On species diversity for a stochastic population model in the presence of competition

A general stochastic model in the presence of colonizations, deaths and replacements is formulated for a population consisting of different species in competition for habitat sites. Assuming that death rates are constant and that replacements follow the hierarchic rule by which species of higher rank outcompete those of lower rank, under the constraint that replacement rates only depend on the types of invading species transient and steady-state probabilities for the occupation site are indicated. The dependence of Shannon-type diversity on the density of unoccupied habitat sites is finally discussed under the assumption of constant rates