Test of Homogeneity in Some Cyclic Predator-Prey Systems

• Activity Number: 99
• Type: Contributed
• Date/Time: Monday, August 4, 2008 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Severien Nkurunziza*+
• Companies: University of Windsor
• Keywords: likelihood ratio test ; Interaction parameter ; Ornestein-Uhlenbeck processes ; Lotka-Volterra system ; ODE system ; predator-prey

Abstract

In this talk, we consider a stochastic model where k deterministic Lotka-Volterra systems of ordinary differential equations (ODEs) are perturbed with k pairs of random errors. Further, we are interested in 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. This stochastic model extends that suggested in Froda and Colavita (2005) as well as in Froda and Nkurunziza (2007), where k=1. Under this statistical model, we propose a likelihood ratio test and study the asymptotic properties of this test.