Re: We believe in design

On 5/31/05, Dr. David Campbell <amblema@bama.ua.edu> wrote:
>
> > So ... to return back to my original point - if the space of viable
> > phenotypes were densely populated (designed that way as Glenn said in
> > his article) so there were caverns of viability connected by viable
> > paths, then evolutionary search can work, and indeed the neutrality
> > idea would improve the efficiency of that search by spreading out
> > over neutral networks.
>
> If much of the theoretical space is significantly worse than the
> region of interest, this may help the search work more efficiently,
> because many suboptimal options can quickly be eliminated. This also
> means that a uniform sampling of the space is not a very good
> approach.
>
> David, I think we're talking at cross purposes here. I'm not talking about
sub-optimal regions being eliminated quickly (presumably you mean by natural
selection). I'm talking about the space of neutral mutations, where there is
no selective advantage for one individual over any other in the same
(sub)-space, because they all translate to the same phenotype. This is how I
understood the paper cited by Pim.

Do you agree that there can't be a selective advantage between two
individuals that have different genotypes (due to neutrality), but the same
phenotype?

If there can't be any selective advantage between members of this subset of
genotype space, then the neutral mutations amount to nothing more than a
random walk. Going back to my "SPQ" formulation, suppose the bit string is:

SPPPPPPPPPPPPPPPPPPPPQQQQQQQQQQQQQQQQQQQQ

and each of these letters can be a 0 or a 1. The value of S determines
whether the P bits go into the phenotype or the Q bits. Suppose that S is
such that the P bits are in the phenotype. Then any mutation of a P bit can
affect the fitness as it changes the phenotype, whereas any change of the Q
bits won't affect it as they are not expressed. Thus, while S remains at
that value, the Q's perform a random walk over a 20-dimensional hypercube.
At some stage they may just happen to get to a value that would be
advantageous over the current P value, and at that point, if the S bit
changes to express Q rather than P, then you will get a selective advantage.
This is my understanding (from the papers Pim quoted) of what is meant by a
"neutral network".

In this case, I would argue that in looking for those elusive values of Q
that give an advantage, that a uniform sampling of Q-space, which is the
region of neutral mutations, is going to be the most likely to find them.
Any non-uniformity will actually be significantly worse and will reduce the
chance of getting an improvement. Think of the problem of finding a needle
in a haystack where there are no clues anywhere - you just find it at the
point it's at. Given no other knowledge of where it is, then a uniform
sampling strategy has to be the one which finds it most quickly on average
because your prior knowledge has told you that it's equally likely to be
anywhere.

In another post, Pim raises the point that evolution is not supposed to find
the optimal solution. I don't recall I ever said it could. I'm talking about
finding a region on genome-space that provides any improvement, not what
finds the optimal one. I may have been misleading here, because I have
worked in the area of optimization, and if so, I'm sorry to have misled
everyone. The topic of "global optimization", for which genetic algorithms
have been proposed as one solution, is a vast one with many unsolved
problems. In this case, too, one never knows if one has found the globally
optimal solution, but one is interested in finding a better one than the
current one. There are several benchmark problems in Mixed Integer-Linear
programming on the web where the optimal solution is not found but as
algorithms improve and the speed of computers improve, occasionally someone
finds a better solution than the previously known best one.

Iain
Received on Wed Jun 1 03:36:22 2005