Combined influences of environmental enrichment and harvesting mediate rich dynamics in an intraguild predation fishery system

Natural resources and its enrichment activities are often being associated with the paradoxical effects in ecology such as in predator–prey and fishery models. Several studies have shown that an increase in resources can cause the “Paradox of Enrichment” i.e., the destabilization of certain species population as the system is enriched. This situation is rather contradictory to our logical intuition. Parallel with this view, harvesting effort and the intensity of enrichment activities are among crucial factors in shaping the sustainability of fishery activities and natural resources. This is because an extreme harvesting effort could lead to resource depletion and threaten vulnerable marine ecosystems. In this work, we investigate the joint effects of enrichment and harvesting activities in an intraguild predator–prey fishery model that incorporates the Michaelis–Menten type of harvesting of predatory fishes. We study the existence and stability of the steady states in this system analytically and conduct numerical simulations, together with bifurcation analysis to verify our analytical findings. Our co-dimension one bifurcation analysis shows that the system can exhibit local bifurcations such as transcritical, saddle–node, subcritical, and supercritical Hopf bifurcations. Co-dimension two bifurcation analysis further demonstrates the existence of global dynamics through the appearance of Generalized Hopf (GH) and Zero-Hopf (ZH) bifurcations, which occur due to the interactions of distinct local bifurcations in this ecological system. The limit point bifurcation of cycles that emanates from the GH point has a bounded parameter space region in which tristability phenomenon (between stable steady states and stable limit cycles) occurs. In a scenario where the resources are enriched in the presence of harvesting activity, bistability emerges with the long-term outcomes lead to the exclusion of either prey or predator population, depending on the initial conditions of species. Based on these findings, we propose another interpretation to the “Paradox of Enrichment” as postulated in ecological theories: this predator–prey fishery system can be destabilized through an alternative stable states phenomenon, which results in the extinction of certain species as the ecosystem is further enriched.