论文标题
选择Wright-Fisher模型中的固定时间的指数积分解决方案
Exponential Integral Solutions for Fixation Time in Wright-Fisher Model With Selection
论文作者
论文摘要
在这项工作中，我们在Wright-Fisher模型中为固定时间提供了新的分析表达式。考虑了三种标准固定情况：固定为零，为一个或两个。固定时间的二阶微分方程仅使用总概率和泰勒扩展的法律来获得简化的方法。获得的解决方案是通过指数积分函数与基本函数的组合给出的。然后，我们陈述仅涉及基本功能的公式近似公式，该功能可用于小选择效应。在整个广泛的仿真研究中，探索了我们的结果质量。我们表明，即使对于较小的人口（数百个）和较大的选择系数，我们的结果也非常准确地近似离散问题。
In this work we derive new analytic expressions for fixation time in Wright-Fisher model with selection. The three standard cases for fixation are considered: fixation to zero, to one or both. Second order differential equations for fixation time are obtained by a simplified approach using only the law of total probability and Taylor expansions. The obtained solutions are given by a combination of exponential integral functions with elementary functions. We then state approximate formulas involving only elementary functions valid for small selection effects. The quality of our results are explored throughout an extensive simulation study. We show that our results approximate the discrete problem very accurately even for small population size (a few hundreds) and large selection coefficients.
