Coalescent theory is a model of how alleles sampled from a population may have originated from a common ancestor. In the simplest case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure, meaning that each variant is equally likely to have been passed from one generation to the next. The model looks backward in time, merging alleles into a single ancestral copy according to a random process in coalescence events. Under this model, the expected time between successive coalescence events increases almost exponentially back in time (with wide variance). Variance in the model comes from both the random passing of alleles from one generation to the next, and the random occurrence of mutations in these alleles.
The mathematical theory of the coalescent was developed independently by several groups in the early 1980s as a natural extension of classical population genetics theory and models, but can be primarily attributed to John Kingman. Advances in coalescent theory include recombination, selection, overlapping generations and virtually any arbitrarily complex evolutionary or demographic model in population genetic analysis.
