Although there seems to be photographic evidence that some cows DO wear underwear (you can find any sort of foolishness you are gullible enough to believe on the internet), my neighbors in the Mad River Valley of Vermont are not accustomed to seeing this.
Cows are much larger than humans, but why does this mean that humans must wear clothes to stay warm, and cows don’t? The explanation lies in Mathematics and Physics, as it so often does for questions of Biology.
To explain this, instead of considering a complex shape like a cow or a human, think of a simple cube, as shown in the figure to the right. The smallest cube is 1 cm. x 1 cm. x 1 cm. The area of one side is 1 square centimeter (1 x 1 ). However, there are six sides, so the total surface area is 6 square centimeters. The volume is 1 cubic centimeter (1 x 1 x 1). Therefore the ratio of surface area : volume is 6. However as the cubes get larger, the ratio of surface area : volume declines! This is because so much of the surface of the individual cubes is now “buried” on the inside of the larger cubes.
Now imagine that the cubes are actually animals. They will lose heat from the skin which covers their surface. They will produce heat from the volume of their internal tissues. Going back to the geometry, this means that the amount of heat lost, compared to what is produced, is much greater in a small animal than a larger one. So how would a cubic-cow compare to a cubic-woman? An average Holstein cow weighs 1500 lbs., while an average american woman weighs 169 lbs. I will elide the geometry, which is simple, but boring. However, the result is that the cubic-cow will lose 4.3 times more heat than the cubic-woman, but will produce 8.9 times more heat. The cow's ratio of surface area : volume is 2.07, so another way to view this is that either the cubic-woman would need to cut her heat loss by half, or double her amount of heat production.
In the real world, we use both strategies. In cold weather humans add layers of clothing to cut their heat loss. Few women - perhaps with the exception of Lindsey Vonn – would be comfortable in a bikini at temperatures when cows are perfectly fine. Alternatively humans can burn more sugars to produce more heat by contracting their muscles, either through intentional exercise, or by involuntary shivering.
Theory is all well and good, but the essential question of Science is whether it explains reality? If the mathematical theory is meaningful, it would be expected that in any biological taxon, members would become larger as their range moves from tropical, to temperate, to polar regions. In fact, the long-nosed bears of the northern hemisphere are an excellent example of this very thing. As shown in the figure to the right, the long-nosed bears diverged from the short-nosed bears (of which the spectacled bear of South America is the only remaining example) around 12 million years ago, and form a genus of six closely related species.
The figure to the right shows the ranges of the long-nosed bears. The Malaysian Sun Bear is the most tropical species, inhabiting Indonesia and southeastern Asia. The Sloth Bear is a tropical-subtropical species which occurs primarily in India. The Asiatic Black Bear is a temperate species inhabiting China, Korea and Japan. Its range overlaps with the Malaysian Sun Bear in southeast Asia. The American Black Bear is a close relative of the Asiatic Black Bear and occupies a similar temperate habitat in North America. Its range overlaps with the Brown Bear throughout western Canada and Alaska. The Polar Bear is the northernmost species.
So is it true – as the geometry would predict - that the size of long-nosed bear species correlates with the temperature of their habitat? The graph to the right shows the average weight for males and females in these six species.
The correlation is not perfect, because it would be expected that the Asiatic Black Bear would be larger than the Sloth Bear, and the American Black Bear somewhat larger still. This is not really surprising because Biology is so complex that there is rarely a perfect correlation until we get down to the molecular level. Other factors may include additional physiological or behavioral adaptations to cold or heat, food size and availability, or the biomechanical conformations necessary to increase predatory success or avoid predation.
For example, Yoda’s species, which evolved in a tropical swamp, is appropriately small, but also has other adaptations such as large ears and reduced head and body hair to facilitate heat loss (presumably this is why he was never present on the ice-planet Hoth).
Nonetheless it is quite clear that the bears living in cold climates are the largest by far, the tropical species is much the smallest, and those from temperate regions are intermediate.
This concept is known as Bergmann’s Rule after the German biologist Carl Bergmann who described it in 1847, Although it is surprisingly difficult to find solid statistical examples in other families (at least ones that I can understand!), it is tempting to speculate that it applies to other taxa as well. For example the smallest member of the feline family is Felis negripes, which occupies arid tropical and sub-tropical habitats in South Africa, Namibia and Zimbabwe. The largest member is the Siberian Tiger. Among members of the dog family, the smallest is the Fennec Fox, weighing only a bit over 2 lbs., which occurs throughout northern Africa and the Middle East. The largest species is the Grey Wolf in which males may weigh up to 145 lbs. and inhabits temperate and arctic ranges throughout North America, Europe and Asia.
Of course the object which most fascinates us is ourselves. Does Bergmann’s rule apply to Homo sapiens? The answer appears to be a nuanced “yes”. The figure to the right shows the mean height for human males by country. The tallest men are found in Holland and Scandanavia followed closely by western Europe. The next tallest are in Canada, the US and Russia. The shortest are in equatorial Africa and Indonesia.
While it is true that it is not the only mechanism, the mathematics of surface : volume ratio, are undoubtedly one way by which evolution drives adaptation of a species to different climates - including our own!
William S. Barnes
Jan. 6, 2018