稀有抗性突变下获救种群的位点频率谱
Site frequency spectrum of a rescued population under rare resistant mutations
AI总结：
本文用双类型分支过程建模治疗压力下稀有抗性突变导致的细胞种群获救，推导中性突变SFS期望的渐近表达式，并借助带叶子标记的亚临界二元Galton-Watson树分析亲缘关系影响。
摘要：
本文旨在研究在治疗压力下，抗性获得对细胞种群中中性突变分布的影响。细胞种群由一个双类型分支过程建模。最初，所有细胞均携带类型0，并与负增长率相关。向类型1的突变被假定为稀有且随机的，并导致细胞在治疗下存活，即类型1与正增长率相关，因此模拟抗性的获得。细胞还携带在出生时获得并通过遗传积累的中性突变，这些突变不影响其类型。在抗性获得为稀有事件且初始种群较大的渐近情形下，我们描述了“位点频率谱”（Site Frequency Spectrum，SFS）的期望，该指标是种群中中性突变分布的一个指数。具体而言，我们给出了由少量细胞和大量细胞共同携带的中性突变期望数量的渐近等价表达式。为了识别亲缘关系对SFS的影响，我们的工作还促使我们详细研究亚临界二元Galton-Watson树，其中每片叶子都以一个小概率被标记。作为该研究的副产品，我们因此给出了在此类以标记数量为条件的Galton-Watson树中随机选取一片叶子时，其世代数的分布规律。
英文摘要：
The aim of this article is to study the impact of resistance acquisition on the distribution of neutral mutations in a cell population under therapeutic pressure. The cell population is modeled by a bi-type branching process. Initially, the cells all carry type 0, associated with a negative growth rate. Mutations towards type $1$ are assumed to be rare and random, and lead to the survival of cells under treatment, i.e. type $1$ is associated with a positive growth rate, and thus models the acquisition of a resistance. Cells also carry neutral mutations, acquired at birth and accumulated by inheritance, that do not affect their type. We describe the expectation of the "Site Frequency Spectrum" (SFS), which is an index of neutral mutation distribution in a population, under the asymptotic of rare events of resistance acquisition and of large initial population. Precisely, we give asymptotically-equivalent expressions of the expected number of neutral mutations shared by both a small and a large number of cells. To identify the influence of relatives on the SFS, our work also lead us to study in detail subcritical binary Galton-Watson trees, where each leaf is marked with a small probability. As a by-product of this study, we thus provide the law of the generation of a randomly chosen leaf in such a Galton-Watson tree conditioned on the number of marks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
