Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

TY - JOUR

T1 - Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

AU - Hey, Jody

AU - Nielsen, Rasmus

N1 - Keywords: Animals; Bayes Theorem; Genealogy and Heraldry; Genetics, Population; Markov Chains; Models, Genetic; Monte Carlo Method; Pan troglodytes

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1073/pnas.0611164104

DO - 10.1073/pnas.0611164104

M3 - Journal article

C2 - 17301231

SN - 0027-8424

VL - 104

SP - 2785

EP - 2790

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 8

ER -