Re: The Living Dead
- From: Steve Schaffner <sfs@xxxxxxxxxxxxxxxxxxxxxxxx>
- Date: 03 Jan 2006 14:10:11 -0500
"Seanpit" <seanpitnospam@xxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:
> Steve Schaffner wrote:
> > "Seanpit" <seanpitnospam@xxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:
> >
> > [On palindromic repeats on the Y chromosome:]
> >
> > > Can you elaborate on this a bit more? Or, are there any fairly easily
> > > accessible papers that describe this process? Thanks . . .
> >
> > Here's a brief description (including an appropriately skeptical note
> > -- this is still pretty speculative stuff), and has references to the
> > original papers:
> >
> > http://www.wellcome.ac.uk/en/genome/thegenome/hg01f015.html
> >
> > This is more of a press release, but provides more info:
> >
> > http://www.brightsurf.com/news/june_03/HHMI_news_061903.html
>
> Interesting. I'm still a bit skeptical myself about how beneficial
> internal Y-chromosome shuffling would actually be. I'll have to think
> about it a bit more.
>
> I've also been thinking a bit more about the numbers in your last
> example. In the first generation you start off with 10,000 individuals
> with 97 detrimental mutations. In the second generation you end up
> with ~7,300 individuals with < = 97 detrimental mutations and ~2,700
> with more than 97 detrimental mutations. Every level contributed far
> more individuals to the lower than to the higher levels. I'm just
> wondering what the 3rd and 4th and 5th . . . etc. generations would
> look like? Is there a simulation available where these parameters can
> be plugged in and tested? Sure, some sand does indeed roll uphill, but
> the majority does indeed seem to roll downhill. How is equilibrium
> reached like this?
Well, you can try to write down equations, which is what that Rice
paper did. If you look at his equation for the necessary load in
diploids, you'll find a factor for the new mutation rate, one for the
spread in the number of deleterious mutations carried (which is just
the statistical scatter from sampling), and one for the dependence of
fitness on the number of mutations.
Or you can, as you suggest, use a simulation. I've got one I wrote a
year or two ago, if you have the ability to compile C code.
> You explain:
>
> > Now apply selection. How much
> > more likely are the 7285 offspring (or the 6265 offspring with < 97
> > deleterious alleles) to survive and reproduce than the ones with more
> > deleterious mutations (some of them with many more)? That depends on
> > the selection coefficient. If the coefficient is high, so that, say,
> > the average lightly loaded offspring is twice as likely to reproduce
> > as the average heavily loaded offspring, then the lightly loaded
> > offspring will actually contribute more to the next generation
> > than the heavily loaded ones, and the mean number of deleterious
> > alleles will decrease.
>
> For argument's sake, lets say that no offspring with more than 97
> mutations are able to reproduce at all. Now, instead of 5,000 couples
> mating to populate the next generation, we only have about 3,600.
> True, these are more fit, but there are fewer of them. If they still
> have the same maximum reproductive rate of 4 per couple, then only
> about 14,500 offspring will be produced instead of the 20,000 produced
> by the original parent population. Of these, won't most go downhill
> instead of uphill? Won't most of these cross the boundary and end up
> below the 97 detrimental mutation threshold?
If there is a hard threshold at 97, then considering a population that
starts with exactly 97 deleterious mutations each is not a good model
for thinking about the situation. Think about a hard limit at, say,
110 instead. You will have more than enough offspring surviving to
produce the next generation, and the really highly loaded tail will be
completely removed. The effect is to increase the overall fitness of
the population at equilibrium, not decrease it.
What you describe is known as truncation selection, and is one extreme
solution proposed to explain how humans could support a high
deleterious mutation rate. (See the discussion section of the Nachman
and Crowell paper, where they mention it.) An ideal poplulation with
3.0 deleterious mutations per gen (2x reproductive capacity, Npop =
10,000, selection coeff = 0.01) comes to equilibrium at around 300
deleterious mutation per individual. (I think I reported that number
incorrectly previously.) With truncation selection operating, with a
threshold of 97 mutations, the population reaches equilibrium with 87
mutations per individual.
> > Note that this is well within the reproductive capacity that I
> > specified. Take the extreme case: all 7285 lightly loaded offspring
> > form part of the next breeding generation, along with 2715 heavily
> > loaded ones. Has the mean number of deleterious alleles in the
> > population increased or decreased?
>
> The mean number has indeed decreased, but so has the absolute number of
> offspring at or above the 97 starting point. What happens in the
> subsequent generations?
Mating in each generation tightens the distribution (combining two
randomly selected individuals from the population reduces the variance
on their average by 1/sqrt(2)), as does selection (which also biases
the distribution towards the low end). Production of new offspring
broadens the distribution, as random numbers of new mutations and
random sampling of existing mutations introduce scatter. Since we
started with zero variance in our thought experiment, initially the
variance will increase, and then stabilize. Selection keeps the high
tail from expanding indefinitely, and new mutations keep the low tail
from expanding.
--
Steve Schaffner sfs@xxxxxxxxxxxxx
Immediate assurance is an excellent sign of probable lack of
insight into the topic. Josiah Royce
.
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