and the chance of loss is 1 -

so the chance of fixation is 1

2N 2N

e e neutral mutations are expected to be lost from a population very rapidly since their initial frequency is very near zero. An average of 4Ne generations will elapse before a new mutation reaches fixation. Fisher's geometric model of mutation shows that mutations with small effects on phenotype are more likely to be fixed by natural selection since these are the mutations with the greatest chance of improving fitness.

The combination of mutation, genetic drift, and natural selection in genomes where recombination is absent or restricted leads to a growing accumulation of deleterious mutations in a phenomenon known as Muller's Ratchet. The infinite alleles model assumes discrete allelic states where each mutation creates an allele not currently present in the population. The infinite sites model assumes alleles are DNA sequences and that each mutation changes a single nucleo-tide at a site that has never before experienced mutation. Since mutation cannot form the same allele twice in both of these models, identity in state is always equivalent to identity by descent. Irreversible mutation will eventually lead to loss of the original allele in a population since there is no process to restore the original allele. Bi-directional mutation leads to a net balance of two alleles changing state and an intermediate allele frequency that depends on the forward and reverse mutation rates. Both models show that mutation alone will take thousands or tens of thousands of generations to attain equilibrium allele frequency in a population, depending on the mutation rate.

• The process of mutation can be added to coalescent genealogies by modeling the waiting time to any event with an appropriate cumulative exponential distribution. When an event does occur, it can be either a coalescence or a mutation that is then reflected in the genealogy. More mutations are likely to occur on longer branches in genealogies since the chance of mutation is constant through time.

• Each mutation event in a genealogy can be interpreted under a specific mutation model such as infinite alleles or infinite sites. The combination of a coalescent genealogy containing mutations and a mutation model yields a prediction for the number and frequency of alleles expected under the process or processes that produced the genealogy.

Further reading

For a detailed review of mutation rate estimates and the processes influencing the evolution of mutation rates see:

Drake JW, Charlesworth B, Charlesworth D, and Crow JF. 1998. Rates of spontaneous mutation. Genetics 148: 1667-86.

For an overview of the numerous evolutionary and population genetic phenomena related to mildly deleterious mutation see:

Charlesworth B and Charlesworth D. 1998. Some evolutionary consequences of deleterious mutation. Genetica 102/103: 3-19.

A full explanation of the experimental methods, assumptions, and statistical analysis used in mutation-accumulation studies along with a critical review of past results can be found in:

Lynch M, Blanchard J, Houle D, Kibota T, Schultz S, Vassilieva L, and Willis J. 1999. Perspective: spontaneous deleterious mutation. Evolution 53: 645-63.

This paper provides an overview of the role mutation plays as the source of genetic variation in the larger process of adaptation by natural selection:

Orr HA. 2005. The genetic theory of adaptation: a brief history. Nature Reviews Genetics 6: 119-27.

For more detail on incorporating mutation into genealogical branching models see:

Hein J, Schierup MH, and Wiuf C. 2005. Gene Genealogies, Variation and Evolution. Oxford University Press, New York.

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