# Are mutation rates normally distributed? If not, what are they?

On average, there are 64 mutations per generation in the human genome. Is this constant, or can we expect variation in the number of mutations?

• You have posed a different question in your title and in the main text which is a bit confusing. As a short hint: Quantities that are bounded (i.e. mutation rate can only be a positive number) cannot be normally distributed. But they can be, for example, distributed by the log-normal distribution. Commented Jun 12, 2023 at 11:24
• this depends a lot on the mutation, different types of mutations have different probabilities. Its all based on the laws of chemistry.
– John
Commented Jul 13, 2023 at 22:26

## 2 Answers

Mutations in this context are being treated as discrete count data (there either happen or they don't). So the number of mutations per person in a given generation should form a discrete probability distribution. Because they are a single count variable bounded at zero (can't have negative counts) and finite (genomes don't go on forever), a Poisson distribution(pwɑːsɒn/) is probably the expected best fit. A Poisson distribution can sometimes be approximated by a normal distribution when the Poisson count mean (λ) is large (some say λ>20, some say λ>100).

Note: there are 60ish substitutions per generation, on average. There are probably many times that number including all mutations (e.g. microsatellites, centromeric satellite repeats, etc). There is almost by definition a telomeric mutation on every chromosome end at every cell division, which alone is comparable to substitution number per generation.

Figure 1d of this paper suggests that the distribution of substitutions alone is log-normal in cancer, as suggested by the commenter.

I am not aware of a reference for distribution of other mutations.

• What does log normal mean Commented Jun 18, 2023 at 9:27
• @ShannonT The lognormal is a distribution that looks normal after a logarithmic transformation of the underlying data. For more info I'd suggest googling it. Commented Jun 18, 2023 at 21:39