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Mutation: Selection vs. Mutation

Typically, selection and mutation are opposing forces. The reason for this is that most mutations are disadvantageous. Thus, selection acts to rid the population of these alleles; The strength of this selection is usually denoted by s, the selection coefficient. The change in the frequency of the mutant allele in the next generation, due to selection, is calculated as:

where h is the degree of dominance.

However, mutation occurs at a relatively constant rate, , which acts to increase the frequency of the mutant allele in the population. Mutation rates are typically between and . The change in the frequency of the mutant allele in the next generation, due to mutation, is calculated as:

Because were talking about deleterious alleles here, selection invokes a negative change in q, whereas mutation invokes a positive change. When these two forces come into balance with each other, q comes to an equilibrium value (no change in q). When this is true, we can calculate the mutation rate for a particular allele given q,s, and h:

Mutation: Selection vs. Mutation

Adjust the selection coefficient s, and the mutation rate m to the right:

When the mutation rate is set to 0.0, q remains at 0.0 because no mutant alleles are introduced into the population. As m is increased, the equilibrium value of q becomes greater as mutation becomes a stronger force. As s is increased, conversely, the equilibrium value of q decreases. The opposing forces of selection and mutation balance out after only a few generations, where q remains relatively constant.

In this simulation, the yellow line represents the frequency of q in a population of 5000 individuals. The current q value is also displayed in the top right of the figure. The red line represents the frequency as calculated using the first two equations in the background section simultaneously.

Because the population size isn't infinite, there is some variation in q after equilibrium has been reached. Note, however, that the frequency never deviates too far from the projected value. This can be seen by pressing the run button several times for a set of conditions without pressing reset button. The frequency is held in check by the opposing forces of selection and mutation.