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Modern Genetic Analysis Chapter 17. Population and Evolutionary Genetics The Sources of Variation
Genetics In Process 17-3: The effect of mutation on allele frequency

Let µ be the mutation rate from allele A to some other allele a (the probability that a gene copy A will become a during the DNA replication preceding meiosis). If pt is the frequency of the A allele in generation t, if qt = 1 pt is the frequency of the a allele, and if there are no other causes of gene frequency change (no natural selection, for example), then the change in allelic frequency in one generation is

where pt1 is the frequency in the preceding generation. This tells us that the frequency of A decreases (and the frequency of a increases) by an amount that is proportional to the mutation rate µ and to the proportion p of all the genes that are still available to mutate. Thus D p gets smaller as the frequency of p itself decreases, because there are fewer and fewer A alleles to mutate into a alleles. We can make the approximation that, after n generations of mutation,

where e is the base of the natural logarithms. This relation of gene frequency to number of generations is shown in the adjoining figure for µ = 105. After 10,000 generations of continued mutation of A to a,

If the population starts with only A alleles (p0 = 1.0), it would still have only 10 percent a alleles after 10,000 generations at this rather high mutation rate and would require 60,000 additional generations to reduce p to 0.5. Even if mutation rates were doubled (say, by environmental mutagens), the rate of evolution would be very slow. For example, radiation levels of sufficient intensity to double the mutation rate over the reproductive lifetime of an individual human are at the limit of occupational safety regulations, and a dose of radiation sufficient to increase mutation rates by an order of magnitude would be lethal, so rapid genetic change in the species would not be one of the effects of increased radiation. Although we have many things to fear from environmental radiation pollution, turning into a species of monsters is not one of them.

The change over generations in the frequency of a gene A due to mutation from A to a at a constant mutation rate (µ) of 105.

© 1999 by W. H. Freeman and Company. All rights reserved.