Coalescent theory

Coalescent theory is a model of how gene variants sampled from a population may have originated from a common ancestor. It is a retrospective model of population genetics that traces all alleles of a gene shared by all members of a population back to a single ancestral copy, known as the most recent common ancestor (MRCA). The theory was developed in the 1980s by John Kingman.

Overview

Coalescent theory provides a framework for understanding the genealogical relationships between alleles in a population. It is particularly useful for modeling the genetic diversity of populations over time and for making inferences about population history and structure.

The basic idea of coalescent theory is to trace the lineage of alleles backward in time to their common ancestor. This is done by considering the genealogical tree, or "coalescent tree," that describes the ancestry of a sample of alleles. The coalescent process is stochastic, meaning it involves random events, and it is influenced by factors such as population size, selection, mutation, and recombination.

Mathematical Formulation

In mathematical terms, the coalescent process is a continuous-time Markov process. The time to the most recent common ancestor of a sample of alleles is a random variable that depends on the effective population size. The expected time to coalescence for two alleles is approximately 2N generations, where N is the effective population size.

The coalescent process can be extended to include various biological factors:

• Mutation: The infinite sites model assumes that mutations occur at a constant rate and each mutation occurs at a unique site.
• Recombination: The coalescent with recombination considers the breaking and rejoining of DNA strands, which can complicate the genealogical tree.
• Selection: The coalescent with selection incorporates the effects of natural selection on allele frequencies.

Applications

Coalescent theory is widely used in population genetics and phylogenetics. It is used to:

• Estimate population parameters such as effective population size and growth rates.
• Infer demographic history, such as population bottlenecks and expansions.
• Study the effects of natural selection on genetic variation.
• Reconstruct the evolutionary history of species.

Limitations

While coalescent theory is a powerful tool, it has limitations. It assumes a constant population size and random mating, which may not be realistic for all populations. Additionally, the model can become complex when incorporating factors like recombination and selection.

Also see

• Population genetics
• Phylogenetics
• Genealogy of genes
• Most recent common ancestor
• Effective population size