[From Bill Powers (940916.1610 MDT)]
Martin Taylor, Rick Marken, Tom Bourbon, Gary Cziko, and
anyone else who has some thoughts about simulating evolution.
I obviously have to do some reading, but while waiting to do that I have
some problems that others may be able to help with. I've been thinking
about how to set up a model of natural selection for beak size among the
finches, using crossovers only and no mutations.
Here we have a population of birds with different beak sizes. If each
finch passes down the same beak size to the next generation, as Weiner
says, then in generation 2 we have the same selection of beak sizes as
in generation 1, minus any lines that have been wiped out. I'm just
taking what Weiner said literally, that beak size is inherited with
great precision.
Suppose we arrive at generation n, in which only certain beak sizes have
survived. Now conditions get better again, so birds with beak sizes that
have been selected against could now survive in generation n+1. My
problem is, where do they come from? We've wiped out the lines of
descent that would have produced those beak sizes, so it seems to me
that we can't get the missing beak sizes back. To get back the wiped-out
lines, we would have to assume that beak sizes are not passed down with
high fidelity, but can vary around a mean even in birds that survive in
a single line of descent. This means that the original assumption, that
beak sizes are passed down the generations with high fidelity, can't be
true.
The obvious answer is to say that each bird carries the genes for all
possible beak sizes from the largest to the smallest ever observed. But
in that case, why don't we ever see a big finch with a ridiculously tiny
beak, or a little one with a great overdeveloped hooter? I should think
that the Grants would have mentioned that as a selection factor if it
had been observed, and since they could identify every individual finch
on the island, and its parentage, it hardly seems likely that they would
have missed such a phenomenon.
It's beginning to look as if we need tables of probabilities for each
beak size, with secondary probabilities of deviation from that beak size
across an average generation. And if such tables exist, or could be got
from raw data, it seems to me that we end up proposing some pretty
complex and interactive genes. Why should it be that a male with a large
beak mating with a female with a medium beak should produce offspring
with beaks averaging between those sizes (as Weiner hints in a couple of
places)? Do genes add like vectors? And how do we reconcile such a
result of mating with the idea that beak sizes are passed down the
generations "faithfully?" Which beak size, the father's or the mother's?
What's rearing its ugly head in my mind is the suspicion that genes as
carriers of "traits" such as beak size don't really exist. It looks more
as if there is a gene for beak size that can produce any beak size
depending on how strongly it is activated. A control system, in other
words. With this idea we don't have to worry about probability tables or
how we get back to characteristics that have been wiped out. The beak
size is simply varied in the E. coli manner to make whatever error is
affected by it as small as possible under the circumstances. It might
take several generations for that control system to change its state
substantially enough to measure, so we would see relatively slow changes
down the generations. The lines of descent in which these control
systems have somewhat higher gain would adapt faster and fare better
than those that are slower.
While this model probably wouldn't fit the data any better than the old
model, it raises fewer questions about the properties of genes. The
apparent model behind the accepted interpretation raises a lot of
questions.
How many separate genes for different beak sizes would there have to be?
Ten? A hundred? A thousand? There would have to be as many different
genes as there are measurably different beak sizes, and I suspect that
that is a rather large number. And we would also have to propose that
genes for one size combine with genes of the sexual parter for different
sizes in some arithmetic way that tends toward a size between those
limits. This says that the probability of propagating a gene for a
different size in the progeny depends on its proximity to a gene for the
parent's beak size. And somehow the gene for one of the parents' beak
size would have to influence the effects of the gene for the other
parent's beak size. Woah!
Somebody must have worked all this out in a way that makes sense. I'm
just managing to confuse myself. When you just say "let the probability
of survival be p," you bypass all these questions, but you run the risk
of tailoring your let-s to produce the answer you want. I think we have
to start a level deeper and propose mechanisms, first to see if we get
the observed phenonema out of the mechanisms we propose, and second to
see if the mechanisms we have to propose to make the model work fall
within range of believability.
Help, anyone?
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Best,
Bill P.