koalescent

The coalescent, also called the koalescent, is a retrospective stochastic process describing the genealogical history of a sample of gene copies from a population by tracing their lineages backward in time until they merge at common ancestors. The standard model, the Kingman coalescent, assumes neutral evolution, random mating, non-overlapping generations, and a constant effective population size Ne. For a sample of k lineages, any pair can coalesce, with total rate C(k,2)/2Ne; waiting times between coalescent events are exponentially distributed. Time is measured in units of 2Ne generations in diploids. As time proceeds backward, the number of ancestral lineages declines from k to k-1, until all lineages meet at the most recent common ancestor.

Coalescent theory links genealogies to patterns of genetic variation and population history. It underpins methods for inferring past population size changes, migration, and structure from DNA data. When recombination is present, different genomic regions can have different genealogies, described by the Ancestral Recombination Graph (ARG). Extensions address deviations from neutrality and simple demographics, including multiple-merger (Lambda- or Xi-coalescents) for species with highly skewed offspring distributions, and structured coalescents for subdivided populations.

Limitations include departures from assumptions (selection, variable Ne, recombination, linkage). Despite these limitations, the coalescent remains foundational in population genetics and phylogenetics, providing a tractable framework for interpreting genetic diversity.