The allele frequency spectrum (AFS), or site frequency spectrum, is commonly used to summarize the genomic polymorphism pattern of a sample, which is informative for inferring population history and detecting natural selection. In 2013, Chen and Chen developed a method for analytically deriving the AFS for populations with temporally varying size through the coalescence time-scaling function. However, their approach is only applicable to population history scenarios in which the analytical form of the time-scaling function is tractable. In this paper, we propose a computational approach to extend the method to populations with arbitrary complex varying size by numerically approximating the time-scaling function. We demonstrate the performance of the approach by constructing the AFS for two population history scenarios: the logistic growth model and the Gompertz growth model, for which the AFS are unavailable with existing approaches. Software for implementing the algorithm can be downloaded at http://chenlab.big.ac.cn/software/.

中文翻译：

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大小可变的人群等位基因频谱建模的一种计算方法。

等位基因频谱（AFS）或位点频谱通常用于总结样本的基因组多态性模式，这对于推断种群历史和检测自然选择很有帮助。2013年，Chen和Chen开发了一种方法，可通过合并时间标度函数来分析得出随时间变化的人口的AFS。但是，它们的方法仅适用于时标函数的分析形式易于处理的人口历史场景。在本文中，我们提出了一种计算方法，通过数值逼近时间标度函数，将该方法扩展到具有任意复杂变化大小的总体。我们通过为两个人口历史场景构建AFS来演示该方法的性能：逻辑增长模型和Gompertz增长模型，而现有方法无法使用AFS。可以从http://chenlab.big.ac.cn/software/下载实现该算法的软件。