In an ecosystem, many species exist. Their mutual interactions may cause the complexity in population dynamics. In the present article, we propose a dynamical model for three freshwater species: mussel, gobies and bitterling. These creatures have the relationship similar to rock-paper-scissors game. We show that the system has two conservation laws, and its dynamics resembles the Lotka-Volterra model. We obtain time averages of population sizes for parameter values, and find that the average sizes frequently show paradoxical responses. For example, when the predation rate of a target species is increased, its population size is decreased. We discuss the relation between paradoxical response and conservation policies for endangered species.

population dynamics, rock-paper-scissors game, conservation laws, time average, endangered species, paradoxical response.