论文标题
关于$λ$ - wright-fisher流程的边界分类，与频率相关选择
On the boundary classification of $Λ$-Wright-Fisher processes with frequency-dependent selection
论文作者
论文摘要
我们构建具有频率依赖性选择（带有选择的$λ$ -WF流程）的纯跳跃$λ$ - wright-fisher流程的扩展，超出了边界$ 1 $的第一个通道时间。我们表明，它们与简单可交换片段钙化过程（EFC）的块计数过程（EFC）满足了一些二元性关系。建立了带有选择的$λ$ -WF进程的边界$ 1 $与块计数过程的边界$ \ infty $之间的一一对应关系。从这些对应关系中推导了具有选择和简单EFC过程的块计数过程的$λ$ -WF进程的新属性。提供了一些条件，以使选择要么足够弱，要么对于边界$ 1 $作为出口边界，要么足以使$ 1 $成为入口边界。当该度量$λ$和选择机制满足某些常规变化属性时，请找到条件，以便使用选择的扩展$λ$ -WF流程可从边界$ 1 $乘坐乘坐，然后以$ 0 $的$ 0 $吸收。在后一个过程中，$ 1 $是瞬态常规反射边界。这与有害等位基因的新现象相对应，该现象可以在零勒贝斯（Lebesgue）度量的一组时代扩散到人群中，然后几乎可以肯定地在有限的时间内消失。
We construct extensions of the pure-jump $Λ$-Wright-Fisher processes with frequency-dependent selection ($Λ$-WF processes with selection) beyond their first passage time at the boundary $1$. We show that they satisfy some duality relationships with the block counting process of simple exchangeable fragmentation-coalescence processes (EFC). One-to-one correspondences between the nature of the boundary $1$ of the $Λ$-WF process with selection and the boundary $\infty$ of the block counting process are established. New properties for the $Λ$-WF processes with selection and the block counting processes of the simple EFC processes are deduced from these correspondences. Some conditions are provided for the selection to be either weak enough for boundary $1$ to be an exit boundary or strong enough for $1$ to be an entrance boundary. When the measure $Λ$ and the selection mechanism satisfy some regular variation properties, conditions are found in order that the extended $Λ$-WF process with selection makes excursions out from the boundary $1$ before getting absorbed at $0$. In the latter process, $1$ is a transient regular reflecting boundary. This corresponds to a new phenomenon for the deleterious allele which can spread into the population in a set of times of zero Lebesgue measure, before vanishing in finite time almost surely.
