Coalescent Theory

Abstract

The coalescent process is a powerful modeling tool for population genetics. The allelic states of all homologous gene copies in a population are determined by the genealogical and mutational history of these copies. The coalescent approach is based on the realization that the genealogy is usually easier to model backward in time, and that selectively neutral mutations can then be superimposed afterwards. A wide range of biological phenomena can be modeled using this approach.Whereas almost all of classical population genetics considers the future of a population given a starting point, the coalescent considers the present, while taking the past into account. This allows the calculation of probabilities of sample configurations under the stationary distribution of various population genetic models, and makes full likelihood analysis of polymorphism data possible. It also leads to extremely efficient computer algorithms for generating simulated data from such distributions, data which can then be compared with observations as a form of exploratory data analysis.

The Pattern of Polymorphism on Human Chromosome 21

“…Because it is unlikely that ancient hominids lived in a single random-mating population, this finding is likely to reflect the remarkable robustness of the standard population genetics model to deviations from its assumptions (Nordborg 2001).…”

“…species, and is typically found to be of order 10 ‫9מ‬ in mammals (Li 1997). Both rates are scaled using a scaling constant often known as the "effective population size", N e , so that = 4N e u and = 4N e r (e.g., Nordborg 2001). It should be noted that it is not necessary for and to be constant over the genome for the model to be a good approximation: It suffices that their averages over windows long enough to have been subject to mutation or recombination are constant.…”

“…The main motivation for doing this is that "positive" selection on a particular site can leave a footprint in the pattern of variation surrounding the site (for review, see Kreitman 2000;Nordborg 2001). For example, whenever directional selection causes a favorable allele to go to fixation, variation in the surrounding chromosomal region will be decreased (a so-called "selective sweep").…”

“…The canonical approach is to compute a summary statistic of the data, and compare its value to the distribution under a neutral null model. A serious drawback of this approach is that the neutral null model may be rejected for reasons other than selection: Demographic history and population structure can cause deviations similar to those expected under selection (Nordborg 2001).…”

“…One may be interested in forces that influence all loci, such as migration, mutation, and recombination, or one may be interested in the history of selection on a particular locus. Many years of research in population genetics (empirical as well as theoretical) have led to a sophisticated mathematical theory for this type of analysis (for review, see Li 1997;Kreitman 2000;Nordborg 2001;Stephens 2001). Arguably the most fundamental insight that has emerged from this work is that in order to overcome the enormous variance that is due to random history and estimate evolutionary parameters accurately, data from surprisingly large numbers of loci are needed.…”