论文标题
在空间上不均匀的种子群体：双重性，存在和聚类
Spatially Inhomogeneous Populations with Seed-banks: Duality, Existence and Clustering
论文作者
论文摘要
我们考虑了一种与种子银行相互作用的模型的系统。一个人居住在殖民地中，只要$ active $ $。每个殖民地都有一个种子银行，个人可以撤退到休眠$，暂停其重新采样和迁移，直到他们再次活跃起来。菌落由$ \ mathbb {z}^d $，$ d \ geq 1 $标记，扮演$ geographic \ space $的角色。活跃人口和休眠人群的尺寸为$有限$，取决于殖民地的$位置$。迁移是由随机步行过渡内核驱动的。我们的目标是研究系统的平衡行为，这是基础模型参数的函数。 在本文中，我们表明，在有效人群的大小的温和条件下，该系统定义明确并且具有双重。双重组成的系统由$互动的系统组成，在$不均匀的$环境中，在活动和休眠之间切换。我们分析了$共存$（=多类型平衡）的二分法与$聚类$（= =单型型平衡），并显示聚类在且仅当两次随机步行在双重步行中从任意状态开始时最终以概率为一种。种子银行$的存在增强了\，遗传\，多样性$。在双重的情况下，这是由随机步行处于休眠状态且不会移动的时间段的存在反映的。
We consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are $active$. Each colony has a seed-bank into which individuals can retreat to become $dormant$, suspending their resampling and migration until they become active again. The colonies are labelled by $\mathbb{Z}^d$, $d \geq 1$, playing the role of a $geographic\, space$. The sizes of the active and the dormant population are $finite$ and depend on the $location$ of the colony. Migration is driven by a random walk transition kernel. Our goal is to study the equilibrium behaviour of the system as a function of the underlying model parameters. In the present paper we show that, under mild condition on the sizes of the active population, the system is well-defined and has a dual. The dual consists of a system of $interacting$ coalescing random walks in an $inhomogeneous$ environment that switch between active and dormant. We analyse the dichotomy of $coexistence$ (= multi-type equilibria) versus $clustering$ (= mono-type equilibria), and show that clustering occurs if and only if two random walks in the dual starting from arbitrary states eventually coalesce with probability one. The presence of the seed-bank $enhances\, genetic\, diversity$. In the dual this is reflected by the presence of time lapses during which the random walks are dormant and do not move.
