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An ecological system with multiple stable equilibria is prone to undergocatastrophic change or regime shift from one steady-state to another. It shouldbe noted that, if one of the steady states is an extinction state, thecatastrophic change may lead to extinction. A suitable manual measure maycontrol the prevention of catastrophic changes of different species from oneequilibrium to another. We consider two stochastic models with linear andnonlinear harvesting terms. We inspect either density regulation or Allee typedensity regulated models [Saha et al., Ecological Modelling, 2013], which havesubstantial applications in the herring fish population's viability study. Boththe deterministic models we consider here contain bi-stability under certainrestrictions, and in that case, one of the stable states is the extinctionstate. We assume that the dynamical system under consideration is closed, i.e.,immigration and emigration are absent. The demographic noise is introduced inthe system by substituting an ordinary differential equation with a stochasticdifferential equation model, where the birth and death rates of thedeterministic process are used to obtain the instantaneous mean and variance inthe stochastic differential equation. Our study reveals that, the catastrophicchanges can be avoided manually by a suitable choice of handling time that willeventually help to prevent the sudden extinction of the harvested population.The entire study is illustrated through the herring population size dataobtained from the Global Population Dynamics Database (GPDD) and simulationexperiment.

Recognizing and prevention of probable regime shift in density regulated  and Allee type stochastic harvesting model with application to herring  conservation