Extinction of metastable stochastic populations
Extinction of metastable stochastic populations
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DOI：
10.1103/physreve.81.021116
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发表时间：
2010-02-01
影响因子：
2.4
通讯作者：
Meerson, Baruch
中科院分区：
文献类型：
--
作者：
Assaf, Michael;Meerson, Baruch
我们调查灭绝的长寿的自我调节随机人口的现象，所造成的内在（人口）噪声。消光通常通过两种情况之一发生，这取决于吸收状态n=0是确定性速率方程的排斥点（情况A）还是吸引点（情况B）。在场景A中，亚稳态随机种群位于排斥点n=0旁边的吸引不动点附近。在情形B中，在吸引点n=0和另一个吸引点n=n（2）之间存在中间排斥点n =n（1），亚稳态布居在该吸引点附近。该理论的关键是WKB（Wentzel-Kramers-Brillouin）近似的耗散变体，该近似假设亚稳态中的典型布居大小是大的。从主方程开始，我们计算的准平稳概率分布的人口规模和（指数长）的平均时间灭绝的两种情况。必要时，WKB近似是补充（i）在小n和（ii）由货车坎彭系统大小的扩展，有效的确定性速率方程的不动点附近的准稳态主方程的递归解。该理论产生的熵障碍灭绝和指数前的因素，并持有一套一般的多步过程时，详细的平衡被打破。结果大大简化了单步过程和附近的情况A和B的特征分叉。
We investigate the phenomenon of extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n=0. In scenario B there is an intermediate repelling point n=n(1) between the attracting point n=0 and another attracting point n=n(2) in the vicinity of which the metastable population resides. The crux of the theory is a dissipative variant of WKB (Wentzel-Kramers-Brillouin) approximation which assumes that the typical population size in the metastable state is large. Starting from the master equation, we calculate the quasistationary probability distribution of the population sizes and the (exponentially long) mean time to extinction for each of the two scenarios. When necessary, the WKB approximation is complemented (i) by a recursive solution of the quasistationary master equation at small n and (ii) by the van Kampen system-size expansion, valid near the fixed points of the deterministic rate equation. The theory yields both entropic barriers to extinction and pre-exponential factors, and holds for a general set of multistep processes when detailed balance is broken. The results simplify considerably for single-step processes and near the characteristic bifurcations of scenarios A and B.