The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and patchy agglomeration

Abstract

In aquatic ecosystem, plankton populations are easily affected by environmental fluctuations due to the unpredictability of many physical factors such as nutrient availability, acidity, water temperature and so on. To reveal how environmental fluctuations influence plankton populations, in this paper, we develop and analyze a stochastic toxin-producing phytoplankton (TPP)-zooplankton model with patchy agglomeration. We first perform the survival analysis of the model, including the persistence and extinction as well as the existence of ergodic stationary distribution. Then, for the scenario when the model exhibits bistability between a positive equilibrium or a limit cycle and TPP-only equilibrium in the absence of noise, we further study the phenomenon of noise-induced transition from plankton coexistence to zooplankton extirpation. Also, we numerically estimate the critical values of noise intensities for the occurrence of transitions with the aids of the technique of stochastic sensitivity functions. Our research indicates that zooplankton population becomes more vulnerable and easily goes to extinction in the presence of environmental noise, and as a result, phytoplankton could benefit from the decrease of grazing pressure. This partially explains the often seen phenomenon in aquatic ecosystems that many toxin-releasing microalgal species with patchy agglomeration are more likely to cause blooms.