### Bergmann's rule

June 3, 2024

Animal size varies over a large range as evolution fills every ecological niche. Focusing our attention on the range of mass of land mammals, the smallest is the Etruscan shrew (1.8 grams), and the largest is the African bush elephant (6,500 kilograms). Some megafauna that existed about 40 million years ago had a mass up to 10,000 kilograms. The largest of these animals were Paraceratheriidae long-limbed, hornless rhinocerotoids, and Proboscidea (extinct elephants).

As Galileo Galilei (1564-1642) wrote in his 1638 book, Discourses and Mathematical Demonstrations Relating to Two New Sciences, mechanics applies to living as well as non-living materials. The square-cube law, which relates a material's surface area and volume, and may have been an inspiration for the spherical cow model, describes the reason why a large structure can't be just an enlarged version of a smaller structure.

Large animals are proportioned differently from smaller animals. For example, if an elephant were proportioned as a mouse, it would be a very weak animal. That's because the cross-section of its muscles would increase by the square of its size, while its mass would increase by its cube. The movie monster giants, such as King Kong[1] and the giant ants from Them!,[2] could not exist, since they are just scaled versions of their smaller counterparts, gorilla and ants.

Movie poster by Reynold Brown (1917-1991) for Attack of the 50 Foot Woman (1958) starring Allison Hayes (1930-1977).[3]

Because of the square–cube law, a fifty foot woman would not appear as comely as her human-sized counterpart.

(Movie poster for Attack of the 50 Foot Woman, via Wikimedia Commons. Click for larger image.)

Bergmann's rule is another rule involving animal size. It was stated by German biologist, Carl Bergmann (1814-1865), in 1847, and it applies to homeothermic (for example, warm-blooded) animals. This correlation is most apparent for animals above a certain size, since small animals can have adaptations, such as burrowing to protect from cold. In this rule, species within a genus have a larger size in cold environments, and smaller size in warmer environments. Bergmann's rule is often generalized to populations within a species, and latitude is used as an alias for temperature.

Interestingly, temperature changes during some geological periods have caused a temporary, reversible dwarfing of mammals. Bergmann's rule applies to humans, as can be seen in the difference between the large body size of the Inuit, Aleut, and Sami people of the polar regions, and the small body size of pygmy people of Africa.

Bergmann theorized that the same reasoning of the square-cube law applies to this rule. In this case, body volume predicts the degree of metabolism that leads to generation of body heat, while the surface area predicts how much of that heat is lost. As a consequence, larger animals radiate less body heat per unit of mass, and they will stay warmer in cold climates, and smaller animals have a proportionately larger surface area that allows more cooling. It's been noted that temperature also has an affect on food availability, and this would cause an evolutionary pressure for smaller body size.

Bergmann's rule has been questioned in a recent study by scientists from the University of Alaska Museum (Fairbanks,Alaska), the University of Alaska, Fairbanks (Fairbanks,Alaska), the University of Reading (Reading, UK), Montana State University (Bozeman, Montana) the University of Bristol (Bristol, UK), the Chinese Academy of Sciences (Beijing, China), and Florida State University (Tallahassee, Florida).[4-5] This study began with the question of whether Bergmann's rule applied to dinosaurs posed to her undergraduate advisor by Lauren Wilson, first author of the paper describing this research.[5]

The study used data for 62 Mesozoic mammaliaforms and 339 dinosaurs, including the the northernmost discovered dinosaur fossils from the Late Cretaceous Prince Creek Formation of northern Alaska.[4-5] Such dinosaurs experienced freezing temperatures and snowfalls in their lifetimes, but the study found no notable increase in body size for any of the Arctic dinosaurs.[5] The Mesozoic dinosaurs and the ancient mammaliaforms were the ancestors of extant homeothermic birds and mammals.[4] Says University of Alaska, Fairbanks graduate student, Lauren Wilson,
We found that Bergmann's rule is only applicable to a subset of homeothermic animals (those that maintain stable body temperatures), and only when you consider temperature, ignoring all other climatic variables. This suggests that Bergmann's ‘rule' is really the exception rather than the rule."[5]

As a further part of their study, the research team analyzed Bergmann's rule for modern mammals and birds, the descendants of extinct mammals and dinosaurs, and found that latitude was not a predictor of body size for these species.[5] They did find a small relationship between the body size of modern birds and temperature, but not for Mesozoic birds.[4-5] This suggests that body size in modern birds was influenced by Bergmann's rule during climatic change in the Cenozoic.[4]

mean annual temperature and body size evolution among extant birds and mammals. On the left is the estimated branch-wise changes in body mass on a logarithmic scale as a function of mean annual temperature (°C) along branches of the avian phylogeny. On the right, the same data analysis along branches of the mammalian phylogeny. No apparent trend is noted in either. (Portions of fig. 3 of ref. 4,[4] released under the Creative Commons Attribution 4.0 International License. Click for larger image.)

### References:

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