Download article on surface to volume ratios.

Surface to Volume Ratios
Organisms and cells exchange nutrients, waste products, and gasses (O2, CO2) with the environment. Such
materials have to move across the surface of a cell, so the amount of surface area is very important. More
precisely, it is the amount of surface area relative to the total volume of the cell. This is called the surface to
volume ratio, or the S/V ratio. The S/V ratio determines how rapidly materials can flow into and out of a cell or
how rapidly heat can be radiated from a large mammal.
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The illustration on the previous page shows that a larger cube has less surface area exposed in proportion to
volume. Functionally this means that as an object becomes larger, it has less surface area relative to volume.
Cell size is limited by surface to volume ratios. A single cell or a single celled organism relies on diffusion
across the cell surface for exchange of materials. Beyond a certain volume, a cell would not have enough
surface area to import and export all the materials it needs. This effectively sets an upper limit of how big cells
can be and helps explain why most cells in an elephant are no bigger than those in a mouse, although an
elephant has more cells than a mouse. Larger organisms must develop supplementary mechanisms, like
respiratory, circulatory, and excretory systems to transport oxygen and nutrients to cells and remove wastes.
Surface to volume ratios are related to heat loss in endothermic (warm-blooded) animals. The larger the
animal the lower the amount of surface area exposed in proportion to volume. For a large animal like an
elephant, heat cannot flow rapidly in or out of the large body since there is such a small surface area exposed
in proportion to the elephant's volume. Thus elephants are easily overheated when they are active. When this
happens they dump heat by sending large volumes of blood flowing to their ears and waving them to promote
cooling.
The smaller the animal, the greater the amount of surface area exposed in proportion to volume. Thus
hummingbirds, that weigh about the same as a penny, have a huge problem with heat loss on a cold night.
They cannot eat enough to maintain their body temperature throughout the night. Thus they allow their body
temperature to drop which reduces their metabolic rate (O2 consumption). This short term reduction in
metabolic rate is called "torpor". Torpor is analogous to overnight hibernation. The reduction in metabolic
rate reduces the body temperature of hummingbird. This reduces the difference in temperature between the
animal and the environment which reduces the energy needed to get the animal through the night.
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There are two ecological rules or principles, based on surface to volume ratios that relate to temperature
regulation. These rules are based on minimizing heat lost or gained by radiation. Bergmann's rule states that
within a given species, body size tends to increase in colder climates. Allen's rule states that within a given
species, limbs tend to become longer in warmer climates.
The picture on the left is a black-tailed jackrabbit that I photographed in the Mojave desert. Their long limbs
and long ears are ideal surfaces for dissipating heat away from their bodies. You would expect endothermic
mammals in the desert to have long appendages (note the ears) to help them dissipate heat (Allen's Rule). The
picture on the right is a "high elevation rabbit" called a pika. I photographed this pika near timberline in the
Sierra Nevada. Alpine environments are found at high elevations where temperatures are cool in the summer
and cold in the winter. Note how short the ears of the pika are. This reduces heat loss by radiation.
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