论文标题
带有种子银行的空间种群：适应性，二元性和平衡
Spatial populations with seed-bank: well-posedness, duality and equilibrium
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Fisher-Wright扩散的系统。个人生活在殖民地中，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，我们认为具有离散拓扑结构的一个可数的Abelian组$ \ Mathbb {G} $。感兴趣的关键示例是Euclidean Lattice $ \ Mathbb {G} = \ Mathbb {Z}^D $。我们的目标是根据基础模型参数对系统的长期行为进行分类。特别是，我们想了解种子银行以什么方式增强遗传多样性。 我们介绍了三种越来越多的普遍性的模型，即，个体处于休眠状态：（1）在其殖民地的种子银行中； （2）在其菌落的种子银行中，采用随机颜色决定其唤醒时间； （3）在采用随机颜色的同时，在随机菌落的种子银行中。 （2）中的扩展使我们能够用脂肪尾巴对唤醒时间进行建模，同时保留Markov的演变特性。对于三个模型中的每一个，我们都表明，该系统会根据由初始状态确定的单个密度参数收敛到独特的平衡，并表现出共存性（=局部多类型平衡）与聚类（=本地单单型平衡）的二分法，这取决于迁移和迁移和种子播种机的二分法。模型1中聚类和共存之间的二分法仅由迁移确定。在模型（2）和（3）中，当唤醒时间具有无限的平均值时，二分法是由与种子银行和迁移的交换确定的。事实证明，种子银行在定量和定性上都会影响长期行为。
We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals 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 $\mathbb{G}$ endowed with the discrete topology. The key example of interest is the Euclidean lattice $\mathbb{G}=\mathbb{Z}^d$. Our goal is to classify the long-time behaviour of the system in terms of the underlying model parameters. In particular, we want to understand in what way the seed-bank enhances genetic diversity. We introduce three models of increasing generality, namely, individuals become dormant: (1) in the seed-bank of their colony; (2) in the seed-bank of their colony while adopting a random colour that determines their wake-up time; (3) in the seed-bank of a random colony while adopting a random colour. The extension in (2) allows us to model wake-up times with fat tails while preserving the Markov property of the evolution. For each of the three models we show that the system converges to a unique equilibrium depending on a single density parameter that is determined by the initial state, and exhibits a dichotomy of coexistence (= locally multi-type equilibrium) versus clustering (= locally mono-type equilibrium) depending on the parameters controlling the migration and the seed-bank. The dichotomy between clustering and coexistence in model 1 is determined by migration only. In models (2) and (3), when the wake-up time has infinite mean, the dichotomy is determined by both the exchange with the seed-bank and migration. It turns out that the seed-bank affects the long-time behaviour both quantitatively and qualitatively.
