Re: Percolation theory

tchow@xxxxxxxxxxxxx wrote:

What I've just described for Z^n holds for a variety of other random graph
models. The result is remarkably robust. Under a wide variety of
conditions we observe a sharp phase transition from dust to a giant
component.

Stuart Kauffman has tried to apply this idea to the origin of life.
See "At Home In The Universe", etc for details.

Now for the vague idea of how this might be relevant to evolutionary
biology. In the simplest model, the points of the graph represent
genotypes. Edges represent mutations that could occur in a single
generation. The survival probability represents something like the
probability that one genotype will produce a viable organism, given
that the genotype at the other end of the edge produces a viable
organism. Finally, the phase transition would indicate what rate of
viable mutations are needed for the genotype to evolve to arbitrarily
distant genotypes, as opposed to getting "stuck" in some island and
being unable to evolve beyond certain limits.

I'm rather sceptical. For one thing:

"The survival probability represents something like the probability
that
one genotype will produce a viable organism, given that the genotype
at
the other end of the edge produces a viable organism."

There is no such global variable in biology - that figure is
enormously
variable, across different situations. The use I see of the model
would be to identify the value of that variable. However, ISTM that
it will be a meaningless average value, of little real significance.

Biology needs there to be at least one big tree, with a simple root.
However, it doesn't need the whole space to be reachable. 99.99% of
possible genomes are dead organisms, with no connections to anything -
it seems like a lot of "dust".
--
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|im |yler http://timtyler.org/ tim@xxxxxxxxxxx Remove lock to
reply.

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