Published online by Cambridge University Press: 15 December 2009
The present paper is based on a more extensive study published a few years ago in a chapter in the book Paleoclimate and Evolution with Emphasis on Human Origins (Vrba et al., 1995). It is thought appropriate both by the author and the editors to republish the most important aspects of that article in the framework of the present volume, even though no new points of view are presented here.
The study of the paleoecological relevance of shrews is ruled by an extremely simple mathematical principle. Imagine a cube with sides of 4cm each. The total surface of the cube (six squares of 4 × 4 = 16cm2 each) is 6 × 16 = 96cm2. The volume or content of the cube is 4 × 4 × 4 = 64cm3. A second cube has sides of 2cm each. Its surface is 6 × 2×2 = 24cm2. Its volume is 2 × 2 × 2 = 8cm3. A third cube has sides of 1cm each, a surface of 6cm2. and a volume of 1cm3.
The first cube has a surface-to-volume (S/V) ratio of 96:64 = 1.5. The second cube has an S/V ratio of 24:8 = 3. The third cube has an S/V ratio of 6:1 = 6. This simple sequence shows that when a body acquires dimensions that are smaller by a factor of two, its S/V ratio doubles. Evidently such simple calculations not only apply to cubes, but to all three-dimensional objects, including mammals. Thus, if a mammal becomes smaller, its surface becomes larger in relation to its volume. The surface of a mammal (or of any object for that matter) is the location of temperature exchanges with the surrounding environment.
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