# Mullers ratchet

Jonah Thomas JEThomas at ix.netcom.com
Mon Mar 6 11:29:02 EST 1995

```In <3j2l2n\$drt at newsbf02.news.aol.com> ehsim at aol.com (Ehsim) writes:

>
>Help!!!!  I am doing a presentation on P. formosa and I need to know
what
>Mullers ratchet.  Please eme asap.
>
>Thanks.
>

Here's an explanation of Muller's Ratchet:

I'll give an example of it working, examples are probably best.

Start with a uniform asexual population of 10^8 individuals.  Assume
there are 10^8 different additive mutations they could get, that each
have a selective disadvantage of about 1%.  (We'll ignore all the other
mutations, and just look at the 1% ones.)  Assume each of these
mutations occurs at a rate of 10^-9 per generation.  And assume the
back-mutation to the "wild-type" also occurs at 10^-9.

The original genome has an overall mutation rate of 10% per
generation, but it's only selected 1%.  The number of mutants will
tend to increase; at equilibrium the population will be 10%
"wild-type" and 90% mutant.

But that isn't really the equilibrium, because the individuals with
mutations will also mutate at 10%.  Their mutations will have about a
2% selective disadvantage relative to the wild-type, but they don't
compete just against the wild-type -- they compete mostly against
their parents.

If you work out the figures, the wild-type won't reach equilibrium
until the average fitness is down low enough to give it a 10%
selective advantage.  At that point the individuals with 9 mutations
will be 1/10 as common as those with 10, those with 8 will be 1/10 as
common as those with 9, and so on.  At equilibrium the wild-type will
be 10^-10 of the population.  But the population is only 10^8
individuals.  At equilibrium the wild-type is gone.

So here's the ratchet -- with the wild-type gone, the cells with 1
mutation are the best.  All the previous calculations apply to them
too.  They will go extinct and the average fitness will decline --
the wild-type would have an 11% advantage if it was still there.  A
turn of the ratchet.  So then the cells with 2 mutations are the
best.  And so on.

This logic doesn't apply to sexual populations.  Sexual populations
don't depend on the few best individuals to outcompete the rest, they
can regenerate good genomes easily, and they can pile a lot of
unfavorable mutations into one individual and, removing that one,
select against the bunch.

###

Muller's Ratchet is good for illustrating some things, but it may be
generally unrealistic.  Here's the question to ask:  How did that
asexual population ever get a perfect "wild-type" in the first place?
Not through selection on that population.

If you instead assume that the population has only stumbled onto half
of the 1% favorable mutations, you get a very different result.  Then
the mutation rate for 1% disfavorable mutations is 5%, and that for
1% favorable mutations is 5%, and the number of favorable ones
increases -- although you can't predict ahead of time which ones will
increase.

!!!  This is important  !!!

It can sometimes allow a sort of selective fine-tuning.

Fisher's Fundamental Law of Natural Selection says that the increase in
fitness due to selection is directly proportional to the variance in
fitness.  It turns out that when a single very-favorable mutation
increases fast, the variance in fitness drops for everything linked to
it.  (It drops across the whole genome in asexual populations.)
There's a balance -- select too strongly and you lose the variability
that lets you select more.  But when there are a _lot_ of
weakly-selected mutations available, they can increase without cutting
the variability at all, and lots of them can increase at once.

Whenever you get down to the level of fitness that hasn't been selected
much already, you can expect to find about 50% favorable mutations
relative to unfavorable ones. (This is similar to another argument by
Fisher.  Mutations with small phenotypic effect reach 50% favorable in
the limit.  Which is the mutation and which the back-mutation?  It
depends on what's already there.  For each pair of choices, there's
about a 50% chance you get the good one by accident.  So if
strongly-selected mutations carry with them whatever weakly-selected
mutations they happened to be linked to, mostly preventing selection at
the weakly-selected sites, about half of those will have the
less-favorable version present.)

See!  It looks like nothing is happening.  No highly-favorable
mutations taking over fast.  Variability staying high, maybe
increasing.  Phenotypic diversity increasing, but not in ways that are
obviously selected.  But given time, the population incorporates a lot
of favorable genes, a sort of incremental improvement.

I stumbled onto this doing simulations of evolving bacterial
populations.  I haven't seen it in the literature, but I haven't
searched that hard.

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