空间连续体演化的新模型
A new model for evolution in a spatial continuum
摘要：
我们研究了一个新的模型，人口在空间连续演化。这个模型可以被认为是Lambda-Fleming-Viot过程的空间版本。它明确地包括小规模的再生产事件和大规模的再生产-再生产事件。根据这一模型演化的种群样本的祖先谱系可以用λ-聚结的空间版本来描述。利用Evans（1997）的技巧，我们证明了该模型的存在性和唯一性.然后，我们调查的渐近行为的家谱的一个有限数量的个人抽样均匀随机（或更一般的“远不够分开”）从一个二维环面的L侧L趋于无穷大。在适当的条件下（在一个合适的时间尺度上），我们可以得到作为限制系谱过程的一个金曼聚结，一个更一般的拉姆达聚结或一个系统的聚结布朗运动（与非局部聚结机制）。
英文摘要：
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans(1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of side L as L tends to infinity. Under appropriate conditions (and on a suitable timescale), we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).
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