Open Access
June 2017 Exact simulation of the Wright–Fisher diffusion
Paul A. Jenkins, Dario Spanò
Ann. Appl. Probab. 27(3): 1478-1509 (June 2017). DOI: 10.1214/16-AAP1236

Abstract

The Wright–Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article, we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright–Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming–Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright–Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion.

Citation

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Paul A. Jenkins. Dario Spanò. "Exact simulation of the Wright–Fisher diffusion." Ann. Appl. Probab. 27 (3) 1478 - 1509, June 2017. https://doi.org/10.1214/16-AAP1236

Information

Received: 1 June 2016; Published: June 2017
First available in Project Euclid: 19 July 2017

zbMATH: 1385.65006
MathSciNet: MR3678477
Digital Object Identifier: 10.1214/16-AAP1236

Subjects:
Primary: 65C05
Secondary: 60H35 , 60J60 , 92D15

Keywords: diffusion bridge , exact algorithm , Fleming–Viot process , Kingman’s coalescent , Monte Carlo , Population genetics , retrospective simulation , simulation , Wright–Fisher diffusion

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 3 • June 2017
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