SCI:ALIFE: the walk is not random, nor is it a walk

Eugene Leitl (
Mon, 13 Jan 1997 17:56:09 +0100 (MET)

I lost the tail of the last post:


I feel confirmation of these results to be very important. From countless
possible physical machinery the one supporting above fitness function
shape has crystallized. If we are to harness darwinian evolution for
autochthonous system design we must choose one boasting above features.
At least we should give the system opportunity to precipitate a
near-optimal shape spontaneously via ALife methodology. If proteins (as
it is to be supposed) mimick RNA in their folding/function antics, de
novo protein design is equivalent to solving the protein folding problem
(indeed doing it pretty rapidly (on minute scale), so we can apply darwinian
evolution to select for those shapes we need.


"An Evolutionary Approach to Synthetic Biology", Thomas S. Ray, in
"Artificial Life -- an Overview", Christopher G. Langton, MIT Press
(1995), pp. 181-182.


3.1 Evolution in Sequence Space

Think of organisms as occupying a "genotype space" consisting of all
possible sequence of all possible lengths of the elements of the genetic
system (i.e., nucleotides or machine instruction), When the first
organism begins replicating, a single self-replicating creature, with a
single sequence of a certain length, occupies a single point in genotype
space. However, as the creature replicates in the environment, a
population of creatures forms, and errors cause genetic variation, such
that the population will form a cloud of points in the genotypic space
centered around the central point.

Because the new genotypes that form the cloud are formed by random
processes, most of them are completely inviable and die without
reproducing. However, some of them are capable of reproduction. These new
genotypes persist, and, because some of them are affected by mutation,
the cloud of points spreads further. However, not all of the viable
genomes are equally viable. Some of them discover tricks to replicate
more efficiently. These genotypes increase in frequency, causing the
population of creatures at the corresponding points in the genotype space
to increase.

Points in the genotype space occupied by greater populations of
individuals will spawn large numbers of mutant offspring; thus, the
density of the cloud of points in the genotype space will shift gradually
in the direction of the more fit genotypes. Over time, the cloud of
points will percolate through the genotype space, either expanding
outward as a result of random drift or by flowing along fitness gradients.

Most of the volume of this space represents completely inviable
sequences. These regions of the space may be momentarily and sparsely
occupied by inviable mutants, but the cloud will never flow into the
inviable regions. The cloud of genotypes may bifurcate as it flows into
habitable regions in different directions, and it may split as large
genetic changes spawn genotypes in distant but viable regions of the
space. We may imagine that the evolving population of creatures will take
the form of wispy clouds flowing through this space.

Now imagine for a moment the situation that there was no selection. This
implies that every sequence is replicated at an equal rate. Mutation will
cause the cloud of points to expand outward, eventually filling the space
uniformly. In this situation, the complexity of the structure of the of
the cloud of points does not increase through time, only the volume that
it occupies. Under selection by contrast, through time the cloud will
take on an intricate structure as it flows along fitness gradients and
percolates by drift through narrow regions of viability in a largely
uninhabitable space.

Consider that the viable region of the genotype space is a very small
subset of the total volume of the space, but that it probably exhibits a
very complex shape, forming tendrils and sheets sparsely permeating the
otherwise empty space. The complex structure of this cloud can be
considered to be a product of evolution by natural selection. This
thought experiment appears to imply that the intricate structure that the
cloud of genotypes may assume through evolution is fully deterministic.
Its shape is predefined by the physics and chemistry and the structure of
the environment [here T.S. Ray forgets to mention (in another passage he
does) that the major share of the environment (=fitness function) is
modulated by another individuals, which makes it uncomfortably
hyperactive (Red Queen phenomenon ("Well, in _our_ country", said Alice,
still panting a little, "you'd generally get to somewhere else -- if you
ran very fast for a long time as we've been doing." "A slow kind of
country!" said the Queen. "Now, _here_, you see, it takes all the running
_you_ can do, to keep in the same place. If you want to get somewhere
else, you must run at least twice as fast as that!" -- "Through the
Looking Glass", C.L. Dodgson) ], in much the same way that the form of the
Mandelbrot set is predetermined by its defining equation. The complex
structure of this viable space is inherent in the medium and is an
example of "order for free" [44].

No living world will ever fill the entire viable subspace, either at a
single moment of time, or even cumulatively over its entire history. The
region usually filled will be strongly influenced by the original
self-replicating sequence and by stochastic forces that will by chance
push the cloud down a subset of possible habitable pathways. Furthermore,
coevolution and ecological interactions imply that certain regions can
only be occupied when certain other regions are also occupied. This
concept of the flow of genotypes throught the genotype space is
esentially the same as that discussed by Eigen [22] in the context of
"quasispecies". Eigen limited his dicussion to species of viruses, where
it is also easy to think of sequence spaces. Here, I am extending the
concept beyond the bounds of the species to include entire phylogenies of

P.S. T.S. Ray arguments that the brittleness of GA-growing machine code
is due to its degeneracity. I rather think it to be an intrinsic
property of the system itself: some of the instructions are simply
too powerful. Overall, the system lacks that intricate webwork of
neutral paths, and mutation rate maps, etc. this is what makes it
brittle. (This also might be a rather unwelcome property of
FPGA-flavoured EHW).