Richard Hudson and Norman Kaplan on the Coalescent Process

MANY important questions in genetics involve looking back in time using data sampled in the present. The coalescent process describes the ancestry of a sample of genes: as lineages trace back, they coalesce at a rate inversely proportional to the effective population size. This remarkably simple approximation now dominates population genetics, both because it gives a direct intuition into the evolutionary process and because it allows efficient simulation.

The coalescent predicts the genealogical relationships between sampled genes, and it depends only on the effective population size, regardless of the detailed life history. The coalescent was first described by Kingman (1982), but was developed independently by Hudson (1983) and Tajima (1983); its influence on population genetics came primarily through Hudson. The coalescent is rooted in older concepts: Malécot’s (1948) idea of identity by descent, which is central to quantitative genetics (Kempthorne 1954), and the diffusion approximation (Kimura 1955), which depends on the same effective population size. The coalescent emerged not through radically new concepts, but, rather, because it gives a natural way to analyze the samples of DNA sequences that were just becoming available. Hudson and Kaplan (1988), with its companion (Kaplan et al. 1988), extended the coalescent to include selection and used it to interpret data on sequence variation around the alcohol dehydrogenase (Adh) locus of Drosophila melanogaster (Kreitman 1983).

Under the coalescent, lineages coalesce at a rate equal to the inverse of the effective number of genes in the population, 1/2N_e. Migration, recombination, and mutation can be included by allowing ancestral lineages to jump between locations, genetic backgrounds, or allelic states; this extension is known as the structured coalescent (Hudson 1983). Selection is much harder to incorporate because the ancestry now depends on the allelic state. However, Kaplan et al. (1988) showed that, if the selected backgrounds are taken as given, then the structured coalescent describes the genealogy of linked neutral alleles; random fluctuations in the frequency of the selected backgrounds can be treated by a diffusion that couples to the coalescent. A surprising conclusion from this method is that selection has to be extremely strong relative to random drift to distort neutral genealogies (Barton and Etheridge 2004). This is a fundamental obstacle to detecting selection from sequence data.

The fast and slow (F/S) alleles of the Adh locus of D. melanogaster differ by a single amino acid. Kreitman (1983) sequenced 11 copies of the locus and found a sharp peak of polymorphism around the amino-acid difference. This is consistent with maintenance of these alleles by long-term balancing selection. Hudson and Kaplan (1988) showed that divergence between the F and S alleles is consistent with balancing selection, albeit with a lower-than-average recombination rate. However, there was also excess variation among the S alleles, which was not expected. Even though Adh in Drosophila is one of the most intensively studied polymorphisms, we still do not know how its sequence variation has been shaped by selection (Begun et al. 1999).

Population genetics is now focused on understanding the abundance of sequence data that has recently become available. Since the first work of Kreitman (1983), the goal has been to infer the nature and strength of selection across the genome directly from the DNA sequence; “genome scans” of the kind introduced by Hudson and Kaplan (1988) are now being carried out for an enormous range of organisms. However, it is disconcerting that even the first and best-studied example is still unresolved.