  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.
