| Abstract: | In this paper we propose a new perspective of population dynamics of plankton, by considering some effects of global ecological cycles, in which a mixed population of plankton is embedded. The propagation of plankton is extremely influenced by various material cycles, such as Nitrogen cycles. Taking this global effect into consideration, we will construct a mathematical model of non‐linear system. Our model is a non‐linear, non‐equilibrium system based on a stochastic model realizing population dynamics of a mixed population of two species of plankton which is placed in a global nitrogen cycle. We show, in this article, that our model gives a new mathematical foundation of phenomena such as water blooms and the predominance of one type of plankton against the other. We calculate the probability of the occurrence of the water bloom of a mixed population and that is where one type of plankton predominates. We show, as a characteristic feature of our model, that the function of predominance has some discontinuity and that there exists a threshold point among the initial values, with respect to the type of plankton that predominates the other. In other words, there is a sort of phase transition in dynamic changes of plankton population, as a result of global ecological cycles. Copyright © 2000 John Wiley & Sons, Ltd. |
