ESTIMATING PREDATOR‐PREY SYSTEMS VIA ORDINARY DIFFERENTIAL EQUATIONS WITH CLOSED ORBITS

Summary This paper considers periodic regression functions, which are solutions to a planar system of differential equations. In particular, it introduces a simple stochastic model which describes the interaction between predator and prey populations. The regression functions are solutions to the classical Lotka-Volterra system of equations, which admits closed orbits. The proposed method of estimation can be applied whenever pairs of predator-prey data are available, and the prey is the main source of food of the predator. Canadian mink-muskrat data are analysed from this new viewpoint. The estimation method is based on the existence of closed trajectories that describe the relationship between the two population sizes, and the paper shows how it can be extended to other systems of differential equations which admit closed orbits (e.g. Hamiltonian systems).