Exact densities for a class of stochastic circular food chain

Abstract

Variants of the Lotka-Volterra equations have been frequently used to describe population dynamics with predator-prey relations. However, real ecosystems are often probabilistic systems rather than deterministic paradigms. In a stochastic framework, the issue of persistence could be best studied through the stationary probability density of the system. This technical note presents a class of circular stochastic food chains with general functional structures of predation rates and closed-form solution for its stationary probability density.