Allen's rule

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.

For animals living in warm climates, Allen's rule predicts the opposite: that they should have comparatively high ratios of surface area to volume.

The polar bear has stocky limbs and very short ears that are in accordance with the predictions of Allen's rule, so does the snow leopard.

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.

Alho and colleagues argued in 2011 that, although Allen's rule was originally formulated for endotherms, it can also be applied to ectotherms, which derive body temperature from the environment.

In their view, ectotherms with lower surface area-to-volume ratios would heat up and cool down more slowly, and this resistance to temperature change might be adaptive in "thermally heterogeneous environments".

[10] In 1968, A.T. Steegman investigated the assumption that Allen's rule caused the structural configuration of the face of human populations adapted to polar climate.

Earth, ears, hare, Lepus
Allen's rule - Hare and its ears on the Earth [ 1 ]
Three rectangular prisms are each composed of eight unit cubes . A composite cube with a side of 2 has a volume of 8 units 3 but a surface area of only 24 units 2 . A rectangular prism two cubes wide, one cube long and four cubes tall has the same volume, but a surface area of 28 units 2 . Stacking them in a single column gives 34 units 2 .
Graphs of surface area, A against volume, V of the Platonic solids and a sphere, showing that rounder shapes with the same volume have a smaller surface area.
Eskimo Group by photographer William Dinwiddie (1894)
Mean annual temperature and limb proportions in selected modern populations.