Applied Mathematics & Information Sciences

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A three level trophic fish web model is proposed, consisting of clupeiforms pilchard (Sardina pilchardus) and anchovy (Engraulis encrasicolus), at the bottom, mackerel (Scomber scombrus) in the intermediate trophic level and tunny (Thunnus thynnus) as top predators. The model includes human harvesting. The clupeiforms population is further partitioned into three age classes, eggs, larvae and the adult fishes to account for possible cannibalism but mainly for the fact that these larvae in the Mediterranean countries are highly appreciated as a delicacy for human consumption. In the absence of fisheries, to prevent total extinction and maintaining coexistence it is important that a sufficient amount of eggs fertilize to form larvae. The predation rate of larvae by other fish populations also has an important role, especially for the occurrence of periodic solutions. Different harvesting policies are then numerically simulated. Independently of the harvesting policy used, even a small amount of selective harvesting of larvae may cause total extinction of the system. To prevent it, fishing that avoids the catch of the larvae should be adopted. With non selective harvesting the system is preserved, but for certain parameter ranges oscillations arise, which under unfavorable environmental perturbations may lead the food chain to collapse.

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