Re: random walk mutation

Gil Lawton wrote:
"Anon." <bob.ohara@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:eqqfs8$drt$1@xxxxxxxxxxxxxxxxxxxxxx
Well, if the boundaries are far enough away, they will approximately
have a 3D normal distribution: proof from central limit theorem.

If the boundaries are close enough, it will be a bit different, but
exactly what happens depends on the type of boundary.


(snipped my words to leave, and respond to, your, Bob)
Isn't that what Gavrilets is doing (I really ought to read his book!)?
Certainly, with no selection, what will happen is obvious from the
theories of stochastic processes, but is also the obvious place to start
building the theory from. With selection, the shape of the fitness
landscape is probably more important.

Bob, I have not read Gavrilets.

Please understand that I am a layman who gets strong intuitive feelings that
there are flys in some ointments, involving not mathematics but the nature
of the mechanism whereby what is called "natural selection" physiologically
does its things. Spookily often, such intuitions of mine turn out to have
some actual basis ultimately, if I pursue and learn enough to confirm that.

My current intuition (which could be totally wrong) is that there are
numberous assumptions made by biologists and paleontologits on basis of a
simplistic view of "natural selection" which has never (so far) been borne
out at the DNA level. The details are BEGINNING to be mapped, which is
wonderful; but molecular biology impresses me as being in its infancy.

Perhaps you would be willing to help me get an accurate picture in my mind
of how distribution of mutations would radiate over time
in a spherical grid. The picture I intuit would tend to be ratable, that is
to simply expand out into the sphere fairly equably in all directions.

Indeed, that would be true under neutrality, hence my references to 3D
normals: they would imply diffuse through the space. if you want some
intuition on your model, then look into diffusion and stochastic processes.

On the other hand, what little I have understood clearly from reading about
mutations indicates to me that most mutations, by far, are
deleterious.

Yes.

Follow my reasoning here, and correct me if you can... but I envision a lot
of mutations *RANDOM IN MORPHOLOGICAL IMPACT, AS WELL IN CAPABILITY OF
SUCCESS vs FAILURE POTENTIAL" to be enormously unlikely to produce lines of
genetic change that lead anywhere in particular.

A lot would just lead to the grave, yes.

Let me pick the example of the evolution into contemporary horses from a
dog-like creature. It is a popular misconception (I have read) that the
progression was a linear one or a smooth one.) The illusion it might have
been so is nothing more than what I might (with a weak attempt at humor)
term "paleontological selection," i.e., selection of specimins to connect
the dots, as it were, from a quadripedally five-toed, dog-like creature to a
creature with one toe contacting the ground, and running only on the toe
nail of that... which we call a "hoof." Actually (I have read) there were
many other variations and branchings off in the process which were somewhat
random... and which failed. To this extent, random mutation and the
possibility *realized* of four hooves do seem to have followed a course of
*PASSIVE* trials of different things MOST of which did not work.

It's more complex than that: the branches that survived did work
(otherwise they would have died out straight away). However, they might
have survived less well than others which appeared subsequently, and
hence went extinct due to competition, or the environment changed, and
they survived less well in the new environment.

Note that we're not talking about selection. Although the initial
mutations may be random, what we see after selection will not be. The
cloud of mutants diffusing through morphospace will become lumpier, as
there are regions where they are not fit, and others where they are fitter.

Okay, but what I intuit to be a fly in the ointment of a clear random
distribution of mutations, selected for by various natural factors (not
merely survival of the fleetist of foot but, also, survival as "screened" by
an enormous number of other factors... predation, disease, not having the
area one had to run on cut off from a main continental shelf and sink below
sea level, and at least a hundred more...

.... is that if most mutations are deleterious... then what are the odds that
anything -- even POST HOC capable of appearing to be linear or ratable over
time -- occur *AT ALL* ?

"Most" is not the same as "all".

For one thing, if a creature were experiencing *RANDOM MUTATIONS*, then it
is unlikely that it would have progressed from five toes being used on each
foot, to three in back and four in front, etc., etc., etc., to a hoof.
Random would not be simply foot mutations. It would be mutations ANYWHERE
in the morphology of descendants. How could so many *RANDOM* mutations have
a focus on the feet?

If you play the lottery, it's unlikely that you will win. BUT that does
not mean that nobody wins the lottery.

Now, mind you, I am not saying they COULDN'T. My point is to say that the
statistical odds would seem to me to be enormously against it.

Not if you have enough horses! The time scales that evolution occurs
over are large, and the populations sizes are much large than one or two
individuals. I think your problem is caused by not appreciating the
scales that you need to look over: it's not one individual, but many
over a long time.

Bob

--
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: http://www.jnr-eeb.org


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