Mutations are errors in DNA synthesis that lead to changes in the DNA code. Although rare events, mutations help generate genetic variation and allow evolution to occur. The effect of a specific mutation depends both on where in the DNA code the mutation occurs, how that mutation changes the trait (or traits) of the offspring, and what environmental factors the offspring is exposed to.

Many mutations have no effect on the organism, often because the change does not significantly alter the phenotype of the offspring. A small portion of mutations confer a selective advantage and persist in future generations. Most mutations, however, decrease the fitness of the organism and tend to be eliminated. Such deleterious mutations should be eliminated from the population. However, a small population of these "bad alleles" persist because selection cannot purify them all. The equilibrium frequency of a given allele can be calculated using a power function.

The wild type Mediterranean fruit fly has white eyes (right) and the mutant has red eyes (left). Photo credit: Al Handler, courtesy of the U.S. Department of Agriculture, Agriculture Research Service.

Mutation-selection balance refers to the equilibrium formed by removal of deleterious alleles by selection, and the addition of deleterious alleles by mutation. For this exercise, we will assume that all mutations are deleterious.

Suppose there is a single locus with two alleles, A and a, with frequencies p and q = 1 - p, respectively. We will assume that allele a is deleterious and recessive, and that mutations only occur in a forward direction at a rate of μ per generation. If s is the selection coefficient corresponding to allele a, where s = 0 implies neutrality and s = 1 implies lethality, the equilibrium frequency of allele a (given by q*) is approximated by,

where 0 < s < 1.