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----- Original Message -----
From: "Steve Shaw" <srshaw@DAL.CA>
To: <naturens@chebucto.ns.ca>
Sent: Sunday, October 03, 2010 1:38 PM
Subject: Re: [NatureNS] Wasp question (long)
> Hi Paul, Derek, Andy, Dave and all,
So if you
> double the width of the insect, you double the length of the tube
> pathway (*2), but the rate of movement of the gases O2 and CO2 will
> drop to one quarter of what it had been before, at the tissue end
> (1/(2 squared) = 1/4). This is believed to be one of the main factors
> that limits the ultimate size of insects, such that at large size they
> simply cannot supply O2 to the tissues fast enough by passive
> diffusion. The most energetically expensive tissue known is insect
> flight muscle, to give an idea of why this might be important.
Hi Steve & All, Oct 7, 2010
It is correct that if delivery of a gas by diffusion to the end of a
tube (of uniform diameter) is J then delivery to the end of same diameter
tube will be J/4, if tube length is doubled.
And-- the above applies (I think) whether removal of gas from the sink
end of the tube is at a very rapid rate relative to the rate of diffusion or
at a slow rate; if removal is rapid then the concentration gradient will be
steep and if slow then shallow.
But if this dimensional effect were relevant, why over all these years,
would not evolutionary pressures have developed sufficient branching in
larger insects to compensate for this effect ?
Unless I have missed something, the answer is quite simple. Most insects
have evolved with flight somewhere in the background and if you are going to
fly then small is beautiful. For example, fairly large Mayflies can almost
float in thermals generated by a canoe or wharf at calm twilight. And
smaller insects can ride the tiny thermals generated by shrubs or other
localized heat sources.
Also, unless transfer of O2 from the trachea to tissue fluids, followed
by flow away from the trachea, is very efficient, and it is difficult to see
how it could be*, then the really steep concentration gradient would be at
the gas/liquid interface.
*Based on O2 solubility in water at 20oC; 20% O2 in air would be in
equilibrium with about 0.6% O2 by volume in water.
Insects, especially rapid fliers, can often be seen sunning themselves.
And it has seemed reasonable to me (from first principles) that this
provides time to digest the last meal and deliver the products of digestion
to the points of use; this delivery must be less satisfactory as size
increases unless offset by better circulation
Just shooting from the hip,
Dave Webster, Kentville
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