论文标题

带有种子银行的空间种群:有限系统计划

Spatial populations with seed-bank: finite-systems scheme

论文作者

Greven, Andreas, Hollander, Frank den

论文摘要

我们考虑了一种与种子银行相互作用的Fisher-Wright扩散的系统。个体携带两种类型中的一种,生活在殖民地中,只要活跃就可以重新采样和迁移。每个菌落都有一个结构化的种子银行,个体可以撤退到休眠状态,暂停其重新采样和迁移,直到再次活跃。作为殖民地标记的地理空间,我们认为一个具有离散拓扑结构的可数值的阿贝利安群体。在较早的工作中,我们表明该系统具有由两种类型的相对密度控制的一个参数系列。此外,这些平衡表现出共存的二分法(=局部多类型平衡)与聚类(=局部单型平衡)。我们确定了这两个阶段发生的参数状态,并发现当休眠个体的平均唤醒时间是有限的或无限的时,这些机制是不同的。 本文的目的是建立有限的系统方案,即确定系统(在地理空间和种子银行中)的有限截断,因为时间和截断水平都趋于无限,并正确调整了截断水平。如果唤醒时间有有限的平均值,则有一个用于缩放限制的单个通用类别。另一方面,如果唤醒时间具有无限的平均值,那么与地理空间的截断水平相比,种子银行的截断水平的增长速度有两个。

We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals carry type one of two types, live in colonies, and are subject to resampling and migration as long as they are active. Each colony has a structured seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. As geographic space labelling the colonies we consider a countable Abelian group endowed with the discrete topology. In earlier work we showed that the system has a one-parameter family of equilibria controlled by the relative density of the two types. Moreover, these equilibria exhibit a dichotomy of coexistence (= locally multi-type equilibrium) versus clustering (= locally mono-type equilibrium). We identified the parameter regimes for which these two phases occur, and found that these regimes are different when the mean wake-up time of a dormant individual is finite or infinite. The goal of the present paper is to establish the finite-systems scheme, i.e., identify how a finite truncation of the system (both in the geographic space and in the seed-bank) behaves as both the time and the truncation level tend to infinity, properly tuned together. If the wake-up time has finite mean, then there is a single universality class for the scaling limit. On the other hand, if the wake-up time has infinite mean, then there are two universality classes depending on how fast the truncation level of the seed-bank grows compared to the truncation level of the geographic space.

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