An Introduction to Allometric Scaling

To paraphrase Stephen J. Gould, allometry is the consequence of size upon shape. When science fiction and fantasy films depict giants they typically show them as well-proportioned, larger than normal individuals. Such scaling is termed isometric (``iso-'' same, ``metric'', having to do with measures)--all proportions are respected and all dimensions are increased by the same amount. Isometric scaling is a special case of allometric scaling, where dimensions may grow differentially.

Today you will examine the consequences of scaling and learn some of the ways biologists see scaling and shape as relating to biological function. We will look at surface area to volume ratios in some simple shapes to determine the consequences of increased (or decreased) size.

Surface area is commonly used as an indicator of supply: all materials that a cell needs must come across the cell membrane and the area available for such transport ultimately limits the rate of transport and therefore the material available to the system. But surface is also used as an indicator of capacity to get rid of material as occurs in excretion (or heat loss in thermoregulation). Volume is used as an indicator of need. The metabolically active space is assumed to be the three dimensional space enclosed by the cell membrane.

How realistic are these assumptions? Can you see ways in which surface area would not be a good indicator of supply, or volume of need? Does the discrepency involved mean that we will underestimate, or overestimate their effect?