Substitution rate

We can now do what we set out to do, which is to relate the within-population allele dynamics to between-population patterns of genetic variation. Having set up our model for the dynamics of a mutation within a population, we need a model to describe how mutations arise in the first place. There are several possible choices in wide use, including:

• k-alleles model (mutation among k possible types)
• infinite alleles model (all mutations create a unique allelic type)
• infinite sites model (similar to the infinite alleles model, except at a finer scale-- nucleotide or amino acid sites along a sequence)

Whatever we imagine these mutations look like, however, they are assumed to occur with mean rate generation (on whatever scale we are assessing mutations-- transitions, transversions, third-base mutations, etc·). We want to know the rate at which these mutations that are entering the population become established in the population-- the fixation process described above. This is known as substitution (a new type is substituted for an old). Then we can use the above results to show that

This simple result, that the rate of substitution equals the rate of mutation, has been instrumental in the study of molecular evolution, for good reason. Population genetics is notorious for its reliance on difficult to measure (and often confounded) parameters such as effective population size, mutation rate, and selection coefficients. Here is a formula which tells us that the data we observe (substitutions) is dependent only on one of these, mutation rate.

• Molecular clocks
• Other results from neutral models