Re: scaling laws

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 13:20 -0400 10/10/03, Robert Cohen wrote:
> It doesn't appear to me that this "immediately" answers the
> question of why an elephant's heart doesn't have to beat faster.
> Don't you have to know something about metabolism?  Or am I
> missing a more "immediate" connection?
The smaller mouse has a much higher surface are to volume ratio than
does the larger elephant, hence the energy generated within the
mouse's body is much more easily radiated away through the body
surface. If both generated heat at the same rate, either the elephant
would fry itself because it couldn't radiate the energy away as
rapidly as would be necessary, or the mouse would freeze itself
(figuratively) because it couldn't generate energy within the body as
rapidly as its body could radiate it away.

Humans may be a better example, because a baby is more nearly a
scaled down adult than a mouse is a scaled down elephant. But the
size difference isn't as great so the effect won't be as great.
Typical adult heart rates are around 70, while those of infants are
around 110-120. The difference can be accounted for by the difference
in surface to volume ratio between infants and adults.

There is a nice book on scaling laws in biology called "Newton Rules
Biology," by C. J Pennycuick (Oxford, 1992), that deals with these
issues and more. There are lots of nice examples of scaling as
applied to biological systems in it.

Hugh
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Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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