Testing concerning the homogeneity of some predator-prey populations

In this paper, we study an inference problem for a stochastic model where k deterministic Lotka-Volterra systems of ordinary differential equations (ODEs) are perturbed with k pairs of random errors. The k deterministic systems describe the ecological interaction between k predator-prey populations. These k deterministic systems depend on unknown parameters. We consider the testing problem concerning the homogeneity between k pairs of the interaction parameters of the ODEs. We assume that the k pairs of random errors are independent and that, each pair follows correlated Ornstein-Uhlenbeck processes. Thus, we extend the stochastic model suggested in Froda and Colavita [2005. Estimating predator-prey systems via ordinary differential equations with closed orbits. Aust. N.Z. J. Stat. 2, 235-254] as well as in Froda and Nkurunziza [2007. Prediction of predator-prey populations modeled by perturbed ODE. J. Math. Biol. 54, 407-451] where k=1. Under this statistical model, we propose a likelihood ratio test and study the asymptotic properties of this test. Finally, we highlight the performance of our method through some simulations studies.