2013 年 25 巻 4 号 p. 101-109
A mathematical model of a microcosm consisting of a producer, a decomposer, and a consumer was employed to simulate a case of inhibition of growth rates of producer and consumer upon exposure to chemical substances. This analysis focused on the entropy production rate and the material circulation phase in order to examine how changes in the growth rate of organisms affect transitions in systems. The results of these calculations were compared with results in an experimental system, and the following four conclusions were reached: First, reducing the growth rate of producer caused the entropy production rate to converge to a minimum value. There were two cases of results from reducing the ratio of the growth rate of consumers; in one, the ratio of the entropy production rate increased to maximum values, then decreased, and in the other, it converged to maximum values. Second, varying the growth rate of organisms caused a transition to the stable set of a frequency of interaction and a strength of interaction allowing coexistence of all three types of organisms. The entropy production rate in the system also fell to a minimum value. Third, the entropy production rates at the mature stage while the growth rate of both consumer and producer were varied together was scattered along a surface lying between a group of linear lines and a group of non-linear curves. It was shown impossible to predict the No-Observed-Effect Concentration in the system without accounting for interactions between the organisms making up the system. Fourth, the time-dependent changes in entropy production rate found in the mathematical model resembled the time-dependent changes in respiration by actual microcosms exposed to Al3+ ion.