NDLI: Finding the best resolution for the Kingman–Tajima coalescent: theory and applications

Content Provider	Springer Nature Link
Author	Sainudiin, Raazesh Stadler, Tanja Véber, Amandine
Copyright Year	2014
Abstract	Many summary statistics currently used in population genetics and in phylogenetics depend only on a rather coarse resolution of the underlying tree (the number of extant lineages, for example). Hence, for computational purposes, working directly on these resolutions appears to be much more efficient. However, this approach seems to have been overlooked in the past. In this paper, we describe six different resolutions of the Kingman–Tajima coalescent together with the corresponding Markov chains, which are essential for inference methods. Two of the resolutions are the well-known $$n$$ -coalescent and the lineage death process due to Kingman. Two other resolutions were mentioned by Kingman and Tajima, but never explicitly formalized. Another two resolutions are novel, and complete the picture of a multi-resolution coalescent. For all of them, we provide the forward and backward transition probabilities, the probability of visiting a given state as well as the probability of a given realization of the full Markov chain. We also provide a description of the state-space that highlights the computational gain obtained by working with lower-resolution objects. Finally, we give several examples of summary statistics that depend on a coarser resolution of Kingman’s coalescent, on which simulations are usually based.
Ending Page	1247
Page Count	41
Starting Page	1207
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	6
Volume Number	70
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-05-14
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical and Computational Biology Tree shape statistics Protein sequences, DNA sequences Applications of Mathematics $$n$$ -Coalescent resolutions Computationally efficient and statistically sufficient inference Problems related to evolution Markov chains (discrete-time Markov processes on discrete state spaces)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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