Genealogical trees, coalescent theory and the analysis of genetic polymorphisms

Key Points

  • Genetic polymorphism results from mutations along the branches of unknown genealogical trees, so genealogical models are needed for the analysis of polymorphism data.

  • The stochastic process known as 'the coalescent' has become the primary tool for modelling genealogies.

  • An extension of classical population-genetics models, the coalescent views lineages as randomly choosing parents going backwards in time.

  • The coalescent is a flexible model that accommodates phenomena such as recombination, age structure, geographical structure and population size change.

  • Efficient simulations and inference based on the coalescent allow tests about causes of genetic variation and estimation of demographic parameters, such as migration rates.

  • Unlike methods borrowed from phylogenetics that attempt to draw inferences from estimated genealogies, the coalescent treats genealogies as random and can naturally handle complex models that incorporate phenomena such as migration, selection and recombination.

  • In the age of genomic polymorphism data, coalescent-based methods will acquire greater roles in such areas as the inference of evolutionary history, the study of linkage disequilibrium in the human genome and the population genetics of infectious disease.


Improvements in genotyping technologies have led to the increased use of genetic polymorphism for inference about population phenomena, such as migration and selection. Such inference presents a challenge, because polymorphism data reflect a unique, complex, non-repeatable evolutionary history. Traditional analysis methods do not take this into account. A stochastic process known as the 'coalescent' presents a coherent statistical framework for analysis of genetic polymorphisms.

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Figure 1: The source of genetic variation.
Figure 2: Random genealogical trees.
Figure 3: A simulated sample of six haplotypes using the standard coalescent with recombination.
Figure 4: The basic principle behind the coalescent.
Figure 5: Simulated random genealogies with a sample size of ten.


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We thank H. Innan and J. Pritchard for comments, and M. Tanaka, C. Wiuf and an anonymous reviewer for careful reading of the manuscript.

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Correspondence to Magnus Nordborg.

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Data that include the genotypes of many individuals sampled at one or more loci; here we consider a locus to be polymorphic if two or more distinct types are observed, regardless of their frequencies.


The allelic configuration of multiple genetic markers that are present on a single chromosome of a given individual.


The merging of ancestral lineages going back in time.


A mathematical description of the random evolution of a quantity through time.


Genetic recombination in prokaryotes that is mediated through direct transfer of DNA from a donor to a recipient cell.


The random fluctuations in allele frequencies over time that are due to chance alone.


The transfer of genetic material between members of the same generation, or between members of different species.


A function that produces an estimate of some parameter.


The selection that maintains two or more alleles in a population.


The evolution of new species or subspecies to fill unoccupied ecological niches.


A statistical perspective that focuses on the probability distribution of parameters, before and after seeing the data.


A statistical perspective that focuses on the frequency with which an observed value is expected in numerous trials.


A function that produces values from data for comparing with expected values under various models.


A statistic that quantifies the dispersion of data about the mean.


A temporary marked reduction in population size.


A statistical method that considers the likelihood of observing the data under alternative models.


A computational technique for efficient numerical calculation of likelihoods.


A computational technique for efficient numerical calculation of likelihoods.


A function that summarizes complex data in terms of simple numbers (examples include mean and variance).


A DNA base-pair position at which polymorphism is observed in a population.


The mixing of two genetically differentiated populations.


The use of estimated gene genealogies to study geographical history and structure of populations and species.

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Rosenberg, N., Nordborg, M. Genealogical trees, coalescent theory and the analysis of genetic polymorphisms. Nat Rev Genet 3, 380–390 (2002).

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