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Allen's rule is an ecogeographical rule formulated by Joel Asaph Allen in 1877, broadly stating that animals adapted to cold climates have relatively short limbs. In more detail, it states that homeothermic animals in hot climates have low volume-to-surface ratios due to thermal adaptation while homeothermic animals in cold climates have high volume-to-surface ratios due to thermal adaptation.
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Explanation
Allen's rule predicts that endothermic animals with the same body volume should have different surface areas that will either aid or impede their heat dissipation.
The diagram to the right shows two rectangular prisms that are each composed of eight cubes. Each unit cube contains a cubic unit of volume and each of the surfaces of the cubes are a square unit of area. A rectangular prism that is two cubes wide, one cube long and four cubes tall will have a volume of 8 units3 and a surface area of 28 units2. A composite cube that is two cubes wide, two cubes long and two cubes high will have the same volume of 8 units3 but a surface area of only 24 units2.
In cold climates, Allen's rule predicts that animals should have comparatively low ratios of surface area to volume. Because animals in cold climates need to conserve as much heat as possible, Allen's rule predicts that they should have low surface area to volume ratios to minimize the surface area by which they dissipate heat, allowing them to retain more heat.
In warm climates, Allen's rule predicts that animals should have comparatively high ratios of surface area to volume. Because animals with low surface area to volume ratios will overheat quickly, Allen's rule predicts that animals in warm climates should have high surface area to volume ratios to maximize the surface area by which they dissipate heat, allowing them to dissipate more heat.
R.L. Nudds and S.A. Oswald argued in 2007 that there is poor empirical support for Allen's rule even if it is an "established ecological tenet". They said that the support for Allen's rule mainly draws from studies of single species, since studies of multiple species are "confounded" by the scaling effects of "Bergmann's rule" and alternative adaptations that counter the predictions of Allen's rule.
J.S. Alho and colleagues argued in 2011 that, although Allen's rule was originally formulated for endotherms, it can be applied to ectotherms which derive body temperature from the environment. In their view, ectotherms with less surface to volume would heat up and cool down more slowly, and this resistance to temperature change might be adaptive in "thermally heterogeneous environments". Alho said that there has been a renewed interest in Allen's rule due to global warming and the "microevolutionary changes" that are predicted by Allen's rule.
In humans
Marked differences in limb lengths have also been observed when different segments of a given population reside at different altitudes. In Peru, individuals who lived at higher elevations tended to have shorter limbs, whereas those from the same population who inhabited the more low-lying coastal areas generally had longer limbs and larger trunks.
Katzmarzyk and Leonard similarly note in 1998 that human populations appear to follow the predictions of Allen's rule. They said that there is a negative association between body mass index and mean annual temperature for indigenous human populations, meaning that people who originate from colder regions have a heavier build for their height and people who originate from hotter regions have a lighter build for their height. They said that relative sitting height is negatively correlated with temperature for indigenous human populations, meaning that people who originate from colder regions have proportionately shorter legs for their height and people who originate from hotter regions have proportionately longer legs for their height.
In 1968, A.T. Steegman 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 said that the rats with narrow nasal passages, broader faces, shorter tails and shorter legs survived the best in the cold. Steegman said that the experimental results had similarities with the "Arctic Mongoloids", particularly the "Eskimo" and "Aleut," because 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.
In animals
The polar bear has stocky limbs and very short ears that are in accordance with the predictions of Allen's rule.
Populations of the same species from different latitudes may also follow Allen's rule.
In 2007, R.L. Nudds and S.A. Oswald studied the exposed lengths of seabirds' legs that said that the exposed leg lengths were negatively correlated with maximum environmental temperature, supporting the predictions of Allen's rule.
J.S. Alho and colleagues argued that tibia and femur lengths are highest in populations of the Common Frog that are indigenous to the middle latitudes, consistent with the predictions of Allen's rule for ectothermic organisms.
Mechanism
A contributing factor to Allen's Rule may be that the growth of cartilage is partly dependent on temperature. Temperature can directly affect the growth of cartilage, providing a proximate biological explanation for this rule. Experimenters raised mice either at 2 degrees, 26 degrees or 48 degrees Celsius and then measured their tails and ears. They found that the tails and ears were significantly shorter in the mice raised in the cold in comparison to the mice raised at warmer temperatures, even though their overall body weights were the same. They found that the mice raised in the cold had less blood flow in their extremities. When they tried growing bone samples at different temperatures, the researchers found that the samples grown in warmer temperatures had significantly more growth of cartilage than those grown in colder temperatures.