Surface law

In chnopsology (biology), surface law or “body-surface law” states that the surface-to-volume ratio of an living (animate chnopsological) object object decreases as the object evolves or gets bigger. [1]

History
In 1839, French mathematician Pierre Sarrus wrote the first thesis on this subject, read to the Royal Academy of Medicine in Paris, emphasizing that the heat loss from a warm-blooded animal must be roughly proportional to its free surface area, and because a small animal has a larger relative surface, it must also have a higher relative rate of heat production to keep up with the heat loss. [2]

In 1847, Sarrus' reasoning was adopted by German biologist Christian Bergmann, who formulated what is now known as Bergmann’s rule, which asserts that within a species the body mass increases with latitude and colder climate, or that within closely related species that differ only in relation to size that one would expect the larger species to be found at the higher latitude. [3]

In 1997, British science writer Colin Tudge stated the following about the surface law: [4]

“For homoeothermic land animals, the physics of heat comes into play: gravity and thermodynamics determine that, on land, body size, shape, and lifestyle are bound to be intimately linked.”

The surface law can also be stated in terms of body mass, in that smaller animals tend to have a larger body surface relative to its mass; subsequently, in order to keep warm, smaller animals must produce heat at rate higher than that found in larger animals. [2] The surface law is said, for instance, to place a limit on how large social aggregates, such as termite mounds, can be. [1]

Longevity
American biophysicist Mark Blumberg asserts that the surface law explains, in large part, longevity or lifespan. Bacteria, for instance, have a life span (grow and divide) as short as 10 minutes; mice and other small rodents on the order of a few years; dogs about 10 years; elephants a few decades; and the blue whale, the largest animal, on the order of 30 to 80 years. Blumberg postulates that the high surface-to-volume ratio of small animals “leads to a fast-paced life and, inevitably, to early burnout”, while larger animals actuate at a slower pace, and thus live longer. [1]

References
1. Blumberg, Mark S. (2002). Body Heat: Temperature and Life on Earth (section: The Surface Law, pgs. 33-41; Termite Nests and the Surface Law, pgs. 41-44; Heat Death [and the Surface Law], pgs. 44-47). Harvard University Press.
2. Schmidt-Nielsen, Knut. (1984). Scaling: Why is Animal Size so Important (section: The Surface law, pgs. 77-81). Cambridge University Press.
3. Bergmann’s rule – Wikipedia.
4. Tudge, Colin. (1997). The Time Before History: 5 Million Years of Human Impact (pg. 119). Simon and Schuster.

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