Sub-Lethal Effects of HAB Toxin on Reef-Fish Population

Abstract

Harmful algal blooms (HABs) associated with fish morbidity and mortality have increased in frequency and severity over the past several decades. We investigate the effects of low level (sub-lethal) HAB stressor exposure on reef fish 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 input limiting nutrient. At the first trophic level the toxin producing phytoplankton are growing on the limiting nutrient with Holling type II functional response, whereas at the second trophic level the toxin-sensitive fish are growing on the toxin producing phytoplankton with Holling type III functional response. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive, even in absence of competition. Also, we prove that under certain conditions the system is permanent in presence of all the organisms and obtains conditions for permanence under which the toxin-sensitive organism becomes extinct. Local stability of the system is obtained in absence of toxin-sensitive species and in presence of both toxin-sensitive and toxin-resistant species. Computer simulations have been carried out to illustrate different analytical results.