Prediction of predator–prey populations modelled by perturbed ODEs
In this paper we explore a stochastic model in continuous time for predator–prey interactions, which accounts for the periodical behaviour observed in many animal populations. More precisely, we consider a solution to the classical Lotka–Volterra system of equations, but we view the actual population sizes as random perturbations of the solutions to this ODE system. Namely, we assume that the perturbations follow correlated Ornstein–Uhlenbeck processes; this approach generalizes the one of Froda and Colavita [Aust N Z J Stat 2:235–254, 2005] who considered only i.i.d. errors. This type of perturbed deterministic model allows to perform parameter estimation and to predict population sizes at future times. On the other hand, the present model refines the previous one since it takes into account the variability due to external factors and the time dependence in the random component. Moreover, this more flexible model improves the predictions of population sizes at future times. In order to illustrate this last point, we analyse two data sets.