Adaptive evolution of body size subject to indirect effect in trophic cascade system

Dynamics of a nutrient-phytoplankton model with random phytoplankton mortality

This study formulates a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution, stochastic boundedness, and stochastically asymptotic stability are well explored. A stochastic ecological reproductive index R₀^s is formulated to characterize the global dynamics. The theoretical analysis demonstrates that, if R₀^s<1, then phytoplankton dies out with probability one; if R₀^s>1 and some other conditions hold, then there exists an invariant and asymptotically stable density of the system and the approach involves integral Markov semigroups theory. Numerical simulations are presented to illustrate the analytical findings and to investigate the long-time effect of water temperature, light, nutrients, and environmental noise on the dynamic evolution of phytoplankton.