Coalescent theory is a probabilistic framework

Wessen-Simulating-human-origin-evo.pdf Simulating Human Origins and Evolution by Ken Wessen (2005) pp 13: The study of a population is generally retrospective in nature, starting with a sample from an existing population and then attempting to describe the observed features in terms of the population’s prior evolution. Results are then generalised from the sample to the entire population. Coalescent theory (Kingman, 1982b; Hudson, 1990) provides a probabilistic framework perfectly suited to this approach, and has therefore become an extremely important tool in population genetics over the past 20 years. In brief, coalescent theory describes the merging of lineages from a sample of a population as one goes backwards in time, to the point where only a single lineage remains, i.e. the common ancestor. It is particularly well suited to molecular data, and although the usual formulation is based on the neutral model (Kimura, 1968) and a single, randomly mating population of constant size, extensions to cover recombination (Hudson, 1983), population growth (Kuhner et al., 1998), population subdivision (Hudson, 1990; Donnelly and Tavaré, 1995) and selection (Neuhauser and Krone, 1997) are well developed and are the subject of much ongoing research. A good review may be found in Fu and Li (1999).

Coalescent theory in a nutshell

From Coalescing into the 21st century: An overview and prospects of coalescent theory. Theor. Popul. Biol. 56, 1–10. By Fu and Li (1999) To infer the past from a sample taken from a present population, a new approach is required. Coalescent theory arose from this necessity. The essence of coalescent theory is to start with a sample, and trace backward in time to identify events that occurred in the past since the most recent common ancestor of the sample. Since the seminal work of Kingman (1982a, b), coalescent theory has been the most active topic in theoretical population genetics, and it is now widely recognized as the cornerstone for various statistical analyses of molecular population samples. The usefulness of the theory comes mainly from three features. First, it is a sample-based theory. Since the study of a population usually relies on a sample of individuals from that population, a theory that describes the properties of a sample is more relevant than the classical population genetics theory that describes the properties of the entire population. Second, it is a highly efficient approach. An important by-product of coalescent theory is the development of highly efficient algorithms for simulating population samples under various population genetics models, allowing various aspects of a model to be examined numerically. Third, coalescent theory is particularly suitable for molecular data, such as DNA sequence samples, which contain rich information about the ancestral relationships among the individuals sampled.