Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics
- †Department of Genetics, Rutgers, The State University of New Jersey, Piscataway, NJ 08846; and
- §Center for Comparative Genomics, Department of Biology, University of Copenhagen, DK-1017 Copenhagen, Denmark
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Communicated by Daniel L. Hartl, Harvard University, Cambridge, MA, December 15, 2006 (received for review October 17, 2006)
Abstract
In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided.
Footnotes
- ‡To whom correspondence should be addressed at: Department of Genetics, Rutgers, the State University of New Jersey, 604 Allison Road, Piscataway, NJ 08846. E-mail: hey{at}biology.rutgers.edu
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Author contributions: J.H. and R.N. designed research; J.H. performed research; J.H. and R.N. contributed new reagents/analytic tools; J.H. analyzed data; and J.H. and R.N. wrote the paper.
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The authors declare no conflict of interest.
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This article contains supporting information online at www.pnas.org/cgi/content/full/0611164104/DC1.
- Abbreviation:
- MCMC,
- Markov chain Monte Carlo.
- © 2007 by The National Academy of Sciences of the USA
