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From: cgl@t13.lanl.GOV (Chris Langton)
Newsgroups: comp.theory.cell-automata
Subject: Re:  CA extensions
Message-ID: <9102071416.AA14396@t13.lanl.gov.>
Date: 7 Feb 91 14:16:03 GMT
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  John Gossman describes observing punctuated equilibria in the course of
the evolution of his CA system. 

  David Hiebeler correctly cautions that observing this phenomenon
in CA systems alone does not really constitute much support for PE
in biological evolution.

  However, this phenomenon is being seen in many different artificial
evolving systems, when people take care to record what happens along the
evolutionary path, instead of just noting that ``fitter-critters''
result at the end of the process.

  Indeed, many of the papers submitted for the proceedings of the most
recent workshop on Artificial Life note this phenomenon. Thus, is
appears that punctuated equilibrium behavior may well be ``generic''
for evolutionary processes.

These punctuation events are often accompanied by population crashes and 
``species'' crashes. This is important, because it suggests that extinction 
events on many different scales can occur due to the natural dynamics of 
the evolutionary process alone, without having to evoke catastrophes like
asteroid impacts. 

This is one of the better illustrations of the way in which Artificial 
Life can contribute to theoretical biology. By viewing evolutionary 
processes (and other biological processes) as dynamical systems, 
identifying what class of dynamical systems they are (if possible),
charting out the different regimes of dynamical behavior that such 
systems exhibit under different parameter settings and with different 
initial conditions, and even by altering the rules of the dynamical
system (for instance by allowing Lamarckian inheritance), we
can derive universal principles from an *ensemble* of examples, 
rather than trying to derive universals from the *single* examples 
that nature has given us of most biological processes.

  Viewing the evolutionary process as a dynamical system allows one 
to make an analogy between punctuated equilibrium dynamics and what 
is known as ``intermittency'' in dynamical systems. Intermittency is
a generic behavior for many dynamical systems near a phase-transition 
between periodic and chaotic behavior. Thus, the fact that evolutionary
processes exhibit dynamical intermittency suggests that evolution naturally
brings populations to some sort of phase-transition. This has a number
of interesting implications which I won't go into here, but suffice it
to say that the love affair between dynamical systems theory and biology
is only just beginning.

Cheers!

Chris Langton

Complex Systems Group
MS B213, Theoretical Division		Phone: 505-667-9471
Los Alamos National Laboratory		Email: cgl@t13.lanl.gov
Los Alamos, New Mexico, USA
87545