Catastrophy Theory (mas)

COUTTS David dcoutts at macadam.mpce.mq.edu.au
Tue Mar 21 16:49:50 EST 1995


Eight years ago I went to a lecture by a Prof. Zeeman (I think) who talked
about evolution in terms of catastrophy theory.  This was a mathematical 
approach to explain transitions from stability to runaway processes. For
example the theory explains the capsizing of a ship, through to speciation
events. He presented a clear graphical (simplified) picture explaining
some of the processes whereby speciation events (and adaptive radiation) can
occur. Indeed, all this was before terms like *punctuated equilibrium*
were popularised. 
The theory (as applied to evolution) was based on population dynamics, and
I guess measurable phenotypic characteristics (ie multi allelic traits). 
Any population was assumed to have some distribution function of *length
of nose etc...* (normally Gaussean), and an inverse fitness function
plotted as a function of the measured characteristic (eg nose length). 
Population genetics/mutaions ensure phenotypic variability. 
What I liked about this approach, was that it offered a very visual and
simple picture which could show how a population followed the potential
curve, how the curve could be modified by the environment, or just be
biased towards being different from the norm (having a nose slightly linger
than everyone else or any such arms race).

There was nothing in this approach that was not part of standard evolutionary
theory, however, I have not come across any written reference which so
clearly presents this approach.  I realise that this is a standard
way of viewing population dynamics, however, is there a reference that 
makes explicit use of this very visual approach to evolutionary theory?

I would be grateful if anyone could point me in the right direction to both
technical and non-techinical references.

It is quite possible that the name Catastrophy Theory is no longer used
(he was a mathematician after all), and from the positngs I have seen here,
Catastrophy Theories these days relate to something totally different.
Chaos is perhaps the modern buzzword relating to these ideas.
Thanks,
David Coutts



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