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Under an infinite sites mutation model, two variable sites on one unrecombined rooted tree have nested or disjoint derived-allele clades. At most three of the four biallelic haplotypes can then occur. Observation of all four haplotypes proves that the single-tree, single-mutation-per-site model cannot hold: some ancestral genetic recombination is necessary if recurrent mutation is excluded. The test gives no proof of absence of recombination when only three haplotypes occur.

// Target: biology.bigb

A mutation changes inherited genetic sequence. Under an infinite sites mutation model, every mutation occurs at a previously unmutated position, so mutations below the sample's common ancestor correspond to segregating sites.

// Target: biology.bigb

A segregating site is a position at which at least two states occur in the sampled chromosomes. Under an infinite sites mutation model, mutations below the sample's common ancestor correspond one-to-one to segregating sites. Their number is commonly denoted $S$.

A single-nucleotide polymorphism is variation at one nucleotide position in sampled genomes. Under an infinite sites mutation model, the number of such variable positions in a sample equals the number of mutations on the genealogy below its most recent common ancestor.