Re: attempt of illustration of the role of sexual recombination in (partly, at least) solving Haldane's dilemma


"Danniel Soares" <dannielsc@xxxxxxxxxxxx> wrote in message news:1157737661.633945.290180@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
I was discussing the subject with a creationist (or something like it)
in another forum, and he objected to an argument given in "an index to
creationists claims", of Talk Origins

( http://www.talkorigins.org/indexcc/CB/CB121.html ).

The argument from talk origins was specifically:

"[Haldane] also assumed that two mutations would take twice as long to
reach fixation as one, but because of sexual recombination, the two can
be selected simultaneously and both reach fixation sooner."

I believe that that is a distortion of Haldane's argument. Haldane
argued that fixing two mutations would incur twice the 'cost of selection'
(ie. selective deaths of individuals) as fixing one mutation. Haldane
was quite aware that, particularly in a sexual population, multiple
alleles can be proceeding to fixation simultaneously. He was also
aware that very-advantageous alleles move to fixation quickly, but
that marginally-advantageous alleles take some time. But he argued
that selectively fixing any allele - marginal or otherwise - requires
the same number of selective deaths (roughly equal to the population
size).

Haldane further argued that in situations in which many alleles are
moving to fixation simultaneously, selective deaths can be a limiting
resource, and hence that the rate of fixation of alleles would be
limited by this limiting resource.

His argument is valid if one selective death, on average, only advances
the advantageous allele at only one locus. One can imagine selective
regimes (truncation selection) in which selective deaths really do
perform 'double duty' in this way, but such schemes are not the way
that the standard population genetics models of selection work.

So the 'problem' you are trying to solve is a non-problem. Haldane
did not assume that serial processing of loci was the case. He
definitely was already assuming that the population was sexual and
that selection on multiple alleles was taking place simultaneously.

To which the creationist objected:

"in sexual reproduction, the descendants do not inherit intact
chromosomes of their parents. Because of this, each mutation has to pay
its fixation cost independently."

Which is basically correct. That is exactly the problem that Haldane
analyzed - the sexual one.

In order to try to explain this, I made an "illustration" in phpbb-like
code of that specific forum, and I present here in an snapshot:

http://img107.imageshack.us/img107/4737/selectioneh8.jpg

Each three-letter string in a line is an individual represented by
three loci of its genome taken in account, and lines are generations.

That is a simple illustration by no means intended to deal with all the
real populational dynamics. Basically, there are the generic genes
always called X, at any locus, and the A, B, and C, advantageous
mutations, each one which increase their frequency in one after each
generation, no matter what. The population size is assumed to be
constant, all the deaths by selection are equaly compensated by the
improved fitness of the mutations being selected. (Which, as far as I
could grasp, is more or less in accord with Haldane's assumptions).

Then, as the illustration hopefully illustrates, due to sexual
recombination, despite of the mutations originating first in diferent
individuals, eventually they met in the same individuals, and can reach
fixation "at the same time" (or more or less, in a more realistical
situation). Despite of the illustration not dealing with the departure
of mutations after they´re been joined in the same individuals (which
I think that would probably be the overall rule, not an exception), I
think that the logic is essentially the same of the joining of
mutations originally arisen in different individuals.

Is that basically correct? Any additional suggestion or note?

You are attacking a straw man. Neither Haldane nor ReMine is unaware
of sex and what it does in terms or recombining genes. But your
diagram seems to illustrate that you *don't* understand what sex
does. Yes, I understand that you actually *do* understand, but
your diagram says otherwise.

Sorry if this seems harsh.

(ps.: the third or fourth generation has an accidental extra "B", but
it´s okay since it retains the same number in the following
generation)


Danniel Soares



.

Relevant Pages