论文标题
一种最佳的质量传输方法，用于随机遗传漂移
An Optimal Mass Transport Method for Random Genetic Drift
论文作者
论文摘要
我们提出并分析了一种最佳的质量传输方法，用于在弱选择下由MORAN过程驱动的随机遗传漂移问题。连续限制为一种称为木村方程的反应添加扩散方程式，遗传了从离散的随机过程中脱颖而出的扩散，该过程将传达到爆炸到dirac-delta奇异性中，因此给分析和数值研究带来了巨大的挑战。所提出的数值方法可以一方面定量捕获dirac-delta奇异性的发展，以一方面的遗传分离，并保留了另一组随机遗传漂移的生物学相关和计算偏爱特性的几组。此外，数值方案指数式地将与网格大小无关的速率及时收敛到唯一的数值固定状态，直至网格误差。提供数值证据以说明和支持这些特性，并证明随机通用漂移的时空动力学。
We propose and analyze an optimal mass transport method for a random genetic drift problem driven by a Moran process under weak-selection. The continuum limit, formulated as a reaction-advection-diffusion equation known as the Kimura equation, inherits degenerate diffusion from the discrete stochastic process that conveys to the blow-up into Dirac-delta singularities hence brings great challenges to both the analytical and numerical studies. The proposed numerical method can quantitatively capture to the fullest possible extent the development of Dirac-delta singularities for genetic segregation on one hand, and preserves several sets of biologically relevant and computationally favored properties of the random genetic drift on the other. Moreover, the numerical scheme exponentially converges to the unique numerical stationary state in time at a rate independent of the mesh size up to a mesh error. Numerical evidence is given to illustrate and support these properties, and to demonstrate the spatio-temporal dynamics of random generic drift.
