Re: Nonlinear dynamics

Gordon Simons (simons@stat.unc.edu)
Tue, 6 Jun 1995 12:26:24 -0400 (EDT)

Thanks Bill, Russ, Glenn, and Brian for your responses to my inquiry on
"nonlinear dynamics" and model building. There is much more there than I
am likely to be able to take on. But it does help me clarify issues. I
trust it has also been helpful to others.

Glenn, you wrote:

"One final important point, when the model is run, one MUST compare the
output to the behavior of reality. This is what Russ Maatman did with his
baseball model. His model matched reality. (Russ, I bet you could sell
that program to bookies for a lot of money. :-) ) If the model does not
match reality, then the model must be altered. In the case of my CAMBEXPL
and EVOLVE programs, the things I wanted to model was punctuated
equilibrium and disparity before diversity. These are two features of the
fossil record that Christian apologists say disprove evolution. Both
those programs use the same algorithm and they matched the behavior of the
fossil record on both counts! Thus, my model was successful (what else
can you expect of a model?)

Since I have a reproductive algorithm which can match reality, it seems to
me that Christian apologists should be careful in their statements that
there is no mechanism for punctuated equilibrium and disparity before
diversity."

I believe this clarifies where things stand: What you have shown is that
there exist (nonlinear dynamical) mathematical models which behave in ways
that mimic punctuated equilibrium.

I was mistakenly assuming you are somehow translating random mutations in
your model into specific morphologies according to *some well understood
biological mechanism*. You have stated earlier that a single mutation can
produce a large change in morphology. You seem to be taking this as a
given, which you model somehow in your program (pretty much arbitrarily, I
gather), and then showing that the consequent behavior is something akin
to what punctuated equilibrium asserts.

It seems to me that much more remains to be modeled before one can
properly view punctuated equilibrium as "validated". But it is no straw
man, waiting for skeptics to blow down with a few words of argumentation.

Gordie