Survival, extinction and ergodicity in a spatially continuous population model
Survival, extinction and ergodicity in a spatially continuous population model
复制标题
空间连续种群模型中的生存、灭绝和遍历性
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Martin Hutzenthaler
中科院分区：
文献类型：
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作者：
N. Berestycki;Martin Hutzenthaler
我们考虑了巴顿和埃斯里奇最近提出的一个模型，该模型是关于一个种群在空间连续体中进化的，在这个连续体中，一系列不同强度的灾难性事件允许大规模灭绝和重新定居的可能性。这些繁殖事件是基于空间事件（而不是个体）的泊松过程，在这种事件中产生的潜在数量是具有一定强度的泊松。我们证明，如果这个强度足够大，当从R d中的平移不变初始条件开始时，种群以概率1存活，而对于低强度，种群灭绝。此外，我们还证明了遍历性即使在低维中也是成立的。这与道森-渡边过程和其他传统模型形成鲜明对比，在这些模型中，不同个体的繁殖是不相关的。
We consider a model recently introduced by Barton & Etheridge for a population evolving in a spatial continuum, in which a succession of catastrophic events of varying intensity allows for the possibility of large-scale extinction and recolonisation. These reproduction events are based on a Poisson process of spatial events (rather than individuals) and the potential number of ofispring produced during such an event is Poisson with a certain intensity. We show that if this intensity is su‐ciently large the population, when started from a translation invariant initial condition in R d , survives with probability one, whereas for low intensities the population dies out. Moreover we prove that ergodicity holds even in low dimensions. This contrasts sharply with the Dawson-Watanabe process and other traditional models in which reproduction of difierent individuals is uncorrelated.