The Influence Of Cell Volume Size On The Growth Dynamic Of Phytoplankton

Most of phytoplankton belong to unicellular organisms,and a few belong to multicellular organisms,the study showed that the size of algae cell has different effects on the growth of phytoplankton under different environmental conditions,but the mechanism is not clear.Consequently,it is of great significance to reveal the growth law of phytoplankton by clarifying the influence mechanism of phytoplankton cell volume size on the growth of phytoplankton.Based on the theories of cell growth dynamics and stochastic dynamics,this paper studied the impact of cell volume size on the dynamics of phytoplankton growth in deterministic and stochastic environments by using the methods of dynamic modeling,dynamic analysis and numerical experiment.the main results are as follows:1.A nutrient-phytoplankton deterministic dynamic model with phytoplankton cell volume size effect was studied,and its corresponding stochastic dynamic model was further considered.In the deterministic environment,the research showed that very small phytoplankton cell volume or very large phytoplankton cell volume can destroy the long-term survival of phytoplankton,but the intermediate level of phytoplankton cell volume size is capable to maintain the long-term survival of phytoplankton.In the stochastic fluctuation environment,the study found that the small random environmental disturbance and the intermediate size phytoplankton cell volume have similar positive feedback effect on the long-term survival of phytoplankton,but the very large phytoplankton cell volume,the very small phytoplankton cell volume and the very large random environmental disturbance have similar negative feedback effect on the long-term survival of phytoplankton.Furthermore,the study also found that the intermediate level of phytoplankton cell volume size is the optimal value to promote the phytoplankton growth,which is in good agreement with the experimental finding.In addition,the study also indicated that phytoplankton density and nutrient concentration decrease with the increase of phytoplankton cell volume,which provides a possible biological strategy for controlling the phytoplankton blooms.2.A phytoplankton-zooplankton deterministic dynamic model with phytoplankton cell volume size effect was studied,and its corresponding stochastic dynamic model was further considered.In the deterministic environment,the study indicated that the relationship between the phytoplankton density as well as zooplankton density and the phytoplankton cell volume is a single peak function with opening downward.In the stochastic fluctuation environment,in addition to the stochastic persistence of phytoplankton and zooplankton,the study also found that the weak stochastic stability(stationary distribution)of phytoplankton also depends largely on the phytoplankton cell volume size and the random environmental disturbance intensity.In addition,the study also showed that with the increase of phytoplankton cell volume,the irregular random variation frequency of phytoplankton density and zooplankton density and their random disturbance amplitude caused by random environmental disturbance are decreasing.According to the results,in the real aquatic ecosystems,the phytoplankton with larger cell volume may have stronger ability to resist the disturbance of external environmental random factors.3.A nutrient-phytoplankton-zooplankton deterministic dynamic model with phytoplankton cell volume size and zooplankton body size effects was studied,and its corresponding stochastic dynamic model was further considered.The research found that very small phytoplankton cell volume or zooplankton body size can cause the extinction of phytoplankton and zooplankton in both deterministic and stochastic fluctuation environments.The study also indicated that when phytoplankton cell volume size and zooplankton body size lie in the intermediate size range,which can produce rich and complex effects on the phytoplankton and zooplankton growth:1)the increase of phytoplankton cell volume size or zooplankton body size can inhibit the proliferation of phytoplankton;2)the increase of phytoplankton cell volume size is conducive to the stable coexistence of nutrient,phytoplankton and zooplankton,but not conducive to the stable coexistence of nutrient and phytoplankton;3)the increase of zooplankton body size is not conducive to the stable coexistence of nutrient,phytoplankton and zooplankton,nor conducive to the stable coexistence of nutrient and phytoplankton;4)the increase of phytoplankton cell volume size can cause the stationary distribution of nutrient and phytoplankton to be left skewness,but the increase of zooplankton body size can cause the stationary distribution of nutrient and phytoplankton to be right skewness;5)The increase of phytoplankton cell volume size or zooplankton body size has no impacts on the stationary distribution of zooplankton to be right skewness.4.A phytoplankton-zooplankton deterministic dynamic model with phytoplankton cell volume size,zooplankton body size and Allee effect was studied.The study indicated that when phytoplankton cell volume size is relatively small,Allee effect plays a decisive role in the growth of phytoplankton and zooplankton,when phytoplankton cell volume size is relatively large,however,the phytoplankton cell volume size plays a decisive role in the growth of phytoplankton and zooplankton,and the influence of zooplankton body size on the growth of phytoplankton and phytoplankton under Allee effect is similar to that of phytoplankton cell volume size.Additionally,the study also found that under the Allee effect,the increase of zooplankton body size or phytoplankton cell volume size may cause periodic oscillation of phytoplankton density,but the increase of phytoplankton cell volume size may also end the periodic oscillation of phytoplankton density.Therefore,the phytoplankton cell volume size and zooplankton body size may be a key factor for initiating or terminating phytoplankton blooms.