发表机构
Johns Hopkins University; University of California, Berkeley; University of Minnesota; University of Iceland（约翰斯·霍普金斯大学; 加州大学伯克利分校; 明尼苏达大学; 冰岛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有突变和选择的指数增长种群中的‘驱动’位点频率谱，通过推导精确矩、构建近似证明强大数定律等方法，考察其各区域，找到截止频率，可用于估计相关进化参数。
AI 中文摘要
我们考虑一个具有突变和选择的超临界两类型连续时间线性生死过程，其中野生型个体产生具有更大净增长率的突变后代。在此设定下，我们研究‘驱动’位点频率谱（SFS），即记录种群中突变等位基因频率的随机测度。我们考察了SFS的各个区域。首先，我们推导了精确矩，并证明了关于大时间和频率下驱动SFS平均行为的结果。通过构建合适的\(L^2\)近似证明了驱动SFS的强大数定律。这些结果被扩展到每个克隆相关的适应性增加是随机的设定。接下来，我们允许频率随时间变化以考察‘中间’和‘大’克隆的数量。利用此，我们找到了一个截止频率，在该频率处克隆数量为1阶。我们的结果允许估计相关的进化参数，如突变体与野生型细胞的适应性增加。
英文摘要
We consider a supercritical two-type continuous-time linear birth-death process with mutation and selection, in which wild-type individuals give rise to mutant offspring with a larger net growth rate $λ_1$. In this setting, we investigate a component of the site frequency spectrum (SFS), describing the number of driver mutations present at any given frequency in the population. We establish asymptotic convergence results at large times and detection sizes. We examine three distinct regions of the SFS: (1) the small frequency region occupied by clones of size $\mathcal{O}(1)$, (2) the intermediate frequency region occupied by clones of size $1\ll j(t)\ll \exp(λ_1 t)$, and (3) the large frequency region occupied by clones of size at least $\exp(λ_1 t).$ We obtain strong laws of large numbers for the driver SFS in the small- and large-frequency regions by constructing suitable $L^2$-approximations. In the intermediate frequency region, we identify a cutoff frequency $j(t)$ growing with time at which there are an order-one number of mutant clones. At this frequency, we obtain a Poisson convergence theorem as $t\to\infty$. Overall, our results provide quantitative insights into how selection shapes the site frequency spectrum both at small and large frequencies, which can in principle be leveraged to construct estimators of relevant evolutionary parameters. As an example of this, we propose and show asymptotic consistency of a new estimator of the fitness increase.
CommentsChanges from v2: added more description of proof strategy, shortened introduction
