A new model for evolution in a spatial continuum
A new model for evolution in a spatial continuum
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DOI：
10.1214/ejp.v15-741
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发表时间：
2010-02-24
影响因子：
1.4
通讯作者：
Veber, A.
中科院分区：
文献类型：
--
作者：
Barton, N. H.;Etheridge, A. M.;Veber, A.
我们研究了一个新的种群在空间连续体中进化的模型。这个模型可以被认为是Lambda-Fleming-Viot过程的空间版本。它明确地结合了小规模的繁殖事件和大规模的灭绝-再殖民化事件。根据该模型进化的种群样本的谱系祖先可以用Lambda-coalescent的空间版本来描述。利用Evans（1997）的技术，我们证明了模型的存在性和唯一性。然后，我们研究了从边长L为L ->∞的二维环面均匀随机抽样（或更一般地“距离足够远”）的有限数量个体的谱系的渐近行为。在适当的条件下（在适当的时间尺度上），我们可以得到一个金曼聚结，一个更一般的λ聚结或一个聚结布朗运动系统（具有非局部聚结机制）作为有限的谱系过程。
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 sidelength L as L -> 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)