Should All the Species of a Food Chain Be Counted to Investigate the Global Dynamics?

A fairly realistic three-species food-chain model based on Lotka±Volterra and Leslie±Gower schemes is investigated assuming that just a single scalar time series is available. The paper uses tools borrowed from the theory of nonlinear dynamical systems. The quality of the di€erent phase portraits reconstructed is tested. Such a situation would arise in practice whenever only a single species is counted. It is found that the dynamical analysis can be safely performed when a single species involved in the food chain is counted if many thousands of observations are available. If not, a global model can be obtained from the available data and subsequently used to produce all the data required for a detailed analysis. In this case, however, the choice of which species to consider in order to obtain a model is crucially important.