Document Detail

Exact coalescent for the Wright-Fisher model.
MedLine Citation:
PMID:  16426654     Owner:  NLM     Status:  MEDLINE    
The Kingman coalescent, which has become the foundation for a wide range of theoretical as well as empirical studies, was derived as an approximation of the Wright-Fisher (WF) model. The approximation heavily relies on the assumption that population size is large and sample size is much smaller than the population size. Whether the sample size is too large compared to the population size is rarely questioned in practice when applying statistical methods based on the Kingman coalescent. Since WF model is the most widely used population genetics model for reproduction, it is desirable to develop a coalescent framework for the WF model, which can be used whenever there are concerns about the accuracy of the Kingman coalescent as an approximation. This paper described the exact coalescent theory for the WF model and develops a simulation algorithm, which is then used, together with an analytical approach, to study the properties of the exact coalescent as well as its differences to the Kingman coalescent. We show that the Kingman coalescent differs from the exact coalescent by: (1) shorter waiting time between successive coalescent events; (2) different probability of observing a topological relationship among sequences in a sample; and (3) slightly smaller tree length in the genealogy of a large sample. On the other hand, there is little difference in the age of the most recent common ancestor (MRCA) of the sample. The exact coalescent makes up the longer waiting time between successive coalescent events by having multiple coalescence at the same time. The most significant difference among various summary statistics of a coalescent examined is the sum of lengths of external branches, which can be more than 10% larger for exact coalescent than that for the Kingman coalescent. As a whole, the Kingman coalescent is a remarkably accurate approximation to the exact coalescent for sample and population sizes falling considerably outside the region that was originally anticipated.
Yun-Xin Fu
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Publication Detail:
Type:  Journal Article; Research Support, N.I.H., Extramural; Research Support, U.S. Gov't, Non-P.H.S.     Date:  2006-01-19
Journal Detail:
Title:  Theoretical population biology     Volume:  69     ISSN:  0040-5809     ISO Abbreviation:  Theor Popul Biol     Publication Date:  2006 Jun 
Date Detail:
Created Date:  2006-05-02     Completed Date:  2006-10-05     Revised Date:  2007-11-14    
Medline Journal Info:
Nlm Unique ID:  0256422     Medline TA:  Theor Popul Biol     Country:  United States    
Other Details:
Languages:  eng     Pagination:  385-94     Citation Subset:  IM    
Human Genetics Center, School of Public Health, University of Texas at Houston, 77030, USA.
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MeSH Terms
Genetics, Population / statistics & numerical data*
Linkage (Genetics)*
Markov Chains
Models, Genetic*
Population Density*
Population Dynamics*
Recombination, Genetic*
Grant Support

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