In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by Hidden-Markov-Model (HMM) literature is used to compute exact sample allele frequency spectra for three demographic scenarios: single changes in (effective) population size, boom-bust dynamics, and stochastic fluctuations in (effective) population size. An approach for fully agnostic demographic inference from these sample allele spectra is explored, and sufficient statistics for step-wise changes in population size are found. Further, convergence behaviours of the polymorphic sample spectra for population size changes on different time scales are examined and discussed within the context of inference of the effective population size. Joint visual assessment of the sample spectra and the temporal coefficients of the spectral decomposition of the forward diffusion process is found to be important in determining departure from equilibrium. Stochastic changes in (effective) population size are shown to shape sample spectra particularly strongly.

翻译：本文利用谱表示方法，将（有效）群体大小的离散和随机变化纳入漂移与低突变率下的双等位基因扩散过程。受隐马尔可夫模型（HMM）文献启发，我们提出了一种前向算法，用于计算三种人口统计学情景下的精确样本等位基因频率谱：（有效）群体大小的单一变化、盛衰动态以及（有效）群体大小的随机波动。我们探索了一种完全不可知的人口统计学推断方法，利用这些样本等位基因谱进行推断，并找到了群体大小逐步变化的充分统计量。此外，我们研究了不同时间尺度上群体大小变化的多态样本谱的收敛行为，并在有效群体大小推断的背景下进行了讨论。研究发现，对样本谱与前向扩散过程谱分解的时间系数进行联合可视化评估，对于判断是否偏离平衡状态至关重要。结果表明，（有效）群体大小的随机波动对样本谱的形成具有特别强的影响。