论文标题
准平衡和单击穆勒棘轮变体的时间
Quasi-equilibria and click times for a variant of Muller's ratchet
论文作者
论文摘要
考虑一个$ n $个人的人口，每个人都携带$ \ Mathbb n_0 $的类型。人口根据带有选择和突变的Moran动力发展，其中$ k $的个体与所有具有$ k'> k $的个人具有相同的选择性优势，而类型的$ k $突变型则以恒定速度为$ k+1 $。因此，该模型是经典Muller棘轮的变体：选择性优势与$ k'-k $成正比。对于选择强度和突变率的制度，即弱选择/突变的制度之间，我们获得了棘轮的{\ em点击时间}的渐近率（即，在人群中迄今丢失了迄今为止最小的（“最佳”）类型的时间），并揭示quasi station station station station typeary类型的点击率之间的频率。该轮廓的较大人口限制的特征是``双重''层级多型逻辑系统的标准化吸引子，也是通过在分支随机步行中以单方面步骤的分支随机步行的最小位移的分布。在证明中，在次数的图形表示中扮演的重要作用是在时间上向前和向后的，而中央工具是通过突变装饰的祖先选择图。
Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over all individuals with type $k' > k$, and type $k$ mutates to type $k+1$ at a constant rate. This model is thus a variation of the classical Muller's ratchet: there the selective advantage is proportional to $k'-k$. For a regime of selection strength and mutation rates which is between the regimes of weak and strong selection/mutation, we obtain the asymptotic rate of the {\em click times} of the ratchet (i.e. the times at which the hitherto minimal (`best') type in the population is lost), and reveal the quasi-stationary type frequency profile between clicks. The large population limit of this profile is characterized as the normalized attractor of a ``dual'' hierarchical multitype logistic system, and also via the distribution of the final minimal displacement in a branching random walk with one-sided steps. An important role in the proofs is played by a graphical representation of the model, both forward and backward in time, and a central tool is the ancestral selection graph decorated by mutations.
