Nonlinear historical superprocess approximations for population models with past dependence
Nonlinear historical superprocess approximations for population models with past dependence
复制标题
具有过去依赖性的总体模型的非线性历史超级过程近似
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
V. Tran
中科院分区：
文献类型：
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作者：
S. M'el'eard;V. Tran
我们对具有特征结构和生态相互作用的出生和死亡过程不断演变的谱系感兴趣。除非发生突变，否则性状会从父母遗传给后代。这种动态可能取决于祖先的特征及其过去，并允许个体之间通过血统进行互动。我们定义了一个相互作用的历史粒子过程，描述了活着的个体的谱系；它采用无限维 cadlag 路径空间上的点测量空间中的值。在大群体、小个体和异速人口统计的假设下，这种基于个体的过程可以通过非线性历史超级过程来近似。由于相互作用，分支属性失效，我们使用鞅问题以及种群和独立分支粒子之间的精细耦合。我们的收敛定理通过当前生物学感兴趣的两个例子来说明。第一个涉及人口的生物多样性历史及其系统发育，而第二个则处理个体通过过去的轨迹进行竞争的空间模型。
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend on the trait of the ancestors and on its past and allows interactions between individuals through their lineages. We define an interacting historical particle process describing the genealogies of the living individuals; it takes values in the space of point measures on an infinite dimensional cadlag path space. This individual-based process can be approximated by a nonlinear historical superprocess, under the assumptions of large populations, small individuals and allometric demographies. Because of the interactions, the branching property fails and we use martingale problems and fine couplings between our population and independent branching particles. Our convergence theorem is illustrated by two examples of current interest in biology. The first one relates the biodiversity history of a population and its phylogeny, while the second treats a spatial model where individuals compete through their past trajectories.
影响因子：
2
作者：
A. Greven;P. Pfaffelhuber;A. Winter
通讯作者：
A. Winter
影响因子：
1.4
作者：
Evans, Steven N.;Steinsaltz, David
通讯作者：
Steinsaltz, David