论文标题
中央限制定理描述在各种形式的幂律传播下隔离的隔离
Central limit theorems describing isolation by distance under various forms of power-law dispersal
论文作者
论文摘要
在本文中，我们通过在后代的远程分散下发现的距离模式发现了新的渐近分离。我们扩展了第一作者的最新作品，其中使用新型随机偏微分方程方法用于空间$λ$ -FLEMING-VIOT模型，从而从远期动力学中获得了这些信息。后者是由Barton，Etheridge和Véber引入的，作为建模空间结构种群遗传组成的演变的框架。复制是通过由泊松点过程驱动的灭绝回合事件进行的。在事件中，在某些球形区域，对父母进行采样，并更换了一定比例的人口。我们通过允许在事件期间对父母采样的区域的区域与后代分散的区域不同，从而概括了第一作者的先前方法，而这些区域的半径遵循幂律分布。特别是，尽管在先前的工作中，祖先谱系和合并行为的运动紧密相连，但我们证明了由分数和标准laplacians控制的祖先谱系的局部和非本地聚集。
In this paper, we uncover new asymptotic isolation by distance patterns occurring under long-range dispersal of offspring. We extend a recent work of the first author, in which this information was obtained from forwards-in-time dynamics using a novel stochastic partial differential equations approach for spatial $Λ$-Fleming-Viot models. The latter were introduced by Barton, Etheridge and Véber as a framework to model the evolution of the genetic composition of a spatially structured population. Reproduction takes place through extinction-recolonisation events driven by a Poisson point process. During an event, in certain ball-shaped areas, a parent is sampled and a proportion of the population is replaced. We generalize the previous approach of the first author by allowing the area from which a parent is sampled during events to differ from the area in which offspring are dispersed, and the radii of these regions follow power-law distributions. In particular, while in previous works the motion of ancestral lineages and coalescence behaviour were closely linked, we demonstrate that local and non-local coalescence is possible for ancestral lineages governed by both fractional and standard Laplacians.
