Allen's rule is a biological rule posited by Joel Asaph Allen in 1877. It states that endotherms from colder climates usually have shorter limbs (or appendages) than the equivalent animals from warmer climates.
The theory behind Allen's rule is that endothermic animals with the same volume may have differing surface areas, which will aid or impede their temperature regulation.
Consider eight cubical boxes of unit volume and unit area of a side. A rectilateral stack two boxes wide, one long and four tall will have a volume of 8 units and a surface area of 28 units. A cubical stack two boxes wide, two long and two high will have the same volume of 8 units but a surface area of only 24 units.
In cold climates, the greater the exposed surface area, the greater the loss of heat and therefore energy. Animals in cold climates need to conserve as much energy as possible. A low surface area to volume ratio helps to conserve heat as there is a smaller surface area for the heat to pass through.
In warm climates, the opposite is true. An animal will overheat quickly if it has a low surface area to volume ratio. Therefore, animals in warm climates will have high surface area to volume ratios so as to help them lose heat.
R.L. Nudds and S.A. Oswald (2007) of the Institute of Integrative and Comparative Biology at the University of Leeds claimed that there is poor empirical support for Allen's rule despite being an "established ecological tenet". They claim the support for Allen's rule mainly draws from single-species studies, since multiple species studies are "confounded" by the scaling effects of "Bergmann's rule" and alternative adaptions that go against the predictions of Allen's rule.
According to J.S. Alho et al. of the Ecological Research Unit of the University of Helsinki, Finland, although Allen's rule was originally formulated for endotherms, it can be applied to ectotherms which derive body temperature from the environment. The reason for this is that ectotherms with less surface to volume would heat up slower and cool down slower which they claim might be adaptive in "thermally heterogeneous environments".
According to J.S. Alho et al. of the Ecological Research Unit of the University of Helsinki, Finland, there has been a renewed interest in Allen's rule due to global warming and the "microevolutionary changes" it predicts.
A contributing factor to Allen's Rule may be that the growth of cartilage is partly dependent on temperature. "Researchers at Pennsylvania State University have shown that temperature can directly affect cartilage growth, providing a biological explanation for this rule. It was a simple experiment. They raised mice either at 2 degrees, 26 degrees or 48 degrees Celsius and then measured their tails and ears. They found that they were significantly shorter in the mice raised in the cold, compared with the mice raised at warmer temperatures, even though their overall bodyweights were the same. They found that the mice raised in the cold had less blood flow in their extremities. And when they tried growing bone samples at different temperatures, the researchers found that the samples grown in warmer temperatures had significantly more cartilage growth than those grown in colder temperatures."
In humans 
According to William R. Leonard of the Department of Anthropology at the University of Florida, human populations follow Allen's rule. As evidence, Leonard cites a study by D.F. Roberts of the Anthropology Laboratory at Oxford University that showed human populations follow Allen's rule. A.T. Steegman of the Department of Anthropology at State University of New York investigated the assumption that Allen's rule caused the structural configuration of the "Arctic Mongoloid" face. Steegman did an experiment that involved the survival of rats in the cold. Steegman found the rats with narrow nasal passages, broader faces, shorter tails and shorter legs survived the best in the cold. Steegman paralleled his findings with the "Arctic Mongoloids", particularly the "Eskimo" and "Aleut," by claiming these "Arctic Mongoloids" have similar features in accordance with Allen's rule: a narrow nasal passage, relatively large heads, long to round heads, large jaws, relatively large bodies, and short limbs. Kenneth L. Beals of the Department of Anthropology at Oregon State University claimed that human head length should theoretically follow "Allen's rule" with people indigenous to colder climates having heads more like a "sphere". In a study that measured the cephalic index of multiple human populations around the globe, Beals confirmed his hypothesis and concluded that the "value of the cephalic index is positively correlated with the intensity of cold stress and is negatively correlated to the intensity of heat stress." Beals notes that the indigenous people of the Americas are an exception to this rule, since the indigenous people of the hot climates of North and South America have cold-adapted, high cephalic indexes. Beals explanation is that these peoples have not yet evolved the appropriate cephalic index for their climate, being, comparatively, only recently descended from the cold-adapted "Arctic Mongoloid".
Examples in the animal kingdom 
An example of this rule among mammals is the Polar bear, Ursus maritimus; this species exhibits stocky limbs and very short ears. The limbs are predictable from a ratio of surface area to body mass, while the outer ear architecture reflects the need to minimize surface area of heat radiating elements. Populations of the same species from different latitudes may also follow Allen's rule. R.L. Nudds and S.A. Oswald (2007) of the Institute of Integrative and Comparative Biology at the University of Leeds performed a study on seabird exposed length that found exposed leg length was negatively correlated with maximum environmental temperature, supporting the predictions of Allen's rule. According to a study done by J.S. Alho et al. of the Ecological Research Unit of the University of Helsinki, Finland, on the Common Frog, tibia and femur length peaked in populations indigenous to the mid latitudes, consistent with the predictions of Allen's rule for ectothermic organisms.
Other factors 
Exposure of exterior surface area is only one of many mechanisms by which animals retain or dispose of body heat. The following mechanisms are also important:
- Skin color
- Behavior (e.g., gathering insulation when it is cold, moving into shade when it is hot)
See also 
- Bergmann's rule - that correlates latitude with body mass in animals.
- Gloger's rule - that correlates humidity with pigmentation in animals.
- Hesse's Rule
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- Lopez, Barry Holstun (1986). Arctic Dreams: Imagination and Desire in a Northern Landscape. Scribner. ISBN 0-684-18578-4.
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- ALHO, J. S., HERCZEG, G., LAUGEN, A. T., RÄSÄNEN, K., LAURILA, A. and MERILÄ, J. (2011), Allen’s rule revisited: quantitative genetics of extremity length in the common frog along a latitudinal gradient. Journal of Evolutionary Biology, 24: 59–70. doi:10.1111/j.1420-9101.2010.02141.x
- "Hot weather for longer legs". The Naked Scientists. December 2008.
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- Steegmann, A. T. and Platner, W. S. (1968), Experimental cold modification of cranio-facial morphology. American Journal of Physical Anthropology, 28: 17–30. doi:10.1002/ajpa.1330280111
- Beals, K. L. (1972), Head form and climatic stress. American Journal of Physical Anthropology, 37: 85–92. doi:10.1002/ajpa.1330370111
- Hogan, C. Michael (2008). In Nicklas Stromberg. "Polar Bear: Ursus maritimus". globalTwitcher.com.
- Hurd PL & van Anders SM. 2007. Latitude, digit ratios, and Allen's and Bergmann's rules: A comment on Loehlin, McFadden, Medland, and Martin (2006). Archives of Sexual Behavior 36: 139-141.