Mutation Rates from Genome Resequencing

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?

Case 1: Mutations with many identical sites

Assumptions:

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

Example: Single-base substitutions

Calculation:

  1. 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
    
  2. 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
    

Case 2: One-time mutations

Assumptions:

  1. The mutation can only happen once per genome.
  2. 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:

  1. 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
    
  2. Calculate a maximum likelihood value and 95% exact (Clopper-Pearson) confidence limit for the fraction of independently evolved lineages that do not have the mutation from your observations.
    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
    
  3. 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.

Issues: Pseudo-replication

Issues: Different mutation rates in different lineages


This topic: Lab > WebHome > ProtocolList > ProceduresCalculatingMutationRatesFromGenomicData
Topic revision: r3 - 25 Jul 2012 - 15:09:39 - Main.JeffreyBarrick