Information Technology Reference
In-Depth Information
Allometric scaling indicates that the size of animals is clearly important, but, per-
haps more significantly, a clue to understanding the web of life may be found in how
the sizes of different animals are interconnected. In 1929 Haldane made the following
observation on the importance of scale [
14
]:
You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a
slight shock and walks away. A rat would probably be killed, though it can fall safely from the
eleventh story of a building, a man is broken, a horse splashes.
Of course, the recognition of the importance of scaling did not begin with Haldane,
or even with Thompson, but it did reach a new level of refinement with their studies.
Consider the observations of Galileo Galilei, who in 1638 reasoned that animals cannot
grow in size indefinitely, contrary to the writings of Swift. It was recognized by the
Lilliputians that since Gulliver was 12 times their stature his volume should exceed
theirs by a factor of 1,728 (12
3
and he must therefore be given a proportionate amount
of food. Galileo observed that the strength of a bone increases in direct proportion to the
bone's cross-sectional area (the square of its linear dimension), but its weight increases
in proportional to its volume (the cube of its linear dimension). Consequently, there is a
size at which the bone is not strong enough to support its own weight. Galileo captured
all of this in one prodigious sentence [
11
]:
)
From what has already been demonstrated, you can plainly see the impossibility of increasing
the size of structures to vast dimensions either in art or in nature; likewise the impossibility of
building ships, palaces, or temples of enormous size in such a way that their oars, yards, beams,
iron bolts and, in short, all their other parts will hold together; nor can nature produce trees of
extraordinary size because the branches would break down under their own weight; so also it
would be impossible to build up the bony structures of men, horses, or other animals so as to hold
together and perform their normal functions if these animals were to be increased enormously in
height; for this increase in height can be accomplished only by employing a material which is
harder and stronger than usual, or by enlarging the size of the bones, thus changing their shape
until the form and appearance of the animals suggest a monstrosity.
A variation of Galileo's bone-crushing example has to do with life and size. The
weight of a body increases as the cube of its linear dimension and its surface area
increases as the square of the linear dimension. This principle of geometry tells us that,
if one species is twice as tall as another, it is likely to be eight times heavier, but to have
only four times as much surface area. This raises the question of how larger plants and
animals compensate for their bulk. Experimentally we know that respiration depends on
surface area for the exchange of gases, as does cooling by evaporation from the skin and
nutrition by absorption through membranes. Consequently the stress on animate bodies
produced by increasing weight must be compensated for by making the exterior more
irregular for a given volume, as Nature has done with the branches and leaves on trees.
The human lung, with 300 million air sacs, has the kind of favorable surface-to-volume
ratio enjoyed by trees. We discuss this in some detail later.
A half century after Lotka, the biologist MacDonald [
20
] and zoologist Calder [
6
]
both adopted a different theoretical approach to the understanding of natural history,
shying away from the dynamic equations of physics and explicitly considering the
