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on necks and crows (was Re: rearing up and Re: Drom. beh. Pack hunting!)

Ken Clay (clayke@pacbell.net) wrote about the Poiseuille equation
describing laminar flow through a tube and asked "someone please let
me know if this reasoning is flawed."  Aside from Frank Galef's
(tyra-rex2@nctimes.net) response that circulatory systems are made up
of viscoelastic elements, I fear that your argument is precisely
backwards.  You note that Poiseuillian flow is proportional to the
fourth power of the radius and then claim that thus the radius could
be quite small and give you a sizeable flow.  However, to think about
comparative anatomy, what you'd need to think about his how a
reduction in the radius of the vessel will effect the flow rate.  That
fourth power dependence means that if the radius goes down a small
amount then either the pressure drop has to go up or the length of the
tube or viscosity of the fluid have to go down by a hellatious amount
in order for the flow to remain the same.  In most sauropods, the
length of the tubes is actually larger than the length of the tube in
pretty much any other animal, and I doubt there's all that much they
could do with the viscosity of their blood and still be able to
function (keep in mind also that blood cells tend to make the
rheological properties of blood different from the ideals modelled by
Poiseuille's equation, particularly at low shear rates).

Or to look at this another way, Ken wrote:

> I argue that flow requirements for rearing sauropod brains to
> function are small, that cerebral artery radiuses (radii?) are
> correspondingly small,

In the ideal situation you've described, if the flow rate is reduced
by some percentage and everything else is to stay the same except for
the radius of the arteries then that radius must go down by that
percentage raised to the 1/4th power.  For example, if flow in a
sauropod artery should be 10% of the flow in a mammal artery, the
sauropod's artery should still be 56% the size of the mammal artery...
That fourth power gives you less bang for the buck than if it was a
1st power in wich case 10% of the flow would mean 10% of the radius.

Frank also suggested:

} I have read that dinosaurs probably didn't fill their braincases
} with brains as much as birds and mammals,

The recent description of an _Allosaurus_ endocast (check the archives
from last week for a reference) is in accordance with this statement.
Dinosaurs were apparently more like crocodiles than like birds and
mammals in this regard.

And now for something completely different.  Gus Derkits
(gejd@concentric.net) writes:

] The old idea that clusters of crows around a feeding site are just
] disorderly "mobs" is being revised NOW.

Are you referring to the work of Bernd Heinrich?  If so, then my
understanding (gleaned largely from John Alcock's description in the
6th edition of _Animal Behavior_) would be closer to disorderly mobs
than fammily gatherings at least for Ravens.  Specifically, it appears
that when a Raven finds a carcass before any other Ravens, it will
keep quiet about it.  If there are more than two Ravens feeding at the
carcass, they will generally squawk to high heaven.  As I understand
the situation, this occurs because Ravens are territorial, and if only
one or two birds have found a carcass it is likely to either be in
their territory or they're interloping and don't want to attract the
attention of the territory's owner.  In either case it "belongs" to
the bird that first found it.  The owner of the territory will harrass
interlopers away from the carcass if it can do so effectively.  In
such situations the interlopers call out to attract more interlopers
in order to make sure that the territory owner cannot effectively
deter them from feeding thus making the carcass up for grabs.  Is the
behavior of crows different from this?  Either way, keep in mind that
I've used motivational statements as a shorthand -- I don't actually
attribute motive or conscious decision making processes to the birds
(though by making this disavowal I do not deny the possibility that
such decision making processes exist...)

Mickey Rowe     (mrowe@indiana.edu)