The Infinite sites model (ISM) is a mathematical model of

molecular evolution Molecular evolution describes how Heredity, inherited DNA and/or RNA change over evolutionary time, and the consequences of this for proteins and other components of Cell (biology), cells and organisms. Molecular evolution is the basis of phylogen ...

first proposed by

Motoo Kimura (November 13, 1924 – November 13, 1994) was a Japanese biologist best known for introducing the neutral theory of molecular evolution in 1968. He became one of the most influential theoretical population geneticists. He is remembered in ge ...

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 Zygosity (the noun, zygote, is from the Greek "yoked," from "yoke") () is the degree to which both copies of a chromosome or gene have the same genetic sequence. In other words, it is the degree of similarity of the alleles in an organism. Mos ...

, or

genetic diversity Genetic diversity is the total number of genetic characteristics in the genetic makeup of a species. It ranges widely, from the number of species to differences within species, and can be correlated to the span of survival for a species. It is d ...

, in a finite population and for the estimation of

genetic distance Genetic distance is a measure of the genetics, genetic divergence between species or between population#Genetics, populations within a species, whether the distance measures time from common ancestor or degree of differentiation. Populations with ...

s 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 Homoplasy, in biology and phylogenetics, is the term used to describe a feature that has been gained or lost independently in separate lineages over the course of evolution. This is different from homology, which is the term used to characterize ...

, or back-mutation to an allele that previously existed. All identical alleles are

identical by descent Identical may refer to: * Identical, when two things are the same, see Identity (philosophy) * ''Identical'' (Hopkins novel), a 2008 young adult novel by Ellen Hopkins * ''Identical'' (Turow novel), a 2013 legal drama novel by Scott Turow * '' Th ...

. 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 (

\theta

) can be estimated as follows, where

\mu^*

is the number of mutations found within a randomly selected DNA sequence (per generation),

N_e

is the effective population size. The

coefficient In mathematics, a coefficient is a Factor (arithmetic), multiplicative factor involved in some Summand, term of a polynomial, a series (mathematics), series, or any other type of expression (mathematics), expression. It may be a Dimensionless qu ...

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 The effective population size (''N'e'') is the size of an idealised population that would experience the same rate of genetic drift as the real population. Idealised populations are those following simple one- locus models that comply with ass ...

which is, for most species, roughly half of

N_e

\theta=4N_e\mu^*

When considering the length of a DNA sequence, the expected number of mutations is calculated as follows

\mu^*=k\mu

Where k is the length of a DNA sequence and

\mu

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

chromosome A chromosome is a package of DNA containing part or all of the genetic material of an organism. In most chromosomes, the very long thin DNA fibers are coated with nucleosome-forming packaging proteins; in eukaryotic cells, the most import ...

s. Chromosomes are made up of ''sites'', which are

nucleotide Nucleotides are Organic compound, organic molecules composed of a nitrogenous base, a pentose sugar and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both o ...

s 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: * ''k'' breaks are made in these chromosomes, which leaves ''2k'' free ends available. The ''2k'' free ends will rejoin in a new manner rearranging the set of chromosomes (i.e. reciprocal translocation, fusion, fission,

inversion Inversion or inversions may refer to: Arts * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ''Inversions'' (novel) by Iain M. Bank ...

, circularized incision, circularized excision). * No break point is ever used twice. * A set of chromosomes can be duplicated or lost. * DNA that never existed before can be observed in the chromosomes, such as

horizontal gene transfer Horizontal gene transfer (HGT) or lateral gene transfer (LGT) is the movement of genetic material between organisms other than by the ("vertical") transmission of DNA from parent to offspring (reproduction). HGT is an important factor in the e ...

of DNA or viral integration. * If the chromosomes become different enough, evolution can form a new species. * Substitutions that alter a single base pair are individually invisible and substitutions occur at a finite rate per site. * The substitution rate is the same for all sites in a species, but is allowed to vary between species (i.e. no

molecular clock The molecular clock is a figurative term for a technique that uses the mutation rate of biomolecules to deduce the time in prehistory when two or more life forms diverged. The biomolecular data used for such calculations are usually nucleot ...

is assumed). * Instead of thinking about substitutions themselves, think about the effect of the substitution at each point along the chromosome as a continuous increase in evolutionary distance between the previous version of the genome at that site and the next version of the genome at the corresponding site in the descendant.

References

Further reading