On the evidence of an Allee effect in herring populations and consequences for population survival: A model-based study

We propose a deterministic model for a population subject to a strong Allee effect and undertake a model based study on commercially valuable herring fish population. We analyze the time series of two herring populations from the Icelandic and Canadian regions from the Global Population Dynamics Database with GPDD Id 1765, 1759. The parameters for the proposed models are estimated using Nonlinear Least Squares and Grid Search procedures. Confidence intervals for the parameters are computed using both Nonlinear Least Squares and regression bootstrap estimates. In the stochastic counterpart of the model we consider demographic noise to estimate different extinction measures viz. probability of extinction and expected time to extinction. The data histogram of population size is well approximated through the quasi-stationary distributions of the proposed stochastic model. The hypothesis of the presence of a strong Allee effect is prominent in both of the herring populations. The presence of a strong Allee effect in these two populations makes them more vulnerable to extinction. External perturbation or uncontrolled harvesting may drive the populations below the Allee threshold where the probability of extinction is high. We suggest that, our analysis can have a huge impact on understanding extinction patterns and enable us to identify demographic threats and guide decision making in conservation management. In addition, a similar analysis can be used in understanding the conservation status for other species.