**Motivation:** You have re-sequenced several genomes after a mutation accumulation or adaptive evolution experiment. How do you infer the rates of different types of mutations from these data? What are the 95% confidence intervals on these values?

**Assumptions:**

- The number of mutations is small compared to the number of sites.
- There are no back mutations (reversions).
- Mutations rates are constant over time and across sites.

**Example:** Single-base substitutions

**Calculation:**

- If you restrict your data to one genome per experimental population, then you can calculate the maximum likelihood value and 95% confidence limits from a Poisson distribution. Count the total number mutation (
*m*) and the total elapsed generations or time of independent evolution (*T*). Example: 22 point mutations found in 6 genomes that each evolved for 10,000 generations.

>m = 22 >T = 10000 * 6 >rate = poisson.test(m) >rate$estimate/T event rate 0.0003666667 >rate$conf.int/T [1] 0.0002297880 0.0005551377 attr(,"conf.level") [1] 0.95

- If you know the number of sites at risk for the mutation (
*s*), then you can calculate a per-site mutation rate. Example: Assume these 22 point mutations are A to G substitutions and there are 1,342,726 A bases in the original genome.

>s = 1342726 >rate$estimate/(T*s) event rate 2.730763e-10 >rate$conf.int/(T*s) [1] 1.711355e-10 4.134408e-10 attr(,"conf.level") [1] 0.95

**Assumptions:**

- The mutation can only happen once per genome.
- The mutation rate is constant per unit time or generation

**Example:** Deletion of an unstable chromosomal region. Once deleted, it can never be deleted again.

**Calculation:**

- Count the number of independent genomes that have the mutation (
*m*) and total number of genomes analyzed (*n*) at a given time (*T*). Example: 5 of 12 independently evolved genomes have the mutation after 10,000 generations.

> m = 5 > n = 12 > T = 10000

- Calculate a maximum likelihood value and 95% exact (Clopper-Pearson) confidence limit for the fraction of independently evolved lineages that
the mutation from your observations.*do not have*

p = binom.test(n - m, n) >p Exact binomial test data: n - m and n number of successes = 7, number of trials = 12, p-value = 0.7744 alternative hypothesis: true probability of success is not equal to 0.5 95 percent confidence interval: 0.2766697 0.8483478 sample estimates: probability of success 0.5833333

- If the mutations happen at a constant rate per unit time, then you can calculate the rate that gives this fraction of independent lineages without a mutation up to the given time point using the zero event term from a Poisson process:

> -log(p$estimate) / T probability of success 5.389965e-05 > -log(p$conf.int) / T [1] 1.284931e-04 1.644646e-05 attr(,"conf.level") [1] 0.95

This is a particularly simple type of survival analysis.

Barrick Lab > ProtocolList > ProceduresCalculatingMutationRatesFromGenomicData

Topic revision: r3 - 25 Jul 2012 - 15:09:39 - Main.JeffreyBarrick

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