Random disturbance and diversity of competitive systems
Population size distribution within a community of species with a competitive hierarchy, is studied. With the introduction of a stochastic model of invasion and extinction due to random environmental disturbance, the stationary population size distribution is derived as a function of the parameter, which denotes the ratio of rates of random extinction and invasion. From this result it is shown that the Shannon-type diversity takes the maximum value under the situation that 10 ≈ 20 percent of habitat sites remain unoccupied, and the number of species also becomes maximum at intermediate levels of disturbance. The dynamical properties of a one-sided competitive system are also discussed by use of the Lotka-Volterra equations.