The role of Allee effect in cannibalistic species: An action plan to sustain the declining cod population

¹ Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab
² Applied Mathematics and Computational Sciences, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia

^* Corresponding author: parimita.roy@thapar.edu

Received: 22 July 2023
Accepted: 1 May 2024

Abstract

Atlantic cod collapsed in the late 20th century after being harvested heavily for 50 years. This paper aims to design conservation guidelines for the cod population, which is diminishing due to predation by grey seals and cannibalism. For this purpose, we first designed a continuous time ecological model (with and without the Allee effect) using a system of differential equations consisting of juvenile Atlantic cod, adult Atlantic cod, and grey seals. The developed model has set forth global existence, non-negativity, and long-term behavior. Subsequently, to handle the extinction problem cost-effectively, Pontryagin’s principle is employed to construct the optimal control, which is then numerically solved using an iterative forward–backward method. We numerically explored the impact of the Allee effect on cod survival within the original model and its two extended versions (i) stochastic and (ii) reaction–diffusion, to thoroughly understand the possible consequences wherein a population has cannibalistic tendencies. The numerical comparison between the non-Allee and Allee models (Ordinary, Stochastic, Reaction–Diffusion) reveals that the Allee effect may significantly promote recovery and benefit the cannibalistic population. We adopted a partial rank correlation coefficient (PRCC) to conduct a global sensitivity analysis to estimate the most sensitive parameters responsible for cod prevalence.