标题： 伯努利工厂与种群遗传学的Wright-Fisher和Allen-Cahn模型中的对偶性 显示英文标题

标题： Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics

摘要： 数学模型的遗传进化通常成对出现，通过所谓的对偶关系连接。 最具有开创性的例子是Wright-Fisher扩散和Kingman共祖过程，前者描述了在大种群中中性等位基因频率随时间向前的随机演化，后者描述了从种群中随机抽样个体的遗传祖先随时间向后的演化。 除了比单独使用任一模型提供更丰富的描述外，对偶性通常能得出感兴趣的量所满足的方程。 我们采用所谓的伯努利工厂——一种在基于模拟的计算中享有盛誉的工具——来推导广泛类别的遗传模型的对偶关系。 作为具体的例子，我们介绍了具有通用漂移函数的Wright-Fisher扩散，以及具有通用非线性强迫项的Allen-Cahn方程。 漂移函数和强迫函数可以被解释为频率依赖选择的作用。 据我们所知，这项工作是首次在种群遗传学模型中将伯努利工厂与对偶性联系起来。 显示英文摘要

摘要： Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Bernoulli factory - a celebrated tool in simulation-based computing - to derive duality relations for broad classes of genetics models. As concrete examples, we present Wright-Fisher diffusions with general drift functions, and Allen-Cahn equations with general, nonlinear forcing terms. The drift and forcing functions can be interpreted as the action of frequency-dependent selection. To our knowledge, this work is the first time a connection has been drawn between Bernoulli factories and duality in models of population genetics.