Effects of Egricultural Insecticide Runoff on Reef-fish Population

Abstract

Chemical contamination from agricultural runoff associated with fish morbidity and mortality have increased in frequency and severity over the past several decades. We investigate the effects of exposure of insecticide on a zooplankivorous reef-fish and its prey by means of a continuous time model of the dynamics of organisms in a food chain in presence of a constant rate of flow of an insecticide. The insecticide is sub-lethal to the fish but is lethal to zooplankton. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the species associated with the system cannot thrive even in absence of predation. Also, we prove that under certain conditions the system is permanent in presence of all the organisms and obtain conditions for permanence under which one of the two organisms is extinct. Local stability of the system is obtained in absence of sensitive species and in presence of both sensitive and resistant species. Computer simulations have been carried out to illustrate different analytical results.