# Box 2 | Removal of deleterious mutations by truncation selection

## From the following article:

The origins, patterns and implications of human spontaneous mutation

James F. Crow

Nature Reviews Genetics 1, 40-47 (October 2000)

doi:10.1038/35049558

A mildly deleterious mutation can persist in the population for many generations,
the number being related to the reduction in fitness caused by the mutation.
We have very little idea of what the average persistence of mildly deleterious
human mutations is. In Drosophila, it is estimated at 50 to several
hundred generations. As an example, I will take 100. Three new mutations per
generation, each persisting for 100 generations, means that the average person
carries 300 mutations. If these are independently inherited, the number per
person will have a distribution that is roughly POISSON
(actually with a little less spread because of incomplete randomization
during meiosis)^{54}. I shall assume a standard deviation of 15
(the Poisson value is the square root of the mean, or about 17), that the
distribution is normal (entirely reasonable with this many mutations) and
that those with a number above one standard deviation from the mean, about
16% of zygotes, fail to survive and reproduce. In the next generation new
mutations occur and existing ones are shuffled by recombination so that the
original normal distribution is restored.

Mean number of mutations

This is illustrated in the figure. The mean number of mutations per person is 300. With 16% eliminated, the mean number among these is 322.7. The mean number in the 84% not eliminated is 295.7. Three new mutations are not quite enough to bring the number back to 300, so 16% selective elimination is more than enough to balance mutation accumulation. Truncation selection is indeed an efficient method for eliminating harmful mutations.

Of course, nobody thinks that this is a realistic model — nature
does not truncate precisely. For this reason, I was once reluctant to regard
this as a reasonable possibility. Then I was surprised to find^{55}
that a very fuzzy approximation to truncation selection (quasi-truncation
selection) works nearly as well. All that is required is that the probability
of removal increases monotonically with the number of deleterious mutations.
Until recently in our evolutionary past, the population was nearly stable
and every generation produced more progeny than could survive and reproduce.
To some extent those who failed would have been those with the largest number
of deleterious mutations. So, I think it quite likely that in the past such
quasi-truncation selection has been an efficient means of eliminating deleterious
mutations. Without belabouring the specific assumptions, it seems reasonable
that elimination of harmful mutants was far more efficient than would have
been expected if they were eliminated independently as proposed by Haldane^{49}.