The Matrix Coalescent and an Application to Human Single-Nucleotide Polymorphisms

The Matrix Coalescent and an Application to Human Single-Nucleotide Polymorphisms

Stephen Wooding^a and Alan Rogers^b
^a Eccles Instititute of Human Genetics, University of Utah, Salt Lake City, Utah 84112-5330
^b Department of Anthropology, University of Utah, Salt Lake City, Utah 84112-0060

Corresponding author: Stephen Wooding, University of Utah, 15 N. 2030 E., Salt Lake City, UT 84112-5330., swooding{at}genetics.utah.edu (E-mail)

Communicating editor: Y.-X. FU

The "matrix coalescent" is a reformulation of the familiar coalescentprocess of population genetics. It ignores the topology of thegene tree and treats the coalescent as a Markov process describingthe decay in the number of ancestors of a sample of genes asone proceeds backward in time. The matrix formulation of thisprocess is convenient when the population changes in size, becausesuch changes affect only the eigenvalues of the transition matrix,not the eigenvectors. The model is used here to calculate theexpectation of the site frequency spectrum under various assumptionsabout population history. To illustrate how this method canbe used with data, we then use it in conjunction with a setof SNPs to test hypotheses about the history of human populationsize.

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