>The classical probability argument is one of the main stays of the
>anti-evolutionary position. It is one of the main reasons I became a
>young-earth creationist in the first place.
[creationist examples intended to show the odds against evolution finding
the combinations of alleles needed for improved fitness snipped]
>I have suggested that the odds are not so bleak for the formation of these
>structures because all these calculations depend on the premise that one and
>only one sequence will perform the function. I have thought of an analogy
>which illustrates what I am trying to say.
>
[Glenn's nice analogy snipped]
Suppose you have a genome with N sites and two alleles (e.g. 0 and 1) at
each site. Define a fitness function arbitrarily and randomize the
alleles. Then changing the state of any single allele is equally likely to
improve or degrade fitness. The probability that _some_ single allele will
improve fitness by having its state changed is 1-2**(-N), which is very
close to unity for N > 10 or so. (I am assuming the contribution of each
allele to fitness is uncorrelated with the contributions of other alleles.
This is not a realistic assumption, but removing it only adds complexity
without really changing the result). Consequently, early in an adaptation
process, the probability that variations will result in improvements in
fitness is very high. Furthermore, there are many ways to improve fitness.
Consequently the natural behavior in the early stages of a process in
which a population is adapting should lead to numerous different
improvements, each resulting from a different set of successful variations.
Later in the process, when most of the alleles in the population have been
set to (probably local) optimal values, a given change in the state of an
allele is more likely to yield a degradation in fitness. Thus the pace of
adaptive optimization slows down and variants don't proliferate as much.
The point is that there is a range of fitness values over which there are
many solutions to the problem of improving fitness, and this leads to many
variants. (This is a very much simplified rendition of Kauffman's
discussion explaining phenomena like the Cambrian Explosion and convergent
evolution)
Bill Hamilton | Vehicle Systems Research
GM R&D Center | Warren, MI 48090-9055
810 986 1474 (voice) | 810 986 3003 (FAX)