期刊
THEORETICAL POPULATION BIOLOGY
卷 79, 期 4, 页码 184-191出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.tpb.2011.03.003
关键词
Population genetics; Diffusions; Neutral allele frequency spectrum; Forward- and backward-in-time solution
资金
- Volkswagen Foundation [I/84232]
- DFG Research Unit [Ste 325/12, 1078]
The allele frequency spectrum has attracted considerable interest for the simultaneous inference of the demographic and adaptive history of populations. In a recent study, Evans et al. (2007) developed a forward diffusion equation describing the allele frequency spectrum, when the population is subject to size changes, selection and mutation. From the diffusion equation, the authors derived a system of ordinary differential equations (ODEs) for the moments in a Wright-Fisher diffusion with varying population size and constant selection. Here, we present an explicit solution for this system of ODEs with variable population size, but without selection, and apply this result to derive the expected spectrum of a sample for time-varying population size. We use this forward-in-time-solution of the allele frequency spectrum to obtain the backward-in-time-solution previously derived via coalescent theory by Griffiths and Tavare (1998). Finally, we discuss the applicability of the theoretical results to the analysis of nucleotide polymorphism data. (C) 2011 Elsevier Inc. All rights reserved.
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