Re: Haldane's Dilemma and quantitative genetics

Jim and ErikW ask:

Geographical structure in the population slows fixation of neutral
mutations to a standstill? Interesting suggestion. First I've heard
of it. But your verbal argument leaves me unconvinced. Perhaps if
you expressed your reasoning in a mathematical model? ;-)

The mathematics of the process is simple enough. A neutral mutation is
by definition a mutation that has neither any selection for or against
it within the population, thus its persistence represents the most
"honest" of games, a "fair" coin flipped a thousand times.

Because of this attribute, its persistence is a Markov process, where
its transition probabilities are equally balanced, for and against.

The classical illustration of a selectively neutral Markov process is a
drunk initially standing at a lightpole, taking a random step to the
left or the right at each tick of the clock. As time proceeds to
infinity, eventually the drunk will have walked the entire universe,
but on average, he will remain where he started, at the lightpole.

The situation is changed however if there is an absorbing barrier
anywhere along his path, no matter how far away it might be from his
original starting point. In real life, absorbing barriers are such
things as death, extinction or bankruptcy, holes you can't climb out
of. At infinite time, the drunk is absolutely guaranteed of falling
into the absorbing barrier, if one exists.

"Gambler's Ruin" is a slightly modified version of the random walk with
an absorbing barrier. Imagine two players coming to a table, one with
100 pennies and the other with 10,000, and they engage in a perfectly
honest game, flipping a fair coin at each tick of the clock. Both
players will enact the same random walk, although they will be the
symmetric opposites of each other. More importantly, they will have the
same variances (measured in absolute terms), and they will explore the
state space of all possible values at the same rate.

The question then becomes: who will hit the bankruptcy absorbing
barrier first? In all probability, it will be the fellow with 100 cents
rather than the one with 10,000 pennies. Indeed, that's the moral of
Gambler's Ruin: in honest games, poor men invariably leave the table
(go extinct) first.

Now imagine a tessellated map (a checkerboard of triangles, squares,
hexagons or whatever geometry you like; the process is robust). On this
inifinitely large map, imagine that each cell is populated by a single
phenotype (an "A"), but also imagine that at the center we put a single
neutrally mutated phenotype (an "a"). Remember, only we know that this
phenotype is neutrally mutated. Selection can't tell the difference.

Now let each population within each cell reproduce and spread out into
the immediately adjoining cells, as do all of the other cells'
populations. The persistence of the a's at the next tick of the clock
depends on their random selection. If the tessellation is hexagonal,
the a's progeny stand only one chance in 6 of surviving in any one the
adjacent cells in the next generation, which is also the same chance of
persistence that the original population is offered.

The process becomes Gambler's Ruin on steroids, with the end result
that the "a" population is extincted almost immediately.

You can futz with the geometries of the map, as well as the rules for
reproduction and competition, but it won't much change the outcome, so
long as the game remains completely "honest," which is nothing more
than saying that it remains selectively neutral.


Jim also writes:

But if your
point is simply that pop-gen and mathematical models generally are
not the royal road to the truth, then your point is taken.

That is exactly the point. Science is not speculation about how many
angels might dance on the head of pin. It is about experimentally
verifiable truths. Once a model is formulated by its codifying its
various assumptions, the answer is cast in stone, whether you
immediately know the answer or not. It only remains to explore the
nooks and crannies of the model with theorem and lemma in hand. People
rarely make mistakes in the algebra of that exploration. That isn't
where the common problem lies; the truth or falsity of the models
invariably lie in the underlying assumptions back at step one.
Mathematical genetics has become so sufficiently dogmatized over the
last 70 years that no one bothers much any more to ask if the "angels"
even exist, but that is exactly the question that should be being
asked. Mathematical genetics is based on a simplfied 1920's
misunderstanding of the genetics of populations that we now outrightly
know to be wrong.


Larry also writes:

This is my opportunity to be the group's curmudgeon for the fortieth
time, but these models are not at all representative of how evolution
works and have almost no value in advancing any physical understanding
of the evolutionary process. If I can't be any more blunt and offensive
than that, I don't know how.

The evolutionary clock does not run at any where near a constant speed.
Filled ecological niches occupied by highly coevolved communities are
very difficult to invade, and thus evolution tends to come to almost a
dead stop in such situations. Intense competitive interaction doesn't
allow much change.

That's a false view of evolution. You don't know what you're talking
about.

How's that for blunt and offensive? :-)

That's not bad, Larry, and I would be both sincerely offended and
chastened if I agreed with you.



Your false view of evolution includes the ridiculous idea that species
become perfectly adapted to their environment and will stop evolving.
Can you identify a single modern species that has become so perfectly
adapted that it has stopped evolving and therefore contains no significant
variation?

"Perfect adaptation" isn't what I was arguing. Perfection implies
optimality, but that's not the point. Rather what I was arguing is that
species commonly become evolutionarily stuck, hemmed in by their
environments and most especially by their ecological competitors for
substantial periods of time.

The notion that adaptive radiations occur only during those periods of
competitive release that are associated with environmental disruptions
is merely the flip side of the punctuated equilibrium argument, which
of course argues that quite long episodes of phyletic stability are
commonplace. "Punk eke" is the paleontological view of the process, but
we have a thousand matching examples of adaptive radiations in the
evolutionary ecological literature as well, instances which have
occurred essentially in "now" time, the evolutionary radiation of the
Felidae that I mentioned earlier being only one of them.

I'm certainly not the only one to argue these points. Indeed, I believe
it to be the consensus view among evolutionary biologists, given the
mass of data we now possess.

By chance, another evolutionary biologist, Olivia Judson, someone of
whom I hadn't heard of before (and I'm sure that she can say the same
of me), has begun writing a blog for the New York Times on evolutionary
biology. Last week she wrote virtually the same thing under the rubric,
"Evolution 101: No Vacancy. No Evolution."

To save Josh and s.b.e. from being sued by the NY Times, I've put up
this one entry of hers on one of our auxiliary web servers:

http://67.41.4.238/evo101-no-vacacny-no-evol.html

It's worth reading.


Another completely false idea is that natural selection is the only
mechanism of evolution.

The third false idea is that "the evolutionary clock does not run at
any where near a constant speed." This silly statement is directly
contradicted by real data in the scientific literature. I can only assume
that you are using some strange definition of evolution that eliminates
all change at the molecular level. Perhaps you meant to say that the
rate of "positive natural selection" isn't clocklike over millions
of years?

Moreover, the presence of a biogeographic map, which is ignored in
standard mathematical genetics, renders the substitution of neutral
changes almost impossible. A novel neutral mutation in an individual
must compete with its sibling competitors coming from all directions,
and because the change is neutral, it has no selective advantage for or
against it by definition, thus if it is to survive, it must climb
against the Gambler's Ruin tide, a Markovian process that virtually
guarantees not only the new mutation's relatively immediate elimination
but also a very short time on the biogeographic map.

Hmmm ... you have just eliminated random genetic drift as a mechanism of
evolution. Why don't you try and publish this? :-)

Walk the streets of any large city. Look at the people. Do they all look
the same? Can you recognize people whose ancestors came from Afica, Europe,
Asia, or North America? Have all of the differences been selected? You
*must* assume that every genetic feature is an adaptation of some sort
otherwise your "theory" is refuted. Are you prepared to make that claim
and defend it?

In the absence of any contradictory evidence, the first presumption has
to be that almost variation among populations is due to selection, not
drift.

To use your example, two hundred years ago, before global transporation
became facile, it was obvious to the first European explorers that the
human phenotypes that they encountered in their travels were tightly
coupled to their environments. Skin color is among the most obvious of
these differences in human populations.

Of even greater interest, Darwin noted that the females of every
population that he encountered were lighter skinned than their
corresponding males. He tentatively attributed that fact to sexually
selected preferences.

Nina Jablonski and Greg Chaplin (1999) have recently offered a more
cogent explanation, although one that may still be amplified by
Darwin's speculation of active sexual selection: Vitamin D3 production
is regulated by a delicate balance in skin pigmentation between too
much absorption, necessarily limiting folic acid degradation, and
insufficient vitamin D3 synthesis. They write regarding the
sex-specific differences in pigmentation:

"Pregnant or lactating women and small
children undergoing rapid bone growth are
most susceptible to changes of UV radiation
regime (Bachrach et al., 1979; Fogelman
et al., 1995; Gessner et al., 1997; Namgung
et al., 1998; Waiters et al., 1999). Vitamin
D3 deficiencies are also common among the
elderly, where they render individuals more
susceptible to osteoporosis and its sequelae
(Davies et al., 1986; Thomas et al., 1998).
The key point here is that overwhelming
clinical evidence demonstrates that even a
relatively minor decrease in endogenous
synthesis of vitamin D3 as a result of
reduced annual UV radiation exposure can
trigger vitamin D3 deficiencies in moderately
to deeply pigmented people. These
deficiencies are more marked in reproductive
females, growing children and the
elderly. Because moderately to deeply pigmented
people require from two to six times
as much UV radiation as lightly pigmented
individuals to catalyze the synthesis of an
equivalent amount of previtamin D3 (Table
2; Figure 2) (Holick et al., 1981; Clemens
et al., 1982), they are highly susceptible to
vitamin D3 deficiencies caused by a change
of UV radiation regime. We therefore conclude,
contrary to Robins, that moderately
to deeply pigmented modern human populations
are optimally tuned for endogenous
synthesis of vitamin D3 under the specific
UV radiation regimes under which they
evolved. This fine-tuning is easily disrupted
by changes of lifestyle or locale. This
situation applies equally to populations of
early Homo sapiens that undertook migrations
from eastern Africa into the circum-
Mediterranean region and Europe. Their
original levels of pigmentation would have
precipitated vitamin D3 crises in their new
environments, especially among females and
infants, and these crises would have been
more severe the farther north the populations
ventured."

http://www.bgsu.edu/departments/chem/faculty/leontis/chem447/PDF_files/Jablonski_skin_color_2000.pdf

Wirt Atmar


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