Coalescentie

Coalescentie, also known as coalescent theory, is a framework in population genetics for describing the genealogical relationships of a sample of alleles by tracing their lineages backward through time until they converge to common ancestors. The standard model, Kingman’s coalescent, assumes neutral evolution and random mating in a population with an effective size N_e. When there are k lineages present, coalescence events occur at rate λ_k = C(k,2)/N_e, so the waiting time to the next coalescence is exponential with mean 1/λ_k. The resulting genealogy is a rooted binary tree with n−1 coalescent events for a sample of size n. Times are typically measured in generations scaled by N_e.

Key assumptions include neutral mutations, no recombination within the locus, constant N_e, and random mating. In practice, recombination is common, which causes genealogies to vary along the genome and is described by the ancestral recombination graph (ARG) for local genealogies.

Extensions of the basic model address more complex biology. Multiple merger coalescents permit simultaneous coalescence of more than two lineages; the structured coalescent incorporates population structure and migration; the serial coalescent handles samples collected at different times; and coalescent methods can incorporate selection via the ancestral selection graph.

Applications span the inference of past population sizes and growth, demographic events, migration rates, and population structure; the detection of natural selection; and the timing of common ancestry from DNA sequence data. Kingman introduced the framework in the 1980s, and coalescent theory remains a central tool in population genetics and evolutionary biology.