Coalescent theory

Coalescent theory is a retrospective model of population genetics that relates genetic diversity in a sample to demographic history of the population from which it was taken. That is, it is a model of the effect of genetic drift, viewed backwards in time, on the genealogy of antecedents. It comprises a probabilistic assessment of variation in time to common ancestry of alleles in a relatively small sample of individuals, from a much larger population. This includes consideration of all pathways of inheritance through which sampled copies of a homologous DNA element are traced back to a single ancestral copy, known as the most recent common ancestor (MRCA; sometimes also termed the coancestor to emphasize the coalescent relationship). The inheritance relationships among alleles are typically represented as a gene genealogy, or gene tree, similar in form to a phylogenetic tree. The probabilistic expectation of this gene genealogy is also known as the coalescent. Understanding the statistical properties of the coalescent under different assumptions forms the basis of coalescent theory. Because of recombination, different gene loci follow different pathways of ancestry, resulting in different gene genealogies. The coalescent is also relevant to phylogenetics, as incomplete lineage sorting between speciation events results in conflict among gene-loci in phylogenetic relationships inferred among species.

The mathematical theory of the coalescent was originally developed in the early 1980s by John Kingman. In the simplest case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure. The gene genealogy is independent of the mutational process, such that changes in the DNA sequence do not affect inheritance and can be considered separately (even if all gene copies are identical in sequence they are not equally related in the gene tree). Under this model, the expected time between successive coalescence events, by which two gene copies arise from a single ancestral copy, increases almost exponentially back in time (with wide variance). Advances in coalescent theory include recombination, selection, and virtually any arbitrarily complex evolutionary or demographic model in population genetic analysis.

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