随机环境中种群稀有性和共性的时间尺度
Timescales of population rarity and commonness in random environments
摘要：
本文研究了环境噪声对密度依赖种群动力学特征时间尺度的影响。一般的结果是在稀有性和常见性所花费的时间的统计上得到的。所考虑的非线性随机模型在状态空间$]0, \infty[$上形成一类马尔可夫链，当内禀增长率为负时，该链是瞬态的，当内禀增长率为正或为零时，该链是常返的.在常返情形下，我们得到了正常返的一个充要条件以及稀有次数和常见次数分布的精确估计。在适用于生态中性物种的零递归临界情况下，稀有时间的分布是指数为-3/2的普适幂律。这些非平凡的结果应该感兴趣的生物学家参与保护受威胁的人口，并面临需要更好地了解害虫或疾病爆发的动态流行病学家。
英文摘要：
This paper investigates the influence of environmental noise on the characteristic timescale of the dynamics of density-dependent populations. General results are obtained on the statistics of time spent in rarity and time spent in commonness. The nonlinear stochastic models under consideration form a class of Markov chains on the state space $]0, \infty[$ which are transient if the intrinsic growth rate is negative and recurrent if it is positive or null. In the recurrent case, we obtain a necessary and sufficient condition for positive recurrence and precise estimates for the distribution of times of rarity and commonness. In the null recurrent, critical case that applies to ecologically neutral species, the distribution of rarity time is a universal power law with exponent -3/2. These non- trivial results should be of interest to biologists involved in the conservation of threatened populations, and to epidemiologists facing the need to better understanding the dynamics of pest or disease outbreaks.
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