Dynamic Models For Scyphozoa Population Based On The Life Cycle

Jellyfish blooms, one of the largest disasters in marine ecosystem following the harmful algal blooms, have caused extreme problems for both marine ecosystems and human being . For most of scyphozoan, the proliferation of medusae derives from the complex life cycle. Without the supplement of the benthic, blooms cannot appear even with optimal conditions. The existence of polyps is a sufficient condi-tion for jellyfish blooms. To characterize and analyze life cycle models of syphozoa is the first step and a key step to reveal the mechanism of jellyfish outbreak.In this paper, dynamic models of scyphozoan life cycle will be formulated. By qualitative analyses and numerical simulations, the effect of key processes, such as strobilation and excystment on stages of the life cycle will be discussed, and blooming mechanisms triggered by crucial environmental factors will be analyzed.Based on the life cycle of scyphozoa, the food web model, including plankton,fish and jellyfish, will be proposed to elucidate the inherent relationship among functional groups and to reveal the ecological response after jellyfish blooms.First, We formulate a general dynamic model for the life cycle of scypho-zoa(PM model) , and investigate the significant effect of some biotie and abiiotic factors such as temperature, substrate, and predation on population dynamics.The analyses confirm that, compared with the decrease of predators, the scypho-zoan species are explicitly and sensitively affected by the expansion of substrates and the benthic phase contributes much more to the abundance of the medusa.Within a suitable range of temperature, the increase of temperature might lead to the explosion of polyps and medusae, but much higher temperatures would be detrimental to both forms.Second, the study focuses on the giant jellyfish Nemopilema nomurai, whose massive aggregation has caused severe damage to the East Asian seas. The three-state life cycle models with constant delay, distributed delay and density depen-dence are formulated to elucidate the population dynamics and to reveal what roles of podocyst play in the blooms. The study reveals that, with the increment of podocysts dormancy, the system goes through the Hopf bifurcation from stabili-ty to oscillation. The fluctuations of podocyst can cause changes in the polyp, but not for the medusa. Based on the surface temperature of Dalian sea, our study shows that the number of podocyst is affected by temperature and the dormant period synergistically. The dormancy and excystment of podocysts should not have a discernible effect on the system for a long time. Parametric sensitivity analysis shows that the polyp is the most sensitive to the expansion of substrates, while the recurrence of medusa has the strongest dependent relationship to strobilation rate. Furthermore, control strategies are discussed in detail, and controlling the expansion of the offshore artificial substrate as one of the effective and practicable control strategies is derived. In fact, if ocean sprawl were restricted, that means the living space for the bottom stages would descend, the successful settlement of planulae would reduce , and the intraspecific competition of polyps would increase,then the size of stages of Nemopilema nomurai would be cut down.Jellyfish blooms, are they increasing robustly or a consequence of oscillations?At last, we formulate a four-dimensional food web model governed by ODEs to characterize the population dynamics. Our analyses indicate that the increment of strobilation rate is not always beneficial to medusae, the density of medusa will increase with the algae aggregating. With medusa proliferating,the plankton and fish will be damaged and the fish can be excluded. If we control the strobilation rate and reduce the growth rate of algae, then the fish can recur. The model not only demonstrates the periodic oscillation of jellyfish but gives some control strategies to protect and recover the fish resources.By the dynamic models,we try to depict the life cycle of scyphozoa and the marine food web, to expound the effect of environmental factors on the life cycle,to investigate inner relations of red tides and jellyfish blooms, and to research the effect of jellyfish blooms on the other functional groups. We hope we can provide new models and methods for studying mechanisms of jellyfish blooms.