Coalescent experiments I: Unlabeled n-coalescent and the site frequency spectrum
| dc.contributor.author | Sainudiin, R. | |
| dc.contributor.author | Thornton, K. | |
| dc.contributor.author | Griffiths, R. | |
| dc.contributor.author | McVean, G. | |
| dc.contributor.author | Donnelly, P. | |
| dc.date.accessioned | 2009-10-08T20:09:39Z | |
| dc.date.available | 2009-10-08T20:09:39Z | |
| dc.date.issued | 2009 | en |
| dc.description.abstract | We derive the transition structure of a Markovian lumping of Kingman’s n-coalescent [1, 2]. Lumping a Markov chain is meant in the sense of [3, def. 6.3.1]. The lumped Markov process, referred as the unlabeled n-coalescent, is a continuous-time Markov chain on the set of all integer partitions of the sample size n. We derive the backward-transition, forward-transition, state-specific, and sequence-specific probabilities of this chain. We show that the likelihood of any given site-frequency-spectrum (SFS), a commonly used statistics in genome scans, from a locus free of intra-locus recombination, can be directly obtained by integrating conditional realizations of the unlabeled n-coalescent. We develop a controlled Markov chain for importance sampling such integrals from an augmented unlabeled n-coalescent forward in time. We apply the methods to population-genetic data to conduct demographic inference at the empirical resolution of the site-frequency-spectra. We also extend a family of classical hypothesis tests of standard neutrality at a non-recombining locus based on any statistics of the SFS to a more powerful version that conditions on the topological information contained in the SFS. We formalize a graph of coalescent experiments to set a decision-theoretic stage for population genetic inference across different empirical resolutions. | en |
| dc.identifier.citation | Sainudiin, R., Thornton, K., Griffiths, R., McVean, G., Donnelly, P. (2009) Coalescent experiments I: Unlabeled n-coalescent and the site frequency spectrum. UCDMS Research Report 2009/7. 29pp.. | en |
| dc.identifier.uri | http://hdl.handle.net/10092/2949 | |
| dc.language.iso | en | |
| dc.publisher | Department of Mathematics & Statistics | en |
| dc.publisher | University of Canterbury. Mathematics and Statistics | en |
| dc.rights.uri | https://hdl.handle.net/10092/17651 | en |
| dc.subject | Statistical decision theory of population genetic experiments | en |
| dc.subject | partially ordered n-coalescent experiments graph | en |
| dc.subject | controlled Markov chain for importance sampling | en |
| dc.subject.marsden | Fields of Research::230000 Mathematical Sciences::239900 Other Mathematical Sciences::239901 Biological Mathematics | en |
| dc.subject.marsden | Fields of Research::270000 Biological Sciences::270200 Genetics | en |
| dc.title | Coalescent experiments I: Unlabeled n-coalescent and the site frequency spectrum | en |
| dc.type | Reports |
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