with how they go about their oxygen, becomes clearer with the aid of this law. Experts associated with the study believe these findings are valuable as they will provide scientists with more insights into how sharks respond to climate change.