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We're now going to calculate the rate of molecular evolution, i.e.,
the rate of allelic substitution, under the hypothesis that mutations
are selectively neutral. To get that rate we need two things: the rate
at which new mutations occur and the probability with which new
mutations are fixed. In a word equation
Surprisingly,1 it's pretty easy to calculate
both
and
from first principles.
In a diploid population of size
, there are
gametes. The
probability that any one of them mutates is just the mutation rate,
, so
 |
(1) |
To calculate the probability of fixation, we have to say something
about the dynamics of alleles in populations. Let's suppose that we're
dealing with a single population, to keep things simple. Now, you have
to remember a little of what you learned about the properties of
genetic drift. If the current frequency of an allele is
, what's
the probability that is eventually fixed?
. When a new mutation
occurs there's only one copy of it,2so the frequency of a newly arisen mutation is
and
 |
(2) |
Putting (1) and (2) together we find
In other words, if mutations are selectively neutral, the substitution
rate is equal to the mutation rate. Since mutation rates are (mostly)
governed by physical factors that remain relatively constant, mutation
rates should remain constant, implying that substitution rates should
remain constant if substitutions are selectively neutral. In short, if
mutations are selectively neutral, we expect a molecular clock.
Next: Diversity in populations
Up: Neutral mutations
Previous: Neutral mutations
Kent Holsinger
2008-09-04