Drury Kevin L S
Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA.
Theor Popul Biol. 2007 Aug;72(1):153-66. doi: 10.1016/j.tpb.2007.03.010. Epub 2007 Apr 4.
Predicting crossings between stable states is a central issue in population biology. Crossings from low-density to high-density equilibria are often associated with pest outbreaks, while the opposite crossings are often associated with population collapse of harvested species. Here I use a simple, bistable model to demonstrate a technique for estimating mean first passage times (MFPT) of thresholds, including boundaries between stable equilibria. The approach is based on stochastic "shot-noise" perturbations to the population and the MFPTs compare favorably with mean crossing times from Monte Carlo numerical solutions of the stochastically perturbed model. This agreement suggests that MFPT approximations can be used to quantify expected effects of species manipulations, whether the goal is pest control or sustainable harvest.
预测稳定状态之间的转变是种群生物学中的一个核心问题。从低密度平衡到高密度平衡的转变通常与害虫爆发有关，而相反的转变则通常与被捕捞物种的种群崩溃有关。在这里，我使用一个简单的双稳态模型来演示一种估计阈值平均首次通过时间（MFPT）的技术，包括稳定平衡点之间的边界。该方法基于对种群的随机“散粒噪声”扰动，并且MFPT与随机扰动模型的蒙特卡罗数值解的平均穿越时间相比表现良好。这种一致性表明，MFPT近似可用于量化物种操纵的预期效果，无论目标是害虫控制还是可持续捕捞。
