Infinite sites model

The Infinite sites model (ISM) is a mathematical model of molecular evolution first proposed by Motoo Kimura in 1969. Like other mutation models, the ISM provides a basis for understanding how mutation develops new alleles in DNA sequences. Using allele frequencies, it allows for the calculation of heterozygosity, or genetic diversity, in a finite population and for the estimation of genetic distances between populations of interest.
The assumptions of the ISM are that (1) there are an infinite number of sites where mutations can occur, (2) every new mutation occurs at a novel site, and (3) there is no recombination. The term ‘site’ refers to a single nucleotide base pair. Because every new mutation has to occur at a novel site, there can be no homoplasy, or back-mutation to an allele that previously existed. All identical alleles are identical by descent. The four gamete rule can be applied to the data to ensure that they do not violate the model assumption of no recombination.
The mutation rate (formula_1) can be estimated as follows, where formula_2 is the number of mutations found within a randomly selected DNA sequence (per generation), formula_3 is the effective population size. The coefficient is the product of twice the gene copies in individuals of the population; in the case of diploid, biparentally-inherited genes the appropriate coefficient is 4 whereas for uniparental, haploid genes, such as mitochondrial genes, the coefficient would be 2 but applied to the "female" effective population size which is, for most species, roughly half of formula_3.
formula_5
When considering the length of a DNA sequence, the expected number of mutations is calculated as follows
formula_6
Where k is the length of a DNA sequence and formula_7 is the probability a mutation will occur at a site.
Watterson developed an estimator for mutation rate that incorporates the number of segregating sites (Watterson's estimator).
One way to think of the ISM is in how it applies to genome evolution. To understand the ISM as it applies to genome evolution, we must think of this model as it applies to chromosomes. Chromosomes are made up of "sites", which are nucleotides represented by either A, C, G, or T. While individual chromosomes are not infinite, we must think of chromosomes as continuous intervals or continuous circles.
Multiple assumptions are applied to understanding the ISM in terms of genome evolution: