We shall consider a stochastic model, which is used to analyze competitive population dynamics. This cyclic and non-transitive model is based on the well-known rock-paper-scissors game. It can be viewed as the stochastic analog of the Lotka-Volterra deterministic model for predator-prey interactions. It has been observed that in order to maintain species richness it is essential for the system to be nonhierarchical in nature. One of the central goals of ecology is to figure out strategies that help to maintain biodiversity or species richness in the long term. The rock-paper-scissors game mimics this natural structure. In this game, each object is more powerful than one and less powerful than the other. Thus, there is no clear winner in this game. In the first half of the talk, we shall discuss the limiting properties of an urn scheme based on this game.
The second half of this talk will be based on simulation studies for more generalized setups that need to be explored further.