"Guy Hoelzer"  wrote in message
news:cftapo$1t5u$1{at}darwin.ediacara.org...
> in article cfh517$13kd$1{at}darwin.ediacara.org, Perplexed in Peoria at
> jimmenegay{at}sbcglobal.net wrote on 8/12/04 6:20 PM:
> > Does the genome act by digging channels or by constructing dams?
> >
> > Dr. Hoelzer seems to have been inspired in his speculation by:
> > http://fsweb.berry.edu/academic/mans/jgraham/Emlen%20Chaos_1998.pdf
> >
> > To be honest, this paper does not impress me very much.  My main complaint
> > is that it fails to make clear the distinction between phase space (where
> > the attractors live and within which trajectories are traced) and parameter
> > space (which controls and determines the geography of phase space).
> > Evolution consists of changes in the genome, which determines a point in
> > parameter space, which then interacts with the environment and the starting
> > state to determine a trajectory in phase space.
>
> I had plenty of problems with the Emlen et al. paper, too, most of which
> faded into unimportance as the central argument (as I read it) became
> clearer (after several readings).  I had not thought of it in the terms you
> describe.
>
> > When viewed correctly, it is easy to see that changes in parameter space
> > always involve both kinds of changes in phase space - channel
digging and dam
> > creation.  There are frequently Thom "catastrophes",
>
> "Thom catastrophes"?
>
> > with new attractors appearing, or old ones disappearing or merging.
> > Evolutionary change involves both kinds of changes in the
attractor structure
> > (as well as simple shifts of the attractor).  There is no
particular reason to
> > focus on just one of these.

Dynamical systems theory distinguishes endogenous variables from exogenous
ones.  The endogenous variables are determined dynamically as the
state changes along a trajectory.  The endogenous variables collectively
determine the phase space.

The exogenous variables are determined outside of the dynamical system.
Nothing that the system does affects the values of these variables.  This
set of variables collectively determine the parameter space.

For some particular fixed set of values of the exogenous variables,
i.e. for a particular point in parameter space, we can look at the
phase space geometrically.  We can draw trajectories, identify attractors,
and delimit basins of attraction.  Notice that there is a discrete
qualitative aspect to this.  There are (generically) a small finite
number of basins of attraction, each containing a single attractor,
which may be a point, a limit cycle, or some fractile "strange
attractor".

Now, consider what happens to this picture in phase space when we make
a small continuous change to the chosen point in parameter space.
The point attractors shift position slightly, the boundaries between
basins shift a little, etc.  But qualitatively, there is no real change.
All of the old attractors and basins continue to exist.  They have
simply moved a little as the chosen point in parameter space has moved
a little.

But now, make a larger change in parameter space such that attractors
merge or split.  Such a change is qualitative.  We can now impose
a geometric interpretation on the parameter space.  In some regions
of parameter space, there are three attractors (in phase space).  In
other regions of parameter space there are four.  We can distinguish
different regions of parameter space, and draw boundaries between these
regions based on the qualitative properties of the phase spaces that
they determine.

The French mathematician Rene Thom made a study of such qualitative
changes in phase space resulting from a continuous "movement" in
parameter space.  He called such transitions "catastrophes".  In
the 1970's, "catastrophe theory" was THE hot topic for math/physics
junkies - though it was later (1980s) absorbed by "chaos theory".

Back to evolution!  I am imagining organism development as taking
place in phase space.  I am imagining that development is controlled
by the genetic changes that determine parameter space.  But, to
really understand things, we probably need to partition the
parameter space into two parts - one for those exogenous variables
that constitute the immediate (variable) environment of development,
and another part for the genetic control.

> > At the biochemical level, an enzyme is more in the nature of a channel than
> > a dam.  Nonetheless, progress in evolution is frequently made by modulating
> > the expression of an enzyme.  This is more dam-like.  Both processes occur.
>
> Should I be thinking of your "dam-like" and
"channel-like" in thermodynamic
> flow terms?  I will for now.
>
> My argument was that natural selection results more in dam-like effects than
> channel-like ones, and you just gave me an example of a dam-like effect.
> Can you provide an example of a channel-like effect?

Any erosion of a dam.  For example, the Baldwin effect is easily interpreted
as the progressive removal of a barrier - it becomes easier and easier
for the environment to switch the system to the new mode, until eventually
the new mode becomes innate.

> [snip]

> To get back to the point of this new thread, what do you see as the basis
> for adaptive phenotypic plasticity in organisms?

The basis in terms of mechanism?  Whatever works.

> Do the mechanisms need to be honed by natural selection,

Yes.  Of course.  Are you asking whether first there is a qualitative
choice of "mechanism architecture" followed by further "tuning of
the mechanism"?  Yes, I think that that frequently happens.

> ... or is it plausible for a novel mechanism to
> manifest and achieve an adaptive response to changing conditions, as argued
> by Emlen et al.?

Not plausible to me.  Their argument, and Kauffman's as well, seems to
be that physics strongly biases the choices available for the initial
"mechanism architecture".  I am unconvinced.  Even if some architectures
are more likely to be chosen initially, based on physics, I don't see
that this is an "adaptive physics".  And, I think that NS has a lot of
freedom during the "honing phase" to morph one architecture into a
different one.  So, I see the physics as playing a passive role and
NS as the only active player.
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