| In aquatic ecosystem,plankton growth and evolution are inevitably affeced by the environmental stochasticity,by utilizing the energy flow and element cycling modelling principles,we respectively establish a stochastic plankton model with toxin-producing phytoplankton and patchy agglomeration,a stochastic algal growth model with stoichiometric constraints and seasonal variation,a stochastic evolutionary phosphorusalgae-zooplankton model with phosphorus recycling.Moreover,for benthonic organisms,we formulate a stochastic coral reef benthic system with grazing intensity and immigrated macroalgae.Based on the stochastic differential equation theory and adaptive dynamic theorey,we study the effects of environmental fluctuations on the survival of plankton populations and adaptive evolution of plankton phenotypic traits,which provided a theoretical basis for explaining the mechanism of algal blooms and seeking for effective control methods as well as protecting the biodiversity of plankton species and promote the sustainable development of oceans and lakes.More specific contents are as follows:1.Considering the influence of environmental stochasticity on harmful algae blooms,a stochastic plankton model with toxin-producing phytoplankton(TPP)and patchy agglomeration is investigated.We first obtain the conditions for the persistence and extinction of plankton populations,the existence of the ergodic stationary distribution is also proved.Moreover,when bistability occurs,we study the noise-induced transition phenomena from plankton coexistence to zooplankton extirpation.The results show that zooplankton population becomes more vulnerable to extinction due to the existence of environmental fluctuations,and consequently TPP could benefit from the reduction 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.2.Considering that the growth of algae is inevitably affected by environmental stochasticity and usually limited by light and nutrient elements,we study a stochastic algal growth model with stoichiometric constraints and seasonal variation.The threshold which determines the persistence and extinction of algal population is first obtained,the existence and global attractiveness of the positive stochastic periodic solution are also proved.The results show that noise intensity and nutrient concentration could determine the survival and extinction of algae,and thus play a decisive role in the termination of algal blooms.We also investigate two effective methods to control algal blooms,which are removing algae periodically and blocking nutrient input constantly respectively.The results show that blocking nutrient inflow could inhibit algal bloom more effectively.3.Considering that the processes of algal growth and evolution are inevitably disturbed by environmental stochasticity,we consider a stochastic evolutlionary phosphorus-algae-zooplankton model with phosphorus recycling.Ecological thresholds that determine the persistence and extinction of the model are first obtained.We then introduce fitness functions with stochastic fluctuations and obtain the evolutionary conditions for CSS and evolutionary branching.The results predict that environmental fluctuations will drive plankton evolution toward smaller traits;With a moderate phosphorus inflow,small environmental fluctuations result in evolutionary branching,while large ones lead to CSS.In eutrophic environment,when algae species evolve only,environmental fluctuations potentially benefit algal biodiversity,and for the coevolution of algae and zooplankton with small environmental fluctuations,algal cell size and zooplankton body size can coevolve to a stable limit cycle.Moreover,environmental stochasticity could narrow the cell size difference between the new emerging algal species,when evlolutionary branching occurs.4.As the most productive but vulnerable marine habitats,coral reefs are easily affected by the ubiquitous environmental fluctuations,we consider a coral reef benthic system,where macroalgae,corals and algal turfs compete for the available space on a given region of the seabed with grazing intensity and immigrated macroalgae.For the deterministic system,we analyze the existence and stability of equilibria as well as the bifurcations.For the stochastic system,sufficient conditions for the existence of the ergodic stationary distribution and the extinction of coral population are obtained.Moreover,for the scenario that bistability occurs in the corresponding deteriminstic model,we investigate the irreversible noise-induced transition from macroalgal-coral coexistence to coral extirpation,numerically estimate the critical noise intensity for the transition,with the aids of the technique of stochastic sensitivity functions. |
