Role of toxin and nutrient for the occurrence and termination of plankton bloom--results drawn from field observations and a mathematical model.
The termination of harmful algal blooms (HABs) and coexistence of phytoplankton-zooplankton populations are of great importance to human health, ecosystem, environment, tourism and fisheries. In this paper we propose a three-component model consisting of dissolved limiting nutrients (N) supplied at constant rate and partially recycled after the death of plankton by bacterial decomposition, phytoplankton (P) and zooplankton (Z), where the growth of zooplankton species reduce due to toxic chemicals released by phytoplankton species. Our analysis leads to different thresholds which are expressible in terms of model parameters and determine the existence and stability of various states of the system. We observe that phytoplankton-zooplankton persist if the maximal zooplankton ingestion rate exceeds a lower threshold value. It is shown that the coexistence equilibrium loses its stability when the dilution rate of the nutrient concentration passes through a critical value and Hopf bifurcation occurs that induces oscillations of the population. Our results indicate that the occurrence of bloom increases when the nutrient concentration is very high, and in that case toxin produced by the phytoplankton plays a very crucial role towards the termination of the planktonic bloom.
Pal
S
S
Ramakrishna Mission Vivekananda Centenary College, Rahara, Kolkata 700118, India.
Chatterjee
Samrat
S
Chattopadhyay
J
J
D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D005068:Eutrophication; D007194:India; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D010839:Phytoplankton / Q000378:metabolism; D010933:Plankton; D049490:Systems Biology; D013997:Time Factors; D014118:Toxins, Biological; D015048:Zooplankton / Q000378:metabolism
D014118:Toxins, Biological