Asymptotic absorption-time distributions in extinction-prone Markov processes

Demographic stochasticity and extinction in populations with Allee effect

We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean-time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dyna…

Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment

The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their time-averaged empirical flows over a large time-window $T$. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood via the Doob generator of the process conditioned to survive up to time $T$. The large deviation pr…

固定与灭绝在时间波动的时空结构元种群中

Fixation and extinction in time-fluctuating spatially structured metapopulations

研究分析了时间波动环境中元种群中固定与灭绝现象的影响因素，揭示了迁移率和环境切换率对突变体固定概率的非单调影响。

Scaling features of two special Markov chains involving total disasters

Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the parameters range, the two models can show up a recurrence/transience transition and, in the critical case, a positive/null recurrence transition. The collapse transition probabilities are chosen in such a way that the models are exactly solvable and, in case of positive recurrence, intimately related to the extended Sibuya and Pareto-Zipf distributions whose divi…

非马尔可夫种群动力学中从亚稳态的逃逸

Escape from a metastable state in non-Markovian population dynamics

本文研究含厚尾等待时间记忆的非马尔可夫单种群随机动力学，用 WKB 方法分析有限均值情形的亚稳态逃逸，并揭示无限均值下双稳态系统的两种标度机制。

多物种生态波动作为从灭绝边缘出发的跳跃过程

Many-species ecological fluctuations as a jump process from the brink of extinction

本研究发现在小迁移率下，多物种生态系统呈现大波动和长时间尺度的标度区间，物种丰度轨迹遵循非马尔可夫跳跃扩散过程，可作为高多样性生态系统内源性波动的指纹。