Overexploitation of commercially beneficial fish is a serious ecological problem around the world. The growth profiles of most of the species are likely to follow density regulated theta-logistic model irrespective of any taxonomy group [Sibly et al., Science, 2005]. Rapid depletion of population size may cause reduced fitness, and the species is exposed to Allee phenomena. Here sustainability is addressed by modelling the herring population as a stochastic process and computing the probability of extinction and expected time to extinction. The models incorporate an Allee effect, crowding effects which reduce birth and death rates at large populations, and two possible choices of harvesting models viz. linear harvesting and nonlinear harvesting. A seminal attempt is made by Saha [Saha et al., Ecol. Model, 2013] for this economically beneficial fish, but ignored the vital phenomena of harvesting. Moreover, in this model, the demographic stochasticity is introduced through the white-noise term, which has certain limitations when harvesting is introduced into the system. White noise is appropriate for such a system where immigration and emigration are allowed, but a harvesting model is rational for a closed system. The demographic stochasticity is introduced by replacing an ordinary differential equation model with a stochastic differential equation model, where the instantaneous variance in the SDE is derived directly from the birth and death rates of a birth-death process. The modelling parameters are fit to data of the herring populations collected from Global Population Dynamics Database (GPDD), and the risk of extinction of each population is computed under different harvesting protocols. A threshold for handling times is computed beneath which the risk of extinction is high. This is proposed as a recommendation to management for sustainable harvesting.

商业性鱼类的过度开发是世界范围内的严重生态问题。不论任何分类学组别，大多数物种的生长情况都可能遵循密度调节的θ逻辑模型[Sably et al。，Science，2005]。种群数量的快速耗尽可能会导致适应性降低，并且该物种暴露于Allee现象。在这里，可持续性通过将鲱鱼种群建模为随机过程并计算灭绝的概率和预计的灭绝时间来解决。该模型具有阿利效应，拥挤效应（可降低大批人口的出生率和死亡率）以及两种可能的收获模型选择。线性收获和非线性收获。Saha进行了开创性的尝试[Saha等，Ecol。模型，2013]，因为这种经济上有利的鱼，却忽略了捕捞的重要现象。此外，在该模型中，人口随机性是通过白噪声项引入的，当将收获引入系统时，这具有一定的局限性。白噪声适用于允许移民和迁出的此类系统，但是对于封闭系统而言，收集模型是合理的。通过用随机微分方程模型代替普通的微分方程模型来引入人口统计的随机性，其中SDE中的瞬时方差直接从出生和死亡过程的出生率和死亡率得出。建模参数适合从全球人口动态数据库（GPDD）收集的鲱鱼种群数据，在不同的采伐方式下计算每个种群灭绝的风险。计算出处理时间的阈值，在该阈值以下，灭绝的风险很高。提议将其作为对可持续收获管理的建议。