ArticleTheoretical population biology2013
An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection.
Article in Theoretical population biology, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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Who cites it
15 citing papers in PubMed.
- Bounds for survival probabilities in supercritical Galton-Watson processes and applications to population genetics.Journal of mathematical biology · 2026Article
- GENERAL MOMENT CLOSURE FOR THE NEUTRAL TWO-LOCUS WRIGHT-FISHER DYNAMICS.bioRxiv : the preprint server for biology · 2026Article
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- A Path Integral Approach for Allele Frequency Dynamics Under Polygenic Selection.bioRxiv : the preprint server for biology · 2024Article
- Article
- Article
- Scaling the Discrete-time Wright Fisher model to biobank-scale datasets.bioRxiv : the preprint server for biology · 2023Article
- Article
- Quantifying evolutionary dynamics from variant-frequency time series.Scientific reports · 2016Article
- SpectralTDF: transition densities of diffusion processes with time-varying selection parameters, mutation rates and effective population sizes.Bioinformatics (Oxford, England) · 2016Article
- Article
- Transition Densities and Sample Frequency Spectra of Diffusion Processes with Selection and Variable Population Size.Genetics · 2015Article
- A NOVEL SPECTRAL METHOD FOR INFERRING GENERAL DIPLOID SELECTION FROM TIME SERIES GENETIC DATA.The annals of applied statistics · 2014Article
- General triallelic frequency spectrum under demographic models with variable population size.Genetics · 2014Article
- Analysis and rejection sampling of Wright-Fisher diffusion bridges.Theoretical population biology · 2013Article
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3 authors.
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Abstract
Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known partial differential equations. For a multi-allelic model with general diploid selection, various theoretical results exist on representations of the transition density, but finding an explicit formula has remained a difficult problem. In this paper, a technique recently developed for a diallelic model is extended to find an explicit transition density for an arbitrary number of alleles, under a general diploid selection model with recurrent parent-independent mutation. Specifically, the method finds the eigenvalues and eigenfunctions of the generator associated with the multi-allelic diffusion, thus yielding an accurate spectral representation of the transition density. Furthermore, this approach allows for efficient, accurate computation of various other quantities of interest, including the normalizing constant of the stationary distribution and the rate of convergence to this distribution.
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