Sau Anurag, Saha Bapi, Bhattacharya Sabyasachi
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T Road, Kolkata 700108, India.
Govt. College of Engg. & Textile Technology, Berhampore, 4 Cantonment Road, PIN-742101, India.
J Theor Biol. 2020 Oct 21;503:110375. doi: 10.1016/j.jtbi.2020.110375. Epub 2020 Jun 25.
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 effect 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.
对具有商业价值鱼类的过度捕捞是全球一个严重的生态问题。无论属于何种分类群，大多数物种的增长曲线可能都遵循密度调节的θ-逻辑斯蒂模型[西布利等人，《科学》，2005年]。种群数量的迅速减少可能导致适应性下降，该物种会面临阿利效应。这里通过将鲱鱼种群建模为一个随机过程并计算灭绝概率和预期灭绝时间来探讨可持续性问题。这些模型纳入了阿利效应、拥挤效应（在大种群中会降低出生率和死亡率）以及两种可能的捕捞模型选择，即线性捕捞和非线性捕捞。萨哈[萨哈等人，《生态模型》，2013年]针对这种具有经济价值的鱼类进行了开创性尝试，但忽略了捕捞的关键现象。此外，在该模型中，通过白噪声项引入了人口统计随机性，当将捕捞引入系统时，这有一定局限性。白噪声适用于允许迁入和迁出的此类系统，但对于封闭系统而言，捕捞模型更为合理。通过用随机微分方程模型取代常微分方程模型来引入人口统计随机性，其中随机微分方程中的瞬时方差直接从生死过程的出生率和死亡率推导得出。将建模参数拟合到从全球种群动态数据库（GPDD）收集的鲱鱼种群数据，并在不同捕捞方案下计算每个种群的灭绝风险。计算出一个处理时间阈值，低于该阈值时灭绝风险很高。这被作为可持续捕捞管理的一项建议提出。
