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.

翻译：Wright-Fisher扩散过程族是一类广泛应用的进化模型。然而，由于不存在已知的转移函数闭式表达式，其模拟十分困难。本文证明，对于一大类Wright-Fisher扩散过程及其桥过程，实际上可以实现精确模拟。针对可逆中性进化对应的扩散过程，我们的核心思想是利用转移函数的特征函数展开；该方法甚至适用于其无穷维类比——Fleming-Viot过程。随后，我们基于回顾模拟思想，为包含自然选择等更一般漂移函数的过程开发了精确拒绝算法。该方法还可用于Wright-Fisher扩散的矩对偶——无限叶Kingman溯祖树的祖先过程——的精确模拟。我们相信，这种扩散模拟的新视角对其他具有转移特征函数展开的模型具有应用前景。