密度调节和Allee型随机收获模型中可能状态转移的识别和预防及其在鲱鱼保护中的应用
Recognizing and prevention of probable regime shift in density regulated and Allee type stochastic harvesting model with application to herring conservation
摘要：
一个具有多个稳定平衡点的生态系统往往会发生灾难性的变化或从一个稳定状态向另一个稳定状态的转变。应该注意的是，如果其中一个稳定状态是灭绝状态，则灾难性变化可能导致灭绝。适当的人工措施可以控制防止不同物种从一个平衡到另一个平衡的灾难性变化。我们考虑两个随机模型的线性和非线性收获项。我们检查密度调节或Allee型密度调节模型[Saha等人，Ecological Modelling，2013]，其在鲱鱼种群的生存力研究中具有实质性应用。我们在这里考虑的两个确定性模型在一定的限制下都包含双稳定性，在这种情况下，其中一个稳定状态是灭绝状态。我们假设所考虑的动力系统是封闭的，即，没有移民和迁出。通过用随机微分方程模型代替常微分方程，在系统中引入人口统计噪声，其中确定性过程的出生率和死亡率用于获得随机微分方程中的瞬时均值和方差。我们的研究表明，灾难性的变化可以通过选择适当的处理时间手动避免，最终将有助于防止收获种群的突然灭绝。通过全球种群动力学数据库（GPDD）中鲱鱼种群大小数据和模拟实验，说明了整个研究。
英文摘要：
An ecological system with multiple stable equilibria is prone to undergo catastrophic change or regime shift from one steady-state to another. It should be noted that, if one of the steady states is an extinction state, the catastrophic change may lead to extinction. A suitable manual measure may control the prevention of catastrophic changes of different species from one equilibrium to another. We consider two stochastic models with linear and nonlinear harvesting terms. We inspect either density regulation or Allee type density regulated models [Saha et al., Ecological Modelling, 2013], which have substantial applications in the herring fish population's viability study. Both the deterministic models we consider here contain bi-stability under certain restrictions, and in that case, one of the stable states is the extinction state. We assume that the dynamical system under consideration is closed, i.e., immigration and emigration are absent. The demographic noise is introduced in the system by substituting an ordinary differential equation with a stochastic differential equation model, where the birth and death rates of the deterministic process are used to obtain the instantaneous mean and variance in the stochastic differential equation. Our study reveals that, the catastrophic changes can be avoided manually by a suitable choice of handling time that will eventually help to prevent the sudden extinction of the harvested population. The entire study is illustrated through the herring population size data obtained from the Global Population Dynamics Database (GPDD) and simulation experiment.
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